policy analysis in transmission-constrained …
TRANSCRIPT
The Pennsylvania State University
The Graduate School
College of Earth and Mineral Sciences
POLICY ANALYSIS IN TRANSMISSION-CONSTRAINED
ELECTRICITY MARKETS
A Dissertation in
Energy and Mineral Engineering
by
Mostafa Sahraei-Ardakani
2013 Mostafa Sahraei-Ardakani
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
August 2013
ii
The dissertation of Mostafa Sahraei-Ardakani is to be reviewed by the following:
Seth A. Blumsack
Assistant Professor of Energy Policy and Economics
Dissertation Advisor
Chair of Committee
Andrew N. Kleit
Professor of Energy and Environmental Economics
Anastasia V. Shcherbakova
Assistant Professor of Energy Economics, Risk, and Policy
Terry L. Friesz
Harold and Inge Marcus Chaired Professor of Industrial Engineering
Luis F. Ayala H.
Associate Professor of Petroleum and Natural Gas Engineering
Associate Department Head for Graduate Education
*Signatures are on file in the Graduate School.
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Abstract
The existence of transmission constraints introduces complexities in electricity markets, the
understanding of which is important in policy applications. One of the major impacts of these
constraints is the locational price disparities. This dissertation addresses two policy relevant
problems in transmission-constrained electricity markets. First, a model is developed for analysis
of supply and demand policies considering the potential distributional impacts caused by the
transmission constraints. Second, a potential market design is studied for upgrading the
transmission system with Flexible Alternating Current Transmission System (FACTS).
Many important electricity policy initiatives, such as imposing emissions taxes or providing
incentives for renewable electricity generation, would directly affect the operation of electric
power networks. Evaluating such policies often requires models of how the proposed policy will
impact system operations. Predictive modeling of electric transmission systems, particularly in
the face of transmission constraints, is difficult unless the analyst possesses a detailed network
model. Such modeling may require data which is not publicly available. Moreover, policy
analysis must often be performed under time constraints, which may prevent the use of complex
engineering models.
First part of this dissertation develops a method for estimating short-run zonal supply curves in
transmission-constrained electricity markets that can be implemented quickly by policy analysts
with training in statistical methods (but not necessarily engineering) and with publicly-available
data. My model enables analysis of distributional impacts of policies affecting operation of
electric power grid. I develop a fuzzy nonlinear statistical model that uses fuel prices and zonal
electric loads to determine piecewise supply curves, each segment of which represents the
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influence of a particular technology type on the zonal electricity price. The domain belonging to
different technologies can overlap, which means a mixture of two fuels can be marginal. The
magnitude of this overlap is a function of the relative fuel prices. My problem thus requires the
simultaneous estimation of the slope of each supply-curve segment, thresholds that define the
endpoints of each segment and the level of marginal fuel overlap. I illustrate my methodology by
estimating zonal supply curves for the seventeen utility zones in the PJM system, a regional
electricity market covering numerous different states.
The zonal supply curves are used to study a state-level energy efficiency and conservation
legislation in Pennsylvania, within the context of PJM. My focus is on the distributive impacts
of this policy – specifically how the policy is likely to impact electricity prices in different areas
of Pennsylvania and in the PJM market more generally. Such spatial differences in policy
impacts are difficult to model and the transmission system is often ignored in policy studies. For
most utilities in Pennsylvania, it would reduce the influence of natural gas on electricity price
formation and increase the influence of coal. It would also save 2.1 to 2.8 percent of total energy
cost in Pennsylvania in a year similar to 2009. The savings are lower than 0.5 percent in other
PJM states and the prices may slightly increase in Washington, DC area.
I also analyze the impacts of imposing a $35/ton tax on emissions of carbon dioxide. My results
show that the policy would increase the average prices in PJM by 47 to 89 percent under
different fuel price scenarios in the short run, and would lead to short-run inter-fuel substitution
between coal and natural gas.
In the second part of this dissertation I investigate a potential market design for operation of
FACTS with the advantages coming from the smart grid technology. Traditionally, electric
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system operators have dispatched generation to minimize total production costs, assuming a
fixed transmission topology within the dispatch horizon. Implementation of smart-grid systems
could allow operators to co-optimize transmission topology alongside generator dispatch; the
technologies that would enable such co-optimization are still regulated as part of the monopoly
transmission system. There are a few proposed mechanisms for compensating transmission
owners based on flexible electrical characteristics and availability; and integrating transmission
into “complete” real-time electricity markets. I discuss why FACTS devices do not fall in the
category of natural monopolies. Then, I propose a sensitivity-based method to calculate the
marginal market value of Flexible Alternating Current Transmission Systems (FACTS). Once
the marginal value is calculated, different compensation mechanisms can be set up. I study two
different such methods for the market-based operation of FACTS, which allows some control
over the electrical topology of transmission lines. The first mechanism, compensates the devices
based on differences in locational prices (effectively with Financial Transmission Rights), while
the second allows FACTS devices to submit supply offers just as generators would, being paid a
market-clearing price for additional transfer capability provided to the system.
My problem formulation suggests a number of regulatory implications for flexible transmission
architecture. First, inclusion of a price signal in the wholesale electricity markets for the FACTS
capacity can lead to a more efficient operation of such devices. Second, the additional transfer
capability offered by FACTS devices may effectively clear the real-time market in some
circumstances (i.e., the additional transfer capability displaces higher-cost generation),
suggesting that FACTS devices have the power to set prices. Third, if FACTS devices are
compensated based on locational price differentials, the owners of such devices may not have the
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right incentive to offer the socially optimal amount of transfer capability to the system. The
market structure is explained and marginal value for the FACTS capacity is calculated in a two-
node and a thirty-bus system. The results show that the outcomes of both payment structures are
equivalent when the congestion is large enough.
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Table of Contents
List of Figures ........................................................................................................................................................ ix
List of Tables .......................................................................................................................................................... xi
Acknowledgements .......................................................................................................................................... xii
Introduction ........................................................................................................................................................... 1
1.1. Zonal Supply Curve Estimation ...................................................................................................... 1
1.2. Market Equilibrium for Flexible AC Transmission Systems ............................................... 7
1.3. Contributions ........................................................................................................................................ 9
2. Distributional Impacts of State-Level Energy Efficiency Policies in Regional
Electricity Markets ............................................................................................................................................ 12
2.1. Introduction ........................................................................................................................................ 12
2.2. Model Description ............................................................................................................................ 14
2.3. Estimation of Zonal Supply Curves in PJM .............................................................................. 19
2.4. Estimating the Impacts of Pennsylvania’s Act 129 .............................................................. 25
2.5. Conclusion ........................................................................................................................................... 32
3. Estimating Zonal Electricity Supply Curves in Transmission-Constrained Electricity
Markets .................................................................................................................................................................. 34
3.1. Introduction ........................................................................................................................................ 34
3.2. Literature Review ............................................................................................................................. 39
3.3. Motivating Example ......................................................................................................................... 40
3.4. Methodology ....................................................................................................................................... 43
3.5. Assigning Membership Functions .............................................................................................. 48
3.6. Application to PJM utility zones .................................................................................................. 50
3.7. Simulation Studies ........................................................................................................................... 54
3.7.1. Carbon Tax ................................................................................................................................. 54
3.7.2. Pennsylvania’s Act 129 .......................................................................................................... 60
3.9. Conclusion ........................................................................................................................................... 63
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4. Active Participation of FACTS Devices in Wholesale Electricity Markets ....................... 65
4.1. Introduction ........................................................................................................................................ 65
4.2. Literature Review ............................................................................................................................. 70
4.3. Market Structure ............................................................................................................................... 72
4.4.1. Market value of FACTS capacity ......................................................................................... 78
4.4.2. Simulation study ...................................................................................................................... 80
4.5. Numerical example .......................................................................................................................... 91
4.6. The complete game .......................................................................................................................... 97
4.7. Conclusion ......................................................................................................................................... 102
5. Conclusion and Policy Implications ............................................................................................. 106
References .......................................................................................................................................................... 110
Appendix 1: Explaining Some Counter-Intuitive Results ................................................................ 119
Appendix 2: Correcting for Electricity Price Over-Estimation in the Fuzzy Gap ..................... 126
Appendix 3- Regression Parameters ........................................................................................................ 130
Appendix 4- Thresholds ................................................................................................................................ 135
Appendix 5- Projected Supply Curves...................................................................................................... 139
Appendix 6- Simulation of Pennsylvania’s Act 129 – Chapter two ............................................... 143
Appendix 7: CMA-ES ....................................................................................................................................... 147
Appendix 6- IEEE 30 BUS System ........................................................................................................... 151
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List of Figures
Figure 1: Estimated system short-run supply curve for the PJM electricity market. The figure is
taken from Newcomer et al. (2008), and includes an adder for transmission and
distribution costs. ................................................................................................................ 4
Figure 2: The variable threshold method defines regions in {qi, qT} space where a given fuel is
on the margin. My approach assumes that these frontiers are linear, and thus the
estimation problem amounts to determining the corner solutions for each frontier ......... 18
Figure 3: Geographical distribution of utility zones in PJM market (www.pjm.com) ................. 20
Figure 4: Estimated thresholds for APS. Shading represents real time prices; darker shading
indicates higher prices....................................................................................................... 23
Figure 5-Top: Dispatch curve for PJM using the following fuel prices: Coal: $2/MMBTU, Gas:
$8/MMBTU, Oil: $15/MMBTU. This set of prices is similar to the situation in late 2008;
Bottom: The supply curve from 120 to 220 GWh of demand. This shows the transition
from coal to natural gas more clearly. .............................................................................. 36
Figure 6: Fuel price trends since January 2006. ........................................................................... 37
Figure 7-Top: Dispatch curve for PJM using the following fuel prices: Coal: $2/MMBTU, Gas:
$3/MMBTU, Oil: $20 /MMBTU. Increases in the price of coal relative to natural gas
price results in a region where a mixture of coal and gas is marginal; Bottom: The same
curve is shown for the region representing 120 to 220 GWh of demand. It shows how a
mixture of two fuels is marginal when demand is between 120 and 200 GWh. .............. 38
Figure 8: Without transmission congestion, there is a single system-wide supply curve and a
single system-wide market price. The presence of transmission congestion segments the
market, so that Nodes 1 and 2 effectively have different supply curves and different
locational market prices. ................................................................................................... 42
Figure 9: Fuzzy variable thresholds: The fuzzy gap depends on the relative fuel prices while the
mean of the distribution is a fixed line in qi-qT space. ..................................................... 47
Figure 10: Fuzzy membership function assignment for coal using analytical geometry
formulation for linear plane. ............................................................................................. 49
Figure 11: Fuzzy thresholds in Dominion .................................................................................... 51
Figure 12: Projected supply curve for APS in central Pennsylvania and West Virginia .............. 59
Figure 13: Projected Supply function for JCPL in eastern New Jersey ........................................ 59
Figure 14: The two-node, two-line system .................................................................................. 75
Figure 15: The transfer capability when both the FACTS devices are used. It is assumed in this
figure that n1=n2 ............................................................................................................... 77
Figure 16: Total amount of reactance change at equilibrium ....................................................... 81
Figure 17: Clearing price for FACTS devices .............................................................................. 82
Figure 18: The profit for FACTS device owners .......................................................................... 82
x
Figure 19: Nodal price at node 1 with and without the FACTS devices ...................................... 84
Figure 20: Nodal price at node 2 with and without the FACTS devices ...................................... 84
Figure 21: Social welfare improvement due to the transfer capability offered by the FACTS
devices............................................................................................................................... 85
Figure 22: Decrease in congestion rent caused by the FACTS devices ....................................... 85
Figure 23: Change in c ustomers’ surplus..................................................................................... 87
Figure 24: Change in generators’ surplus ..................................................................................... 87
Figure 25: Change in FACTS surplus ........................................................................................... 88
Figure 26: Supply and marginal value functions for FACTS capacity at different levels of load.
........................................................................................................................................... 88
Figure 27: IEEE standard 30-bus, 6-generator system ................................................................. 91
Figure 28: Marginal value of FACTS capacity in IEEE-30 bus system. ...................................... 94
Figure 29: Generators’ output when the FACTS devices are used and when they are not used. . 95
Figure 30: Price difference between the case where the FACTS devices are not used and the case
where they are used. .......................................................................................................... 97
Figure 31: Generator's bidding strategies in two-node system assuming a price cap of $3000 per
megawatt hour. The demand at node two is 825 MW. ................................................... 100
Figure 32: Generators’ bidding strategies in the 30 bus system. ................................................ 100
Figure A-1: Three node test system. All transmission lines in the system are assumed to have
equal impedances. ........................................................................................................... 120
Figure A-2: Three node test system with two different types of plants at node 1. ..................... 123
Figure A-3: Gas/Oil threshold at node 1 with positive slope...................................................... 125
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List of Tables
Table 1: PJM Zonal Abbreviations ............................................................................................... 20
Table 2: Estimated zonal supply curve thresholds for the PJM market ........................................ 21
Table 3: Estimated zonal marginal fuel frequencies in the PJM market ...................................... 22
Table 4: F-Test results for significance of quadratic terms .......................................................... 24
Table 5: F-Test results for significance of variable thresholds ..................................................... 25
Table 6: Act 129’s Effect on Zonal Electricity Prices in PJM ...................................................... 29
Table 7: Act 129’s Effect on Zonal Fuel Utilization in PJM ........................................................ 31
Table 8: Membership function parameters ................................................................................... 52
Table 9- Regression parameters: * indicates the significant coefficients with 95% confidence
interval. Note that the coefficients presented in the table are normalized and to get the
actual numbers each row should be multiplied by the elements of the following vector: 53
Table 10: Fuel prices under the two scenarios .............................................................................. 55
Table 11: Average prices before and after imposing a carbon tax of $35 per ton under the two
scenarios ($/MWh)............................................................................................................ 56
Table 12: The frequency with which each fuel is marginal before and after the carbon tax (%). 57
Table 13: Changes in producers’ surplus due to the carbon tax (millions of dollars) .................. 58
Table 14: Savings from Pennsylvania Act 129 in PJM's utility zones. The units are in millions of
dollars. ............................................................................................................................... 62
Table 15: Physical characerisics of the system ............................................................................. 80
Table 16: Cost function coefficients of the generators ................................................................. 92
Table 17: Sensitivity of power flows and prices over the transmission network to the FACTS
devices in IEEE-30 Bus System ....................................................................................... 93
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Acknowledgements
First and foremost, I should thank my advisor, Seth Blumsack, whose excellent mentorship and
caring character made this journey a lot more enjoyable than it usually is. Not only did he teach
me the skills I needed but also he showed me how to think. I could not possibly ask for a better
advisor and very much appreciate his brilliance and helpfulness. I was very lucky to work with
Seth and look forward to a lifetime friendship with him. I would like to thank Andrew Kleit for
his support and contribution. I would also like to thank Zhen Lei, Terry Friesz, and Anastasia
Shcherbakova. I appreciate the helpful discussions I had on my research with Kory Hedman,
Raja Ayyanar, and Michael Henderson.
I could not finish my PhD without the financial supports I received. I am grateful to Center for
Rural Pennsylvania, Department of Energy, and Penn State Energy Institute for funding my
research.
Besides the excellent education, graduate school offered me the opportunity to make lifetime
friends. I still remember my first day at Penn State, when Alisha Fernandez showed me around. I
had the greatest time with Clayton Barrows, Farid Tayari, Mercedes Cortes, Joseph Kasprzyk,
and Qin Fan when we were working or procrastinating. Thanks to all of you and my other friends
that are too many to mention.
Last, and most importantly Razieh Farzad deserves my sincere thanks for being patient with me.
I would not have finished this dissertation without her support. I should also thank my mother,
Narges, for her unconditional love and support.
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Introduction
The annual revenue of the US electricity industry is around 350 billion dollars (US Energy
Information Administration, 2012). The very large economic size of the industry emphasizes the
need for efficient operation of the whole system. Thus different policy initiatives are adopted to
increase the economic and environmental efficiency of the system. North American power grid
has been called “the most complex machine” built by human (Amin 2004). The unique physical
properties of electricity, the complex behavior of the transmission network, and the lack of
practical technology for storage of electrical energy make policy analysis in electric power sector
a complicated task. My motivation is to develop policy analysis tools for the emerging new
electric power system. The focus of my dissertation is on tools specific to these problems:
1. Estimating locational impacts such as price and fuel utilization of electricity policy
changes.
2. Expansion of electricity markets to accommodate new types of players in the
transmission sector. I specifically look at incorporation of Flexible Alternating
Current Transmission System (FACTS) devices into the wholesale electricity
markets.
1.1. Zonal Supply Curve Estimation
Many policy analyses related to electricity markets or electric transmission systems are focused
on the economic or environmental impacts of alternative policies, decisions, or market designs.
Projections of electricity system operations or the estimation of supply curves are thus highly
relevant to these analyses. My motivation is to develop a method for estimating zonal supply
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curves in transmission-constrained electricity markets that can be implemented quickly by policy
analysts with training in statistical methods (but not necessarily engineering) and with publicly-
available data. There is a large body of literature on the estimation of electricity prices. A variety
of approaches have been proposed for the forecast of electricity prices over various time
horizons. The methods include estimation of price duration curves (Valenzuela and Mazumdar,
2005), short-term price estimation with neural networks (Amjady, 2006 and Mandal et al., 2007)
or transfer functions (Mandal et al., 2007), and electricity price forecast with time series (Kian
and Keyhani, 2001; Misiorek et al, 2006). The mentioned techniques either need proprietary data
or are not accurate in the time-frame needed for policy analysis. Some of the models work well
for estimating prices for a week but do not do a good job of estimating prices for several years in
future.
Another method which seems to be popular for policy analysis applications is the construction of
a dispatch curve. Dispatch curve is the short-run marginal cost curve which is used by the system
operator to determine the set of power plants which will be dispatched at a given time. Actual
supply curves based on detailed production-cost data from generation owners or transmission
system operators are not typically made public, so many existing analyses (e.g., Mansur and
Holland, 2006; Apt, et al., 2008; Newcomer, et al., 2008; Newcomer and Apt, 2009; Blumsack,
2009; Dowds, et al., 2010) employ a procedure similar to the following:
1. Data from individual power generators are gathered. This data set usually includes
information at the plant or unit level on capacity, annual utilization (or capacity factor),
fuel usage, emissions and average efficiency. The e-GRID database published by the
Environmental Protection Agency, or data from the U.S. Energy Information
3
Administration, are often utilized to assemble these data sets. I note here that these data
sets, while detailed, offer far less information than a true production-cost model.
2. Data on fuel prices are gathered and used in conjunction with the power-plant data set to
generate a single number representing the marginal cost foe each generator.
3. The plants are sorted from the cheapest to the most expensive to generate a single supply
curve for a given electricity system. The modeled electricity systems are often regional
in scope, such as the PJM system.
An example of a supply curve generated in this fashion is shown in Figure 1. These estimated
supply curves may represent short-run supply curves (as in Newcomer et al., 2008 and
Blumsack, 2009) or in some cases long-run supply curves (as in Newcomer and Apt, 2009).
The supply curves are used in scenario analysis to estimate the impacts of various policies on
electricity prices, emissions or other variables of interest. For example, Mansur and Holland
(2006) use such a model to examine the welfare implications of real-time electricity pricing.
Newcomer et al. (2008) and Blumsack (2009) model the impacts on electricity costs, generator
utilization and greenhouse-gas emissions associated with different retail electricity pricing
policies. Newcomer and Apt (2009) and Dowds, et al. (2010) examine long-run investment
problems related to new electric generation or the adoption of electrified transportation.
4
Figure 1: Estimated system short-run supply curve for the PJM electricity market. The figure is
taken from Newcomer et al. (2008), and includes an adder for transmission and distribution
costs.
While these models are relatively straightforward to construct and understand, they share a
methodological drawback in that they ignore constraints on the electric transmission network.
In a power system, electricity flows are determined by Kirchhoff’s Laws, so an outside analyst
cannot simply assume that electricity from a given source is delivered to a given sink. When
power systems are constrained in some way, the analyst’s problem becomes more difficult,
because it must be determined whether electricity from a given source can be physically
delivered to a given sink, or whether the customers at that load sink must be served by
dispatching a different set of power plants. Analysis thus becomes more complex when the
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system is transmission-constrained.
In the presence of transmission constraints, prices and marginal fuels can be different at different
locations of the network. Therefore methods which ignore the transmission system are not able
to capture such differences. However in some cases the distributional impacts of policies may be
important policy outcomes. State-level energy efficiency policies are examples where the
distributional impacts are important.
The objective in this research is to fit a piecewise supply curve to data from electricity markets,
effectively creating a price and fuel utilization forecasting tool for policy-analysis purposes
considering the effects of transmission network. I develop a statistical model that uses fuel prices
and zonal electric loads to determine piecewise supply curves, each segment of which represents
the influence of a particular fuel type on the zonal electricity price. To illustrate this method, I
focus on estimating piecewise supply curves with segments representing three major fuels which
are consumed by thermal power plants: coal, natural gas, and oil. Because of technological
differences in power plants and differences in fuels utilization, it is expected that the electricity
price will be more correlated with the price of the relevant fuel at each specific load level.
The aggregated supply curve for PJM electricity market in Figure 1 suggests that the shape of the
supply curve changes when the fuel on the margin switches. The supply curve exhibits jumps in
the level and the slope when the fuel switches from coal to gas and from gas to oil. The proposed
method contributes to the existing literature by simultaneously estimating the thresholds where
the fuel on the margin switches. The method also estimates the partial supply curve (i.e., the
slope parameters of each segment) for each fuel.
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Recent decrease in the price of natural gas has made electricity produced by burning gas
relatively cheaper. This means that efficient natural gas fired power plants are now dispatched
before inefficient coal-fired plants. I further improve my method of supply curve estimation by
utilizing a fuzzy logic approach that allows a mixture of two fuels (e.g. coal and natural gas) to
effectively be on the margin (i.e., to determine the market-clearing price). This enables the model
to estimate fuel utilization and electricity prices more accurately when the natural gas prices are
low.
The method is used to simulate two policies: Pennsylvania’s Act 129, and a carbon tax policy in
PJM. Pennsylvania’s “Act 129,” 1 targets energy efficiency and peak demand reduction. It
requires electric utilities within Pennsylvania to reduce their annual demand (i.e., annual
kilowatt-hmy sales) by one percent, relative to 2010 levels, with an additional 4.5 percent
reduction during the 100 highest-demand hours. As Pennsylvania is part of a regional electricity
market in the Mid-Atlantic and Midwestern U.S. (the PJM Interconnection), this state-level
policy will have both local effects in Pennsylvania and potentially broader effects throughout
PJM. This is an example where the regional impacts are important policy outcomes, and my
method is used to capture them. I find that Act 129 lowers the total cost of generation between
2.1 to 2.8 percent for utilities inside Pennsylvania in a year similar to 2009. The generation cost
has the largest share in consumer’s bills but does not include the distribution charges. Estimated
savings are less than 0.5 percent for the utilities outside Pennsylvania. A previous study suggests
that the benefit to cost ratio associated with Act 129 to be between 1.9 to 2.8 in different utility
zones of PJM with exception of Allegheny Power for which the ratio is 4.1 (Statewide
1 The full text of Act 129 can be found at: http://www.puc.state.pa.us/electric/pdf/Act129/HB2200-Act129_Bill.pdf
7
Evaluation Team, 2009). I estimate that Act 129 may increase prices in Washington, D.C. and
southern Maryland, although these price increases are much smaller than the price declines in
other areas of PJM.
1.2. Market Equilibrium for Flexible AC Transmission Systems
FACTS are power electronic devices used to influence the power flows and voltages in a power
system (G. G. Hug, 2008). In this dissertation I specifically focus on the types of FACTS that
significantly affect the reactance of transmission lines. This would affect the power flows in the
system by changing the admittance matrix which determines the flows over the lines. In the
second part of this dissertation I investigate the potential for active participation of FACTS
devices in wholesale electricity markets.
The entire industry was considered to be a natural monopoly before 1990s and was operated
under regulation. One of the goals of restructuring, which began in the 1990s, is to decentralize
the decision making process and hopefully improve the system’s efficiency. Currently, the
operation decisions in electric transmission are made centrally by the system operator. Some
payments to regulated transmission owners are also made according to a regulated rate of return
that does not necessarily reflect the economic value of a certain transmission line to the system.
The implementation of the “smart grid” could enable the deployment of flexible and adaptive
transmission networks, thus allowing for the transmission topology to be optimized depending
on electricity demand and other system conditions. One technology that would allow this is
Flexible Alternating Current Transmission Systems (FACTS).
In an analogy to the water networks FACTS devices act similar to water pumps (Fairley, 2011).
8
Without water pumps, water only flows from higher altitudes to the lower altitudes based on the
pressure difference which may not always be efficient in a network. Similarly electricity flows
based on voltage and angle differences which may not be economically efficient. Economic
inefficiencies can occur in the form of loop flows or counter intuitive flows from a cheap node to
an expensive one. FACTS devices make it possible to control several parameters of the network
such as lines’ admittance and bus voltages. They facilitate control of the flows by affecting the
admittances of the transmission lines and thus avoid such economically inefficient phenomena.
Having these devices installed on the transmission system can potentially improve the system
without costly and time consuming investment on new transmission lines. These devices could
be seen as non-transmission alternatives which are suggested by FERC order 1000.
Recently, some studies have suggested implementing market-based mechanisms for transmission
sector. This would allow the transmission owners to offer their services to the system operator on
a bid basis, as generators currently do in deregulated electricity markets. Such a market has been
termed a “complete real-time electricity market” (O’Neill et al., 2008). They conclude that it is
not clear whether the FACTS devices are natural monopoly and provide a strong theoretical
background for designing markets with active transmission participation. However there is a
positive externality problem with their payment system. I explain this in more details and
propose a sensitivity-based method to calculate FACTS capacity value to overcome the issue.
Once the marginal value for FACTS capacity is determined, different payment mechanisms
could be set up. I explore the market outcome under two different payment structures. First I use
an LMP based market where the FACTS devices get paid based on the nodal price differences.
This is more or less similar to a Cournot competition for FACTS devices. Second, I set up supply
9
function equilibrium (SFE) model in which FACTS devices can submit supply offers similar to
generations. The market structure can potentially lead to more efficient operation of FACTS
devices compared to the existing regulated procedures. This is in line with the restructuring goals
to improve the efficiency.
1.3.Contributions
This dissertation makes several contributions to the existing methods of policy analysis in the
transmission-constrained electricity markets. It also provides insight into how the FACTS
devices can be incorporated into the current electricity markets. Here is the list of contributions
this dissertation makes to the existing literature in supply and demand policy analysis and
complete electricity market including some transmission assets:
1. I develop a statistical model with publically available data to estimate zonal electricity
supply curves. The model estimates zonal prices and zonal marginal fuel which enables
analysts to measure price changes as well as fuel utilization impacts, such as emissions,
due to implication of a policy. The model implicitly captures the effects of transmission
constraints.
a. The model uses fuzzy logic to estimate conditions under which a mixture of two
fuels sets the electricity prices.
b. I estimate supply curves at utility level for the seventeen utility zones of PJM
regional electricity market.
2. I use the resulted supply curve to study the impacts of two policies:
a. I simulate the potential zonal impacts of Pennsylvania act 129. The results show
that Pennsylvania act 129 would save 1% of the total cost of generating electricity
10
in PJM. The savings would be around 2.4% for utilities in Pennsylvania. Such
study is not possible with a transmission-less model since it cannot distinguish
between different areas.
b. I also study the impacts of a potential carbon tax policy in different utility zones
of PJM. The impacts are not uniform over the different zones.
3. I show the positive externality problem with the payment method proposed by (O’Neill,
et al., 2008) and propose a sensitivity-based mechanism to value the FACTS capacity.
Once this value is calculated, different payment structures can be set up without having to
deal with the positive externality.
4. I study two different payment designs mechanisms allowing FACTS to actively
participate in the market: an LMP based design (Cournot); and a Supply Function
Equilibrium (SFE).
a. The results suggest that both designs improve the social welfare.
b. They also have similar outcome when the congestion is significant enough. Under
such circumstances, the device owners would offer their full capacity at the
marginal value for their devices.
The rest of this dissertation is organized as follows: Chapter 2 presents a deterministic model for
analyzing regional impacts of energy-efficiency policies. The chapter also includes estimation of
the impacts of Pennsylvania’s act 129 on regional prices and fuel utilization. Chapter 3 presents
the application of fuzzy logic to the model presented in chapter 2. This enables the model to
estimate conditions under which a mixture of two fuels sets the electricity price. Such ability is
important especially when the relative prices of two fuels become comparable similar to the
current situation of coal and natural gas. Chapter 3 also includes simulation potential impacts of
11
Pennsylvania’s act 129 and a carbon tax policy under lower natural gas scenarios than presented
in chapter 1. Chapter 4 presents the proposed method for active participation of FACTS devices
in the wholesale electricity markets to provide additional transfer capability. Chapter 5 provides
conclusions and policy implications.
12
2. Distributional Impacts of State-Level Energy Efficiency Policies in
Regional Electricity Markets1
2.1.Introduction
In restructured power systems market forces incentivize better operation of the system in
some ways such as more efficient operation of power plants (Wolfram, C. 2005). However
energy efficiency policies imposed by governmental agencies are appropriate means of capturing
efficiencies that the market alone cannot assure (Vine et al. 2003; Gillingham, Newell, and
Palmer 2009; Benjamin K. 2009). Demand response and energy efficiency can help improve
electric-system operations by reducing the demand peak and driving peak prices to a lower level.
In 2008 there was 38,000 MW potentially available for peak shaving through demand response
programs in the US (Cappers, Goldman, and Kathan 2010). Demand response is considered a
neglected way of solving electricity industry problems (Spees and Lave 2007) and can
potentially be used more significantly in the future (Walawalkar et al. 2010).
An example of such a policy is Pennsylvania’s “Act 129,” 2which targets energy efficiency and
peak demand reduction. It requires electric utilities within Pennsylvania to reduce their annual
demand (i.e., annual kilowatt-hmy sales) by one percent, relative to 2010 levels, with an
additional 4.5 percent reduction during the 100 highest-demand hours. As Pennsylvania is part of
a regional electricity market in the Mid-Atlantic and Midwestern U.S. (the PJM Interconnection),
this state-level policy will have both local effects in Pennsylvania and potentially broader effects
1 This chapter has been published in Energy Policy: Mostafa Sahraei-Ardakani, Seth Blumsack, Andrew Kleit, 2012,
“Distributional Impacts of State-Level Energy Efficiency Policies in Regional Electricity Markets,” Energy Policy, Vol. 49, pp. 365-372 2 The full text of Act 129 can be found at: http://www.puc.state.pa.us/electric/pdf/Act129/HB2200-Act129_Bill.pdf
13
throughout PJM. These regional impacts are important policy outcomes, but capturing these
effects can be complex.
Many previous analyses of electricity policies (e.g., Mansur and Holland, 2006; Apt, et al.,
2008; Newcomer, et al., 2008; Newcomer and Apt, 2009; Blumsack, 2009; Dowds, et al., 2010)
utilize system-wide models that cannot capture locational differences in policy impacts. I refer to
this type of model as the “single dispatch curve model.” This body of literature uses publicly-
available data on generator characteristics and fuel prices to estimate a single system-wide
supply curve, and the supply-curve model is then used to estimate or simulate the impacts of
policy (as shown in Figure 1). Since locational impacts on prices and fuels utilization are
important policy variables for assessing the impacts of Pennsylvania’s Act 129, this research
takes a different approach. I utilize a statistical model to estimate supply curves for electricity in
different utility zones of the PJM market. These zonal supply curves form the basis of my
locational assessment of Act 129’s impacts.
I find that Act 129 lowers the total cost of generation between 2.1 to 2.8 percent for utilities
inside Pennsylvania in a year similar to 2009. The generation cost has the largest share in
consumer’s bills but does not include the distribution charges. Estimated savings are less than 0.5
percent for the utilities outside Pennsylvania. A previous study suggests that the benefit to cost
ratio associated with Act 129 to be between 1.9 to 2.8 in different utility zones of PJM with
exception of Allegheny Power for which the ratio is 4.1 (Statewide Evaluation Team, 2009). I
estimate that Act 129 may increase prices in Washington, D.C. and southern Maryland, although
these price increases are much smaller than the price declines in other areas of PJM.
14
The rest of this chapter is organized as follows: In Section 2 an overview of a model I have
developed in previous work (Kleit, et al., 2011) is provided that allows us to estimate zonal
supply curves in transmission-constrained electricity markets. Section 3 presents my estimated
supply curves and a statistical sensitivity analysis suggesting that my choice of model is
appropriate. The model estimated in Section 3 forms the basis of my analysis of the locational
impacts of Pennsylvania’s Act 129 in Section 4. Section 5 offers some concluding comments.
2.2.Model Description
The existence of transmission congestion implies that locational prices will differ (Wu et al,
1997). A statistical model is utilized that uses fuel prices and zonal electric loads to determine
piecewise supply curves, each segment of which represents the influence of a particular fuel type
on the zonal electricity price. To illustrate this method, I focus on estimating piecewise supply
curves with segments representing three major fuels which are consumed by thermal power
plants: coal, natural gas, and oil. Because of technological differences in power plants and
differences in fuels utilization, it is expected that the electricity price will be more correlated
with the price of the relevant fuel at each specific load level. By estimating the price and fuel
utilization at the zonal level I implicitly account for transmission constraints that inhibit the
movement of electricity between zones and produce order-of-magnitude impact estimates that
are useful for policy evaluation.
I model zonal supply curves in an electricity market as a function of load in the relevant zone,
system-wide load and fuel prices. The goal is to determine load-based thresholds or load
intervals where variations in electricity prices can be explained by variations in specific fuel
prices, i.e., gas, coal or oil (A “nuclear” segment is not estimated, as nuclear energy is almost
15
never the marginal fuel in the PJM system and thus the marginal cost of generating electricity
from fission generally does not set the market price). I will refer to this fuel-type correlation as a
specific fuel being “on the margin.” For example, if my model detects that for some interval of
demands, variation in electricity prices can be explained by variations in natural gas prices, then
I will say that natural gas is “on the margin” for that interval of zonal electricity demand. My
model does not permit multiple fuels to be on the margin simultaneously within a zone.1 Because
my econometric model estimates zonal supply curves by correlating electricity price variation to
fuel-price variation (i.e., I do not use individual plant outputs to estimate zonal electricity prices),
the definition of “marginal fuel” used in this chapter differs from that used in RTO State of the
Market Reports.2 By estimating prices and marginal fuels at the zonal level, rather than at the
system level (as in Newcomer, et al., 2008) I implicitly account for the impact of transmission
constraints on zonal price formation. This enables us to calculate the zonal effects of
Pennsylvania’s Act 129 both on prices and emissions. The statistical model is described in
greater detail in the technical appendix to Kleit, et al (2011), but I outline the basic features here.
My approach is to minimize the sum of squared errors in the following equation:
ikOkTkikOiTkikOiGkTkikGiTkikGi
CkTkikCiTkikCiOkGkCkTkikeik
epqqSFqqMpqqSFqqM
pqqSFqqMpppqqp
),,(),(),,(),(
),,(),(),,,,()12(
1 This is a limitation of our modeling approach that we leave for future methodological work. Data on marginal
fuel in the PJM system as a whole suggests that in the presence of congestion, multiple fuels may be on the margin simultaneously (i.e., the marginal fuel may differ by location). The model that we utilize to study the Act 129 demand-reduction policy implicitly assumes that there is no transmission congestion within a single utility zone. 2 For PJM, these reports are available online at www.monitoringanalytics.com.
16
Where pe is the price of electricity, pC, pG and pO are the prices of coal, gas, and oil. SFC, SFG,
and SFO are the parts of supply function associated with fuel coal, gas, and oil. qi presents the
zonal demand in zone i. Finally MC, MG, and MO are the binary variables indicating whether coal,
gas, or oil is on the margin. Subscript i indicates the zone while subscript k is used for the
indicating the kth
observation. For the sake of simplicity I use i iT qq in my formulation to
account for the demand in the entire market. My Mji variable is defined as follows:
kjMM
M
otherwiseM
izoneatinmtheonisfueljifM
kiji
J
j
ji
ji
th
ji
0
1
0
arg1
)22(
1
Equation (2-2) implies that for each level of demand in each zone, one and only one fuel is on
the margin for which the related M function is equal to 1.
In order to use Equation 1, the SF and M functions need to be specified. I utilize a quadratic
parameterization for the SF functions, as shown in equation (2-3).
2
21
2
210),,()32( TjijiTjijiijijiijijijijijiTiji qpqpqpqpppqqSF
17
where pei and pji are the price of electricity and fuel j in zone i, α and β parameters are the supply
function coefficients. As the notation suggests, fuel prices can be different among the zones.
Equation (2-3) implies that electricity prices are quadratic function of electrical load, while the
coefficients of the function can vary by fuel prices.
I define the M function in equation (2-1), which specifies the thresholds that segment the supply
curve, as regions in on qi-qT space. This method defines the set of values {qi, qT} for which a
given fuel would be on the margin in zone i, as shown conceptually in Figure 2. Intuitively, the
regions define different combinations of zonal load and load in the entire PJM system for which
my model estimates that a specific fuel has the most influence in determining that zone’s
electricity prices. These threshold frontiers are defined mathematically as:
01
0&0&0
0&01
0&0&0
0&0
1
1
1
)42(
/,/,,/
/,,/
/,/,,/
/,,/
/,/,
,/
/,/,
,/
OiCiGi
OGTOGiiOG
OGTiOG
Oi
GCTGCiiGC
GCTiGC
Ci
OGT
T
OGi
i
iOG
GCT
T
GCi
i
iGC
MMM
qqTh
qThM
qqTh
qTh
M
q
q
q
qTh
q
q
q
qTh
When iGCTh ,/ is negative, the observation lays below the threshold frontier for switching from
coal to gas. The same holds for iOGTh ,/ . Figure 2 shows that when both iGCTh ,/ and iOGTh ,/ are
negative, coal is on the margin. When both of the parameters become positive, the observation
18
lays on the last part of the supply curve which belongs to oil. Gas is on the margin when iOGTh ,/
is negative and iGCTh ,/ is positive. By including a constraint I ensure that 0,/ iGCTh and
0,/ iOGTh do not occur simultaneously. The points at which electricity supply shifts from one
fuel to another (coal to gas, or gas to oil) are defined by the locus of points at which Equation (4)
is equal to zero.
Figure 2: The variable threshold method defines regions in {qi, qT} space where a given fuel is
on the margin. My approach assumes that these frontiers are linear, and thus the estimation
problem amounts to determining the corner solutions for each frontier
19
Given a set of thresholds, parameters for supply functions (i.e., equation (2-3)) can be found by
using a least squares regression method. However, different sets of thresholds yield different
sums of squared errors so it is not always clear which choice of thresholds is optimal. To solve
this problem, which is in general non-differential and multi-modal (i.e., featuring many local
minima or maxima), I have used an evolutionary algorithm to find the set of thresholds that
minimizes the overall sum of squared errors in equation (2-1). The particular algorithm that I
use is known as CMA-ES (Hansen et al., 1996, 2001, 2004; Suttorp et al., 2009).
2.3.Estimation of Zonal Supply Curves in PJM
In order to assess the locational impacts of Act 129 in different areas of the PJM electricity
market, I estimate supply curves for electricity on a zonal basis for the PJM electricity market
using the model discussed in Section 2. These zones are shown in Figure 3 and listed in Table 1.
The data requirements for estimating zonal supply curves include hourly electric demand and
real-time electricity prices (obtained from PJM), as well as fuel price data for coal, oil and
natural gas specific to the PJM region (obtained from the U.S. Energy Information
Administration). I use data from January 2006 through December 2009 in my estimation of
zonal supply curves.
20
Figure 3: Geographical distribution of utility zones in PJM market (www.pjm.com)
Table 1: PJM Zonal Abbreviations
Utility Name Abbreviation Utility Name Abbreviation
Allegheny Power Systems
APS Jersey Central Power and Light Company
JCPL
American Electric Power
AEP Metropolitan Edison Company
METED
Atlantic City Electric Company
AECO Philadelphia Electric Company
PECO
Baltimore Gas and Electric Company
BGE Pennsylvania Power and Light
PPL
Commonwealth Edison Company
COMED Pennsylvania Electric Company
PENELEC
Dayton Power and Light Company
DAY Potomac Electric Power Company
PEPCO
Dominion DOM Public Service Electric and Gas Company
PSEG
Delmarva Power and Light Company
DPL Rockland Electric Company
RECO
Duquesne Light DUQ
21
Tables 2 and 3 present the results of my zonal supply curve estimation analysis, in which I have
econometrically estimated piecewise supply curves using equations (1) – (3). Table 2 shows my
estimated thresholds, where the fuel “on the margin” changes for each of the seventeen zones in
PJM. Table 3 shows the frequency with which each fuel is on the margin, without considering
the impacts of Act 129.
Table 2: Estimated zonal supply curve thresholds for the PJM market
qi, C/G qi, G/O qT, C/G qT, G/O R2
APS 3,774 6,035 -279,633 -339,974 0.51 AEP 10,120 32,020 -154,498 470,804 0.51 AECO 1,812 6,826 162,474 210,135 0.50 BGE 1,480 13,298 -58,987 256,953 0.48 COMED 20,835 22,378 136,912 2,539,733 0.48 DPL 912 9,745 -77,058 211,833 0.48 DUQ 4,768 1,838 118,061 -268,531 0.36 JCPL 2,236 21,195 416,978 178,123 0.47 METED 4,193 3,721 100,796 585,047 0.47 PECO 14,194 23,879 95,512 195,971 0.46 PPL 8,784 5,090 123,051 -311,513 0.47 PENELEC -20,111 3,644 64,650 564,001 0.48 PEPCO 7,143 5,854 105,180 -1,663,835 0.47 PSEG 13,427 17,780 88,355 288,573 0.51 RECO 195 1,771 166,196 166,857 0.50 DAY 2,314 4,569 689,243 480,354 0.46 DOM 32,411 31,642 84,371 301,013 0.49
22
Table 3: Estimated zonal marginal fuel frequencies in the PJM market
Coal Gas Oil
APS 21.92 77.69 0.41 AEP 37.66 62.10 0.26 AECO 19.77 80.02 0.22 BGE 13.70 86.11 0.20 COMED 27.38 72.48 0.15 DPL 12.48 87.29 0.25 DUQ 48.57 50.91 0.54 JCPL 7.67 92.11 0.23 METED 17.93 81.96 0.13 PECO 23.40 76.38 0.23 PPL 20.26 78.73 1.02 PENELEC 29.51 70.31 0.20 PEPCO 13.45 86.31 0.25 PSEG 10.62 89.15 0.24 RECO 10.06 89.75 0.20 DAY 47.71 51.98 0.33 DOM 19.42 80.40 0.19
Figure 4 illustrates the estimated thresholds for the APS zone, which covers Central
Pennsylvania and portions of West Virginia.1 The figure illustrates how the fuel on the margin
can be sensitive to the zonal and system load. For example, the slope of the coal/gas threshold
indicates the sensitivity of switching from coal to gas to the demand in APS and the total PJM’s
electrical load. I also observe that the slope of gas/oil threshold is positive. This counter-intuitive
threshold occurs because of the transmission constraints. I explain this phenomenon on a simple
three node test system in an Appendix to this dissertation.
1 Visualizations of the supply curve thresholds for other PJM zones are available from the authors upon request.
23
Figure 4: Estimated thresholds for APS. Shading represents real time prices; darker shading
indicates higher prices.
I employed F-tests to test the null hypothesis that the parameters on quadratic terms in the
regression equations are statistically different from zero. The F-test results are shown in Table 4
suggesting that the quadratic functional form is appropriate.
$/MWh
24
Table 4: F-Test results for significance of quadratic terms
Variable Thresholds
F P-Val
APS 56.16 0.00 AEP 34.55 0.00 AECO 77.14 0.00 BGE 69.84 0.00 COMED 23.72 0.00 DPL 38.34 0.00 DUQ 37.94 0.00 JCPL 8.66 0.00 METED 67.28 0.00 PECO 14.15 0.00 PPL 20.09 0.00 PENELEC 39.85 0.00 PEPCO 48.10 0.00 PSEG 2.34 0.03 RECO 21.85 0.00 DAY 43.92 0.00 DOM 30.37 0.00
I also employ F-tests to examine whether using fixed thresholds, as implied by Figure 1, yields
supply curves that are statistically similar to my model (Figure 2). The fixed threshold approach
assumes that the transition from one marginal fuel to another depends only on the level of
demand in a given zone. While the fixed threshold model yields results that are easier to
visualize, I find that my model provides better fit to the data. The results of these specification
tests are shown in Table 5 for all the utility zones in the PJM market. The results suggest that the
improvement in the fit with variable thresholds is statistically significant at the 95% level for
every zone except BGE.
25
Table 5: F-Test results for significance of variable thresholds
Piecewise Linear Piecewise Quadratic
F P-Val F P-Val
APS 39.12 0.00 6.58 0.00 AEP 23.63 0.00 22.08 0.00 AECO 17.57 0.00 4.47 0.01 BGE 1.16 0.31 5.43 0.00 COMED 23.55 0.00 14.69 0.00 DPL 4.14 0.02 6.61 0.00 DUQ 24.39 0.00 33.66 0.00 JCPL 12.33 0.00 8.21 0.00 METED 21.99 0.00 4.74 0.01 PECO 13.51 0.00 12.58 0.00 PPL 37.10 0.00 29.26 0.00 PENELEC 49.81 0.00 43.43 0.00 PEPCO 5.89 0.00 5.26 0.01 PSEG 13.12 0.00 13.13 0.00 RECO 15.88 0.00 19.33 0.00 DAY 10.10 0.00 5.42 0.00 DOM 11.67 0.00 12.83 0.00
2.4.Estimating the Impacts of Pennsylvania’s Act 129
I estimate the impact of Act 129 on zonal electricity prices in PJM, the frequency with which
each fuel is on the margin in each PJM zone, and the emissions of greenhouse gases by power
generators in the PJM system. I compare my results with those obtained from a single system
dispatch curve model that ignores transmission constraints, as in Figure 1 and Newcomer et al.
(2008). Act 129 requires utilities in Pennsylvania to cut their annual electrical load by 1 percent,
with additional load reductions amounting to 4.5 percent during the 100 highest-load hours each
year. My analysis uses 2009 (the year in which Act 129 was passed) as a base year, so annual
and peak-time load reductions are measured relative to 2009 electricity demand in PJM. The fuel
26
price scenario that is examined assumes prices of coal, gas and oil to be 2$/million BTU,
8$/million BTU, and 10.66$/million BTU respectively (Kleit, et al., 2011). This is similar to
prices prevailing in 2009 in the PJM region. This set of prices is used in my example so that I
can readily compare my results to previous work. Recent shifts in fuel prices may affect my
results.
I first use the single dispatch curve model to estimate the impacts of Act 129 on electricity prices
in PJM, fuels utilization and emissions. These results will be benchmarked against a zonal
analysis of Act 129 later in this Section. To estimate a single short-run supply curve for PJM, , I
use plant-level data from the EPA’s e-GRID database, in conjunction with my assumed fuel
prices. This is approximately the curve that is shown in Figure 1.1 For each hmy in 2009, I
estimate how Act 129 will change the market-clearing point in PJM and calculate the impacts on
prices, fuels utilization and emissions accordingly. I generate hourly electricity demands under
Act 129 using the following procedure:
1. For each hmy in my 2009 data set, I use zonal demand data from PJM to
determine Pennsylvania’s share of total PJM electricity demand.
2. Each hour’s demand in Pennsylvania is reduced by 1 percent; this reduction is
reflected in a reduced PJM-wide level of electricity demand.
3. In the top 100 hours of demand, each hour’s demand in Pennsylvania is further
reduced by 4.5 percent. This reduction is also reflected in a reduced PJM-wide
level of electricity demand during the 100 highest-demand hours.
1 The supply curve shown in Figure 1 is taken from Newcomer, et al. (2008), which uses different fuel
prices than we do in this example.
27
My estimates of Act 129’s impact generated using the single dispatch curve model projects that
total electricity costs in the PJM territory in a year similar to 2009 would decline by $150
million. I do not observe any shifts in the marginal fuel. The reduction in Pennsylvania demand
is sufficiently small relative to the size of the PJM system as a whole that the frequency with
which coal, natural gas or oil is estimated to be the marginal fuel does not change. Using plant-
level average emissions data from the e-GRID database, I calculate that Act 129 would reduce
annual carbon dioxide emissions in the PJM territory by 2.9 million tons in a year similar to
2009.
I next compare the PJM-wide analysis to a zonal analysis of Act 129. I again use 2009 as a test
year, and estimate the zonal impacts of Act 129’s implementation on electricity prices, fuels
utilization and emissions. Specifically, my zonal analysis simulates a scenario where utilities
within Pennsylvania (APS, DUQ, METED, PECO, PPL, PENELEC) comply with the demand-
reduction requirements of Act 129. Electricity demand in other PJM zones is held constant. It is
noted that some of the service territory of APS lies outside Pennsylvania. For simplicity, I
assumed that APS meets Act 129 demand reduction goals in its entire territory. For each of the
Pennsylvania zones, the supply curve for that zone is used to estimate the new market-clearing
point following the Act 129 demand reductions.
Analysis of Act 129 using my estimated zonal supply curves suggests that the savings in PJM
would be $275 million, about $235 million of which would be enjoyed by electricity consumers
in Pennsylvania. This implies that the total cost of electricity in Pennsylvania and territories of
APS outside Pennsylvania would decline by 2.5 percent, while total costs within the PJM system
as a whole would decline by 1.1 percent. The effects on prices and fuel utilization at zonal level
28
are presented in table 6 and 7. My results are of the same order-of-magnitude as existing
analyses of Act 129’s impacts (PennFuture, 2011), which suggest that savings due to Act 129
would be $278 million. The primary reason for the differences between my analysis and that in
PennFuture (2011) is that my analysis assumes that Pennsylvania utilities meet Act 129 demand-
reduction targets exactly, while PennFuture (2011) considers a case where these targets are
exceeded by more than 40 percent.
Applying average CO2 emission factors (emissions per MWh of electricity generated) for
Pennsylvania coal-fired plants, gas plants and oil plants from Blumsack, et al. (2010), I estimate
that annual emissions of carbon dioxide would decline by approximately 4 million metric tons.
29
Table 6: Act 129’s Effect on Zonal Electricity Prices in PJM
Zone
Price ($/MWh) Total Costs ( Millions of dollars)
Without Act 129 With Act 129 BAU Act 129
Savings Savings
Min Average Max Min Average Max (%)
APS 15.9 46.57 189.08 15.57 45.88 109.59 2294 2228 66 2.88
AEP 16.9 38.73 119.47 16.9 38.71 118.44 5445 5441 4 0.07
AECO 15.59 53.54 168.18 15.39 53.25 164.78 637 633 4 0.56
BGE 16.07 55.97 165.29 15.84 55.94 166.12 2017 2017 0 0.01
COMED 13.3 40.47 109.08 13.27 40.33 109.04 4223 4209 14 0.33
DPL 16.77 54 141.15 16.62 53.84 141.06 1072 1069 3 0.28
DUQ 16.82 37.49 103.71 16.59 36.9 87.58 548 532 15 2.78
JCPL 21.42 52.67 121.1 21.4 52.42 119.07 1310 1304 6 0.48
METED 19.5 51.39 138.61 19.48 50.86 132.27 840 822 19 2.21
PECO 17.1 51.91 125.68 17.32 51.22 120.11 2247 2190 57 2.53
PPL 18.04 50.44 164.02 17.86 49.76 150.03 2204 2143 61 2.76
PENELEC 17.98 44.72 105.68 17.78 44.27 102.89 812 795 17 2.1
PEPCO 15.93 57.23 199.59 15.71 57.21 201.15 1957 1957 -1 -0.03
PSEG 18.99 53.6 120.33 18.86 53.34 118.05 2546 2533 13 0.49
RECO 16.56 52.97 112.24 16.34 52.73 109.76 83 83 0 0.46
DAY 18.02 37.68 96.94 17.97 37.64 96.79 687 687 1 0.11
DOM 16.33 55.62 144.97 16.1 55.63 145.71 5650 5654 -4 -0.06
My results show that implementation of Act 129 in Pennsylvania would have the effect of
decreasing wholesale electricity prices in many areas of the PJM territory that lie outside of
Pennsylvania.1 I also observe, however, that in DOM, PEPCO, and BGE the cost of electricity
1 Detailed model results are available from the authors.
30
may increase as load is reduced in Pennsylvania, although the magnitude of the increase (0.04%)
is significantly smaller than the magnitude of the price decreases in other PJM zones. While the
system supply curve in PJM is non-decreasing, locational prices can increase when the demand
is decreased in other areas. This seemingly counter-intuitive result arises as an implication of
Kirchhoff’s Laws and congestion on the transmission network. Intuitively, in a power network
where flows are governed by Kirchhoff’s Laws, a decrease in electricity demand at one location
can increase the transmission availability for exports delivered to another location, and thus the
price of delivered power at that other location. Similar effects are described in Kirschen and
Strbac (2004), and a more detailed description is presented in the Appendix to this dissertation.
31
Table 7: Act 129’s Effect on Zonal Fuel Utilization in PJM
Zone
Fuel Share (percentage)
Without Act 129 With Act 129
Coal Gas Oil Coal Gas Oil
APS 29.13 70.52 0.35 30.91 69.09 0
AEP 55.99 43.99 0.02 55.69 44.29 0.02
AECO 22.55 77.45 0 22.71 77.29 0
BGE 14.98 85.02 0 14.69 85.31 0
COMED 30.74 69.26 0 31.08 68.92 0
DPL 16.58 83.42 0 16.37 83.63 0
DUQ 53.29 46.65 0.06 54.99 45.01 0
JCPL 11.17 88.83 0 11.21 88.79 0
METED 20.37 79.63 0 20.97 79.03 0
PECO 25.12 74.88 0 25.98 74.02 0
PPL 23.24 75.88 0.88 24.05 75.85 0.1
PENELEC 30.73 69.27 0 30.98 69.02 0
PEPCO 15.45 84.52 0.02 15.56 84.42 0.02
PSEG 13.17 86.83 0 13.35 86.65 0
RECO 13.15 86.85 0 13.27 86.73 0
DAY 60.08 39.92 0 60.18 39.82 0
DOM 14.82 85.18 0 15.03 84.97 0
The estimated impacts of Act 129 are uniformly larger using my regional supply curve
estimation method than using the single dispatch curve method. Total estimated electricity cost
savings are 67 percent larger, and estimated carbon dioxide emissions reductions are nearly 40
32
percent larger using the regional supply curve method. Using my regional supply curve
estimation method, I find that 85 percent of the net benefit of Act 129 is enjoyed by
Pennsylvania utilities, in the form of lower electricity costs. When the single dispatch curve
model is used, the region-specific impacts cannot be differentiated.
2.5.Conclusion
Analysis of electricity policies such as Pennsylvania’s Act 129 often requires understanding the
effects of transmission constraints, which can be very complex. Incorporating transmission-
system impacts in engineering models needs detailed information that is neither publicly
available nor practical to use for many economists or policy analysts. Many existing analyses
thus abstract from transmission constraints. I utilize a method that estimates zonal prices and
fuel utilization in a transmission-constrained electricity markets to estimate the impacts of
Pennsylvania’s Act 129 for utilities both inside and outside Pennsylvania. While the assumption
that transmission constraints can be ignored makes policy models more tractable, my analysis of
Pennsylvania Act 129 suggests that these models may underestimate the impacts of electricity
policies.
I find that compliance with Act 129 demand-reduction targets lowers total electric generation
costs in Pennsylvania by 2.1 to 2.88 percent in a year similar to 2009. My cost reduction
estimates are nearly twice as large as those generated by models that do not account for
transmission constraints. I also estimate significantly larger emissions reductions associated with
demand-reduction policy than previous analyses would imply (e.g., Newcomer, 2008). I also
find evidence of both positive and negative pecuniary externalities associated with state-level
energy efficiency policies. While the electricity prices decline in most of the other zones of PJM
33
(the positive pecuniary externality), these price declines are generally smaller than those within
Pennsylvania. In southern parts of Maryland and eastern parts of Virginia, I estimate that Act
129 in isolation would actually increase electricity prices (this is the negative pecuniary
externality). Differences in estimated generation reductions and emissions implications relative
to previous work, combined with the possibility for pecuniary effects, suggests that state-level
energy efficiency policies can have broad regional benefits, but such benefits are unlikely to be
uniform.
34
3. Estimating Zonal Electricity Supply Curves in Transmission-
Constrained Electricity Markets1
3.1.Introduction
Many energy and environmental policy initiatives (including emissions regulations; renewable
portfolio standards; and efficiency policies) would affect the operation of electric power grid.
Analysis of such policies is however difficult in the absence of reliable models of the electric
power system. The North American power transmission grid has been called “the largest and
most complex machine in the world” (Amin, 2004). Detailed modeling of the system requires
complete engineering data on every element of the system such as transmission lines,
transformers and generators. This engineering approach is often not feasible in the context of
policy analysis due to the proprietary nature of the data and engineering model complexity. As a
result, many policy models in the existing literature often neglect the effects of the transmission
system and use the relatively simple dispatch curve models (Mansur and Holland, 2006; Apt, et
al., 2008; Newcomer, et al., 2008; Newcomer and Apt, 2009; Blumsack, 2009; Dowds, et al.,
2010; Borenstein et al., 2002; Joskow and Kahn, 2001).
In order to construct a dispatch curve, power plants in a system are sorted according to their
marginal cost. Figure 1 shows an estimated dispatch curve for PJM and is calculated similar to
(Newcomer, et al., 2008). Given data on electricity demand, the dispatch curve can be utilized to
determine the marginal unit in the system, as well as the market price in the absence of
transmission constraints (the so-called “System Marginal Price”). However because of the
1 This chapter is under review for publication in Energy Economics: Mostafa Sahraei-Ardakani, Seth Blumsack,
Andrew Kleit, 2012, “Estimating zonal supply curves in transmission-constrained electricity markets,” Energy Economics
35
transmission constraints, both prices and marginal technologies can be potentially different at
different locations within the power system. For example in PJM during the peak hours prices
are much higher in eastern areas such as Philadelphia and Washington, D.C. compared to
Western Pennsylvania and West Virginia. At such times coal may be on the margin in the
western areas while oil is on the margin in eastern PJM.
Locational price differences induced by transmission congestion can introduce challenges in the
context of policy analysis. I take as an example Pennsylvania’s Act 129, which is an energy
conservation and efficiency policy that requires the state’s utilities to reduce their annual demand
by one percent with some additional peak demand shaving.1 By looking at the dispatch curve in
Figure 5, one can see that the slope of the supply curve is low when the demand is less than 250
GW, and a policy analyst assessing the price impact of Act 129 would predict that the Act would
not materially reduce wholesale prices in the PJM system (and, consequently, in Pennsylvania).
Such an assessment would ignore important locational price differences, with two potential
consequences. First, the estimated potential impacts of an efficiency policy such as Act 129 are
likely to be biased downwards, since they would not capture the steeper supply curves (higher-
cost generation) used in locations downstream from transmission constraints. Second, the policy
analyst would not be able to estimate locational differences in price impacts and fuels utilization.
These locational impacts may be important for policy analysis.
1 The full text of Act 129 can be found online at http://www.puc.state.pa.us/electric/pdf/Act129/HB2200-
Act129_Bill.pdf
36
Figure 5-Top: Dispatch curve for PJM using the following fuel prices: Coal: $2/MMBTU, Gas:
$8/MMBTU, Oil: $15/MMBTU. This set of prices is similar to the situation in late 2008; Bottom:
The supply curve from 120 to 220 GWh of demand. This shows the transition from coal to
natural gas more clearly.
Figure 1 suggests that I can differentiate the technologies in the supply curve and find thresholds
based on demand levels where the marginal input fuel switches. Recent shifts in relative fuel
prices in the PJM region, however (Figure 6), have resulted in some short-run substitution of
natural gas for coal technologies as the marginal cost of efficient combined-cycle gas plants
declines to levels similar to that of coal fired plants. The threshold between the region where
coal is the marginal technology and natural gas is the marginal technology becomes fuzzy, as
shown in Figure 7. When there is a fuzzy region, the marginal technology is effectively fueled
by a mixture of coal and natural gas. Further changes in relative fuel prices (which may be
caused by additional declines in natural gas prices or increases in other fuel prices) will serve to
37
widen this fuzzy region, which means that a mixture of coal and natural gas will be marginal
over a wider range of load.
Figure 6: Fuel price trends since January 2006.
0
5
10
15
20
25
Jan
-06
May
-06
Sep
-06
Jan
-07
May
-07
Sep
-07
Jan
-08
May
-08
Sep
-08
Jan
-09
May
-09
Sep
-09
Jan
-10
May
-10
Sep
-10
$/M
MB
TU
OIL
GAS
COAL
38
Figure 7-Top: Dispatch curve for PJM using the following fuel prices: Coal: $2/MMBTU, Gas:
$3/MMBTU, Oil: $20 /MMBTU. Increases in the price of coal relative to natural gas price
results in a region where a mixture of coal and gas is marginal; Bottom: The same curve is
shown for the region representing 120 to 220 GWh of demand. It shows how a mixture of two
fuels is marginal when demand is between 120 and 200 GWh.
Here I seek to develop a model with publicly available data that can capture locational
differences in technologies and fuels that are on the margin in transmission-constrained
electricity systems. My method implicitly models transmission constraints by estimating price
and marginal fuel at the zonal level as a function of zonal and system-level electricity demand.
(Large-scale power systems are often divided into geographic “zones” for planning, pricing or
other purposes; see Sahraei-Ardakani, et al., 2011). The rest of this chapter is organized as
follows: section 2 reviews the relevant literature. A simple example which motivates my method
39
is presented in section 3. My econometric model is described in section 4. The results of the
model applied to the seventeen utility zones of PJM are presented in section 5. Section 6 includes
the simulation of Pennsylvania Act 129 and a carbon tax policy. Section 7 concludes this
chapter.
3.2.Literature Review
There are several methods in the literature for forecasting short term electricity prices. These
methods include probabilistic estimation of price duration curves (Valenzuela and Mazumdar,
2005), short term forecast with fuzzy neural networks (Amjady, 2006), transfer functions
(Nogales and Conejo, 2006), linear and nonlinear time series (Kian and Keyhani, 2001; Misiorek
et al, 2006). These methods are designed to forecast short term prices from hours to a week
ahead. These models forecast the prices well but cannot be used in policy analysis where
estimation over longer periods of time is needed. Abstract equilibrium models such as (Ruibal
and Mazumdar, 2008) can provide insights into how the players can raise the prices, but cannot
be applied directly to the real markets.
Many policy analyses in the existing literature employ a simpler approach. They gather publicly-
available information on generator parameters such as heat rate, fuel type and capacity e-GRID
(US EPA, egrid v. 1.1) or other similar data sources. They also collect fuel prices and construct a
simple “dispatch curve” (short-run marginal cost curve) for the system by sorting the plants from
lowest to the highest marginal cost, without considering how transmission constraints may
impact the ability of the system operator to dispatch power plants in an economically efficient
fashion. This approach is more or less used in (Borenstein et al., 2002; Joskow and Kahn, 2001;
40
Mansur and Holland, 2006; Apt, et al., 2008; Newcomer, et al., 2008; Newcomer and Apt, 2009;
Blumsack, 2009; Dowds, et al., 2010).
While the dispatch curve models are relatively straightforward to construct, they ignore
constraints on the electric transmission network. In a power system, electricity flows are
determined by Kirchhoff’s Laws, so it cannot be assumed that electricity from a given source is
delivered to a given sink. When power systems are so constrained, the analyst’s problem
becomes much more difficult.
Here statistical methods and evolutionary optimization are used to construct a model for the
purpose of policy analysis, while focusing on capturing location-specific impacts of electricity
policies. I estimate the technology (which effectively sets the price) in each utility zone based on
the level of demand. In transmission-constrained markets it is possible for multiple technologies
to be simultaneously marginal (Kirschen and Strbac 2004). To address this my model utilizes a
type of fuzzy logic that allows mixtures of technologies to simultaneously be on the margin and
set the price in a given utility zone.
3.3.Motivating Example
The following example shows how transmission constraints introduce complexities in building
supply curves and performing policy analysis. Figure 4 shows a simple electric system with two
nodes. There is a single generator and single customer or “load” at each node. The generators
are assumed to have simple linear marginal cost functions; MC(G1) = 5 + G1 for the generator at
node 1, and MC(G2) = 10 + 2G2 for the generator at node 2. For the purposes of this example,
any capacity constraints on the two generators are ignored but I will assume that the transmission
line connecting the two nodes has a capacity limit of 20 Megawatts (MW). If demand at node 1
41
in a certain hmy is given by L1 = 30 MWh and demand at node 2 is given by L2 = 35 MWh, then
total demand in the system is L = 65 MWh and there is no transmission constraint. The supply
curve for the system is thus the vertical sum of the individual supply curves: G = 1.5P – 10 for
G>5, where G = G1 + G2 and P is the market price of electricity. At a demand of 65 MWh, We
thus have 65 = 1.5P – 10, and the market-clearing price for electricity is $50/MWh. Under this
scenario, G1 = 45 MWh and G2 = 20 MWh. Thus, 10 MWh of electric energy is transferred
across the transmission line from node 1 to node 2. A policy that, for example, would reduce
demand at node 2 by 10 MWh would reduce the market-clearing price for all consumers in the
system to $43.3/MWh.
At higher levels of demand, however, the transmission constraint prevents some lower-cost
generation from being delivered across the transmission line. Higher-cost generation local to the
downstream node must be dispatched instead. This introduces kinks into the supply curve for
each location; the location of the kinks depends on both the demand at the specific location and
the aggregate demand at all locations in the network. The “out-of-merit” dispatch of power
generators in the presence of transmission congestion segments the electricity market into two
zonal sub-markets, each of which have their own supply curve and their own clearing price.
These prices are, in essence, the Locational Marginal Prices (LMP) used in most organized
wholesale markets in the United States. Using my example in Figure 8, if the capacity of the
transmission line is constrained to 5 MW, then the marginal cost functions to supply electricity at
each node are given by Equation (3-1).
42
Figure 8: Without transmission congestion, there is a single system-wide supply curve and a
single system-wide market price. The presence of transmission congestion segments the market,
so that Nodes 1 and 2 effectively have different supply curves and different locational market
prices.
Node 1
MC(G1) = 5 + G
1
Node 2
MC(G2) = 10 + 2G
2
L1
MC(L1)
L2
MC(L2)
L
MC(L)
No Transmission Constraint
With Transmission
Constraint
MC(L=65) =$50/MWh
MC(L1=30) = 40 MC(L
2=35) = 70
43
{
{
Determining each of these supply curves for a two-node example is tractable in closed form,
even if the network is transmission-constrained. Realistic networks, however, are more complex
and far less tractable.
3.4.Methodology
When the system is constrained, different fuels can set the electricity price in different zones. For
each zone this fuel is called “zonal marginal fuel”. The zonal marginal fuel is modeled as a
function of the relevant zonal demand, system-wide demand and relative fuel prices. Then I
assign a separate segment of the zonal supply curve to each fuel type that depends only on the
relevant fuel price and load. Electricity prices are estimated based on a membership function that
relates each observation to the marginal fuels. My approach is to minimize the sum of squared
errors in the following equation:
J
j
ik
F
jikjiTkikji
F
ikjiTkikjiik epqqSFpqqMp1
),,,(),,,()23(
44
The subscript i represents the zone i, j indicates the fuel j, and k is the number of the observation.
Mj is the membership function specifying the influence of fuel j on the price in zone i. pik is the
zonal electricity price, F
ikp
is the vector of zonal fuel prices and qik is the zonal load. For the sake
of simplicity I use ∑ in my formulation to account for demand in other zones of the
market. SFij is the partial supply function regarding fuel j at zone i. ji
and ji
are the parameter
vectors for M and SF functions and eik is the error term for the observation k at zone i.
By estimating equation (3-2) separately for each zone, I am able to capture the zonal price and
fuel utilization differences resulting from transmission congestion. The model is flexible enough
to estimate piecewise supply curves with as many segments as desired (or for which data is
available). For my simulation studies j=3 is chosen to include coal, natural gas and oil, the three
major marginal fuels in PJM (While PJM uses substantial amounts of nuclear power, this
technology is not marginal in the PJM system and therefore never sets the price). Since I
estimate fuzzy membership functions the three segments of the supply curve can potentially
overlap. I refer to this area of overlap as the “fuzzy gap.” The membership functions Mji should
satisfy the following conditions:
J
j
ji
ji
M
M
1
1
10
)33(
Equation (3-3) states the probability principles for the membership functions. The probability of
each fuel being marginal is between 0 and 1, and the probability of all fuels being marginal sums
to 1. Thus equation (3-2) may be rewritten as:
45
),,(),,,(),,(),,,,(
),,(),,,(),,,,()43(
OiTiOiOiGiTiOiGiTiGiOiGiCiTiGi
CiTiCiGiCiTiCiOiGiCiTiei
pqqSFppqqMpqqSFpppqqM
pqqSFppqqMpppqqp
Where pei is the price of electricity and pCi, pGi and pOi are the prices of coal, gas, and oil. SFCi,
SFGi, and SFOi are the parts of supply function associated with fuels coal, gas, and oil, MCi, MGi,
and MOi are the membership functions indicating how much coal, gas, or oil is on the margin. All
these variables are considered at zone i.
In order to use Equation (3-4), the SF and M functions need to be specified. I use quadratic
supply curves as shown in Equation (3-5).
2
21
2
210:),,()53( TjijiTjijiijijiijijijijieijiTiji qpqpqpqppppqqSF
where α and β parameters are the supply function coefficients. As the notation suggests, fuel
prices can differ on a zonal basis. Equation (5) implies that electricity price is a quadratic
function of electrical load, while the coefficients of the function can vary by fuel prices.
In addition to the piecewise supply function I need to assign fuzzy membership functions to each
observation. In my model, the mean of the fuzzy gap is fixed based on quantities, and the width
of the gap is a function of relative fuel prices. As described in Figure 9, the fuzzy membership
functions linearly increase or decrease in the fuzzy gap from 0 to 1. The width of the fuzzy gap
depends on the relative fuel prices as shown in Equation (3-6) for the case of the fuzzy gap
between coal and natural gas.
46
(
) (
)
{
In Equation (3-6), PC is the price of coal, PG is the price of natural gas and
is the minimum
relative price (i.e., the price of coal relative to the price of gas) defining the existence of a fuzzy
gap. For relative prices below this limit, my probabilistic model becomes similar to the model
described and used in (Sahraei-Ardakani, et al., 2012 ; Kleit et al., 2011), where the thresholds
separating segments of the supply curve are defined by single points. The term specifies
how the fuzzy gap widens when the relative prices increase. I can write the same equation for the
transition from gas to oil as shown in Equation (3-7).
(
) (
)
47
Figure 9: Fuzzy variable thresholds: The fuzzy gap depends on the relative fuel prices while the
mean of the distribution is a fixed line in qi-qT space.
Thus to fully identify the fuzzy thresholds I need to find qi,C/G , qi,G/O, qT,C/G , qT,G/O,
, ,
and . Once these parameters are specified an ordinary least squared (OLS) regression
method can be used to estimate the parameters in Equation (3-5). To minimize the sum of
squared errors in Equation (3-2) I need to find the optimal parameters for the fuzzy threshold.
Estimation of the membership functions is an optimization problem with the objective of
minimizing the sum of squared errors. My examinations show that the objective function is non-
(MW)qi
(MW)
(MW)
qT
ΔC/G
Gas / Oil Fuzzy Gap
C/G
qi,G/O
Coal / Gas Fuzzy Gap
48
linear, non-convex, non-differentiable and multi-modal, having multiple local minima. Therefore
classical optimization algorithms fail to handle the problem. I use a powerful evolutionary
optimization algorithm known as Covariance Matrix Adaptation-Evolution Strategy (CMA-ES).
It takes samples from the decision space and approximates the covariance matrix from the fitness
of the samples. In the first step of the algorithm, a number of individual solutions (sets of
parameter estimates) are generated. In each generation, OLS is used to estimate the ω
parameters (see Equation 2) for each individual solution. Then the sum of squared errors is
calculated and fed back to CMA-ES as the fitness of each solution. The fitness values are used to
rank individuals and generate the next generation of parameters for the membership functions.
This process is repeated until the stopping criteria are met (Hansen and Ostermeier 2001; Hansen
et al., 2003).
3.5.Assigning Membership Functions
After specifying all eight parameters needed for the fuzzy thresholds I use them to assign
membership functions to the data points. While the width of the fuzzy gap depends on relative
fuel prices (and thus may vary from observation to observation), I assume that the mean of the
fuzzy gap (the solid lines in Figure 9) is fixed based on own area and PJM quantities. Figure 10
shows how the fuzzy membership function for coal is defined. At points A and B the
membership function gives the value of 1, while at points C and D the function has the value of
zero. The membership function is a linear plane fitting the fmy points. According to analytical
geometry I only need three points to specify the plane. The plane’s formulation is given in
Equation (3-8):
49
|
|
[
] [
] [
]
⇒ |
|
Figure 10: Fuzzy membership function assignment for coal using analytical geometry
formulation for linear plane.
qT,C/G
qi,C/G
qi,C/G
-ΔC/G
qi,C/G
+ΔC/G
qT,C/G
+m.ΔC/G
qT,C/G
-m.ΔC/G
m=qT,C/G
/ q
i,C/G
A
D
B
C
qi (MW)
qT (MW)
50
MC‘ is the unadjusted membership function for coal. The formulation provided in Equation (3-8)
gives negative values for points outside the upper bound of the fuzzy gap. It also gives values
larger than one for observations outside the lower bound of the fuzzy gap. I constrain such
estimates to lie on the upper or lower bound of the fuzzy gap, as shown in Equation (3-9)
{
The membership function for oil is calculated in a similar fashion. I force the fuzzy gaps for
coal/gas and for gas/oil to be disjoint. This is not necessary but it is consistent with the PJM
system, where coal and oil would not be simultaneously on the margin. The membership
function for natural gas is calculated in Equation (3-10).
Implementation of my method also requires some care when estimating zonal electricity prices
within the fuzzy gap, as there is some potential for price estimates to be biased upwards. I
address this issue by adjusting zonal and system loads within the fuzzy gap to bound electricity
price estimates from above. My mechanism for bounding price estimates in this way is
described in detail in Appendix 2.
3.6.Application to PJM utility zones
I utilize my method to estimate supply curves for each of the seventeen utility zones of PJM. A
map of PJM is depicted in Figure 3. The utility names with their abbreviations are presented in
Table 1.
51
Zonal load and real time prices obtained from the PJM website are used. Fuel prices for
electricity industry are also gathered from the U.S. Energy Information Administration. My data
is from January 2006 to December 2010. The membership function parameters obtained by my
method are presented in table 8. I also estimate the regression parameters introduced in Equation
6 for all the zones. These parameters are presented in table 9. With the information provided in
these two tables the zonal supply curves can be constructed and used for policy analysis. The
thresholds are depicted for Dominion (DOM) in Figure 11, in which we can see the areas where
different fuels are marginal. The figure assumes fuel prices of $2.25 /mmBTU for coal,
$5/Thousand cubic feet for gas and $15/mmBTU for oil. Using this set of fuel prices results in no
fuzzy region for a mixture of gas and oil.
Figure 11: Fuzzy thresholds in Dominion
52
Table 8: Membership function parameters
qi,C/G qT,C/G qi,G/O qT, G/O
γC/G γG/O
APS 4885 -756628 5194 -197347 0.13 0.93 4002.64 688.42 AEP 8871 -95663 14237 -163279 0.12 1.08 14160.42 186.91 AECO -57548 71221 4941 249087 0.12 0.21 1390.66 316.77 BGE 1458 -50418 4268 -243677 0.11 1.65 4797.34 37.87 COMED -143706 70960 11011 -109778 0.13 0.88 10454.08 0.00 DPL 2923 208975 4126 808240 0.13 0.17 2074.99 408.27 DUQ 1938 1482810 1463 -127304 0.12 0.61 1338.11 0.20 JCPL -5019 48417 641398 123698 0.12 1.70 3762.50 1361.02 METED 788 -62370 932 -53260 0.12 0.83 2077.84 0.00 PECO 27053 93089 20342 189257 0.12 0.17 3169.76 763.40 PPL 120492 81056 41098 141387 0.12 0.17 3256.10 539.73 PENELEC 3584 211710 5632 316370 0.12 0.91 1958.99 0.05 PEPCO -7420 48750 15243 209766 0.11 0.20 2774.62 546.99 PSEG -17851 57186 197078 127596 0.12 0.21 5045.54 1150.43 RECO -545 55368 53335 122155 0.12 0.21 229.03 38.03 DAY 1462 -147721 2221 -168889 0.12 1.25 2764.00 22.16 DOM 7945 -307678 53161 209121 0.11 0.41 6533.03 671.46
53
Table 9- Regression parameters: * indicates the significant coefficients with 95% confidence interval. Note that the coefficients
presented in the table are normalized and to get the actual numbers each row should be multiplied by the elements of the following
vector:
116 1.34E-2 1.38E-6 1.55E-3 1.91E-8 185 9.37E-4 5.11E-8 1.42E-4 1.09E-9 20.2 1.05E-3 5.52E-8 1.48E-4 1.08E-9
COAL Natural Gas Oil
Coeff 1 qi qi2 qT qT
2 1 qi qi2 qT qT
2 1 qi qi2 qT qT
2
APS 1.05* -2.26* 1.67* -0.31 0.36* 2.29* -7.54* 5.24* 1.26* 0.08 -19.67 109.42 -62.03* -66.80* 40.00*
AEP 1.42* -5.07* 4.33* 1.43* -1.39* 1.31* -4.34* 3.60* 0.64 -0.02 585.16* -1141.35 573.83 -34.66 17.77
AECO 0.84* 0.30 -0.18 -2.19* 1.50* 0.59* -0.43* 0.42* -1.30* 1.58* 45.20* 13.02 -6.17 -107.40* 56.39*
BGE 0.69* -4.27* 3.56* 2.52* -1.98* 0.07 2.11* 0.09 -2.41* 1.11* 3.35 67.25 -31.57 -79.83* 41.76*
COMED 0.78* 1.27* -0.84* -2.86* 2.00* 0.43* -0.12 0.81* -0.90* 1.05* -0.19 -0.44 1.12* 1.31* -0.85*
DPL 0.46* -0.62* 0.52* -0.65 0.64* 0.42* -2.63* 2.15* 1.40* -0.48* -11.85 57.30* -27.32* -38.11* 21.07*
DUQ 1.17* -4.45* 3.11* 1.97* -1.34* -1.21* -0.37 1.17* 2.88* -1.31* 62.98 -115.40 64.96 -18.34 8.55
JCPL 1.43* 0.76* -0.75* -4.19* 3.16* -0.11 0.02 0.04 0.35 0.63* 33.98* -6.88 5.19* -66.73* 35.78*
METED 0.40* -1.27* 1.53* -0.13 0.20 0.24* 4.31* -1.68* -5.39* 3.77* -0.24 -1.14 0.30 1.87 -0.36
PECO 1.02* -2.98* 1.98* 0.23 0.22 1.08* 0.64* 0.10 -3.36* 2.47* 34.72* 12.83 -5.44 -88.80* 47.63*
PPL 0.96* 1.05* -0.55* -3.24* 2.20* 2.41* -2.86* 1.88* -3.05* 2.65* 40.36* -10.28 6.72* -77.40* 41.77*
PENELEC 0.93* -0.95* 0.91* -1.66* 1.50* 5.04* -9.91* 6.35* -2.99* 2.96* 0.00 0.00 0.00 0.00 0.00
PEPCO 1.97* 0.09 -0.17 -4.49* 3.02* -0.03 -1.20* 1.80* 1.28* -0.99* -89.10* 344.47* -181.82* -150.77* 78.07*
PSEG 1.76* -0.67* 0.44* -3.56* 2.57* 0.28* 0.78* -0.57* -1.28* 1.59* 36.78* -11.47* 7.64* -69.21* 37.49*
RECO 1.99* -0.72* 0.43* -4.06* 2.83* 0.19* 1.11* -0.87* -1.15* 1.49* 53.75* 2.67 -0.86 -115.92* 61.46*
DAY 0.84* -2.46* 2.30* 0.24 -0.24* -1.75* 6.21* -2.14* -2.80* 1.67* 0.56* 0.00 0.00 0.00 0.00
DOM 0.88* -3.46* 2.21* 1.55* -0.82* 0.42* -0.91* 2.01* -0.19 -0.18 1083.93* -1773.76* 903.90* -431.76 218.59
54
3.7.Simulation Studies
In this section I use my zonal supply curve to simulate the impacts of two policies in PJM. I first
simulate the effects of imposing a carbon tax on electric generation. Then I study the impacts of
Pennsylvania Act 129 on utility zones in Pennsylvania and other PJM states.
3.7.1. Carbon Tax
The Representative emissions of CO2 produced from each fuel per billion BTU of energy
are as follows (Silverman): 94.35 tons for coal; 53.07 tons for natural gas; and 74.39 tons for oil.
Each thousand cubic feet of natural gas contains 1.03 MMBTU of energy. With the data on
carbon emission by fuel, I can calculate the equivalent fuel prices considering the carbon tax.
PTax
represents the price of fuel including the carbon tax. TaxCarbon has the unit of $/Ton of CO2.
Here I study the impacts of imposing $35 per ton of CO2 tax under two fuel price scenarios: a
high natural gas price scenario similar to (Newcomer et al., 2008) and a low natural gas price
similar to fall 2010. For both scenarios I assume a 10% price elasticity of demand. The fuel
prices under each scenario are presented in table 10.
55
Table 10: Fuel prices under the two scenarios
High gas price scenario
(Newcomer et al., 2008)
Low gas price
scenario (Fall 2010)
Coal ($/MMBTU) 1.73 2.25
Natural Gas ($/MMBTU) 9.95 4
Oil ($/MMBTU) 8.49 15
The estimated effects of a $35 CO2 tax on zonal electricity prices in PJM are shown in table 6.
Lower gas prices shift some of the low marginal cost gas plants to the left side of the supply
curve to serve the base load. This means that more coal fired power plants would be used for
serving shoulder load. Therefore coal would gain more influence in setting the electricity prices
(i.e., coal would be the marginal fuel more often). Imposing a carbon tax would make coal more
expensive relative to natural gas. When coal is on the margin more frequently, the carbon tax
would further increase the price of electricity. Table 6 shows that under the low gas price
scenario the average prices would increase by 89 percent while the same tax would increase
prices by 47 percent under a high gas price scenario. My estimates of overall price increases are
somewhat higher than in Newcomer et al., which estimated the price increase to be 40 percent
over all of PJM under a scenario with high natural gas prices. The model in Newcomer, et al.,
however, is not able to differentiate location-specific price increases, which I estimate to be
between 27 percent and 84 percent as shown in table 11.
56
Table 11: Average prices before and after imposing a carbon tax of $35 per ton under the two
scenarios ($/MWh)
Low gas price scenario High gas price scenario
No Tax
Tax % Change No Tax Tax % Change
APS 36.13 63.13 74.76 60.95 89.07 46.15 AEP 31.94 66.44 107.99 45.87 77.92 69.87 AECO 38.55 63.18 63.89 69.56 92.15 32.47 BGE 40.99 134.80 228.87 71.31 95.17 33.46 COMED 28.15 47.93 70.29 50.66 70.72 39.59 DPL 39.80 64.66 62.45 71.12 94.77 33.26 DUQ 32.56 61.61 89.24 45.78 80.95 76.81 JCPL 37.32 65.81 76.33 68.07 90.73 33.29 METED 40.41 80.21 98.49 62.58 98.00 56.61 PECO 39.91 62.86 57.52 64.19 95.36 48.55 PPL 38.58 62.58 62.21 61.30 92.38 50.70 PENELEC 37.12 73.21 97.20 55.64 90.13 61.98 PEPCO 38.08 70.41 84.92 74.18 94.20 26.99 PSEG 38.08 72.40 90.14 68.50 92.20 34.60 RECO 36.84 66.82 81.38 67.73 90.18 33.15 DAY 32.74 91.92 180.75 42.43 78.23 84.39 DOM 37.78 60.26 59.52 74.42 97.21 30.63
PJM 35.32 67.05 89.52 59.89 86.63 47.15
The carbon tax policy would also change fuels utilization. Table 12 presents my estimates of
how often each fuel is on the margin in each zone of PJM. Under a low gas price scenario, the
carbon tax would shift more low-cost natural gas to serving base-load demand. Under a high gas
price scenario, the carbon tax induces similar fuel-switching, but to a lesser extent in most zones
than under the low gas price scenario.
In the high gas price scenario I estimate a 7.2 percent reductions in CO2 emissions across PJM,
while Newcomer et al. estimated a 10.6 percent reduction. One possible explanation for the
differences relates to the utilization of low-cost coal assets in the presence of transmission
57
congestion; these plants may be constrained by existing congestion in the transmission system
and thus would not be used less intensively in the presence of a carbon tax. I estimate 12.35
percent CO2 reduction under the low gas price. When the gas prices are low, coal fired plants
shift from base load to shoulder load and play a more important role in setting the electricity
prices. Therefore carbon tax would have a larger effect on electricity prices when natural gas
prices are low.
Table 12: The frequency with which each fuel is marginal before and after the carbon tax (%).
Low gas price scenario High gas price scenario
Coal Natural Gas Oil Coal Natural Gas Oil No Tax Tax No Tax Tax No Tax Tax No Tax Tax No Tax Tax No Tax Tax
APS 45.72 55.47 54.04 44.53 0.25 0.00 47.37 55.66 52.36 44.30 0.27 0.05 AEP 58.66 61.45 41.34 38.55 0.00 0.00 65.61 70.97 34.39 29.03 0.00 0.00
AECO 35.64 49.16 63.10 50.78 1.26 0.06 29.98 43.54 68.37 55.86 1.65 0.61 BGE 42.68 49.77 56.34 50.23 0.97 0.00 41.50 46.71 57.53 53.17 0.97 0.11
COMED 42.66 53.21 57.34 46.79 0.00 0.00 41.53 51.88 58.47 48.12 0.00 0.00 DPL 36.47 48.11 61.23 51.64 2.30 0.25 31.64 42.52 65.80 56.31 2.57 1.17 DUQ 60.22 62.75 39.78 37.25 0.00 0.00 70.24 72.82 29.76 27.18 0.00 0.00
JCPL 33.38 48.66 65.13 51.32 1.49 0.02 27.45 41.00 71.05 58.73 1.49 0.27 METED 52.32 55.85 47.68 44.15 0.00 0.00 55.81 60.54 44.19 39.46 0.00 0.00 PECO 43.87 54.65 54.00 45.19 2.13 0.17 43.59 53.92 53.96 45.06 2.45 1.02 PPL 45.41 55.61 52.45 44.26 2.14 0.13 46.17 55.65 51.49 43.51 2.35 0.84
PENELEC 54.41 58.47 45.59 41.53 0.00 0.00 61.17 65.36 38.83 34.64 0.00 0.00 PEPCO 29.79 45.77 69.19 54.23 1.02 0.00 23.91 37.13 74.87 62.57 1.22 0.30 PSEG 35.03 48.82 63.32 51.12 1.66 0.06 29.57 42.63 68.38 56.61 2.05 0.77 RECO 31.74 47.30 66.52 52.62 1.75 0.08 25.88 39.40 72.14 59.93 1.97 0.66 DAY 64.73 61.87 35.27 38.13 0.00 0.00 80.98 76.28 19.02 23.72 0.00 0.00 DOM 34.48 46.37 65.46 53.63 0.06 0.00 35.04 41.68 64.89 58.32 0.06 0.00
I estimated the changes in producers’ surplus for all plants in the system (assuming that nuclear
power plants in the PJM system are always operating at maximum capacity, and neglecting
hydroelectric and wind energy), and for fossil plants only. The results are shown in table 13.
58
Under a low gas price scenario, the total change would create around 4.1 billion dollars in
surplus in a year while the fossil plants lose around 7.6 billion dollars in surplus (the difference
represents increases in producer surplus enjoyed by nuclear power). Under a high gas price
scenario, the total changes would create around 5.7 billion dollars, while the fossil plants lose 4.4
billion dollars in surplus.
Table 13: Changes in producers’ surplus due to the carbon tax (millions of dollars)
Low gas price scenario High gas price scenario
All the plants Fossil plants All the plants Fossil plants
APS 558.99 -189.97 550.63 -236.24
AEP 1879.42 -990.32 2264.46 -356.96
AECO 97.60 -48.40 139.95 -23.10
BGE 865.54 -1015.13 381.75 -108.94
COMED 1141.61 -33.13 970.73 -304.74
DPL -380.19 -430.45 -250.24 -297.79
DUQ 207.81 -68.33 298.04 -35.81
JCPL 71.22 -227.45 243.11 -45.79
METED 225.41 -101.23 261.50 -22.77
PECO 363.02 -222.39 613.66 -180.00
PPL 528.80 -71.66 579.41 -150.78
PENELEC -256.53 -425.60 -68.12 -234.22
PEPCO 195.71 -377.91 234.24 -131.54
PSEG -2076.28 -2402.92 -1101.82 -1359.79
RECO -6.19 -23.67 5.79 -9.34
DAY 173.35 -318.52 251.49 -45.49
DOM 569.74 -694.48 382.79 -869.35
PJM 4159.02 -7641.57 5757.35 -4412.65
The estimated supply curves for APS and JCPL under the low gas price scenario is depicted in
figures 12 and 13. In PJM the prices are higher in eastern parts where there is a larger demand. In
the western PJM, there are cheaper power plants but the electricity cannot be exported to the
eastern PJM due to the congestion in transmission lines.
59
Figure 12: Projected supply curve for APS in central Pennsylvania and West Virginia
Figure 13: Projected Supply function for JCPL in eastern New Jersey
4 5 6 7 80
20
40
60
80
100
120
Load in APS (GW)
Pri
ce i
n A
PS
($/M
Wh
)
No Tax
With Carbon Tax
2 3 4 50
50
100
150
200
Load in JCPL (GW)
Pri
ce i
n J
CP
L (
$/M
Wh
)
No Tax
With Carbon Tax
60
3.7.2. Pennsylvania’s Act 129
I use my method of estimating zonal supply curves in the PJM market to evaluate the impacts of
Act 129, implemented in Pennsylvania in 2009. Act 129 requires utilities in Pennsylvania to cut
their annual electrical load by 1 percent, with additional load reductions amounting to 4.5 percent
during the 100 highest-load hours each year. I apply my supply curve estimation method to
simulating the impact of Act 129 on zonal electricity costs in PJM, the frequency with which
each fuel is on the margin in each PJM zone, and the emissions of greenhouse gases by power
generators in the PJM system. I compare my results with those obtained from a single system
dispatch curve model that ignores transmission constraints, as in Newcomer et al. (2008). My
analysis uses 2010 as a base year, so annual and peak-time load reductions are measured relative
to 2010 electricity demand in PJM. I simulate the impacts of Act 129 under the two fuel price
scenarios described in table 4.
Plant-level data from the EPA’s e-GRID database is used, in conjunction with my assumed fuel
prices, to generate a single short-run marginal cost curve for the PJM territory. This is
approximately the curve that is shown in Figure 1. I generate hourly electricity demands under
Act 129 using the following procedure:
1. For each hour in my 2010 data set, I determine the relative amount of total PJM
demand that represents Pennsylvania utilities.
2. Each hour’s demand is reduced by 1 percent.
3. In the top 100 hours of demand, each hour’s demand is reduced by 4.5 percent.
Given my new set of hourly PJM demands, adjusted to reflect successful implementation of Act
129, hourly market-clearing prices and generator dispatch are obtained by determining the
intersection between the short-run supply curve and a vertical demand curve at each hour’s level
61
of demand. The same procedure is used to obtain hourly market-clearing prices and generator
dispatch for my baseline case, based on the PJM market in 2010.
My estimates of Act 129’s impact generated using the single dispatch curve model projects that
total electricity costs in the PJM territory would decline by $150 million on an annual basis
following the successful implementation of Act 129. In this model we do not observe any shifts
in the marginal fuel, i.e., the reduction in Pennsylvania demand does not change the frequency
with which coal, natural gas or oil is estimated to be the marginal fuel across the PJM system.
Using plant-level average emissions data from the e-GRID database, I calculate that Act 129
reduces annual carbon dioxide emissions in the PJM territory by 2.9 million tons.
For simplicity, I assumed that APS meets Act 129 demand reduction goals in its entire territory.
The fuel prices in my estimation are the ones presented as the low gas price scenario.
Analysis of Act 129 using my estimated zonal supply curves suggests that the energy cost
savings in PJM would be $ 267 million, about $200 million of which would be enjoyed by
electricity consumers in Pennsylvania. This implies that the total cost of electricity in
Pennsylvania and territories of APS outside Pennsylvania would decline by 2.4 percent, while
total costs within the PJM system as a whole would decline by around 1 percent. The zonal
results are shown in Table 14. My results are close to the estimates from an existing study of Act
129’s impacts (PennFuture, 2011), which suggest that savings due to Act 129 amounted to $278
million in 2011. My estimates may be lower than those in the PennFuture study for two reasons.
First, I assume a lower price for natural gas; and second, the magnitude of the demand reduction
used in the PennFuture study is larger than ours (their assumed demand reduction is more than
required under Act 129.)
62
Table 14: Savings from Pennsylvania Act 129 in PJM's utility zones. The units are in millions of
dollars.
Utility Zone Without
Act 129
With Act
129
Saved Percentage
Saved
APS 1833.07 1790.44 42.64 2.33 AEP 4602.33 4586.17 16.17 0.35 AECO 500.19 496.34 3.85 0.77 BGE 1533.36 1531.61 1.75 0.11 COMED 3052.06 3048.98 3.09 0.10 DPL 840.46 837.74 2.72 0.32 DUQ 501.93 492.97 8.96 1.78 JCPL 1005.66 991.47 14.19 1.41 METED 670.16 664.56 5.60 0.84 PECO 1823.39 1748.68 74.70 4.10 PPL 1661.50 1611.37 50.12 3.02 PENELEC 700.15 685.12 15.02 2.15 PEPCO 1364.51 1360.96 3.55 0.26 PSEG 1914.82 1902.89 11.92 0.62 RECO 63.52 62.87 0.65 1.03 DAY 605.70 604.59 1.11 0.18 DOM 3944.99 3933.25 11.74 0.30 PJM 26617.80 26350.01 267.79 1.01
Pennsylvania 8388.27 8188.04 200.23 2.39
The estimated impacts of Act 129 are uniformly larger using my regional supply curve
estimation method than using the single dispatch curve method. Total estimated electricity cost
savings are 78 percent larger. Using my regional supply curve estimation method, I find that 82
percent of the net benefit of Act 129 is enjoyed by Pennsylvania utilities and customers, in the
form of lower electricity costs. When the single dispatch curve model is used, region-specific
impacts cannot be differentiated.
63
3.9.Conclusion
Analysis of electricity policies often requires understanding the effects of transmission
constraints, which can be very complex. Incorporating transmission-system in engineering
models requires detailed information that is neither publicly available nor practical to use for
many economists and policy analysts. Many existing analyses thus abstract from transmission
constraints. While this assumption makes modeling more tractable, it can underestimate the
impacts of electricity policies, sometimes by substantial margins. Moreover, abstraction from
transmission constraints prevents the estimation of location-specific impacts. I develop a method
to estimate zonal prices in a transmission-constrained electricity markets. My method also
estimates the marginal fuel based on zonal load and the total demand in the market. It can also
detect when a mixture of two fuels is on the margin. My model is particularly useful when the
distributional impacts of a policy are of special interest.
I applied my model to the seventeen utility zones in the PJM footprint and calculated the fuzzy
zonal thresholds where the marginal fuel switches. My results show the sensitivity of the
marginal fuel to the zonal and system loads. I found that the price of electricity in PJM is mostly
driven by natural gas prices, although in some zones coal-fired power plants are on the margin
during the majority of hours. I simulated a carbon tax of $35 per ton in PJM and found that such
a policy would increase the prices by 47 to 89 percent in PJM. Such a policy would increase the
influence of coal on formation of electricity prices and reduce the CO2 emissions by 7.2 to 10.6
percent. My example analysis of Pennsylvania’s Act 129 shows that compliance with Act 129
demand-reduction targets lowers total electric generation costs in Pennsylvania by 2.4 percent. I
estimate the total cost reduction in PJM to be around 1 percent which translates to $267 million.
While the assumption that transmission constraints can be ignored makes policy models more
64
tractable, my analysis of Pennsylvania Act 129 suggests that these models may underestimate the
impacts of electricity policies.
65
4. Active Participation of FACTS Devices in Wholesale Electricity Markets
4.1.Introduction
The annual revenue of the US electricity industry is around 350 billion dollars (EIA). The very
large economic size of the industry emphasizes the need for efficient operation of the whole
system. The industry was considered to be a natural monopoly before 1990s and was operated
under regulation. One of the goals of restructuring, which began in the 1990s, is to decentralize
the decision making process and hopefully improve the system’s efficiency. Currently, the
operation decisions in electric transmission are made centrally by the system operator. Payments
to the regulated transmission owners are also made according to a regulated rate of return that
does not necessarily reflect the economic value of a certain transmission asset to the system.
The transmission network in the US is under stress and needs to be upgraded to keep up with the
electricity demand growth (Abraham 2002, Snarr 2009). Building new transmission lines can do
the upgrade; but the process is costly and time-consuming. FERC order 1000 suggests
considering non-transmission alternatives in transmission planning projects (FERC 2011). The
implementation of the “smart grid” could enable the deployment of flexible and adaptive
transmission networks, thus allowing for the transmission topology to be optimized depending
on electricity demand and other system conditions. One technology that would allow this is
Flexible Alternating Current Transmission Systems (FACTS). While the FACTS devices were
available before, the new communication and control technologies as well as efficient
computational algorithms offered by the smart grid make network topology optimization
possible.
66
In an analogy to the water networks FACTS devices act similar to water pumps (Fairley, 2011).
Without water pumps, water only flows from higher altitudes to the lower altitudes based on the
pressure difference which may not always be efficient in a network. Similarly electricity flows
based on voltage and angle differences which may not be economically efficient. Economic
inefficiencies can occur in the form of loop flows or counter intuitive flows from a cheap node to
an expensive one. FACTS devices make it possible to control the flows and avoid such
economically inefficient phenomena by adjusting the lines’ admittances and bus voltages.
FACTS devices can be seen as a non-transmission alternative aligned with FERC order 1000.
Department of Energy’s study of transmission grid in the US acknowledges the benefits of
FACTS devices and their role in the future of the transmission system for improved operation of
the grid (Abraham 2002). (Hauer et al. 2002) indicates that FACTS devices can control power
flows and affect transfer capabilities leading to more efficient utilization of the existing
transmission lines. (Amin 2004) claims that FACTS can increase the transfer capability over the
current transmission lines by a factor of fifty percent.
FACTS devices are already a part of our transmission network. ISO-NE has thirteen installed
and three planned FACTS in its territory (ISO New England 2012). Five EPRI-sponsored
FACTS devices are currently operating in AEP territory in Kentucky, BPA in Oregon, CSW in
Texas, TVA in Tennessee, and NYPA in New York (Basler et al. 2012). In PJM, Primary Power
LCC is developing Grid Plus project, which involves installation of several FACTS devices. The
project aims at increasing the transfer capability from west to east, reducing congestion, and
improving system stability (FERC 2010).
67
Among the different types of FACTS devices, the following three types provide the most control
over the power flows: Thyrsitor Protected Series Compensator (TPSC), Thyrsitor Controlled
Series Compesator (TCSC), and Unified Power Flow Control (UPFC). These devices would
affect admittances, voltage magnitude and angle. (Beck et al. 2006) provides more detailed
information on each type as well as the installed projects worldwide by Siemens. This includes
the first TCSC in the world, which is located in Kayenta substation in Arizona and a UPFC
installed in AEP territory in Kentucky. Here I focus on power flow control provided by line’s
admittance control.
An important feature of the FACTS devices is that they have a controllable set point. This allows
for dynamic control of the system based on its state. The dynamic setting is already being used
for dynamic stability improvement (Beck et al. 2006). It is well recognized that FACTS devices
can increase transfer capability and the application is already commercialized in various regions.
However, the set point of FACTS devices are not changed dynamically for the purpose of
increasing the transfer capability. For example, ISO-NE uses the dynamic setting of FACTS
devices for stability purpose in closed control loops (Henderson et al. 2011), but the set points
are not changed often due to the needs for adjustment of transfer capability. This means that we
have devices in the system, which are capable of lowering the system cost, but we do not utilize
them properly. Providing incentives for the owner of such devices to operate them in a socially
optimal way can improve the system efficiency. In the existing power systems, FACTS devices
are regulated similar to other transmission assets. Once they are built the owner receives the
regulated rate of return, which does not provide proper incentive for efficient operation of the
devices. Moreover, it is against the owner’s interest that the set point of FACTS is changed
dynamically. The reason is that, it increases the stress on the device resulting in higher
68
maintenance costs. Another drawback of regulated rate of return payment to FACTS owners is
that it passes the investment risks to the ratepayers. Once a project is approved the ratepayers pay
for it independent of its actual benefit to the system. A better compensation mechanism can help
avoid such problems. This can be done by means of a price signal (Cardell 2007). Here I propose
a market-based mechanism for valuing the FACTS capacity to signal improved operation of
FACTS devices.
In order for FACTS to participate in the market, it should not fall into the category of natural
monopolies. FACTS devices do not have economies of scale because they are location-specific
devices. The average investment cost of a FACTS device may decrease by the size on a specific
line, but that has nothing to do with another device in another location. Unlike the generators that
provide the same service regardless of their location, the impact of FACTS devices on transfer
capability depends on their location. Thus, if firm A builds a FACTS device on line X, it can
affect the transfer capability to some degree. But if it there is need for another FACTS device on
line Y, firm B has the to spend the same amount of money on the project as firm X. the average
investment cost does not decrease by the size due to the nature of power electronics. There is a
non-linear factor with the maintenance and degradation cost of power electronic devices, which
makes the average operational cost higher for the larger devices. Therefore, in a meshed network
neither of average capital and operational costs decreases by the cumulative size of the FACTS
in the system. The transmission lines themselves may not fall into the category of natural
monopolies either. Rather, the main reason behind regulating them is the excess market power
they would have if allowed participating in the market. This does not necessarily hold for
FACTS devices since their impact is marginal. However if for some reason a FACTS device has
69
such a huge market power, it should be treated similar to reliability must run (RMR) units and
not allowed to participate in the market.
Recently some studies have suggested implementing market-based mechanisms for transmission
sector. This would allow transmission owners to offer their services to the system operator on a
bid basis, as generators currently do in deregulated electricity markets. Such a market has been
termed a “complete real-time electricity market” (O’Neill et al., 2008). They conclude that it is
not clear whether the FACTS devices are natural monopoly and provide a theoretical background
for designing markets with active transmission participation. However there is a positive
externality problem with their payment system. I explain this in more details later in this chapter
and propose a sensitivity-based method to calculate FACTS capacity value to overcome the
issue.
Once the marginal value for FACTS capacity is determined, different payment mechanisms
could be set up. I explore the market outcome under two different payment structures. First I use
an LMP based market where the FACTS devices get paid based on the nodal price differences.
This is more or less similar to a Cournot competition for FACTS devices. Second, I set up a
supply function equilibrium (SFE) model in which FACTS devices can submit supply offers
similar to generations. The market structure can potentially lead to more efficient operation of
FACTS devices compared to the existing regulated procedures. This is in line with the
restructuring goals to improve the efficiency.
The rest of this chapter is organized as follows: Section 2 reviews the relevant literature. Market
structure and marginal value calculations are presented in section 3. Section 4 includes a
comprehensive analytical case study on a simple two-node system. Section 5 presents a
70
numerical case study in a thirty bus system. Section 6 presents a discussion on the challenges in
the complete game problem and finally section 7 concludes this chapter.
4.2.Literature Review
By utilizing communication and automation potentials of the smart grid, the transmission system
topology can be controlled in real-time. This can be done either by the system operator or
distributed decision-makers such as FACTS device owners. Recently some studies have
suggested co-optimizing generation and transmission network topology to obtain a more efficient
level of operation. The majority of research has focused on switching transmission lines
(Hedman et al., 2008; Fisher et al., 2008; Khodaei and Shahidehpour, 2010). Based on the
distribution of load and generation on the power grid switching a line off the network can reduce
loop flows. This can help reducing the power flow on some congested lines resulting to a lower
total operating cost for the system. The findings show that switching the transmission lines can
significantly save energy costs.
The switching control can be improved by using FACTS devices. TPSCs, TCSCs, and UPFCs
can continuously control the reactance of a transmission line (Hug, 2008; Hug and Anderson,
2005, Hingorani and Gyugyi, 2000). Current technology allows for significant adjustment of a
line’s reactance even as high 100% at which point the line becomes capacitive rather than
inductive (Hingorani and Gyugyi, 2000). However, at large levels of reactance adjustments
stability of the system may turn into a concern.
O’Neill et al. used this concept in their complete real-time market design which allows for
transmission bidding (O’Neill et al., 2008). Their design has so far the most complete
71
formulation to my knowledge. They allow for transmission owners to bid in the market for using
their FACTS devices to change the admittance of the lines. They limit their study to the case
where transmission lines are price taker and bid zero into the system. They argue that the right
way to compensate transmission owners is to pay them the difference between nodal prices times
the power flowing along the line. This is similar to the contract for differences of differences
proposed in (Baldick 2007). Their research is a step towards decentralizing the centrally made
optimization decisions regarding the transmission system. I build my research on their work and
address the positive externality problem in their design, where a FACTS device may get
rewarded because of the actions taken by another device. I explain this in the example presented
in section 4. To solve the issue I develop a sensitivity-based mechanism to find the marginal
value of the FACTS capacity in the market. Once the market value is calculated, different
payment structures could be set up.
There is a relevant body of literature on merchant transmission investment. Unlike regulated
transmission, a merchant transmission project recovers its costs via market mechanisms such as
Financial Transmission Rights (FTR). Hogan argues that transmission projects are alternatives to
local generation projects. Therefore having regulatory mechanism for transmission can spread
out to the generation (Hogan, 2003). Yet, merchant transmission faces different classes of
problems (Joskow and Tirole, 2004; Joskow and Tirole, 2005). (Brunekreeft, 2004) argues that
these problems do not exist in the case of controllable flows such as HVDC lines or AC lines
equipped with FACTS devices. A good market design for lines equipped with FACTS devices
can potentially support the idea of merchant transmission. The existing literature on transmission
markets is very limited and deals with unrealistic assumptions and trivial cases (Ernst et al.,
2004).
72
When dealing with transmission lines, the payments can be based on different properties of a
line. A method is introduced in (Gribik et al., 2005) for defining transmission rights under which
the owner of the line (or the holder of the transmission right) receives payments based on the
line’s capacity and its admittance. Currently transmission rights such as FTRs have positive
value only when congestion makes the nodal prices at the delivery bus larger than the source bus.
The authors argue that capacity is not the only valuable characteristic of a transmission line and
admittance should also be taken into account. In my model I use the concept of admittance
payment.
4.3.Market Structure
The market is modeled as a two-level mathematical problem. At the first level Independent
System Operator (ISO) solves a social welfare maximizing problem subject to the system and
firms’ constraints. The formulation is presented in Equation (4-1) which is taken from (O’Neill
et al., 2008).
ISO’s problem (OPF):
∑
{
bk is the offer from demanders and suppliers on their controllable variable uk. For example a
generator would put a negative bid (cost) on its controllable variable, active output power. Kk and
Ks are the vectors of asset and system constraints. An example of a system constraint would be
the power balance equations and generator output maximum limitation is an example of asset
constraints. The Lagrangian for the optimization problem is shown in Equation (4-2).
73
∑[ ]
The first order conditions of optimality are presented in equation (4-3).
Equation (4-1) can be simplified under DC assumptions. The objective function and constraints
under such simplifying assumptions are presented in Equation (4-4).
∑
∑
(
)
(
)
| | (
)
(
)
( )
( )
The objective function minimizes the cost of generation and FACTS devices considering the
constraints, which include power flow and balance equations and max/min limitations.
The correct way of solving the market is simultaneous clearing of generation and FACTS.
However the effect of FACTS devices on the power flow constraints makes the problem non-
74
convex. To avoid the complexities of a non-convex problem I solve a two-stage problem. First,
the market is solved without FACTS. Then, using the obtained dispatch a sensitivity-based
mechanism is employed to find the marginal value of FACTS capacity for each of such devices.
The sensitivity-based marginal value is shown in Equation (4-5).
∑(
)
∑(( ∑ (
)
)
)
This means that the value of each FACTS depends on its impact on the flows and also the
combined effect of all FACTS devices on the price differences at the two ends of the
transmission lines. Having the marginal value, ISO can set up various types of compensation
mechanisms for the owners of the FACTS devices. As long as the price paid to the owners is
equal to or less than the marginal value, it is economically efficient for the system operator to
dispatch FACTS devices.
For instance, ISO can transfer the control over the devices to the owners and pay them the
marginal value for the capacity. This type of competition can be modeled as a Cournot game,
where the generators still submit their offers in the form of supply functions. It should be noticed
that the Cournot game is only played by the FACTS owners by offering their capacity to the
market. The quantity offered by each device owner would be the additional transfer capability on
each line. I assume that each FACTS device owner is paid the nodal price difference times the
incremental transfer capability facilitated by the use of the FACTS device. The profit function
for one of the device owners is presented in Equation (4-6).
75
∑[( )
]
A profit-maximizing firm would choose its level of output by maximizing the function shown in
Equation (4-6). The first order condition is shown in Equation (4-7).
∑[(
)
( )
]
Another alternative, which may seem more natural, would be central control of the FACTS set
point by the ISO. In such a structure the owners are allowed to bid in the wholesale market
alongside the generators similar to what shown in Equations (4-11, and 4-14). In a competitive
market the owners bid zero since there is no cost for operating the devices. The strategic bidding
of players under this structure is beyond the scope of this study. However, there may be market
power issues associated with the design.
4.4.The two-node system with FACTS devices
In this section I apply the theory developed in the previous section to a simple two-node system.
The nodes are connected through two transmission lines. The example is taken from (O’Neill et
al., 2008). The system is shown in Figure 14.
Figure 14: The two-node, two-line system
76
X indicates reactance of the lines and K shows their thermal capacity. Assume the marginal cost
of production is lower for G1 than G2 and the thermal capacity is 400 MW for K1 and 500 MW
for K2. Suppose that the generators have unlimited capacity and both lines have equal base
reactances. They are both equipped with series FACTS devices allowing for the control of their
reactance. The net reactances of the lines are shown in Equation (4-8):
where n shows the percentage by which the reactance of the transmission line is adjusted.
Considering the thermal limit of 400 MW on line one, the maximum amount of power, which
can flow over line two would be limited to 400 MW as well. This is because of Ohm’s law in DC
power flow which states that the relative flow on parallel lines is proportional to the inverse of
their reactances (
). Since the lines initially have equal reactances the power flow would
be equal and the limit on the first line imposes an artificial cap on the second line (
). However by adjusting the reactance of the lines the power flowing along line two can
be increased. The total transfer capability from node 1 to node 2 can be calculated according to
Ohm’s law. Line 1 is congested and can only carry 400 MW. The power flowing along the
second line can be calculated based on the first line’s flow and the relative reactances. The total
transfer capability ( ) is shown in Equation (4-9).
Equation (4-9) suggests a linear relationship between n1 and the transfer capability and a non-
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linear relationship between n2 and the transfer capability. I can use the linear part of the Taylor
series to get a linear approximation (800+400n1-400n2). The transfer capability and its linear
approximation are depicted versus n1 and n2 in Figure 15. It shows that the approximation is
valid for small values of n.
Figure 15: The transfer capability when both the FACTS devices are used. It is assumed in this
figure that n1=n2
I assume linear marginal cost of production at the two nodes of the system. They are shown in
Equation (4-10) with q being the power produced.
Based on the thermal limit of the lines, the nodal prices can be calculated. I assume that
generator 2 is more expensive at the scale of this problem for all the values of demand. The
nodal prices are calculated for the case when generator 2 is needed for serving the load. The
800
810
820
830
840
850
860
870
880
890
900
0 1 2 3 4 5 6 7 8 9 10
Tran
sfe
r C
apac
ity
(MW
)
Percentage Change in Reactance
Real Capacity
Linear Approximation
78
price at each node equals the marginal cost of serving an additional unit of demand at that node.
This equals to the marginal cost of generators at each node. Having the generation levels and
marginal cost functions, the nodal prices are calculated in Equation (4-11).
is the transfer capability between the two nodes without using the FACTS devices.
The formulation developed by (O’Neill et al., 2008) suggests paying the price difference times
the quantity flowing over the line to the transmission lines. However this type of payment
removes the incentive for Line 1 to use its FACTS device in order to increase the transfer
capability. As discussed earlier no matter which FACTS device is used, the additional power
flows along line 2. Under the design presented in (O’Neill et al., 2008) line 2 would be rewarded
even for the actions taken by line 1. This is the positive externality in their formulation, when
independent companies own the FACTS devices.
The payment method I use is based on the incremental transfer capability. Each FACTS device
owner is paid the market price for reactance change times the amount of change. The ISO
calculates the marginal value of FACTS capacity using a sensitivity-based method. Having the
marginal value different payment mechanisms could be set up.
4.4.1. Market value of FACTS capacity
The marginal value of the FACTS devices can be calculated according to Equation (4-6). First, I
need to calculate the nodal price differences. Assuming that generators submit their marginal
cost to the market the nodal price difference is presented:
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The marginal value of the FACTS capacity is calculated in the following equation:
{ ( )
Under Cournot type of competition, it is assumed that each FACTS device owner is paid the
marginal value times the FACTS capacity provided by the FACTS device. Note that Cournot
game is only played by the FACTS devices and generators are still assumed to submit supply
function offers, which here assumed to be equal to marginal cost..
The profit functions for FACTS owners are presented in Equation (4-14).
To find Nash-Cournot equilibrium for this game the following conditions should hold:
The solution to the above set of equation is presented in Equation (4-16).
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Since the FACTS device owners are paid the nodal price difference, the equilibrium shown in
Equation (4-16) never relieves the congestion. The term epsilon ensures that the prices are
always different at the two nodes of the system and FACTS capacity has positive value.
An alternative to Cournot payment mechanism is a method in which FACTS devices submit their
supply offers to the market. Since the marginal cost of the FACTS capacity is zero, I assume that
they bid 0 into the market. The correct way of solving the market would be simultaneous
optimization of FACTS and generation. However because of the non-convexities involved in the
problem, I use the same sensitivity-based mechanism discussed earlier for this payment
mechanism as well.
4.4.2. Simulation study
The discussion here shows how the proposed FACTS device market would work in the context
of a numerical example. Assume that line 1 has a thermal capacity of 400 MW which makes the
equal 800 MW. The other parameters of the system are presented in Table 15. I assume that
each FACTS device can only change the reactance of the relevant line by two percent.
Table 15: Physical characerisics of the system
α1 β1 α2 β2
0.05 $/MW2 18.5 $/MW 0.5 $/MW
2 65 $/MW
The load is increased at node 2 from 800 MW to 830MW. I look at different market variables
such as equilibrium quantities (% reactance changes), nodal prices, FACTS profits, overall social
81
welfare improvement, and congestion rent. Two payment systems are studied: Cournot in which
that the FACTS owners play a Cournot game on the additional transfer capability they provide;
and SFE where the FACTS owners bid zero to the market and the ISO clears both generation and
FACTS capacity. The first set of results is shown in Figures 16 to 18.
Figure 16: Total amount of reactance change at equilibrium
82
Figure 17: Clearing price for FACTS devices
Figure 18: The profit for FACTS device owners
83
The figures show that at equilibrium in SFE model, enough FACTS capacity is offered to relieve
the congestion for loads below 816 MW. In Cournot model the device owners strategically
withhold some capacity in order to collect revenue by keeping the price larger than zero. It seems
from Figure 16 that SFE and Cournot give the same capacity at equilibrium when load is lower
than 816 MW. However, it should be noticed that the capacity offered under Cournot is slightly
below SFE because of the term epsilon in Equation 30. This is why both the prices and profits
for FACTS device owners are larger when they are paid based on LMP difference under a
Cournot model.
In SFE model, FACTS devices are dispatched based on their bids, alongside generation. Since
FACTS devices are assumed to bid zero, the price for FACTS capacity is zero until all of the
capacity is utilized. After this point, the price raises to the market value. Figures 19 to 22 show
nodal prices as well as changes in social welfare and congestion rent.
84
Figure 19: Nodal price at node 1 with and without the FACTS devices
Figure 20: Nodal price at node 2 with and without the FACTS devices
85
Figure 21: Social welfare improvement due to the transfer capability offered by the FACTS
devices
Figure 22: Decrease in congestion rent caused by the FACTS devices
86
Figures 19 and 20 show the nodal prices at the two nodes of the system with and without the
FACTS devices. When the devices are not utilized the price at node one remains at 58.5 $/MWh
which is the marginal cost of production at node 1 when the production level is 800MW. The
price at node 2 without having the FACTS devices comes from the marginal cost of production
at node 2. When the FACTS devices are utilized, SFE gives lower nodal price at node 2. In this
case the price at node 2 equals the price at node 1 plus the price charged by FACTS devices,
which equals zero when the load is less than 816 MW. LMP based compensation results in a
larger price at node 2 compared to the case when the device owners are allowed to actively bid
into the market. This is because of the strategic capacity withholding which occurs under LMP
compensation. Figures 21 and 22 show that both Cournot and SFE models increase the social
welfare and reduce the congestion rent. However as the results show, SFE model makes the
society better off by offering more FACTS capacity. The congestion rent reduction is because of
the decrease in price difference at the two nodes of the system. An important outcome of the
analysis is that both models give the exact same outcome when the congestion is severe enough
that FACTS capacity is well below the necessary amount to relieve the congestion.
Figures 23, 24, and 25 show the change in generators, customers, and FACTS surplus due to the
participation of FACTS devices in the market. They show that all of the three calculated
surpluses increase as a result of FACTS participation. The largest increase occurs in consumers’
surplus. While the additional transfer capability reduces the surplus of the expensive generator at
node 2 it increases the surplus for the other generator. This increase is larger than the decrease in
the other generator’s surplus, resulting in a total increase in the generators’ surplus. Since the
FACTS devices make profit from participating in the market the FACTS surplus is expected to
be positive.
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Figure 23: Change in c ustomers’ surplus
Figure 24: Change in generators’ surplus
88
Figure 25: Change in FACTS surplus
Figure 26 provides better insight into how the market works. The marginal value of FACTS
capacity and the supply function are depicted in the figure.
Figure 26: Supply and marginal value functions for FACTS capacity at different levels of load.
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Figure 26 shows how the price is set at different levels of demand under supply function
equilibrium payment structure. The marginal value function is the price difference at the two
nodes of the system corrected according to the transfer capability offered by the marginal
FACTS device capacity. In this example a percent change offered by the FACTS devices allows
four additional megawatts of power to be transferred from node 1 to node 2. Thus the marginal
value for FACTS capacity would be four times the nodal price difference. The more heavily the
FACTS devices are utilized the lower this value will be. When the demand is low and FACTS
capacity is enough to relieve the congestion, the price is zero. For example the market results in a
price of $0 per percent change in the reactance of each line when the demand is 805 MW.
However when the demand is large enough that FACTS capacity would not be enough for
removal of the congestion, the marginal value of the FACTS capacity sets the price. For example
at 830 MW of demand, the price would be $50.8 per percent change of the reactance which
equals the marginal value of an additional percent of FACTS capacity.
Under Cournot payment structure, the players find their optimal capacity to offer to the market
based on the same demand function. Under this design, even when the FACTS capacity is
enough for relief of the congestion, the device owners would strategically withhold some of their
capacity to keep the marginal value of the capacity positive. If the congestion is removed this
value would go down to zero.
When the congestion constraint is binding by a large margin, so the available FACTS capacity is
much below the capacity needed for removal of the congestion, both Cournot and SFE would
result in the same equilibrium. Under such circumstances all the FACTS capacity is offered at
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the marginal value of capacity.
I assumed that each FACTS device was owned by an independent firm. If they were owned by a
single firm, under both SFE and Cournot payment structures, the owner would find its optimal
output to maximize the profit. With no competition and same marginal value curve both payment
structures would lead to a monopolistic Cournot equilibrium. This would be different from the
competitive equilibrium only if the capacity of FACTS devices is enough for relieving the
congestion. Otherwise both monopoly and competitive markets would lead to the same
equilibrium where all the capacity is offered at the marginal value.
If the FACTS devices are owned by the holders of Financial Transmission Rights (FTR),
potentially the line owners, they do not have any incentive to use them since the profit they get
from these assets are much lower than the congestion rent they lose. FACTS profit shown in
Figure 18 is much lower than congestion rent reduction shown in Figure 22. Therefore the results
suggest that the ownership of FACTS and transmission lines should be separated. Moreover, it
should be noted that heavy utilization of FACTS devices could result in inadequacies in FTR
market similar to optimal transmission switching (OTS) (Hedman et al., 2011). The cheaper
generator on node 1 has an incentive to invest in FACTS capacity to gain profit from FACTS
and also increase its surplus by exporting more energy to node 2. On the other hand similar to
transmission lines the expensive generator at node 2 does not have proper incentive to operate
the FACTS devices since the profit it loses in generation side is larger than the FACTS profit.
Under SFE assumptions, even if the FACTS devices are owned by the transmission lines or the
expensive generator, they cannot impose more costs to the system than the initial cost without
FACTS. However under Cournot assumptions, this could happen by further congesting the lines,
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since the Cournot payment of FACTS would be smaller than the additional rent generated by the
congestion. Thus ownership of FACTS devices by generation or transmission companies may or
may not be harmful to the system.
4.5.Numerical example
In this section I apply the model developed in previous sections on a thirty-bus system. The
system is shown in figure 27. It has thirty busses and six generators. Detailed data on the system
is provided in an appendix. Lines 25 and 26 are taken out of the system and line 15 is the only
transmission line which is constrained in the scale of the problem. Its capacity is limited to 20
MW. The cost function coefficients of the generators are presented in table 16.
Figure 27: IEEE standard 30-bus, 6-generator system
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Table 16: Cost function coefficients of the generators
------ α β
Gen. 1 0.1 16
Gen. 2 0.11 16
Gen. 3 0.12 16
Gen. 4 .13 16
Gen. 5 14 16
Gen. 6 15 16
The generator’s cost function coefficients are changed so that the generation in areas 1 and 2
becomes cheaper than the generation in area 3. Thus, ideally most of the energy demanded in
area 3 would be imported from areas 1 and 2. However, because of the transmission capacity
limit on line 15, the deliverable power from areas 1 and 2 to area 3 is limited.
The generators’ capacities are all limited to 150 MW. Two FACTS devices are installed on the
inter-ties 15 and 32. FACTS capacity is limited to 20% change in the reactance of the linked line.
In order to calculate the marginal value of the FACTS devices the sensitivity of prices and power
flows to the changes made by each device should be calculated. Each device is used with 1%
change in the reactance of its related line and the changes in power flows and prices are
calculated. Table 17 summarizes the sensitivities. For each line ΔF indicates the change in the
flow of that line due to 1% change in the reactance with the FACTS device. ΔF1 corresponds to
changes due to the device installed on line 15 and ΔF2 corresponds to the FACTS installed on
line 32. Δλ represents the price difference at the ends of each line when the FACTS devices are
not used. Δλ1 and Δλ2 show the same variable when the relative FACTS is used. Δ(Δλ)1 and
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Δ(Δλ)2 represent the changes in the price difference at the two ends of each line due to 1% usage
of each device. The lines which are not affected by the FACTS devices are taken out.
Table 17: Sensitivity of power flows and prices over the transmission network to the FACTS
devices in IEEE-30 Bus System
Line #
From To ΔF1 ΔF2 Δλ Δλ1 Δλ2 Δ(Δλ)1 Δ(Δλ)2
1 1 2 -0.0016 0.0064 5.8927 5.871 5.9597 -0.0218 0.067
2 1 3 0.0016 -0.0064 -1.866 -1.8591 -1.8872 0.0069 -0.0212
3 2 4 0.0114 -0.045 -11.6872 -11.6441 -11.8201 0.0431 -0.1329
4 3 4 0.0016 -0.0064 -3.9285 -3.914 -3.9731 0.0145 -0.0447
5 2 5 0.0064 -0.0252 2.1758 2.1677 2.2005 -0.008 0.0247
6 2 6 0.0397 -0.1568 12.1843 12.1393 12.3228 -0.045 0.1385
7 4 6 0.013 -0.0514 23.8715 23.7834 24.1429 -0.0881 0.2714
8 5 7 0.0064 -0.0252 1.3055 1.3006 1.3203 -0.0048 0.0148
9 6 7 -0.0064 0.0252 -8.7031 -8.671 -8.802 0.0321 -0.0989
10 6 8 0.0018 -0.0072 1.709 1.7026 1.7284 -0.0063 0.0194
11 6 9 0.0248 -0.0981 12.1946 12.1496 12.3332 -0.045 0.1386
12 6 10 0.0142 -0.056 18.5822 18.5136 18.7935 -0.0686 0.2112
14 9 10 0.0248 -0.0981 6.3876 6.3641 6.4603 -0.0236 0.0726
15 4 12 0 0 149.6006 149.0484 151.6786 -0.5522 2.0781
16 12 13 0.0359 -0.1371 0 0 0 0 0
17 12 14 -0.0079 0.0302 -7.92 -7.8908 -8.01 0.0292 -0.09
18 12 15 -0.028 0.1069 -14.0123 -13.9606 -14.1716 0.0517 -0.1593
20 14 15 -0.0079 0.0302 -6.0923 -6.0698 -6.1616 0.0225 -0.0693
25 10 20 0 0 93.1345 92.7907 94.5707 -0.3438 1.4362
26 10 17 0 0 107.1468 106.7513 108.7423 -0.3955 1.5955
27 10 21 0.0056 -0.022 9.1252 9.0915 9.2289 -0.0337 0.1037
28 10 22 0.0335 -0.1321 11.7324 11.6891 11.8658 -0.0433 0.1334
29 21 22 0.0056 -0.022 2.6072 2.5976 2.6368 -0.0096 0.0296
30 15 23 -0.0359 0.1371 -27.6497 -27.5476 -27.964 0.1021 -0.3143
31 22 24 0.039 -0.1541 16.4254 16.3647 16.6121 -0.0606 0.1867
32 23 24 -0.0592 0.2335 -37.3271 -37.1893 -38.1289 0.1378 -0.8018
33 24 25 -0.0201 0.0794 -15.5088 -15.4515 -15.6851 0.0572 -0.1763
35 25 27 -0.0201 0.0794 -9.8692 -9.8328 -9.9814 0.0364 -0.1122
36 28 27 0.0201 -0.0794 18.7985 18.7291 19.0122 -0.0694 0.2137
40 8 28 0.0018 -0.0072 0.8545 0.8513 0.8642 -0.0032 0.0097
41 6 28 0.0183 -0.0722 2.5634 2.554 2.5926 -0.0095 0.0291
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Using the information presented in table 17, the FACTS marginal value functions can be
calculated. The marginal value for each device should represent changes in the power flows at
the price difference. This should be summed over all the transmission lines. Equations (4-17) and
(4-18) show the calculations for the two FACTS devices in the system. The marginal value
functions are depicted in Figure 28.
∑((
)
)
∑((
)
)
Figure 28: Marginal value of FACTS capacity in IEEE-30 bus system.
95
Since line 15 is congested, FACTS devices are used to increase the reactance on line 15 and
decrease the reactance on line 32 each by 20%. This way more power would flow along line 32,
increasing the total transfer capability from areas 1 and 2 to area 3. The dispatched output of
generators is shown in Figure 29. If there was no congestion, FACTS would not be used because
there was no need for it.
Figure 29: Generators’ output when the FACTS devices are used and when they are not used.
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The FACTS capacity needed to relieve the congestion is substantially larger than the 20%
capacity installed on the two inter-ties. Therefore as discussed in the previous section, Cournot
and SFE give the same equilibrium with all the capacity offered at the marginal value. The nodal
price differences when the FACTS devices are used are depicted in figure 30. In this system,
generators 5 and 6 are relatively more expensive and because of the limit on the capacity of the
inter-ties there is not enough capacity for the generation in areas 1 and 2 to be exported to zone
3. Thus, the prices in zone 3 would be higher. The FACTS devices can help increasing the
transfer capability and decreasing the price in zone 3. Figure 30 shows that the prices at all the
nodes of zone 3 would decrease as the result of using the FACTS devices and prices in other
zones would slightly increase.
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Figure 30: Price difference between the case where the FACTS devices are not used and the case
where they are used.
The two FACTS devices decrease the generation cost from $19851 to $14868, a 25% decrease.
They also reduce customers’ cost from $23562 to $17284, a 26% decrease. At the same time the
device owners each make $92 and $359 relatively.
4.6.The complete game
Two payment mechanisms where introduced and simulated in previous sections. I solved for
Nash equilibrium under Cournot payment structure. Under SFE set of assumptions, I assumed
that the FACTS owners would bid zero. The generators were assumed to always submit supply
offers equal to their marginal cost functions. This is similar to the assumption of (Joskow and
Tirole, 2005) where they argue that the resulting supply function at each node comes from a
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local competition. They further assume that the changes in transmission network have no
significant effect on the local competition. By this logic the only strategic players that should be
considered are the FACTS device owners. The same set of assumptions is used here in the two-
node example (section 4.4) and thirty-node example (section 4.5). The complete game would
consider both FACTS and generators as strategic players, responding to each others’ strategies.
Moreover, the market considering FACTS and generation should be cleared simultaneously. In
order to avoid the complexities involved with non-convexities of FACTS impacts, I solved the
market without FACTS and use a sensitivity-based method to find the optimal FACTS dispatch
and value. Then, I solve the market with the obtained topology to find the final generation
dispatch. Although, my assumptions are restrictive, they are reasonable to show potential
benefits of a better market design allowing for active participation of FACTS devices. Solving
for Nash equilibrium in a complete market would be interesting but involves some practical
challenges. Here I mention some of these difficulties:
1. The problem of optimal bidding strategy under SFE assumptions can be straightforwardly
solved when the transmission constraints are not binding. Under such circumstances there
is a single price at all the nodes of the system and there would be no need for FACTS
devices to be dispatched to increase transfer capability. The problem becomes
challenging when transmission constraints are binding and nodal prices differ (Day et al.,
2002). In a transmission-constrained market, pure strategy Nash equilibrium may not
exist (Cunningham et al., 2002). There may also be multiple equilibria or local equilibria
(so-called Nash traps). The local equilibria only satisfy equilibrium conditions in a subset
of the strategy domain (Son and Baldick, 2004). Figures 31 and 32 show the best
response dynamics of the generators’ bidding strategies in the two-node and thirty-bus
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system with no FACTS devices. In the figures it is assumed that the generators submit the
slope of their supply function truthfully (equal to the slope of their marginal cost) and just
play with the intercept. The oscillatory behavior means that there is no stable pure
strategy Nash equilibrium. The explanation for figure 31 is that starting from their
marginal cost, the expensive generator at node two only gets to generate 25MW, and so it
increases its bid to the price cap. Generator one then increases its bid so much that still
generates 800 MW but gets a price close to the price at node 2. Then generator 2 reduces
its bid to reduce the price a little bit but gets larger production share and thus increases its
profit. The cheap generator then reduces its bid again to recapture its share of production.
As shown in figure 31 this cyclic behavior does not converge to Equilibrium. Similar
cyclic behavior is observed in the 30-bus system. However, because of the existence of
multiple generators in each area, the bidding strategies do not reach the price cap. The
introduction of FACTS bidding adds to the non-convexity of the problem and calculating
the best response dynamics becomes even more challenging.
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Figure 31: Generator's bidding strategies in two-node system assuming a price cap of
$3000 per megawatt hour. The demand at node two is 825 MW.
Figure 32: Generators’ bidding strategies in the 30 bus system.
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2. The equilibrium in SFE models for generators is shown to be the artifact of the
parameterization of the model (Baldick, 2002). This means that the results can be product
of the choice of the decision variables, e.g. slope or intercept. This would make the
results hard to generalize. In my model, in case of heavy congestion the outcome is not
dependent on the choice of decision variable and the marginal value curve sets the prices.
Further research similar to (Baldick, 2002) is needed for FACTS devices to determine
whether the outcome of SFE model for FACTS is robust to the choice of decision
variable or not in the case of low congestion.
3. A solution to these problems is adoption of a Conjectured Supply Function (CSF)
approach instead of supply function (Day et al., 2002). CSF is a conjectural variation
model with players form conjectures about other players’ supply functions. CSF
equilibrium can be calculated in larger transmission networks and better represents a real
power system than a Cournot model for generators. Again note that the designed Cournot
market for FACTS is different from Cournot game for generators. In this chapter the
generators were always assumed to submit supply offers in the form of supply functions,
which were assumed to be equal to marginal cost. CSF is not as realistic as SFE, since the
assumed conjectures may be different from the actual reaction of the rivals. Using a range
of different conjectures can provide a wider overview of the market’s behavior. However
it will add to the complexity of the model without necessarily enabling the generalization
of the results. The outcome of CSF is sensitive to the choice of the selected conjectures
and thus is not robust.
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The complete game problem is computationally interesting, but more fundamental advances are
necessary to characterize equilibrium, if such a stable equilibrium exists, in the complete
strategic game. Since the focus in this research is on the policy implications of inclusion of
FACTS devices in the electricity market, I keep the assumption that generators are not strategic
players and focus on the behavior of FACTS devices. This assumption may be restrictive for
conclusions especially in the future with potentially larger FACTS capacity. But in order to
prevent the challenges briefly explained in this section I did not try to solve the complete game.
This research fixes the incentive problem identified in previous work (O’Neill et al., 2008) by
offering a new payment mechanism. Further research is needed to address the complete game’s
equilibrium.
4.7.Conclusion
With the smart grid technology, transmission topology can be co-optimized with generation
simultaneously. Here I study the possibility of having a market for FACTS devices in order to
control the admittance of the lines. It was discussed that FACTS devices are not natural
monopoly and can participate in the market. I discussed the positive externality problem in a
recent study aimed at inclusion of transmission in the wholesale electricity market. I addressed
the problem by proposing another method to value the FACTS capacity. The correct way of
calculating the value is simultaneous co-optimization of generation and FACTS. However, to
avoid the complexities of dealing with a non-convex problem, a sensitivity-based method was
used to estimate the value of FACTS capacity. Once the value is calculated, different payment
mechanisms could be set up by the system operator to compensate the owners.
I investigated two different payment structures: first, they were paid based on the LMP
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differences similar to FTR. Second: They were allowed to submit their offers to the market
which means they put prices on the percentage changes in the admittance of the line. Since the
marginal cost of FACTS devices is zero, it was assumed that they would bid zero to the market.
The designs were formulated and simulated on a simple two-node system. It was shown that both
designs can be beneficial to the system and also to the players. However bid-based FACTS
market was more efficient for the society compared to LMP compensation design. It was shown
that when the device owners are being paid based on LMP differences they may strategically
withhold some capacity and may deviate from socially optimal point. If the FACTS capacity is
low enough compared to the congestion, both SFE and Cournot have the same outcome. Under
such circumstances all the available capacity is offered at the marginal value. Simulation of the
market on a 30-bus system with two inter-ties showed that two FACTS devices were able to
reduce the generation and demand costs by 25% via changing the inter-tie reactances by 20%.
These results suggest that providing a proper market-based signal to the FACTS owners can
effectively decrease the system cost.
Participation of dispatchable transmission assets such as FACTS devices would also change the
generation dispatch. As shown both in the two-node and thirty-node system, the FACTS devices
increase the amount of deliverable supply to nodes with higher prices caused by congestion.
They help the cheaper generation to replace some more expensive generation and lower the
market share of the expensive generators. This means that these devices can lower the market
power for some generators by lowering their market share.
However this conclusion alongside other comments made in this study is based on the
assumption of independent ownership of these assets. FACTS devices change the power flows
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and allow for dispatch adjustments to lower the total system cost. This means that some cheaper
generation replaces some expensive generation. Depending on the impacts of FACTS on
different generators, they may or may not have the right incentives to operate FACTS in a
socially optimal way.
The congestion rent is given away by the RTO through its FTR auctions. The revenue from that
auction is allocated to the owners of transmission assets (so-called Auction Revenue Rights). A
profit-maximizing transmission owner that also owned FACTS devices would need to weigh the
lost ARR revenue from operating FACTS devices against the payments given by the RTO to the
FACTS device. Suppose that some market player paid exactly the congestion rent for an FTR,
the two-node example suggests that the lost ARR revenue is much larger than the FACTS profit.
Figure 18 shows the FACTS profit, which is lower by a wide margin that the lost congestion rent
shown in Figure 22. Therefore the transmission lines do not have the right incentive to operate
FACTS in a socially optimal way.
The other assumption is this chapter was the competitive behavior of the FACTS devices with
respect to each other. In the case that the same firm owns more than one device, the outcome of
the market would be closer to a monopolistic behavior. A pure monopoly for FACTS devices
could result in strategic withholding, with prices always as high as the marginal value. The
results presented in previous sections showed that competitive behavior is only observed when
the FACTS capacity is enough to relieve the congestion. If the congestion is large enough and
the capacity constraint for FACTS devices is binding the outcome of competition and monopoly
are the same. Under such circumstances all the FACTS capacity would be offered at the marginal
value. This happens because the system needs more FACTS capacity than the available.
105
Therefore, there would be no competition on the available FACTS capacity and all the device
owners can get paid the marginal value, which is the cap on FACTS price. This was shown both
in the two-node and thirty-bus examples.
The initial results in this chapter show that the ownership of FACTS and transmission lines
should be separated. Even if the congestion is large and would not be relieved by the installed
FACTS capacity, the price change caused by the FACTS devices would lower the congestion
rent. This was shown in the simulation studies in this chapter. While some generators may have
the right incentive to invest in FACTS capacity it is not clear whether the ownership of FACTS
and generation assets should be independent. Further research is needed to better answer the
question of whether ownership of FACTS and other assets would result in a manipulative
adjustment of the network topology or not.
Changing the way FACTS devices operate today would affect some other operational protocols.
For instance by changing the impedance of a line, the protection relay settings should also be
adjusted to represent the correct protection zones. Moreover, the FACTS setting should be
communicated to the neighboring systems so they have the correct model for their transmission
system.
106
5. Conclusion and Policy Implications
Analysis of electricity policies often requires understanding the effects of transmission
constraints, which can be very complex. The constraints on the transmission system cause
locational price disparities in the system. This dissertation has two main parts addressing two
problems regarding the transmission constraints.
The first part (Chapters 2 and 3) develops a supply-demand policy analysis tool which captures
the distributional impacts of the policy in transmission-constrained electricity markets. The
model uses same publically available data and statistical methods used by policy analysts in their
transmission-less models. It also implicitly accounts for the impacts of the transmission
constraints by estimating the price and fuel utilization at the zonal level. The distributional price
and fuel utilization impacts are sometimes important policy outcomes which are not detectable
with transmission-less models. This is especially important when the policy under study is at
state level. The inputs to the model are zonal demand, total demand in the system, and fuel
prices. The model can also capture conditions under which a mixture of two fuels sets the
electricity price using fuzzy logic.
I applied my model to seventeen utility zones in the PJM footprint and calculated the zonal
thresholds where the marginal fuel switches. The results show the sensitivity of the marginal fuel
to the zonal and system loads. They show that the price of electricity in PJM is mostly driven by
natural gas prices. The example analysis of Pennsylvania’s Act 129 shows that compliance with
Act 129 demand-reduction targets lowers total electric generation costs in Pennsylvania by 2.1 to
2.88 percent in a year similar to 2009. While the electricity prices decline in most of the other
107
zones of PJM, southern parts of Maryland and eastern parts of Virginia might face price
increases. Assuming natural gas prices at levels similar to fall 2010, almost half of the prices in
2009, Pennsylvania Act 129 would lower total electric generation costs in Pennsylvania by 2.4
percent. I estimate the total cost reduction in PJM to be around 1 percent which translates to
$267 million. The cost reduction estimates are nearly twice as large as those generated by models
that do not account for transmission constraints. Although the assumption that transmission
constraints can be ignored makes policy models more tractable, the analysis of Pennsylvania Act
129 suggests that these models may underestimate the impacts of electricity policies.
Differences in estimated generation reductions and emissions implications relative to previous
work, combined with the possibility for pecuniary effects, suggests that state-level energy
efficiency policies can have broad regional benefits, but such benefits are unlikely to be uniform.
The simulation of a carbon tax of $35 per ton in PJM shows that such a policy would increase
the prices by 47 to 89 percent in PJM. It would also increase the influence of coal on formation
of electricity prices and reduce the CO2 emissions by 7.2 to 10.6 percent. None of the above
mentioned zonal studies were possible with the models which abstract from the transmission
system.
The second part of this dissertation (Chapter 4) focuses on the improvement of the transmission
system with FACTS devices. With the smart grid technology FACTS devices can be used to
optimize the topology of the network as an alternative to building new transmission lines or
cheap generation. While FACTS can upgrade the system appropriate policies are needed to
facilitate the investment in this technology. I studied the possibility of having a market for
FACTS devices in order to control the admittance of the lines as a potentially more efficient
108
method than regulating them like the wires. I discussed that the FACTS devices unlike the
transmission lines are not necessarily natural monopoly and thus can participate in the wholesale
electricity market to provide transmission services.
I proposed a market based mechanism to identify the value of additional transfer capability
provided by the FACTS devices. Once this marginal value is calculated, different payment
structures can be set up by the system operator. I investigated two different payment structures
for compensating the FACTS devices: first, they are paid based on the LMP differences similar
to FTR. Second: They are allowed to submit their offers to the market which means they put
prices on the percentage changes in the admittance of the line. The designs were formulated and
first order conditions at equilibrium were derived. They were simulated on a simple two-node
system with a comprehensive analysis. It was shown that both mechanisms can be beneficial to
the system and also to the players. However bid-based FACTS payment structure was more
efficient for the society compared to LMP-based compensation method. It was shown that when
the device owners are being paid based on LMP differences they may strategically withhold
some capacity and deviate from the socially optimal solution. If the congestion is severe enough
that FACTS capacity is not enough for relieving it, the outcome of both designs could be
equivalent. Under such circumstances all the FACTS capacity is offered to the market at the
marginal value. This would still improve the social welfare. The marginal value of FACTS
capacity was also simulated on a 30-bus system to present the necessary computational steps.
The results suggest that the transmission system can be improved with FACTS devices as an
alternative to investment in cheaper generation or transmission lines. Proper modifications to the
current wholesale electricity market designs can be made to signal the right incentive for
109
investment and optimal operation of FACTS capacity. The installed FACTS can improve the
transmission network and gain revenue by participating in the market.
From a regulatory standpoint my initial results suggest that the ownership of FACTS devices
should be independent of the transmission lines, they are installed on. Further research is needed
to better answer the question of whether ownership of FACTS and other assets would result in a
manipulative adjustment of the network topology or not. Other market players may or may not
have the right incentive to invest and operate the FACTS devices in a socially optimal way.
Equilibrium conditions in the complete game should be identified to help answering these
questions.
110
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Appendix 1: Explaining Some Counter-Intuitive Results
This appendix discusses in more detail two seemingly counter-intuitive results in chapters two
and three of this dissertation. First, my results indicated that as the demand for power decreased
in Pennsylvania, prices increased in Virginia and the District of Columbia. Second, for some
scenarios I found that some thresholds in quantity in one zone were positively related to
quantities in other zones. While these results may be economically counter-intuitive, they are
relatively simple implications of Kirchhoff’s Laws. In this appendix I use a three-node network
to illustrate how these results can arise.
My simulation of Act 129 suggests that by decreasing load in Pennsylvania, electricity price in
Virginia and Washington, DC area increases. To understand how that could happen consider the
power system shown in Figure A-1 below. In Figure A-1, Node 1 represents the Virginia and
Washington, DC area, while the other two nodes in the network represent the remainder of the
PJM system.
120
Figure A-1: Three node test system. All transmission lines in the system are assumed to have
equal impedances.
Let Qk be power generation at node k; Lkj represent the flow along the transmission line
connecting nodes k and j; and λk be the LMP at node k. For a system without any transmission
congestion I have:
Q1=35 MW Q2=25 MW
λ1= λ2= λ3= 35 $/MWh
Power flows: L1,2=0 MW L1,3=25 MW L2,3=25 MW
RestofPJM
VirginiaandWashington,DC
10MW
MC1=Q1
MC2=10+Q2 50MW
1
2 3
121
Now assume that the line connecting node 1 to node 3 has a thermal capacity of 20 MW. This is
5 MW of power less than what it carries in the unconstrained scenario above. In order to reduce
capacity on line 1-3 while still meeting demand, generator 1 must reduce its output by 15 MW,
while generator 2 has to increase its power output by 15 MW. The resulting prices and quantities
are:
Q1=20 MW Q2=40 MW
λ1= 20 $/MWh λ2=50$/MWh λ3=2 λ2- λ1 = 80 $/MWh 11
Power flows: L1,2=-10 MW L1,3=20 MW L2,3=30 MW
Now assume that load at node 3 decreases to 45 MW. This load reduction in node 3 enables an
increase in output from generator 1. The resulting prices and quantities are:
Q1=25 MW Q2=30 MW
λ1= 25 $/MWh λ2=40$/MWh λ3=2 λ2- λ1 = 55 $/MWh
Power flows: L1,2=-5 MW L1,3=20 MW L2,3=25 MW
11 To consume an extra megawatt of load at node 3, two additional megawatts need to be generated at node 2 and the generator at node 1 must reduce its output by one megawatt. Thus the price at node 3 equals twice the marginal cost at node two minus the marginal cost at node 1.
122
Thus, decreasing load at node 3 actually increases the price of power at node 1.
More generally, reducing load in a particular zone may allow for more exports of power from
another zone. This in turn will increase the marginal cost of power at the exporting zone,
resulting in increased costs for consumers in that zone.
The second seemingly counter-intuitive result in that chapter is that the slope of some fuel
transition thresholds could be positive (as in Figure 6). I now explain this result, again using a
three-node network.
In a system with no active transmission constraints, I expect to have identical prices in all
locations. In such a system it does not matter where the load is, and the marginal unit specifies
the marginal fuel for serving demand at any of the nodes. Thus both qi and qT have the same
effect and the slope of variable threshold line should be negative.
Now consider the following system:
123
Figure A-2: Three node test system with two different types of plants at node 1.
As in the previous example, assume that line 13 has thermal capacity of 20 MW, as well as
qi=10 MWh. Assume that the gas turbine at node 1 has generation capacity of 20 MW. Other
generators are unconstrained and marginal cost of generator at node 2 is 55$/MWh.
For qT = 50 MWh, 10 MWh of the capacity of the gas turbine at node 1 would be in use to serve
the load at node 1. Thus, the maximum zonal load qi for which the marginal fuel is natural gas is
qi=10 MWh. Thus, the maximum amount that can be supplied to node 3 from node 1 (with
natural gas as the marginal fuel) is 10 MWh, with 40 MWh supplied from node 2. For any larger
zonal load at node 1, the system operator would have to use the oil fired plant at node 1 which
would thus become the marginal unit at node 1.
124
Now assume that qT = 45 MWh . In this case, 15 MWh of the gas turbine at node 1 would be in
use for serving the load at node 3, leaving 5 MWh of the gas turbine’s capacity for the zonal load
qi. Thus for any zonal load larger than qi = 5 MWh, oil would be the marginal unit. The
reduction in quantity demanded at node 3 reduces the amount of power required from node 2.
This in turn increases the quantity that can be supplied from node 1. Here the quantity supplied
from node 1 increases from 10 to 15 MWh. This in turn makes oil the marginal fuel at node 1,
increasing the price at node 1 from $20/MWh to $50/MWh.
Once again, reducing demand serves to reduce demand on the transmission system. This, in
turn, may allow for further exports of power from a particular zone, increasing the price of power
in that zone. The gas/oil threshold at node 1 would thus have a positive slope. Figure A-3
depicts this situation. It means that although congestion poses higher costs to the system, it is
beneficial for some nodes.
125
Figure A-3: Gas/Oil threshold at node 1 with positive slope.
126
Appendix 2: Correcting for Electricity Price Over-Estimation in the Fuzzy
Gap
For the sake of simplicity assume that the marginal fuel is just a function of zonal load.
Moreover assume that the electricity price is a linear function of load in each segment. Figure
A1-a shows such a condition when the difference between natural gas and coal price is large
enough that there is no overlap between segments of the zonal supply curve (the threshold
between the coal and gas segments is a single point). At the threshold the most expensive coal
fired power plant sets the price at p1. Now assume that natural gas prices drop to a lower level
resulting in a fuzzy gap between the coal and natural gas segments of the zonal supply curve.
The price is still equal to p1 but it could be set either by a high-cost coal plant with a marginal
cost of p1 at the relevant level of production, or a low-cost natural gas plant, also with a marginal
cost of p1 at the relevant level of production. This situation is shown in Figure A1-b.
In the fuzzy gap, either coal or gas could be the marginal fuel, but in either case the prevailing
price should be p1. The estimation problem arises when projecting the coal portion of the supply
curve to the upper boundary of the fuzzy gap. Within the fuzzy gap, both the coal and gas
segments of the supply curve would predict a price of p1. But on the boundary of the fuzzy gap
the coal segment of the supply curve would predict a higher price. Figure A1-c shows the coal
segment of the supply curve in the fuzzy band. If I use the original supply function as I use it
outside the fuzzy gap I end up with the unadjusted projection shown in the figure, and estimate
an electricity price higher than p1. This is clearly incorrect since the price of coal has not changed
and thus the estimated price of electricity should not change. Thus, I need to adjust the supply
127
function in the fuzzy region so that the price is bounded from above by p1. To do so, I adjust the
load variables (qi, qT) in the fuzzy area, where a mixture of two fuels is marginal.
Figure A1: An example explaining why I need to adjust the load variable in the fuzzy gap.
(a): Coal and gas segments of supply function, assuming deterministic marginal fuels. (b):
The same supply functions assuming lower natural gas prices which results in a fuzzy area
where a mixture of natural gas and coal is marginal. (c): The coal portion of the zonal
supply curve in the fuzzy gap. If I do not adjust the supply curve the estimated electricity
price exceeds p1.
Figure A2 shows two different fuzzy gaps for the coal-gas threshold, with widths Δ1 and Δ2 .
Points A, B and C represent the same marginal coal-fired power plant under three different fuzzy
gap scenarios. In the case with no fuzzy gap (i.e., the membership functions are totally
deterministic), point A represents the most expensive relevant coal power plant in the system.
128
With the fuzzy gap of width Δ1 , point B represents the same power plant. Point C represents the
same power plant when fuzzy gap has width Δ2 . Assuming a fixed coal price for all three of
these cases, Equation (4) should estimate the same coal-related electricity price for all the three
described cases. To do so I utilize a transformation to map point C (associated with a fuzzy gap
of width Δ1) and point B (fuzzy gap of width Δ2) to the reference point A. Such a
transformation should not, however, change the locations of the fuzzy gap boundaries
(represented by points D and E in Figure A2).
Figure A2: Load adjustment in the fuzzy gaps
The transformation for coal is explained by Equation (A1). and
are the equivalent zonal
and system load for coal part of the supply function. and
are the projections of the original
qT,C/G
qT,
qi,C/G
Δ1
Δ2
C B
A
E
D
qi
qT
129
point on the lower fuzzy limit (E or D). Similar transformation is needed for gas and oil. For oil I
need the projection on the higher limit of the fuzzy gap. For natural gas, the projection depends
on whether there is a mixture of coal and gas or gas and oil.
{
130
Appendix 3- Regression Parameters
In this appendix, alpha and beta parameters of Equation 3 in addition to the related test statistics are presented for the fmy models used in chapter
two.
131
Piecewise linear model with fixed thresholds:
Zone Coal Gas Oil
intercept zonal load PJM load intercept zonal load PJM load Intercept zonal load PJM load
APS Parameter -18.40* 5.29E-3* 1.72E-4* -6.49* 3.30E-4* 1.34E-4* -30.90* 5.42E-3* 1.51E-5
T-Statistics -9.87 7.53 4.11 -57.85 8.21 53.56 -2.56 3.61 0.70
AEP Parameter -14.65* 2.66E-3* -9.90E-5* -6.66* 4.92E-4* 5.25E-5* -22.91* 8.31E-4* 1.24E-4*
T-Statistics -18.53 24.46 -5.55 -46.10 30.67 20.61 -2.58 2.23 7.31
AECO Parameter -17.43* 4.07E-5* 5.34E-4* -8.20* 2.11E-3* 1.56E-4* -63.66* -6.70E-3 7.85E-4*
T-Statistics -4.90 7.43E-3 8.87 -59.68 17.71 54.90 -5.98 -1.55 13.54
BGE Parameter -20.15* -6.75E-3* 9.02E-4* -7.32* 4.13E-3* -1.95E-5* 61.76* -0.01* 4.33E-4*
T-Statistics -5.56 -3.24 9.33 -51.56 40.91 -3.53 2.02 -2.97 4.02
COMED Parameter -14.32* 1.07E-3* 2.65E-4* -5.54* 4.47E-4* 7.18E-5* -3.69 1.09E-3 -5.16E-5
T-Statistics -7.92 4.02 11.72 -58.40 33.67 34.38 -0.27 1.52 -1.04
DPL Parameter -15.49* 1.66E-3 4.56E-4* -5.99* 2.83E-3* 8.68E-5* -59.57* 1.12E-3 5.56E-4*
T-Statistics -2.77 0.31 4.01 -48.93 22.77 21.05 -3.92 0.26 7.70
DUQ Parameter -12.15* 0.01* 1.30E-4* -4.23* 4.88E-3* 1.35E-5* -39.36* 0.01* 1.24E-4*
T-Statistics -14.02 9.36 5.51 -28.43 28.16 3.93 -5.04 4.29 4.46
JCPL Parameter -13.68* -0.02* 1.19E-3* -6.12* 4.35E-4* 1.48E-4* -57.97* 8.01E-4 5.47E-4*
T-Statistics -2.01 -5.11 12.68 -48.15 6.51 44.32 -3.38 0.27 5.96
METED Parameter -22.94* 8.06E-4 6.02E-4* -7.08* 1.89E-3* 1.30E-4* -40.38* -0.02* 7.54E-4*
T-Statistics -9.77 0.35 12.79 -54.53 10.34 32.27 -4.27 -4.31 19.74
PECO Parameter -21.35* -5.76E-3* 9.35E-4* -5.79* 1.94E-3* 4.17E-5* -21.79 -4.51E-3 5.79E-4*
T-Statistics -7.63 -4.32 13.98 -47.18 29.24 9.91 -0.97 -1.54 7.11
PPL Parameter -17.60* 2.88E-3* 3.59E-4* -5.76* -3.48E-5 1.57E-4* -29.27* 3.39E-3* 1.62E-4*
T-Statistics -6.45 2.49 5.86 -48.19 -0.73 55.75 -2.53 2.11 8.02
PENELEC Parameter -16.83* 8.10E-3* 2.90E-4* -5.30* 9.16E-4* 1.16E-4* -21.65 9.65E-3 7.10E-5
T-Statistics -11.01 6.73 12.81 -41.80 9.54 61.40 -0.63 0.78 1.16
PEPCO Parameter -18.70* -4.96E-3* 7.79E-4* -7.09* 4.52E-3* -2.71E-5* -61.12* 0.01* 2.88E-5
T-Statistics -4.67 -2.33 9.53 -47.98 44.76 -5.10 -2.05 2.14 0.28
PSEG Parameter -15.88* -8.44E-4 5.67E-4* -6.25* 2.44E-4* 1.50E-4* -46.64* 8.14E-4 4.32E-4*
T-Statistics -2.09 -0.59 7.62 -62.87 6.95 53.64 -2.58 0.43 7.44
RECO Parameter -17.37* -0.04 6.17E-4* -5.51* 6.06E-3* 1.43E-4* -182.70* 0.22* 8.37E-4*
T-Statistics -2.38 -0.56 7.43 -49.01 8.52 56.97 -6.32 4.13 6.01
DAY Parameter -9.61* 0.01* 5.23E-5* -5.55* 3.65E-3* 3.62E-5* -30.65* 6.28E-3* 1.62E-4*
T-Statistics -15.14 19.67 3.48 -40.74 31.06 12.44 -4.56 3.31 9.11
DOM Parameter -18.26* -1.58E-3* 7.54E-4* -5.26* 1.43E-3* -3.99E-5* -16.00 -3.19E-3 7.08E-4*
T-Statistics -4.54 -2.19 9.23 -42.30 57.68 -10.07 -0.40 -1.55 6.12
132
Piecewise quadratic model with fixed thresholds:
Zone Coal Gas Oil
intercept zonal
load
PJM
load
zonal load
squared
PJM load
squared
intercept zonal
load PJM
load zonal load
squared PJM load
squared intercept zonal
load PJM
load zonal load
squared PJM load
squared
APS Parameter 9.86 3.48E-3 2.63E-7 -6.25E-4 6.20E-9 14.83* -7.13E-3* 6.14E-7* 1.56E-4* -1.00E-10 1,702.98* -0.39* 2.39E-5* -1.59E-3* 6.60E-9*
T-Statistics 0.58 0.37 0.24 -1.21 1.58 15.94 -16.82 17.91 7.85 -1.19 3.09 -2.93 2.97 -2.60 2.64
AEP Parameter 18.68* -6.13E-3* 3.27E-7* 6.32E-4* -5.20E-9* 11.41* -1.65E-3* 5.89E-8* 8.12E-5* -2.00E-10 -949.52 0.08 -1.62E-6 1.93E-4 -3.00E-10
T-Statistics 2.40 -4.22 6.06 3.18 -3.72 8.27 -8.28 10.83 3.68 -1.40 -1.92 1.90 -1.88 0.44 -0.16
AECO Parameter 10.52 -0.12 5.90E-5 1.34E-3* -5.60E-9 8.55* -8.37E-3* 2.97E-6* -5.17E-5* 1.30E-9* 2,966.32* -2.38* 4.13E-4* 6.27E-3 -2.02E-8
T-Statistics 0.29 -1.33 1.32 1.96 -1.07 10.25 -10.88 12.45 -2.14 9.31 2.47 -2.90 2.86 1.14 -0.97
BGE Parameter -25.66 -0.03 3.78E-6 2.09E-3 -9.70E-9 -1.47 -7.56E-3* 1.33E-6* 4.20E-4* -2.50E-9* 182.82 0.06 -5.35E-6 -5.14E-3 2.12E-8
T-Statistics -0.44 -0.57 0.43 1.19 -0.68 -1.93 -11.29 17.42 11.06 -11.45 0.10 0.10 -0.13 -1.22 1.32
COMED Parameter -16.36 -1.10E-3 1.17E-7 6.37E-4* -2.80E-9 -7.88* -5.27E-4* 3.59E-8* 2.70E-4* -1.10E-9* 843.48 -0.08 1.85E-6 1.10E-3 -4.70E-9
T-Statistics -0.61 -0.17 0.32 1.98 -1.16 -15.12 -6.14 11.65 17.81 -13.14 1.28 -1.29 1.30 0.85 -0.88
DPL Parameter -63.92 -0.02 7.06E-6 2.64E-3 -1.77E-8 -3.94* -7.81E-3* 2.12E-6* 3.33E-4* -1.40E-9* -2,081.4* 0.96* -1.21E-4* 2.38E-3 -7.20E-9
T-Statistics -1.41 -0.32 0.32 1.90 -1.56 -5.59 -9.95 13.46 11.29 -8.12 -3.32 3.07 -3.06 1.18 -0.91
DUQ Parameter 5.67 -0.05* 2.22E-5* 9.54E-4* -5.60E-9* 9.95* -5.88E-4 1.19E-6* -1.71E-4* 1.00E-9* 97.49 0.08 -1.25E-5 -3.34E-3* 1.39E-8*
T-Statistics 0.69 -2.97 3.69 3.90 -3.35 8.02 -0.35 2.90 -5.33 6.02 0.39 0.44 -0.42 -4.51 4.69
JCPL Parameter 134.86 0.16 -4.54E-5 -9.54E-3* 8.81E-8* -5.03* 9.11E-4* -7.33E-8 1.06E-4* 2.00E-10 -907.38 0.22 -1.85E-5 3.28E-3 -1.08E-8
T-Statistics 1.04 1.10 -1.14 -7.55 8.54 -7.53 2.69 -1.50 4.39 1.80 -1.19 0.95 -0.94 1.14 -0.95
METED Parameter 22.38 -0.04 1.56E-5 -8.65E-5 4.90E-9 8.72* 8.97E-4 3.27E-7 -2.11E-4* 1.90E-9* 974.01 -1.90 3.06E-4 0.03 -1.15E-7
T-Statistics 0.97 -1.13 1.27 -0.15 1.13 10.75 0.58 0.84 -6.84 10.93 0.21 -0.56 0.54 1.16 -1.12
PECO Parameter 12.58 -0.02 1.81E-6 5.40E-4 3.10E-9 1.40 2.78E-3* -9.26E-8* -1.71E-4* 1.20E-9* 832.60 -0.19 1.10E-5 -7.31E-4 5.20E-9
T-Statistics 0.42 -0.89 0.63 0.63 0.46 1.82 6.04 -2.20 -5.42 6.96 0.69 -0.64 0.63 -0.28 0.50
PPL Parameter 25.16 -0.02 3.72E-6 3.50E-4 2.00E-10 4.97* -3.23E-3* 3.10E-7* 9.94E-5* 3.00E-10* 1,668.02* -0.42* 2.92E-5* -2.15E-3* 9.60E-9*
T-Statistics 0.87 -1.21 1.42 0.40 0.03 5.94 -7.37 7.67 4.46 2.50 3.72 -3.51 3.55 -3.19 3.44
PENELEC Parameter 55.72* -0.04* 1.66E-5* -8.17E-4* 8.10E-9* 1.22 3.74E-3* -5.42E-7* -1.06E-4* 1.20E-9* 2,703.41 -1.76 3.07E-4 -2.51E-3 1.03E-8
T-Statistics 3.64 -2.26 2.87 -3.29 4.44 1.17 3.22 -2.08 -6.67 13.95 0.76 -0.72 0.73 -1.27 1.31
PEPCO Parameter -130.01 0.07 -1.47E-5 1.51E-3 -6.30E-9 -5.44* -4.42E-3* 1.09E-6* 3.47E-4* -2.10E-9* -2,065.16 0.86 -6.70E-5 -0.01* 4.43E-8*
T-Statistics -0.75 0.47 -0.50 0.57 -0.28 -7.87 -7.51 15.06 10.04 -10.62 -1.17 1.57 -1.58 -6.08 6.09
PSEG Parameter -9.47 -5.34E-3 7.64E-7 5.69E-4 -1.00E-10 -5.27* 9.73E-4* -6.13E-8* 7.73E-5* 4.00E-10* 279.88 -0.07 3.37E-6 8.21E-4 -1.60E-9
T-Statistics -0.28 -0.50 0.40 0.76 -0.02 -10.52 4.57 -3.51 3.71 3.51 0.33 -0.41 0.41 0.46 -0.22
RECO Parameter -124.90 1.57 -7.53E-3 1.32E-3 -5.60E-9 -3.88* 0.04* -7.62E-5* 3.05E-5 6.00E-10* -1,634.04 5.02 -5.89E-3 8.01E-3 -2.72E-8
T-Statistics -1.47 1.29 -1.33 0.80 -0.41 -6.75 11.57 -9.81 1.64 5.87 -1.49 1.03 -0.98 1.15 -1.03
DAY Parameter 8.97 -0.02* 9.41E-6* 3.16E-4* -1.90E-9 10.91* -7.07E-3* 2.14E-6* -3.11E-5 3.00E-10* -513.01 0.33 -4.65E-5 -1.29E-3* 5.90E-9*
T-Statistics 1.76 -3.04 4.91 2.04 -1.75 10.88 -6.20 9.46 -1.18 2.52 -0.62 0.72 -0.72 -2.13 2.36
DOM Parameter -37.77 -0.01 6.32E-7 2.60E-3 -1.53E-8 -3.33* -4.87E-4* 8.00E-8* 1.75E-4* -1.20E-9* 4,080.49 -0.37 9.79E-6 -0.01* 4.01E-8*
T-Statistics -0.55 -0.55 0.47 1.66 -1.18 -5.29 -2.96 11.69 6.49 -7.97 1.89 -1.55 1.53 -5.08 5.18
133
Piecewise linear model with variable thresholds:
Zone Coal Gas Oil
intercept zonal load PJM load intercept zonal load PJM load Intercept zonal load PJM load
APS Parameter -17.34* 4.8E-03* 2.0E-04* -6.00* 1.0E-04* 1.0E-04 -49.33* 7.0E-03* 1.0E-04*
T-Statistics -10.09 8.32 4.55 -49.92 3.22 55.68 -13.12 10.67 3.36
AEP Parameter -13.90* 2.6E-03* -1.0E-04* -6.57* 5.0E-04* 1.0E-04 -16.76 6.0E-04 1.0E-04*
T-Statistics -16.94 20.97 -5.25 -47.57 27.53 22.48 -1.73 1.58 6.31
AECO Parameter -19.04* -5.1E-03 6.0E-04* -8.04* 2.0E-03* 2.0E-04 -99.96* 6.0E-04 9.0E-04*
T-Statistics -6.88 -1.50 12.52 -54.02 16.92 52.54 -15.39 0.33 13.61
BGE Parameter -19.32* -7.8E-03* 9.0E-04* -7.19* 4.1E-03* 0.0E+00 -23.74 9.0E-04 3.0E-04*
T-Statistics -4.01 -3.47 8.26 -52.32 41.08 -3.72 -0.94 0.27 2.56
COMED Parameter -12.71* 2.0E-04 4.0E-04* -4.76* 5.0E-04* 1.0E-04 6.39 6.0E-04 0.0E+00
T-Statistics -14.81 1.89 22.50 -37.82 35.13 24.24 0.43 0.77 -0.87
DPL Parameter -17.13* -2.1E-03 6.0E-04* -5.97* 2.9E-03* 1.0E-04 -57.11* 2.5E-03 5.0E-04*
T-Statistics -2.77 -0.43 4.56 -48.81 23.02 20.84 -3.12 0.72 4.50
DUQ Parameter -11.79* 9.5E-03* 2.0E-04* -4.20* 5.2E-03* 0.0E+00 -41.05* 0.01* 1.0E-04*
T-Statistics -14.26 7.47 7.78 -28.51 30.80 1.98 -6.54 5.08 4.63
JCPL Parameter -18.14* -2.6E-03 6.0E-04* -5.97* 4.0E-04* 1.0E-04 -26.91 1.1E-03 3.0E-04
T-Statistics -5.37 -1.19 8.46 -42.48 5.87 42.89 -1.09 0.50 1.82
METED Parameter -20.10* 4.7E-03* 5.0E-04* -7.04* 1.7E-03* 1.0E-04 -112.44* -6.9E-03 1.1E-03*
T-Statistics -7.15 2.12 7.45 -55.47 9.80 33.72 -7.49 -1.81 17.06
PECO Parameter -20.37* -6.2E-03* 9.0E-04* -5.67* 1.9E-03* 0.0E+00 -34.39 -2.0E-03 5.0E-04*
T-Statistics -8.14 -5.88 15.06 -44.84 29.28 9.57 -1.37 -0.99 3.72
PPL Parameter -18.17* 2.7E-03* 4.0E-04* -5.59* -1.0E-04* 2.0E-04 -11.89* 1.5E-03 1.0E-04*
T-Statistics -6.62 2.68 5.54 -45.57 -2.84 57.25 -2.16 1.52 6.22
PENELEC Parameter -20.66* 0.01* 2.0E-04* -5.36* 9.0E-04* 1.0E-04 -42.96* 8.4E-03 3.0E-04*
T-Statistics -15.45 12.12 7.09 -41.03 9.72 61.77 -2.04 1.44 2.57
PEPCO Parameter -19.18* -6.5E-03* 9.0E-04* -6.93* 4.5E-03* 0.0E+00 -33.50 -6.1E-03 7.0E-04*
T-Statistics -4.45 -3.96 10.00 -46.41 45.18 -5.54 -1.10 -0.94 4.63
PSEG Parameter -16.08* -2.3E-03* 7.0E-04* -6.21* 2.0E-04* 1.0E-04 -22.20 8.0E-04 3.0E-04
T-Statistics -3.19 -2.14 7.70 -57.84 7.08 52.61 -0.96 0.56 1.86
RECO Parameter -11.78* -0.09* 6.0E-04* -5.36* 6.0E-03* 1.0E-04 -1.83 5.8E-03 1.0E-04
T-Statistics -2.30 -1.98 7.97 -45.29 8.49 55.10 -0.07 0.23 0.76
DAY Parameter -9.65* 0.01* 0.0E+00* -5.62* 3.8E-03* 0.0E+00 -18.40* 2.2E-03 2.0E-04*
T-Statistics -15.04 20.08 3.07 -41.66 33.21 11.84 -1.97 1.09 4.94
DOM Parameter -19.56* -1.9E-03* 8.0E-04* -5.14* 1.4E-03* 0.0E+00 -48.18 -8.0E-04 6.0E-04*
T-Statistics -5.05 -3.46 10.05 -40.37 57.97 -10.53 -1.64 -0.62 5.70
134
Piecewise quadratic model with variable thresholds:
Zone Coal Gas Oil
intercept zonal
load PJM load zonal
load
squared
PJM load
squared intercept zonal
load PJM load zonal
load
squared
PJM load
squared intercept zonal
load PJM load zonal
load
squared
PJM load
squared
APS Prameter 2.15 1.7E-03 0.0E+00 -3.0E-04 0.0E+00 14.49* -7.2E-03* 0.0E+0* 2.0E-04* 0.0E+00 698.47 -0.21 0.0E+00 2.8E-03* 0.0E+00*
T-Statistics 0.13 0.17 0.40 -0.53 0.87 16.61 -16.67 17.66 8.45 -1.49 1.41 -1.68 1.69 4.68 -4.34
AEP Prameter 18.81* -4.7E-3* 0.0E+00* 3.0E-04* 0.0E+00* 10.36* -2.1E-03* 0.0E+0* 2.0E-04* 0.0E+0* 420.39 -0.03 0.0E+00 -1.0E-03 0.0E+00
T-Statistics 2.47 -3.08 4.78 2.34 -3.17 8.70 -11.19 13.80 9.25 -6.50 0.70 -0.61 0.62 -0.89 1.06
AECO Prameter -50.77 0.01 0.0E+00 1.4E-03 0.0E+00 7.13* -5.9E-03* 0.0E+0* -1.0E-04* 0.0E+0* -791.91 0.20 0.0E+00 7.5E-03 0.0E+00
T-Statistics -1.27 0.15 -0.22 1.45 -0.81 8.19 -7.90 9.67 -2.44 9.23 -1.34 0.89 -0.91* 1.01 -0.91
BGE Prameter -51.92 5.4E-03 0.0E+00 1.4E-03 0.0E+00 -1.53* -9.0E-03* 0.0E+0* 5.0E-04* 0.0E+0* -1467.39 0.76* -1.0E-04 -0.02 0.0E+00
T-Statistics -1.44 0.14 -0.28 1.80 -0.79 -2.02 -13.13 19.10 13.05 -13.39 -1.27 2.62 -2.63 -1.82 1.86
COMED Prameter -19.83 8.7E-03* 0.0E+00* -6.0E-04 0.0E+00* -8.32* -5.0E-04* 0.0E+0* 3.0E-04* 0.0E+0* 1216.87 -0.11 0.0E+00 6.0E-04 0.0E+00
T-Statistics -1.15 2.54 -2.41 -1.46 2.21 -13.10 -5.85 11.46 15.88 -11.96 1.94 -1.87 1.87 0.43 -0.47
DPL Prameter -58.73 0.03 0.0E+00 1.3E-03 0.0E+00 -4.24* -8.5E-03* 0.0E+0* 4.0E-04* 0.0E+0* -1600.56* 0.35 0.0E+00 0.01 0.0E+00
T-Statistics -1.63 0.38 -0.36 1.20 -0.80 -6.26 -10.84 14.34 12.40 -9.16 -2.43 1.62 -1.60 1.67 -1.60
DUQ Prameter -8.94 6.4E-03 0.0E+00 2.0E-04 0.0E+00 10.25* 9.2E-03* 0.0E+0* -4.0E-04* 0.0E+0* -119.50 0.20* 0.0E+00* -2.7E-03* 0.0E+00*
T-Statistics -1.05 0.38 0.16 0.56 0.05 8.98 6.28 -3.13 -11.35 11.64 -1.14 2.32 -2.20 -4.93 5.12
JCPL Prameter 230.33 0.09 0.0E+00 -0.01* 0.0E+00* -5.32* 8.0E-04* 0.0E+0 1.0E-04* 0.0E+0 -2252.35 0.11 0.0E+00 0.03 0.0E+00
T-Statistics 1.88 0.63 -0.65 -8.18 9.13 -7.85 2.44 -1.19 4.80 1.35 -1.92 1.12 -1.10 1.80 -1.77
METED Prameter 40.67 -0.03 0.0E+00 -8.0E-04 0.0E+00 7.98* 1.6E-03 0.0E+0 -2.0E-04* 0.0E+0* -3412.84 1.54 -3.0E-04 0.02 0.0E+00
T-Statistics 0.98 -0.92 1.09 -0.50 0.81 10.99 1.23 0.45 -7.33 11.67 -0.70 0.45 -0.47 0.95 -0.90
PECO Prameter 44.87 -0.02 0.0E+00 -5.0E-04 0.0E+00 2.44* 3.7E-03* 0.0E+0* -2.0E-04* 0.0E+0* -1587.06 0.11 0.0E+00 0.02 0.0E+00
T-Statistics 1.52 -1.37 1.05 -0.45 1.34 2.93 8.44 -4.30 -7.35 8.62 -1.72 0.72 -0.72 1.63 -1.58
PPL Prameter 14.07 -2.1E-03 0.0E+00 -4.0E-04 0.0E+00 3.92* -1.0E-03* 0.0E+0* 0.0E+00 0.0E+0* 200.61 -0.05 0.0E+00 -5.0E-04 0.0E+00
T-Statistics 0.46 -0.14 0.37 -0.37 0.71 4.38 -2.14 2.17 -0.34 7.44 1.33 -1.10 1.12 -1.02 1.46
PENELEC Prameter 36.22* -5.8E-03 0.0E+00 -1.1E-03 0.0E+00* 5.61* 9.0E-04 0.0E+00 -1.0E-04* 0.0E+0* 2576.50 -1.72 3.0E-04 -1.6E-03 0.0E+00
T-Statistics 2.14 -0.45 1.42 -1.72 2.10 5.58 0.93 0.48 -7.23 13.73 1.69 -1.90 1.90 -0.23 0.27
PEPCO Prameter -57.77 0.02 0.0E+00 9.0E-04 0.0E+00 -4.28* -3.9E-03* 0.0E+0* 3.0E-04* 0.0E+0* -1838.10 0.81 -1.0E-04 -0.01* 0.0E+0*
T-Statistics -0.69 0.50 -0.66 0.40 -0.05 -5.36 -6.34 13.67 7.93 -8.61 -1.03 1.45 -1.46 -7.13 7.05
PSEG Prameter 10.50 3.0E-03 0.0E+00 -6.0E-04 0.0E+00 -5.23* 9.0E-04* 0.0E+0* 1.0E-04* 0.0E+0* 126.32 -0.08 0.0E+00 4.0E-03 0.0E+00
T-Statistics 0.15 0.46 -0.79 -0.24 0.51 -8.84 4.57 -3.45 3.59 3.18 0.15 -0.85 0.86 0.40 -0.37
RECO Prameter -130.38 1.03 -5.0E-03 2.5E-03 0.0E+00 -3.94* 0.04* -1.0E-4* 0.0E+00 0.0E+0* -993.63 -2.57* 3.3E-03* 0.02* 0.0E+0*
T-Statistics -1.79 1.27 -1.40 1.23 -0.93 -6.11 11.78 -9.99 1.60 5.33 -1.33 -2.76 2.79 2.07 -2.04
DAY Prameter 7.39 -0.03* 0.00* 0.00* 0.00* 10.43* -0.01* 0.00* 0.00 0.0* -317.51 0.22 0.00 0.00 0.0*
T-Statistics 1.42 -3.89 5.79 3.01 -2.79 9.81 -5.86 9.26 -1.37 2.59 -1.33 1.67 -1.64 -1.92 2.22
DOM Prameter -60.98 0.00 0.00 0.00 0.00 -3.89* 0.00* 0.00* 0.00* 0.00* -499.67 0.04 0.00 0.00 0.00
T-Statistics -0.78 0.34 -0.52 0.56 -0.25 -5.97 -3.71 12.88 7.35 -8.93 -0.49 0.48 -0.49 0.18 -0.09
135
Appendix 4- Thresholds
In this appendix, the results of data classification with the two introduced methods in chapter two
are shown. In each figure data points are shown based on the zonal and total PJM load for each
observation. The darkness shows the price. There are fmy vertical lines in each figure which
show the fixed thresholds. The other fmy lines represent variable thresholds. Solid lines are for
the models with piecewise linear supply curves, while the dashed lines are for the models with
piecewise quadratic supply functions.
136
137
138
139
Appendix 5- Projected Supply Curves
Projected supply curves for all the models presented in chapter two are depicted in this appendix.
In order to form these curves zonal demand, total demand and fuel prices are needed. Zonal loads
vary from minimum to maximum demand observed during 2006 to 2009 period. A mostly
expected fuel price scenario which was described in section 5 is used here as well. In order to
find relative total load for each level of zonal demand, these [two variables are regressed against
each other having data from 2006 to 2009.] Then using the regression equation, I have projected
total demand from zonal load.
140
141
142
143
Appendix 6- Simulation of Pennsylvania’s Act 129 – Chapter two
Piecewise linear model with fixed thresholds:
Zone
Price ($/MWh) Total Costs ( Millions of dollars) Fuel Share (percentage)
Without Act 129 With Act 129 Without
Act 129
With
Act 129
Savings Savings
(%)
Without Act 129 With Act 129
Min Average Max Min Average Max Coal Gas Oil Coal Gas Oil
APS 14.59 46.28 182.14 14.21 45.65 155.05 2280 2220 60 2.64 24.60 75.09 0.30 26.00 73.96 0.02
AEP 11.41 38.88 125.89 11.44 38.85 124.24 5471 5465 6 0.11 55.74 44.05 0.21 55.74 44.05 0.21
AECO 18.35 53.55 191.15 18.21 53.28 178.04 638 635 3 0.51 17.69 82.23 0.07 17.69 82.23 0.07
BGE 16.54 56.19 139.38 16.31 56.17 139.63 2026 2026 0 0.00 15.85 84.13 0.00 15.85 84.13 0.00
COMED 13.80 40.47 98.30 13.73 40.34 98.07 4222 4209 13 0.30 26.08 73.91 0.00 26.08 73.91 0.00
DPL 18.67 53.96 161.59 18.55 53.80 152.32 1072 1069 3 0.29 11.01 88.94 0.03 11.01 88.94 0.03
DUQ 16.39 37.66 112.31 16.08 37.06 79.89 550 535 15 2.78 55.32 44.64 0.02 58.45 41.54 0.00
JCPL 11.94 52.67 121.60 11.62 52.40 119.74 1311 1304 7 0.51 11.11 88.88 0.00 11.11 88.88 0.00
METED 15.65 51.22 133.64 15.48 50.80 113.99 838 822 16 1.97 20.48 79.28 0.23 21.69 78.30 0.00
PECO 15.53 52.01 120.00 15.64 51.29 112.72 2253 2194 59 2.62 17.52 82.47 0.00 18.50 81.49 0.00
PPL 16.76 50.15 165.23 16.50 49.72 148.05 2189 2144 45 2.06 18.39 81.30 0.30 19.43 80.52 0.05
PENELEC 15.94 44.49 151.13 15.66 44.10 93.20 809 793 16 1.98 28.38 71.60 0.01 30.28 69.71 0.00
PEPCO 16.57 57.80 218.30 16.37 57.80 217.82 1972 1973 -1 -0.03 14.58 85.39 0.02 14.58 85.39 0.02
PSEG 18.71 53.59 121.20 18.56 53.33 119.31 2546 2533 12 0.48 7.29 92.69 0.00 7.29 92.69 0.00
RECO 18.73 52.89 118.36 18.57 52.64 116.58 83 83 0 0.47 8.87 91.12 0.00 8.87 91.12 0.00
DAY 14.71 37.67 86.59 14.70 37.63 86.47 688 687 1 0.12 60.38 39.61 0.00 60.38 39.61 0.00
DOM 17.50 55.96 127.58 17.31 55.99 127.88 5669 5674 -5 -0.08 12.76 87.23 0.00 12.76 87.23 0.00
144
Piecewise quadratic model with fixed thresholds:
Zone
Price ($/MWh) Total Costs ( Millions of dollars) Fuel Share (percentage)
Without Act 129 With Act 129 Without
Act 129
With
Act 129
Savings Savings
(%)
Without Act 129 With Act 129
Min Average Max Min Average Max Coal Gas Oil Coal Gas Oil
APS 16.13 46.57 184.89 15.80 45.94 158.13 2292 2231 62 2.69 30.08 69.62 0.30 31.61 68.36 0.02
AEP 17.19 38.96 124.97 17.16 38.93 123.29 5475 5470 6 0.10 55.74 44.05 0.21 55.74 44.05 0.21
AECO 16.48 53.74 173.36 16.29 53.45 169.95 639 635 4 0.56 23.50 76.49 0.00 23.50 76.49 0.00
BGE 15.39 55.79 162.99 15.11 55.75 163.71 2012 2012 0 0.02 15.85 84.13 0.00 15.85 84.13 0.00
COMED 13.25 40.49 109.35 13.16 40.36 109.30 4225 4212 13 0.31 26.13 73.86 0.00 26.13 73.86 0.00
DPL 15.87 53.96 145.86 15.65 53.78 137.85 1071 1068 3 0.31 17.64 82.32 0.03 17.64 82.32 0.03
DUQ 17.38 37.72 107.18 17.39 37.16 86.13 551 536 15 2.72 58.46 41.50 0.02 61.80 38.19 0.00
JCPL 20.82 52.66 121.03 20.88 52.41 118.93 1310 1304 6 0.49 10.91 89.08 0.00 10.91 89.08 0.00
METED 18.52 51.46 139.26 18.50 50.92 132.61 841 822 19 2.22 23.01 76.98 0.00 24.54 75.45 0.00
PECO 16.41 52.08 126.47 16.60 51.36 120.04 2253 2195 58 2.58 21.72 78.27 0.00 22.95 77.03 0.00
PPL 18.69 50.26 174.57 18.68 49.81 140.56 2193 2146 47 2.14 21.34 78.35 0.30 22.55 77.39 0.05
PENELEC 20.54 44.44 151.51 20.53 43.99 102.34 808 790 17 2.12 28.09 71.89 0.01 30.09 69.90 0.00
PEPCO 15.91 57.36 198.73 15.69 57.35 199.48 1960 1961 -1 -0.04 9.30 90.66 0.02 9.30 90.66 0.02
PSEG 18.51 53.63 120.46 18.37 53.37 118.15 2547 2535 12 0.48 7.29 92.69 0.00 7.29 92.69 0.00
RECO 17.42 53.02 113.17 17.23 52.78 110.64 83 83 0 0.46 8.88 91.11 0.00 8.88 91.11 0.00
DAY 18.03 37.69 97.26 18.00 37.65 97.11 687 687 1 0.12 60.38 39.61 0.00 60.38 39.61 0.00
DOM 15.22 55.80 143.95 14.95 55.82 144.61 5661 5666 -4 -0.08 12.76 87.23 0.00 12.76 87.23 0.00
145
Piecewise linear model with variable thresholds:
Zone
Price ($/MWh) Total Costs ( Millions of dollars) Fuel Share (percentage)
Without Act 129 With Act 129 Without
Act 129
With
Act 129
Savings Savings
(%)
Without Act 129 With Act 129
Min Average Max Min Average Max Coal Gas Oil Coal Gas Oil
APS 15.08 46.60 184.60 14.73 45.76 149.02 2298 2223 76 3.29 26.77 71.97 1.27 27.70 72.04 0.26
AEP 11.81 38.67 125.69 11.84 38.64 124.15 5441 5436 5 0.10 55.99 43.83 0.18 55.69 44.14 0.17
AECO 17.25 53.52 177.34 17.09 53.24 162.19 638 634 3 0.53 22.19 77.73 0.08 22.29 77.66 0.05
BGE 16.50 56.17 138.88 16.26 56.16 139.14 2025 2025 0 -0.01 13.95 86.05 0.00 14.04 85.96 0.00
COMED 13.84 40.12 98.37 13.75 39.98 98.19 4190 4176 14 0.34 44.99 55.01 0.00 45.38 54.62 0.00
DPL 18.11 53.93 126.53 17.97 53.77 125.45 1071 1068 3 0.28 10.80 89.20 0.00 10.90 89.10 0.00
DUQ 16.39 37.52 111.90 16.14 36.93 80.03 548 533 15 2.79 53.81 46.14 0.06 55.32 44.68 0.00
JCPL 17.62 52.75 120.76 17.46 52.50 118.90 1312 1306 6 0.49 18.26 81.74 0.00 18.39 81.61 0.00
METED 16.28 51.29 125.24 16.06 50.83 114.12 839 822 17 2.04 20.37 79.57 0.06 20.93 79.07 0.00
PECO 15.71 51.84 119.53 15.85 51.13 112.27 2246 2188 58 2.60 21.16 78.84 0.00 21.98 78.02 0.00
PPL 16.62 50.35 159.21 16.37 49.70 150.90 2201 2142 59 2.69 19.96 79.15 0.89 20.74 79.13 0.13
PENELEC 14.22 44.71 95.07 13.84 44.29 93.41 812 796 16 2.00 30.73 69.27 0.00 30.98 69.02 0.00
PEPCO 15.35 57.61 200.32 15.13 57.60 188.40 1968 1968 0 -0.01 16.37 83.61 0.02 16.56 83.42 0.02
PSEG 17.94 53.57 121.08 17.77 53.31 119.20 2545 2532 12 0.49 13.17 86.83 0.00 13.35 86.65 0.00
RECO 19.29 52.86 117.79 19.13 52.61 116.03 83 83 0 0.47 13.15 86.85 0.00 13.29 86.71 0.00
DAY 14.67 37.65 86.96 14.66 37.61 86.85 688 687 1 0.11 59.91 40.09 0.00 59.98 40.02 0.00
DOM 16.66 55.82 127.45 16.45 55.84 127.77 5658 5662 -4 -0.07 15.41 84.59 0.00 15.52 84.48 0.00
146
Piecewise quadratic model with variable thresholds:
Zone
Price ($/MWh) Total Costs ( Millions of dollars) Fuel Share (percentage)
Without Act 129 With Act 129 Without
Act 129
With
Act 129
Savings Savings
(%)
Without Act 129 With Act 129
Min Average Max Min Average Max Coal Gas Oil Coal Gas Oil
APS 15.90 46.57 189.08 15.57 45.88 109.59 2294 2228 66 2.88 29.13 70.52 0.35 30.91 69.09 0.00
AEP 16.90 38.73 119.47 16.90 38.71 118.44 5445 5441 4 0.07 55.99 43.99 0.02 55.69 44.29 0.02
AECO 15.59 53.54 168.18 15.39 53.25 164.78 637 633 4 0.56 22.55 77.45 0.00 22.71 77.29 0.00
BGE 16.07 55.97 165.29 15.84 55.94 166.12 2017 2017 0 0.01 14.98 85.02 0.00 14.69 85.31 0.00
COMED 13.30 40.47 109.08 13.27 40.33 109.04 4223 4209 14 0.33 30.74 69.26 0.00 31.08 68.92 0.00
DPL 16.77 54.00 141.15 16.62 53.84 141.06 1072 1069 3 0.28 16.58 83.42 0.00 16.37 83.63 0.00
DUQ 16.82 37.49 103.71 16.59 36.90 87.58 548 532 15 2.78 53.29 46.65 0.06 54.99 45.01 0.00
JCPL 21.42 52.67 121.10 21.40 52.42 119.07 1310 1304 6 0.48 11.17 88.83 0.00 11.21 88.79 0.00
METED 19.50 51.39 138.61 19.48 50.86 132.27 840 822 19 2.21 20.37 79.63 0.00 20.97 79.03 0.00
PECO 17.10 51.91 125.68 17.32 51.22 120.11 2247 2190 57 2.53 25.12 74.88 0.00 25.98 74.02 0.00
PPL 18.04 50.44 164.02 17.86 49.76 150.03 2204 2143 61 2.76 23.24 75.88 0.88 24.05 75.85 0.10
PENELEC 17.98 44.72 105.68 17.78 44.27 102.89 812 795 17 2.10 30.73 69.27 0.00 30.98 69.02 0.00
PEPCO 15.93 57.23 199.59 15.71 57.21 201.15 1957 1957 -1 -0.03 15.45 84.52 0.02 15.56 84.42 0.02
PSEG 18.99 53.60 120.33 18.86 53.34 118.05 2546 2533 13 0.49 13.17 86.83 0.00 13.35 86.65 0.00
RECO 16.56 52.97 112.24 16.34 52.73 109.76 83 83 0 0.46 13.15 86.85 0.00 13.27 86.73 0.00
DAY 18.02 37.68 96.94 17.97 37.64 96.79 687 687 1 0.11 60.08 39.92 0.00 60.18 39.82 0.00
DOM 16.33 55.62 144.97 16.10 55.63 145.71 5650 5654 -4 -0.06 14.82 85.18 0.00 15.03 84.97 0.00
147
Appendix 7: CMA-ES
In this appendix Covariance Matrix Adaptation-Evolution Strategy (CMA-ES) is
described briefly. I use the same notation as Hansen and Ostermeier, 2001. CMA-ES is an
Evolution Strategy (ES) which is a derivative-free and stochastic numerical optimization method.
ES belongs to the family of evolutionary algorithms. In ES the dependency between members of
a population is described by a covariance matrix. CMA-ES introduces a method for updating this
covariance matrix which is very effective in the sense that it maintains fast convergence yet
preventing pre-mature convergence. It should be noted that if the objective function was convex,
and derivatives were available conventional optimization methods would still converge faster.
(µ,λ)-CMA-ES is designed for a minimization problem:
n
nx
f
xxfA
:
),...,(min)15(
1
where f is the objective function and x=(x1,…,xn) is the n-dimensional decision variable.
In each generation g of the algorithm, λ individuals are generated, from which the µ best
members will be selected. Each individual in the population represents a decision variable (x). In
each generation the individuals are picked from a normal distribution described in equations
(A5-2):
1
1
1
)(
:)(
)1()()()()()1(
1:)25(
,...,1)25(
i
i
i
i
i
g
iig
w
g
k
gggg
w
g
k
wthatsuch
w
xw
xbA
kforzDBxxaA
148
where )1( g
kz is an independent realization of a normal distribution with the mean of 0n
and covariance of In and )(
:
g
ix is the ith
best individual in generation g based on the individuals’
fitness. Equations (A5-2) imply that generation g+1 would be normally distributed around
weighted average of µ best individuals of generation g with the covariance matrix of )(2 gC
where Tgggg BDBC )(2)()()( . This is the Singular Value Decomposition (SVD) of the
symmetrical positive definite n×n matrix )(gC . D determines the relative step size in each
dimension (shape of distribution) while B as a rotation matrix adjusts the coordination of the
distribution. The distribution’s covariance has two parameters that can be adapted. C(g)
is adapted
using evolution path pc(g+1)
and σ which is the global step size is adapted by means of a
conjugate evolution path pσ(g+1)
. Calculation of the paths and adaptation rules are described in
equations (A5-3).
n
n
g
gg
g
w
g
w
ugg
Tg
c
g
c
gg
g
w
gg
i i
i i
uu
g
cc
g
c
p
ddA
zBccpcpcA
ppcCcCbA
zDB
w
wccpcpaA
ˆ
ˆ.
1exp)35(
.).1()35(
.).1()35(
.)2().1()35(
)1(
)1()1(
)1()()()1(
)1()1(
cov
)(
cov
)1(
)1()()(
1
2
1)()1(
where
1
)(
:
1
)1(
:)1(
i
g
ii
i
g
iig
w
xw
zw
z and
221
1
4
11),0(ˆ
nnnn
nINE is the expected
length of a sample from the normal distribution with the mean of 0 and covariance matrix of In.
The algorithm keeps updating new generations until a convergence criterion, such as no
149
improvement in objective function evaluation after a large number of generations, is met. The
evolution path is designed such that consecutive steps be orthogonal in expectation. This helps
preventing premature convergence. Having equations (A5-2) and (A5-3) I only need the
algorithm parameters and initialization values to be able to implement the algorithm. The
algorithm parameters are presented in table A5-I. They can be set differently but the presented
formulas are recommended by Hansen and Ostermeier, 2001. One of the advantages of CMA-ES
over its competitor evolutionary algorithms is that there is no need to adjust these parameters
based on the underlying optimization problem.
TABLE A5-I
CMA-ES PARAMETER SETTING
Parameter λ µ wi=1,…,µ cc ccov cσ dσ
Description Population size Number of
parents
Weights Cumulation
time for pc
Change rate of the
Covariance Matrix C
Cumulation
time for pσ
Damping
parameter
Value )ln(34 n 2 )ln(ln
21 i 4
4n 2)2(
2
n
44n 11
c
The initialization values are presented in table A5-II. * means that the parameters are user
defined and should be chosen based on the knowledge of the problem. Both initial population
and initial step size specify the first generation. Instead of the initial population I can initialize
the mean of the distribution. According to Hansen and Kern, 2004 CMA-ES converges to global
minimum even when it is initialized near a relatively good local minimum in multi-modal test
functions. Therefore initialization reduces to generating a feasible population.
150
TABLE A5-II
INITIALIZATION OF CMA-ES POPULATION AND PARAMETERS
Parameter )(o
kx C0
σ0 )0(
cp )0(
p
Description population Covariance matrix
neglecting σ
Step
size
Evolution
path
Conjugate
Evolution path
Initialization * In×n * 0n 0n
In a more advanced implementation of the algorithm, Auger and Hansen, 2005 have
included a restart feature which improves the global search property. In this approach the
obtained solution is injected to a double-sized population.
151
Appendix 6- IEEE 30 BUS System
baseMVA = 100 MWA;
bus = [ Bus # Load (MW)
1 0 2 21.7
3 2.4
4 7.6
5 94.2
6 0
7 22.8
8 30
9 0
10 5.8
11 0
12 22.4
13 0
14 12.4
15 16.4
16 7
17 18
18 6.4
19 19
20 4.4
21 17.5
22 0
23 6.4
24 8.7
25 0
26 3.5
27 0
28 0
29 2.4
30 12.9545 ]
gen = [ Bus # Max generation (MW) 1 150; 2 150; 22 150; 27 150; 23 150; 13 150; ];
branch = [From To Admittance (p.u.)
1 2 0.02
1 3 0.05
2 4 0.06
3 4 0.01
2 5 0.05
2 6 0.06
4 6 0.01
5 7 0.05
6 7 0.03
152
6 8 0.01
6 9 0
6 10 0
9 11 0
9 10 0
4 12 0
12 13 0
12 14 0.012
12 15 0.07
12 16 0.09
14 15 0.022
16 17 0.08
15 18 0.011
18 19 0.06
19 20 0.03
10 20 0.09
10 17 0.03
10 21 0.03
10 22 0.07
21 22 0.01
15 23 0.01
22 24 0.012
23 24 0.013
24 25 0.019
25 26 0.025
25 27 0.011
28 27 0
27 29 0.022
27 30 0.032
29 30 0.024
8 28 0.006
6 28 0.002]
gencost = [ Qud Lin Fix .1 16 0;
.11 16 0; .12 16 0; .13 16 0; 1.5 8.5 0; 1.4 8.5 0;
];
Mostafa Sahraei-Ardakani ERC 519, Arizona State University, Tempe, AZ, 85281, Tel: 814-321-6259, email: [email protected]
Education
Ph.D. in Energy Engineering – Energy Management and Policy, August 2013 The Pennsylvania State University GPA: 3.93/4.0 Advisor: Dr. S. Blumsack Dissertation: Policy Analysis in Transmission-Constrained Electricity Markets M.S. in Electrical Engineering-Power Systems, November 2008 University of Tehran GPA: 18.36/20 Advisor: Dr. A. Rahimi-Kian Thesis: Dynamic Modeling of Electricity Markets B.S. in Electrical Engineering-Control, September 2005 University of Tehran
Experience
Post-Doctoral Scholar: School of ECEE, Arizona State University, Since Jan. 2013 (Dr. Hedman) Robust Adaptive Topology Control (RATC): optimization of transmission network topology
Research/Teaching Assistant: The Pennsylvania State University, May 2009 – December 2012 Instrumentation and Control Engineer: Moshanir power consultiants, May 2006 – April 2009 Research Associate: Niroo Research Institute, September 2008 – April 2009
Involved in designing reserve ancillary service market for Iran’s electricity market.
Selected Publications
1. M. Sahraei-Ardakani, S. Blumsack, A. Kleit, 2012 “Distributional Impacts of State-Level Energy Efficiency Policies in Regional Electricity Markets,” Energy Policy
2. M. Sahraei-Ardakani, S. Blumsack, A. Keleit, 2013 “Estimating Zonal Electricity Supply Curves in Transmission-Constrained Electricity Markets,” Submitted to Energy Economics,
3. M. Sahraei-Ardakani, A. Rahimi-Kian, 2009 "A Dynamic Replicator Model of the Players' Bids in an Oligopolistic Electricity Market", Electric Power System Research
4. A. Kleit, S. Blumsack, Z. Lei, L. Hutelmyer, M. Sahraei-Ardakani, S. Smith, 2011 “Impacts of Electricity Restructuring in Rural Pennsylvania,” Center for Rural Pennsylvania
5. M. Sahraei-Ardakani, S. Blumsack, A. Kleit, 2011 “Zonal Supply Curve Estimation With Fuzzy Marginal Fuel in Electricity Markets,” in Proc. of 30th USAEE north American Conference
Honors and Awards
Selected as one of the 55 world talents to join Shell’s team in NRG battle-world edition, world gas conference, Kuala Lumpur, Malaysia, June 2012
EEEPI summer research award, April 2012 Outstanding New Student Organization of the Year for PSU IEEE Student Chapter, 2012 Dennis J. O'Brien USAEE Best Student Paper Finalist Award, 30th USAEE American Conference Honorable mention for poster presentation, Penn State EMS welcome ceremony, 2011 & 2012 Third engineering research award at Penn State graduate exhibition, 2011 IFAC Asian student travel award for attending IFAC 2008 in Seoul, Korea.
Activities
IEEE student member, since 2006 IAEE/USAEE student member, since 2011
Graduate Student Liaison, Penn State IEEE student chapter, January 2011 – December 2012 Peer Reviewer: IEEE Trans. on Power Systems, Energy Economics, IFAC Conferences, HICSS