Friday, March 5th, 2021
Economic Dispatch and Unit Commitment Modeling Using PLEXOS
Agenda1. Economic Dispatch and Unit Commitment Overview
2. Introduction to PLEXOS
3. Modeling a case for Economic Dispatch and Unit Commitment
4. Mathematical model and Optimization method used by PLEXOS
5. Importance and Benefits of Economic Dispatch and Unit Commitment
6. Modeling Hydro Electric and Renewable Energy Systems
7. Advanced Modeling features in PLEXOS – Power2X and Electric Vehicles
8. Q&A and Discussions
Economic Dispatch and Unit Commitment Overview
Economic Dispatch
• Definition:Economic dispatch is defined as the optimal operation of generationfacilities to generate electricity at the lowest cost while reliably serving theconsumers as well as respecting the operational constraints of generationand transmission facilities.
• Affordable and reliable electricity service to consumers
• Focuses on short-term operational decisions
• Requires thoughtful, long-term investments in generation andtransmission as well as sophisticated operation of these assets.
Economic Dispatch Problem
• Minimize : 𝐶 𝑃𝐺 = σ𝑡=1𝑇 σ𝑖=1
𝑁 𝐶𝑖 . 𝑃𝐺𝑖(𝑡) - Total Production Cost of‘N’ Gen Units
• Subject to : σ𝑖=1𝑁 𝑃𝐺𝑖(𝑡) = 𝑃𝐷(𝑡) + 𝑃𝑙𝑜𝑠𝑠(𝑡) - Power Balance
𝑃𝐺𝑖𝑚𝑖𝑛 ≤ 𝑃𝐺𝑖(𝑡) ≤ 𝑃𝐺𝑖
𝑚𝑎𝑥- Generator Operating Limits
−𝑃𝐿𝑖𝑚𝑖𝑛≤ 𝑃𝐿𝑖 𝑡 ≤ 𝑃𝐿𝑖
𝑚𝑎𝑥- Transmission Line Limits
Other Constraints
• where,• 𝑃𝐺𝑖 is generation output of generator unit ‘i’
• 𝑃𝐷𝑡𝑜𝑡𝑎𝑙 is total load demand
• 𝑃𝑙𝑜𝑠𝑠 is total transmission losses
3 Bus Example2_GasNode
3_LoadCenter
1_CoalNode
CoalGen_1 GasGen_1
Load = 120MW
Max Capacity = 80MW
Min Stable Level = 0MW
Fuel Price = 1.5 $/GJ
Heat Rate = 10GJ/MWh
Max Capacity = 100MW
Min Stable Level = 0MW
Fuel Price = 3 $/GJ
Heat Rate = 6GJ/MWh
3 Bus Example2_GasNode
3_LoadCenter
1_CoalNode
CoalGen_1 GasGen_1
Load = 120MW
Max Capacity = 80MW
Min Stable Level = 0MW
Fuel Price = 1.5 $/GJ
Heat Rate = 10GJ/MWh
Max Capacity = 100MW
Min Stable Level = 0MW
Fuel Price = 3 $/GJ
Heat Rate = 6GJ/MWh
CoalGen_1 can
dispatch at a cost of
1.5×10 = 15 $/MWh
3 Bus Example2_GasNode
3_LoadCenter
1_CoalNode
CoalGen_1 GasGen_1
Load = 120MW
Max Capacity = 80MW
Min Stable Level = 0MW
Fuel Price = 1.5 $/GJ
Heat Rate = 10GJ/MWh
Max Capacity = 100MW
Min Stable Level = 0MW
Fuel Price = 3 $/GJ
Heat Rate = 6GJ/MWh
CoalGen_1 can
dispatch at a cost of
3×6 = 18 $/MWh
3 Bus Example2_GasNode
3_LoadCenter
1_CoalNode
CoalGen_1 GasGen_1
Load = 120MW
Max Capacity = 80MW
Min Stable Level = 0MW
Fuel Price = 1.5 $/GJ
Heat Rate = 10GJ/MWh
Max Capacity = 100MW
Min Stable Level = 0MW
Fuel Price = 3 $/GJ
Heat Rate = 6GJ/MWh
Objective function:
Min f(x) = [15 × CoalGen_1] + [18 × GasGen_1]
Subject to:
0 ≤ CoalGen_1 ≤ 80MW
0 ≤ GasGen_1 ≤ 100MW
CoalGen_1 + GasGen_1 = 120MW
3 Bus Example2_GasNode
3_LoadCenter
1_CoalNode
CoalGen_1 GasGen_1
Load = 120MW
Max Capacity = 80MW
Min Stable Level = 0MW
Fuel Price = 1.5 $/GJ
Heat Rate = 10GJ/MWh
Max Capacity = 100MW
Min Stable Level = 0MW
Fuel Price = 3 $/GJ
Heat Rate = 6GJ/MWh
Minimize:
f(x) = [15 × 80] + [18 × 40]
= $1920
40 MW
80 MW
Unit Commitment Problem
• Unit Commitment refers to a sequence of generating unit on and offdecisions made across time.
• The Unit Commitment problem is to find an optimal combination of theseon/off decisions for all generating units across a given horizon.
• On/Off decisions must imply both feasible and optimal solution (i.e. minimizethe total system cost)
• In summary, UC is a decision to choose a combination of availablegenerating units to meet demand in order to minimize operating cost
• Constraints that apply to Unit Commitment problem:• Min Stable Level
• Min Up/Down Time
• Ramp Rates
• Fuel Constraints
Unit Commitment Problem• Minimize : 𝐹 = σ𝑡=1
𝑇 σ𝑖=1𝑁 [𝐶𝑖 . 𝑃𝐺𝑖 𝑡 + 𝑆𝑖 . 𝒖𝒊
𝒔(𝒕)] - Total Production Cost
• Subject to : σ𝑖=1𝑁 𝑃𝐺𝑖(𝑡) = 𝑃𝐷(𝑡) + 𝑃𝑙𝑜𝑠𝑠(𝑡) - Power Balance
𝑃𝐺𝑖𝑚𝑖𝑛. 𝑢𝑖(𝑡) ≤ 𝑃𝐺𝑖(𝑡) ≤ 𝑃𝐺𝑖
𝑚𝑎𝑥. 𝑢𝑖(𝑡) - Generator Operating Limits
𝒖𝒊, 𝒖𝒊𝒔 ∈ {𝟎; 𝟏} - Unit Commitment decision variable
−𝑃𝐿𝑖𝑚𝑖𝑛≤ 𝑃𝐿𝑖 𝑡 ≤ 𝑃𝐿𝑖
𝑚𝑎𝑥- Transmission Line Limits
Other Constraints - Ramp Rates, Min Up/Down
• where,• 𝑃𝐺𝑖 is generation output of generator unit ‘i’
• 𝑃𝐷𝑡𝑜𝑡𝑎𝑙 is total load demand
• 𝑃𝑙𝑜𝑠𝑠 is total transmission losses
• 𝑆𝑖 is start up cost of generator unit ‘i’
• 𝑢𝑖 is the unit commitment of generator unit ‘i’
• 𝑢𝑖𝑠 is the start up indicator of generator unit ‘i’
Mixed Integer Linear Programming (MILP)
• Economic Dispatch Problem:• Equations (i.e., objective function and constraints)
are all linear in its decision variables.• Decision Variables are all continuous (e.g.,
generator outputs), i.e., they take their valueswithin a pre-defined closed interval (no holesallowed)
• Unit Commitment Problem (MILP):• Equations (i.e., objective function and constraints)
are all linear in its decision variables.• Decision Variables can be continuous (e.g.,
generator outputs) or integer (e.g., generator unitcommitment), hence it is a ‘Mixed Integer’.
2_GasNode
3_LoadCenter
1_CoalNode
CoalGen_2 GasGen_2
Load = 120MW
GasGen_1
GasGen_3
CoalGen_1
CoalGen_3
?
Solving LP and MILP
• LP:• Relatively Easier to solve using
Simplex or Interior Point Methods
• Solved in Polynomial time
• MILP:• Harder to solve
• Time taken to solve increasesexponentially with increase inthe number of decisionvariables and constraints
MILP
LP
Problem Size
So
lutio
n T
ime
~ 50,000 integers
(MILP case)
Introduction to PLEXOS
• Single unified software solution for fundamental energy modeling
SINGLE UNIFIED ENGINE
• Works across all use cases• Works across all horizons
GLOBAL CO-OPTIMIZATION
• Co-optimizes across all commodities• Co-optimizes across all assets
DIGITAL TRANSFORMATION PLATFORM
• High performance• Advanced analytics
SINGLE
UNIFIED
ENGINE
Congestion
Analysis
Market Price
Forecast
Regulatory
Assessments
Market Analysis
System
Expansion
Gas Portfolio
Planning
Integrated
Resource
Planning
Portfolio
Planning &
Budgeting
Reliability
Assessment
Portfolio ST
Operations
P&L Analysis
Maintenance
Planning
PLEXOS
PLEXOS Typical Use Cases
Single Unified Energy System
GAS PLANNING/OPTIMIZATION
MARKET & PORTFOLIO ANALYSIS
Gas SupplyGas Storage
Gas Demand
LNG Import/ExportsGas Generation Power Generation Hydro Generation
Hydro Topology
Water Demand
Electric Demand
TRANSMISSION PLANNING
Pipeline Network
CHP Plant
Steam Demand
GENERATION PLANNING /OPTIMIZATION
HYDRO OPTIMIZATION
COMBINED HEAT & POWER
Renewable Generation
Energy Storage
RENEWABLES & STORAGE
Modeling a case for Economic Dispatch and Unit Commitment
3 Bus Example2_GasNode
3_LoadCenter
1_CoalNode
CoalGen_1 GasGen_1
Load = 120MW
Max Capacity = 80MW
Min Stable Level = 0MW
Fuel Price = 1.5 $/GJ
Heat Rate = 10GJ/MWh
Max Capacity = 100MW
Min Stable Level = 0MW
Fuel Price = 3 $/GJ
Heat Rate = 6GJ/MWh
3 Bus Example2_HydroNode
3_LoadCenter
1_CoalNode
CoalGen_1
HydroGen_1
Load
GasGen_1
GasGen_2
Mathematical Model in PLEXOS
Solving UC/ED using MILP• Unit Commitment and Economic Dispatch can be formulated as a linear problem
with integer variables representing generator on/off status.
Minimize Cost = generator fuel and VOM cost + energy/AS/fuel/capacity marketpurchase cost + transmission wheeling – energy/AS/fuel/capacitymarket sale revenue + contract purchase + generator start cost –contract sale saving
Subject to:• Energy Balance constraints• Operation reserve constraints• Generator and contract chronological constraints: ramp, min up/down, min capacity• Generator and contract energy limits: hourly/daily/weekly/…• Transmission limits• Fuel limits: pipeline, daily/weekly/…• Emission limits: daily/weekly/…• User defined constraints• Other constraints
Advantages of MILP
PLEXOS’ use of MILP is advantageous in many ways:
• Integers – unlocks many modeling possibilities.
• Any user defined constraint can be seamlessly added to optimizationformulation.
• Integration with reputable solvers: IMB (CPLEX), Gurobi, and FICO(Xpress-MP).
• Can take advantage of latest advances in solver technology.
• Guarantees an optimal solution as opposed to most heuristics.
• The real world – pool markets already operate on MILP. This is what themarket clearing engines solve, and PLEXOS is well-positioned to mimicthem.
Importance and Benefits of Economic Dispatch& Unit Commitment
Benefits of UC/ED
• Reduced Total Fixed and Variable Electricity Production Costs.
• Use of efficient generation units resulting in:• Lower fuel usage
• Better fuel utilization
• Reduced emissions
• Increases additional cost savings from pooled operating reserves, thusincreasing reliability using less total generation capacity.
• Increased Reliability without increasing operating costs.
• Encourage long term investment in transmission and generationexpansion by maintaining reliability and minimizing costs.
Modeling Hydro Electric and Renewable Energy
Systems
Renewable Energy Systems
Why?
• Clean Energy Standards, Renewable Portfolio Standards (RPS)
• 100% renewable futures
• Challenges• Intermittent nature
• Reliability, grid scale storage
• Model and evaluate
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Hydro Optimization
Ensures optimal use of storage down to chronological levelMultiple phase simulation
(Long – Medium – Short)
Major and minor storages and junctions
Natural inflows and spillways and canals
Cascading networks
Minimum releases for environment
Operational constraints and hydro generation efficiency
Constraints
Multistage stochastic optimisation for better modelling of storage release policies under uncertainty
Monte Carlo or Stochastic
Optimisation
0
250
500
750
1000
1250
1500
1750
2000
2250
2500
Storage volume trajectory - Laja Lake (Mm3)
Serie 1 Serie 2 Serie 3 Serie 4 Serie 5 Serie 6
Serie 7 Serie 8 Serie 9 Serie 10 Serie 11 Serie 12
Hydro Operation and Planning
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Challenges:
1) Transmission: High congestions in the
transmission lines due to large supply of solar energy in the north to serve
high demand in the central zone
2) Cycling: Increase in startups between 16 and 21 hours (Solar gen
decrease) and shutdowns between
6 and 12 hours (Solar gen increase).
3) Ramping: High ramping requirements with solar generation
increase/decrease.
4) Hydro constraints: Highly complex irrigation constraints.
2 interconnected systems connected through a 1,700 MVA 2x500 kV line consisting in a system of 3,200 km extension
En
d V
olu
me
(1000 m
3)
Storage Volume Trajectory for 12 series of Natural
Inflow
Advanced Modeling features in PLEXOS:
Power2X and Electric Vehicles
Electricity and Gas Markets ConvergencePrimary Fuels
Convergence/Processing
TechnologiesEnd Use
Coal
Power Generation
Gas Production Facilities
Refineries
Hydrogen Production
Oil
Other: Biomass, Nuclear, etc.
Natural Gas
Renewables
Electricity Modeling
Gas
Modeling
Industrial
Residential
Commercial
Transport
Detailed Modeling of Electricity
Fuel (Gas)
• Fuel is represented as a
TimeSeries datafile
• Fuel availability is not
modeled in detailed but
approximated
• Unable to identify synergy
between gas and power
network
Emissions
Heat
Wind
Solar
Battery
Node C
Node B
Node A
Line A-B
Line B-C
Gas Gen 2
Gas Gen 1
Detailed Modeling of Gas Network
Fuel (Gas)
Emissions
Heat
Wind
Solar
Battery
Node C
Node B
Node A
Line A-B
Line B-C
Gas Gen 2
Gas Gen 1
Gas Storage
Power2X
Gas Node B
𝐻2
Gas Node A
Gas Node C
Gas Node D
Gas Pipeline
Gas Pipeline
Gas Pipeline
Gas Pipeline
Gas Node F
Gas Node E
Gas Field
Gas Contract
Residential Demand
Industrial Demand
Power to Gas (P2X) adds flexibility
• The electricity system is fast real time system, resulting in limited long-term flexibility; whereas the gas system is much flexible and longer termand can provide flexibility to the electricity system
• Surplus renewable energy can’t be effectively stored in the electricitysystem, so “free” renewable generation must be increasingly curtailed.
• Power2X converts this surplus electricity to gas and stores it instead
• Essentially operating as a battery, but large scale and using the current gasinfrastructure with limited additional investment or technological risk
Electric Vehicles
• Electric Vehicle penetration – increasing demand
• Challenge is to develop an optimal charging schedule based on the vehicle usage
• PLEXOS models three levels of complexities with respect to charging and dischargingof electric vehicle batteries:
• 'V0G’
• 'V1G’
• 'V2G'
Unique Business Value
Business Value
• Ability to model a wide range of generating assets – solar, nuclear,
wind, hydro, coal, gas, PPAs etc., their associated properties (Heat
Rates, Max Capacity) and complex constraints associated to the unit
(Ramp Rates, Min up/down time, emission).
• MILP provides the most optimal and feasible solution resulting in large
savings in annual fuel costs and higher annual profits.
• Ability to introduce user defined constraints to the optimization
problem.
• Unified Energy System Model – One Engine for everything.
• Transparent and robust diagnostics and infeasibility resolution.
Asia Pacific Customers
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Questions?