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?