economic assesment of dynamic pricing in smart distribution networks

7/23/2019 Economic Assesment of Dynamic Pricing in Smart Distribution Networks

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Fig. 1. Comparison of specifical power and energy storage potential of eachstorage technology [3]

A.

Energy Storage Systems for Distribution SystemsA short-term scheduling of battery in a thermal-

photovoltaic system is obtained through security constrainedunit commitment in [5]. Electric power users with installed

photovoltaic (PV) and battery systems are considered. In thiswork, the user is not incentivized to use its assets; moreover theDNO centrally dispatches the batteries operation schedule.

The work presented in [6] introduces a heuristic techniquefor scheduling a residential DER installation containing

photovoltaic arrays, and local energy storage, interfaced to thegrid through a single phase voltage source inverter. Theoptimization problem is set to maximize customers daily

profit. The customer is able to sell specified amounts of real

and reactive power to the utility grid. The optimizationalgorithm determines the operating points for the smart inverterfor the next 24 hours of operation based on forecasts of theresidential demand, solar irradiance, and the price of active

power. It may be inferred that this work assumes the use of aHEMS to control the smart inverter.

Works [7] and [8] propose models of automatedmanagement of residential customers appliances. Themechanisms for demand management optimization define a

plan that minimizes the users energy usage costs. The model issimulated considering two types of tariffs: a Time of Use(TOU) rate with two price levels and a time-varying tariffwhere price changes every hour with higher costs at demand

peak hours. Time of Use tariffs allow charging users forelectricity consumption at different prices according to the time

block of consumption.

In work [9], an optimal framework was propose forbidding, scheduling, and deployment of battery systems in theCalifornia ISO energy market. In the analyzed scenarios,

battery systems can participate in day-ahead and real-timemarkets. The problem is formulated as a stochasticoptimization, which is solved by a decompositionmethodology.

Most works reviewed are related to optimal management ofenergy use to minimize clients costs for energy usage ormaximize profits for selling energy; moreover they dontconsider the DNO interests as a part of the problem. In thiswork we assess the effects that different electricity pricings willhave in DNO interests, considering that HEMS are set tomaximize prosumers benefits.

III. PROSUMER MODEL

A scheme of the studied prosumer model is presented inFig. 2. The different power directions are represented. The signconvention in Fig. 2 is used as a reference throughout thewhole paper. The main components of the prosumer model arethe PV generator, the batteries energy storage, the user loads,the distribution grid, and the electronics power converters. The

parameter SOC is the value of the state of charge of thebatteries.

Fig. 2. Power direction and sign convention in the prosumer model [10]

A. Prosumer Optimization Problem

The prosumer optimization problem is completely defined

by (1)-(9). The objective of (1) is to minimize the prosumerscosts (or maximize their benefit). The prosumer can satisfy itselectricity needs by self-consuming the energy he produces or

by buying energy to the distribution network, he can also sellits energy surplus or stored energy to the distribution network.The control variables of this problem are , and ,for 1 (24 hours). Since the prosumer is notcapable to schedule the batteries charge and discharge cycles,as stated previously we assume that a HEMS does this job forhim.

The first member of (1) is the cost of buying energy to theDNO at hourly electricity pricing , and its secondmember is the revenue received for selling energy at a fixed

Feed-in Tariff (FIT). Nowadays utilities engaged in DemandSide Management Programs can charge customers as a passthrough the real time hourly market price [11] or day aheadhourly market price [12]. An overview of the state of the art inelectricity management in response to dynamic pricings andenabling technologies can be found in [13].

Equations (2) and (3) define the power drawn from andinjected to the distribution grid respectively, and are defined insuch way that (1) can be evaluated by the proposedoptimization algorithm, which will be discussed at the end ofthis section. Equations (2) and (3) depend on the sign of (4).


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Equation (5) defines the net power from the PV generatorand/or the batteries. According to the sign convention, the

power balance in the prosumer model is formulated in (4) and(5).

The limitations on the prosumer model are the physicalconstraints formulated by (6)(8). These constraints are set tolimit the batteries degradation and ageing. Additionally,constraint (7) forces the battery to be charged exclusively from

the PV generator. The state of charge of batteries depends onthe preceding charging and discharging cycles, as formulatedin (9). In equations (1)-(9), represents the set of prosumersthat own ESS and represents the set of time slots in theanalyzed time horizon. In this research the prosumer load isconsidered inelastic.

, 1 min , , (1)

, 0 , 0

, , 0(2)

, , , 00 , 0 (3) , , , (4)

, , , , (5), , , (6)

0 , , (7)

, 0 (8) , , , , (9)Equations (2) and (3) where formulated in such way that (1)

is convex. The optimization problem formulated by (1)-(9) isconvex, and can be solved using convex programmingtechniques such as interior point method (IPM)[14].

IV. DNO MODEL

The DNO buys energy to the wholesale electricity market(EM) at the corresponding Locational Marginal Price (LMP) inits frontier node. We assume that the hourly LMPs ($/kWh) are

set for the day ahead for time slots 1 24. The DNO buysthe energy injected by prosumers to the distribution grid at afixed Feed-In Tariff (FIT).

The interest of the DNO consists in buying energy from theEM and prosumers to provide energy to its clients at theminimum cost, complying with quality and continuityregulations. Quality and continuity regulations demand thatvoltage magnitude on distribution network load buses arewithin certain limits and that demand is served at all timesrespectively. Failure to comply with regulations will result inhigh economic penalties for the DNO.

A.DNO Costs Evaluation

The DNO cost for 24 hours is formulated by (10). The firstterm refers to the cost of buying energy to the EM. Thesecond and third terms refer to the penalty costs for supplyingenergy with poor quality and continuity. The failureto supply energy with continuity due to network congestion isrepresented by the cost of energy not supplied. It can benoted that (10) incorporates the prosumers objective function(1) as a subtrahend, denoting opposition to DNO objective. Thefourth term corresponds to the energy sold by the DNO tocustomers with inelastic demand. The last term of (10) is aresult of the prosumer optimization problem formulated by (1)-(9).

(10)The three first terms of (10) are evaluated by means of a

Power Flow. Power Flow considers nodal balance for activeand reactive power [15]. The cost of buying energy to theelectric market [$] is proportional to the active powerflow in DNO/EM frontier node. Whenever the voltage result in

a load node is not within acceptable values, the DNO ispenalized with [$], which is the product of the load powerconnected to the corresponding node and the penalization forenergy with poor quality. Similarly, whenever a line is overcongested, the DNO is penalized with [$]which is the

product of the load power connected to the corresponding nodeand the penalization for energy not supplied.

B. Proposed Evaluation Method

The DNO evaluation method consists in the followingpoints:

1) Set a 24 hour dynamic pricing

2)

Solve the HEMS optimization problem (1)-(9)considering solar generation and demand forecast. TheHEMS schedules the batteries charge and discharge

cycles ,/ ,for 1 24.3) Depending on its sign, , is used to update the

prosumers load or generation data in thecorresponding load node for the power flow (e.g.

prosumers injected power is modeled as negativeload).

4) HEMS and power flow results are used to evaluate theDNO costs (10).

V. NUMERICAL RESULTS

As a test case, a modified IEEE 13 node feeder test system[16] at 13.2 kV as in Fig.3 is considered with 6 MW peak loadand high level of DER penetration (5.1 MW total peakgeneration). Node 650 is the EM frontier node. Loads withdifferent 24 hour demand profiles are connected in every nodeexcept 650, 632, 671 and 684. Load and PV generation profilesfor node 680 are shown in Fig. 4.

Prosumers are connected to nodes 652, 680, 646 and 675. Itis assumed that prosumers PV panels draw only active power.Table 1 shows certain characteristics of prosumers aggregated


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PV-battery storage. Values of penalization for energy notsupplied and energy with poor quality are respectively 2000[$/MWh] and 300 [$/MWh].

Fig. 3. Modified IEEE 13 node feeder test system [16]

TABLE I. PV/STORAGE SYSTEMS CHARACTERISTICS

Table HeadNode

652 680 646 675

PV Max Power [MW] 1.5 1.5 1.5 1.0

Total Daily EnergyProduction [MWh]

10.4 10.4 10.2 7.3

[kW] -300 -300 -300 -300[kW] 300 300 300 300

[MWh] 0.05 0.05 0.05 0.05[MWh] 1.5 1.5 1.5 1.5[$/MWh] 150 150 150 150

Fig. 4. Node 680 forecasted Load and PV generation.

In order to assess the DNO economic interests, we simulatethe HEMS control actions in response to different pricings. The

base case consists in testing the HEMS optimization problemconsidering that DNO charges energy to prosumers hourly atthe corresponding Locational Marginal Price (LMP)( ) shown in Fig. 5. Figure 5 also shows atrivial pricing which will be later analyzed.

Operation schedules of batteries in response to LMP and atrivial pricing are shown for nodes 652 and Fig. 6 and Fig. 7respectively. The charge and discharge cycles due to LMP are

approximately between time intervals 8:00-12:00 and 13:00 to17:00 respectively. The results of LMP in terms of DNO and

prosumers costs is 3468.50 [$] and -585.00 [$]. The high costfor DNO is due to energy not served penalizations for networkcongestions on hours 23:00 and 24:00. The prosumer has ahigh net profit due to high values DER penetration and.

Fig. 5. Day Ahead LMP and Trivial Pricing for 24 hours

Fig. 6. Batteries charge and discharge cycles in response to LMP and TrivialPricing at node 652

Fig. 7. Batteries charge and discharge cycles in response to LMP and TrivialPricing at node 680

To avoid the high costs of energy not served, we triviallymodified the LMP to set peak price levels in hours of highcongestion as in Fig. 5. The HEMS responds to this pricing bydischarging stored energy in hours 23:00 and 24:00 as shownin Figures 6 and 7, contributing to avoid network congestionand costs of energy not served. Nevertheless, the trivial pricingresults in relative improvement in DNO benefits butdeterioration of prosumers benefits as shown in Table II.

0 5 10 15 20 250

0.5

1

1.5

Time[hr]

Power[MW]

Node 680

PV Gen Profile

Demand Profile

15.0

20.0

25.0

30.0

35.0

40.0

45.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Price[$/MWh]

Time [hr]LMP [$/MWh] Trivial Pricing [$/MWh]

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0 1 2 3 4 5 6 7 8 9 1 0 11 12 13 14 15 1 6 1 7 1 8 19 20 2 1 2 2 2 3 2 4

Power[MW]

Time [hr]

Pbat@LMP (Node 652) Pbat@Trivial Pricing (Node 652)

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 1 2 3 4 5 6 7 8 9 1 0 11 12 13 1 4 1 5 1 6 17 18 1 9 20 21 2 2 2 3 2 4

Power[MW]

Time [hr]

Pbat@LMP (Node 680) Pbat@Trivial Pricing (Node 680)


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TABLE II. DNOPROSUMER COSTS RESULTS

Pricing \ Cost DNO Cost Prosumer Cost

DA LMP 3468.50 -585.00

Trivial Pricing 1654.57 -406.52

From this results from Table II, we conclude that trade-offs in

DNO and prosumers benefits in result to different dynamicpricings must be analyzed in order to define an optimal pricing-a pricing that benefits both interests-.

VI. CONCLUSIONS

The intelligent optimization technique proposed in thismethodology, allows the prosumers to optimally schedule their

batteries operation for a 24 hour horizon with previousknowledge of the dynamic pricing, PV system generationforecast and prosumers demand forecast, by the use of aHEMS. In the presented dynamic pricing scenario, manualschedule of batteries charge and discharge would be inefficientand suboptimal.

This work relies on the assumption that prosumers HEMSmaximize their own benefit for selling PV power and buying

power to the DNO, by scheduling optimally the charge anddischarge cycles of batteries. Prosumers can also, deliverservices for voltage control and congestion management if anadequate dynamic pricing is set by the DNO for these

purposes, by means of active power management.Nevertheless, due to the fact that prosumers and DSO haveconflicting interests, trade-offs due to different dynamic

pricings must be exhaustively analyzed.

In this context, in a future work we expect to analyzedynamic pricing trade-offs by the use of a multiobjectiveoptimization algorithm. In addition to distributed generation

and electrical energy storage, also active loads are part of DER.Future research could consider prosumers to schedule flexibleloads in response to dynamic pricing through HEMS.

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economic assesment of dynamic pricing in smart distribution networks

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