Integrated Resource Planning with PLEXOS - Energy...

World Bank Thirsty Energy - A Technical Workshop in Morocco

Dr. Randell M. Johnson, P.E. [email protected]

Integrated Resource Planning with PLEXOS

March 24th & 25th, 2014 Rabat, Morocco

• Multi-Sector Least Cost Planning

– Water Requirements for Power Plant Cooling

– Desalination

– Generation Capacity Planning

– Transmission Expansion

– Gas Pipeline Expansion Planning

– Renewables Integration

– Ancillary Services

– Commodity Storages

• Least Cost Optimizations

– Mixed Integer Programs

– Stochastic Optimizations

– Co-Optimizations

Integrated Planning with PLEXOS

2

Water/Energy Tradeoffs or Opportunities

• Generate a power expansion plan considering aggregated water use limits

• When a desal can be the least cost options for both power supply and water production

• When to use one or the other type of cooling in power plant in response to environmental regulation or water constraints

• When to build a power plant in a different location given water constraints

• When to build a transmission line instead of a water pipe to locate the power plant where it makes sense to least cost expansion plan

4 April, 2014 Energy Exemplar 3

Demand Duration Curves for Co-Optimized Expansion and Operation of Water and Electricity Sectors


Co

un

try

Wat

er D

eman

d (

MG

D)

Co

un

try

Elec

tric

ity

Dem

and

(M

W)

Percent Time

Country Electricity Demand Country Water Demand

- Multi Sector CapEx and OpEx Least Cost Optimization

- Primary and Secondary demand curve optimizations

Vol 1 Vol 2 Vol 3

Load

Water Use

Water Use

Water Use

Cpp1

Ctx pp1

Cpp2 Cpp3

Ctx pp2 Ctx pp3

Ctx Line 1

Ctx Line 2

Flow 1

Aqua Duct

Cad 1

Flow ad 1

Simplified Diagram of a Long Term Expansion Plan Optimization Problem

Thermal Plant 1

Thermal Plant 2

Thermal Plant 3

Cpp4 Thermal Plant 4

C w2 C w4 C w3 C w1

Water Use

Flow 4 Flow 2 Flow 3

Ctx pp4 Thermal

Plant

Coal Supply Capital Costs O&M Costs Fuel Costs Constraints

OR Gas Supply Capital Costs O&M Costs Fuel Costs Constraints

Cooling Type

Once Through

Recirculating

Dry

Capital and O&M Costs - Build cost - Cooling Type - Efficiency - Substation - Others

Fuel Supply Expansion Decision

Generator Type Expansion Decision

Coal Plant Cooling Water Requirement water treatment production cost = water treatment penalty price x flow

Optimized Expansion Decisions • Which power plant(s) to build and when considering water use costs and

constraints? • Which transmission interfaces to expand and when and how much? • Should Aqua Duct be built, when, and what size? • Should the Power Plant be build in a different water area? And build more power

transmission? (co-optimize water pipe and power transmission as well) • In the case above, could we consider as well the cost of building transport facilities

for the fuels (the coal, gas) to the alternative power plant site? • Include combined water-and-power production facilities, so that if one need to

meet a water production target, the opportunity to co-generate water-and-power is exploited to minimize the power cost (INV and O&M) and meet the water targets (these water targets may for a separate and different “type” of water not necessarily the same or connected to the water in the 3 areas shown in the picture)

Expansion with Stochastic Electric and Water Demands

4 April, 2014 8

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Hours over a Week

Stochastic Electric Demand Paths

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16

3

Hours over a Week

Stochastic Water Demand Paths

Stochastic Decomposition

Multi Sector Least Cost Decision Making

Cost $

Investment x

Production Cost P(x)

Investment cost/ Capital cost C(x)

Total Cost = C(x) + P(x)

Minimum cost plan x

9

• Chart shows the minimization of total cost of investments and of production cost

• As more investments made production cost trends down however investment cost trends up

• Minimize capital costs and production costs for electric, water, gas and other demands

Objective: Minimize net present value of the sum of investment and production costs over time

Illustrative Least Cost Optimization

10

Minimize 𝐵𝑢𝑖𝑙𝑑𝐶𝑜𝑠𝑡𝑖 × 𝐵𝑢𝑖𝑙𝑑𝑖,𝑦

𝐼

𝑖=1

𝑌

𝑦=1

+ 𝑃𝑟𝑜𝑑𝐶𝑜𝑠𝑡𝑖 × 𝑃𝑟𝑜𝑑𝑖,𝑡

𝐼

𝑖=1

+ 𝑆ℎ𝑜𝑟𝑡𝐶𝑜𝑠𝑡 × 𝑆ℎ𝑜𝑟𝑡𝑎𝑔𝑒𝑡

𝑇

𝑡=1

VOLL Unserved Energy

Individual Unit Production Cost

Individual Unit Production

subject to

Supply and Demand Balance: 𝑃𝑟𝑜𝑑𝑖,𝑡

𝐼

𝑖=1

+ 𝑆ℎ𝑜𝑟𝑡𝑎𝑔𝑒𝑡 = 𝐷𝑒𝑚𝑎𝑛𝑑𝑡 ∀𝑡

Production Feasible: 𝑃𝑟𝑜𝑑𝑖,𝑡 ≤ 𝑃𝑟𝑜𝑑𝑀𝑎𝑥𝑖 ∀𝑖, 𝑡 Expansion Feasible: 𝐵𝑢𝑖𝑙𝑑𝑖,𝑦 ≤ 𝐵𝑢𝑖𝑙𝑑𝑀𝑎𝑥𝑖,𝑦 ∀𝑖, 𝑦 Integrality: 𝐵𝑢𝑖𝑙𝑑𝑖,𝑦 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 Reliability: 𝐿𝑂𝐿𝐸(𝐵𝑢𝑖𝑙𝑑𝑖,𝑦) ≤ 𝐿𝑂𝐿𝐸𝑇𝑎𝑟𝑔𝑒𝑡 ∀𝑦

Individual Unit Build Cost

Amount Built

Investment Cost Production Cost

27 February, 2014 MA AGO

This simplified illustration shows the essential elements of the mixed integer programming formulation. Build decisions cover generation, generation cooling types, water use costs, transmission, gas pipeline, coal transport, water pipe, as does supply and demand balance and shortage terms. The entire problem is solved simultaneously, yielding a true co-optimized solution.

∀ = for all 𝑦 = year 𝑡 = interval 𝑖 = unit Y = Horizon

PLEXOS Algorithms

• Chronological or load duration curves

• Large-scale mixed integer programming solution

• Deterministic, Monte Carlo; or

• State-of-the-art Stochastic Optimization (optimal decisions under uncertainty)

Stochastic Variables • Set of uncertain inputs ω can contain any

property that can be made variable in PLEXOS: – Load – Fuel prices – Electric prices – Ancillary services prices – Hydro inflows – Wind energy, etc – Discount rates – Others

• Number of samples S limited only by computing memory

• First-stage variables depend on the simulation phase

• Remainder of the formulation is repeated S times

Capacity Expansion Planning 11

Constraints Driving Decisions • Investment Constraints

– Renewable Energy Laws – 10 – 30 year horizon – Minimum zonal reserve margins (% or MW) – Reliability criteria (LOLP Target) – Inter-zonal transmission expansion (bulk

network) – Resource addition and retirement candidates

(i.e. maximum units built / retired ) – Water Pipe – Gas Pipeline – Coal Transport – Build / retirement costs – Age and lifetime of units – Technology / fuel mix rules

• Operational Constraints – Energy balance – Ancillary Service requirements – Optimal power flow and limits – Resource limits:

• energy limits, fuel limits, emission limits, water use, etc.

– Emission constraints

• User-defined Constraints: – Practically any linear constraint can be added

to the optimization problem

Capacity Expansion Planning 12

Gas and Coal Gen Efficiency


MinCap 50% 65% 85% MaxCap

Incr

emen

talH

eatR

ates

(btu

/kW

h)

Ave

rage

Hea

tRat

e (

btu

/kW

h)

Capacity (MWh)

AverageHeatRate(btu/kWh) IncrementalHeatRate(btu/kWh)

Full Load HeatRate(btu/kWh)

System expansion for obtaining higher capacity factors leads to better

over all efficiency and lower carbon intensity

PLEXOS Example: Desalination

14

Seawater

Desalination

Freshwater

Heat Electricity

Example of Desal Expansion


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DES

AL

Elec

tric

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Co

nsu

mp

tio

n

Desal Expansion

Existing Desal Capacity Expanded Desal

Decision Option for power plant expansion

simultaneous with a desal expansion

Water Production Merit Order


1 5 9

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1

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5

Wat

er P

rod

uct

ion

Hours over Week

Unit A

Unit B

Example Desalination Plant • Example of Gold Coast Desalination Plant:

– Maximum Production = 133 ML/day

– Energy Consumption = 3.2 kWh/1000L

• Expression of Demand

– ML/hour (rate)

– ML (quantity)

• Use units consistently:

– 133/24 = 5.5417 ML/hour

– 3.2kWh × 1000 = 3.2 MWh/ML

4 April 2014 Generic Decision Variables 17

• PLEXOS treats water demand as a load on the electrical system • Generation and load are balanced with following equation:

𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑗𝑗

+ 𝑈𝑆𝐸𝑖,𝑡 − 𝐷𝑢𝑚𝑝𝑖,𝑡 − 𝑁𝑒𝑡𝐼𝑛𝑗𝑒𝑐𝑡𝑖𝑜𝑛𝑖,𝑡 = 𝐿𝑜𝑎𝑑𝑖,𝑡 ∀𝑖, 𝑡

• Where 𝑈𝑆𝐸𝑖,𝑡 is unserved energy, 𝐷𝑢𝑚𝑝𝑖,𝑡 is over-generation and 𝑁𝑒𝑡𝐼𝑛𝑗𝑒𝑐𝑡𝑖𝑜𝑛𝑖,𝑡 is the net export from the transmission node

Objects Class Name Cat- Description

Decision Variable Heat - The amount of heat provided to the desalination process in period t

Decision Variable Heat Input - Heat input to storage in period t

Decision Variable Heat Loss - Heat lost from storage in period t

Decision Variable Heat Stored - Amount of heat in stored in period t

Decision Variable Heat Stored Lag - Amount of heat stored in period t-1

Decision Variable Water - Freshwater

Constraint Heat Definition - Definition constraint for "Heat"

Constraint Heat Input Definition - Definition of "Heat Input' as sum of waste heat and ancillary boiler heat.

Constraint Heat Load - Defines the heat load associated with desalination.

Constraint Heat Loss Definition - Defines "Heat Loss" as a proportion of "Heat Stored"

Constraint Heat Stored Definition - Defines "Heat Stored" as a function of previous period "Heat Stored" and "Heat Input" and "Heat Loss"

Constraint Heat Stored Lag Definition - Defines "Heat Stored Lag" as "Heat Stored" in the previous period


Production Cost with Desal


1 5 91

31

72

12

52

93

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54

95

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Demand with Desal (MW) Demand before Desal (MW)


Economic Generation Dispatch to meet Electrical Demand and Water Demand

PLEXOS Example: Co-Optimization of Generation and Transmission Expansion

21

DC-Optimal Power Flow (DC-OPF)

solves network

power flow for given resource

schedules passed from UC/ED

enforces transmission line

limits

enforces interface limits

enforces nomograms

Security Constrained Unit Commit /Economic Dispatch

Energy-AS Co-optimization using

Mixed Integer Programming (MIP)

enforces resource chronological

constraints, transmission

constraints passed from NA,

and others.

Solutions include resource

on-line status, loading levels,

AS provisions, etc.

Unit Commitment /

Economic Dispatch

(UC/ED) Resource Schedules

in 24 hours

for DA simulations, or

in sub-hourly

for RT simulations

Violated Transmission

Constraints

Network Applications

(NA)

• SCUC / ED consists of two applications: UC/ED and Network Applications (NA)

• SCUC / ED is used in many power markets in the world include CAISO, MISO, PJM, etc.

Intermediate/advanced exercises:

1. Create a locational model by defining new GT (operating on Oil) candidate close to the load.

2. Solve the trade-off expansion problem of building Oil-fired GT or reinforcing the transmission system (building a second circuit L1-3 at 10 Million $$). WACC = 12% and Economic Life Year = 30, not earlier than 1/1/2015

23

Simple Example: G&T Co-Optimization

Gas_Gen (2x)

Load

3-Load_Center

2-River & Market

1-Coal_Mine

Coal_Gen

x2

L1-2 L2-3

L1-3

New_GT

New CCGT

GT-oil

L1-3_new

Line Max Flow (MW)

L1-2 500

L2-3 500

L1-3 500

Enable following Line expansion properties:

Generation and Transmission Expansion Results

24

Generation Expansion Transmission Expansion

Australian ISO Use of PLEXOS of Co-Optimization of Generation and Transmission in planning

25

Least-cost expansion modelling delivers a co-optimized set of new generation developments, inter-regional transmission network augmentations, and generation retirements across the NEM over a given period. This provides an indication of the optimal combination of technology, location, timing, and capacity of future generation and inter-regional transmission developments. The least-cost expansion algorithm invests in and retires generation to minimize combined capital and operating-cost expenses across the NEM system. This optimization is subject to satisfying: • The energy balance constraint, ensuring supply

matches demand for electricity at any time, • The capacity constraint, ensuring sufficient

generation is built to meet peak demand with the largest generating unit out of service, and

• The Large-Scale Renewable Energy Target (LRET) constraint, which mandates an annual level of generation to be sourced from renewable resources.

PLEXOS Example: Co-Optimization of Ancillary Services for Energy Storage to Balance Renewables

26

Co-Optimization of Ancillary Services Requirements for Renewables

• Integration of the intermittency of renewables requires study of Co-

Optimization of Ancillary Services and true co-optimization of Ancillary services is done on a sub-hourly basis

• More and more the last decade, it has been recognised that AS and

Energy are closely coupled as the same resource and same capacity have to be used to provide multiple products when justified by economics.

• The capacity coupling for the provision of Energy and AS, calls for joint optimisation of Energy and AS.

27

28

Ancillary Services Reliable and Secure System Operation requires the following product and Services (not exhaustive):

1. Energy

2. Regulation & Load Following Services – AGC/Real time maintenance of system’s phase angle and balancing of supply/demand variations.

3. Synchronised Reserve – 10 min Spinning up and down

4. Non-Synchronised Reserve – 10 min up and down

5. Operating Reserve – 30 min response time

6. Voltage Support – Location Specific

7. Black Start – (Service Contracts)


Energy Storage Providing Ancillary Services and Time Shift of Energy

PLEXOS Example: Sub-Hourly Energy and Ancillary Services Co-Optimization

30

31

PLEXOS Base Model Generation Result

• Peaking plant in orange operating at morning peak

• Some displacement of hydro to allow for ramping

• Variable wind in green

Spinning Reserve Requirement

32

• CCGT now runs all day to cover reserves and energy

• Coal plant 2 also online longer

• Oil unit not required

• Less displacement of hydro generation for ramping

PLEXOS higher resolution dispatch – 5 Minute Sub-Hourly Simulation

33

• Oil unit required at peak for increased variability

• Increased displacement of base load to cover for ramping constraints

Energy/AS Stochastic Co-optimisation!!!

34

So far the model example has had perfect information on future wind and load requirements.

Uncertainty in our model inputs should affect our decisions – Stochastic optimisation (SO)

• The goal of SO then is to find some policy that is feasible for all (or almost all) the possible data instances and maximise the expectation of some function of the decisions and the random variables

What decision should I make now given the uncertainty in the inputs?

Energy/AS Stochastic Co-optimisation

35

• Even though load lower (wind unchanged) more units must be committed to cover the possibility of high load and low wind

• These units must then operate at or above Minimum Stable Level

References for Ancillary Co-Optimization Applications of PLEXOS

36

• WECC Balancing Authority Cooperation Concepts to Reduce Variable Generation Integration Costs in the

Western Interconnection: Intra-Hour Scheduling (using PLEXOS), DOE Award DE-EE0001376, 02:10 – 12:12 • Integration of Wind and Solar Energy in the California Power System: Results from Simulations of a 20%

Renewable Portfolio Standard (using PLEXOS) • Examination of Potential Benefits of an Energy Imbalance Market in the Western Interconnection (using

PLEXOS), Prepared under Task Nos. DP08.7010, SM12.2011 sponsored DOE

PLEXOS Example: Consideration of Adequacy of Supply for System Expansion Planning

37

Calculated 1-in-10 LOLE for ISO-NE Control Area

12-13 March, 2014

32000 33000 34000 35000 36000 37000 38000

28325

28590

28940

29340

29790

30265

30750

31445

32210

32900

Installed Capacity (MW)

Sum

mer

20

17

Pea

k Lo

ad F

ore

cast

Dis

trib

uti

on

(M

W)

Forecast Probability

2017 Peak Load Forecast

10/90 28,325

20/90 28,590

30/70 28,940

40/60 29,340

50/50 29,790

60/40 30,265

70/30 30,750

80/20 31,445

90/10 32,210

95/5 32,900

160 PLEXOS Simulations of High Level ISO-NE Control Area Model

Results: NICR = 33,855 MW LOLE ~ 0.1

MA AGO 38

- Simulated load risk in calculating Loss of Load Expectation (LOLE) - Simulated multiple capacity levels

12-13 March, 2014 MA AGO 39

0

0.1

0.2

0.3

0.4

0.5

0.6

$0

$500,000,000

$1,000,000,000

$1,500,000,000

$2,000,000,000

$2,500,000,000

$3,000,000,000

$3,500,000,000

$4,000,000,000

95

%

96

%

97

%

98

%

99

%

10

0%

10

1%

10

2%

10

3%

10

4%

10

5%

10

6%

10

7%

10

8%

10

9%

11

0%

LOLE

(d

ays)

Co

st o

f Lo

st L

oad

($

)

% NICR

Cost of Lost Load

Value of Lost Load LOLEAssumption: VOLL = $20,000/MWh

PLEXOS calculation of average load weighted cost of lost load

PLEXOS calculation of average load weighted LOLE

• System LOLE degrades rapidly below Net Installed Capacity Requirement (NICR)

Applications of Integrated Planning Tools

40

Planning Objectives PLEXOS Capability

Environmental Policies • Optimization of Annual, Mid-Term, and Short Term constraints • Water usage, Environmental Constraints, others

Generation Capacity Planning • Least cost capacity expansion planning, cooling types (once through, recirculating, dry), Capacity Expansion Type, Minimization of Production Costs including water treatment costs

Renewables Integration and System Flexibility Requirement Assessments

• Sub-Hourly Co-Optimization of Ancillary Services with Energy and Transmission Power Flows • Stochastic Optimization and Stochastic Renewables Models • PHEV, EE, DR, SG, Energy Storage Models

Least Cost Resource Change within and Across Regions

• Co-Optimization of Generation and Transmission Expansion • Generation Retirements and Environmental Retrofit Models • Reliability Evaluation, Interregional Planning

Minimizing production costs and consumer costs

• Co-Optimization of Production cost of Water, Electrical, and Natural Gas Sectors • Electrical Network Contingencies and Natural Gas Network Contingencies

Sizing Natural Gas Network Components and Natural Gas Storage

• Co-Optimization of Natural Gas Network Expansion along with Electricity Sector Expansion • Electrical Network Contingencies and Natural Gas Network Contingencies

Integrated Reliability Evaluation • Integrated Reliability Evaluation to Ensure LOLE and other Metrics Maintained with Co-Optimization of Electric and or Gas Sector Expansion or True Monte Carlo

Appendix

PLEXOS Optimization Methods

• Linear Relaxation - The integer restriction on unit commitment is relaxed so unit commitment can occur in non-integer increments. Unit start up variables are still included in the formulation but can take non-integer values in the optimal solution. This option is the fastest to solve but can distort the pricing outcome as well as the dispatch because semi-fixed costs (start cost and unit no-load cost) can be marginal and involved in price setting

• Rounded Relaxation - The RR algorithm integerizes the unit commitment decisions in a multi-pass optimization. The result is an integer solution. The RR can be faster than a full integer optimal solution because it uses a finite number of passes of linear programming rather than integer programming.

• Integer Optimal - The unit commitment problem is solved as a mixed-integer program (MIP). MIP solvers are based on the Branch and Bound algorithm, complemented by heuristics designed to reduce the search space without comprising solution quality. Branch and Bound does not have predicable run time like linear programming. It is difficult in all but trivial cases to prove optimality and guarantee that the integer-optimal solution is found. Instead the algorithm relies on a number of stopping criteria that can be user defined in determining unit on and off states.

• Dynamic Programming - Dynamic programming (DP) is a technique that is well suited to the unit commitment problem because it directly resolves the min up time and min down time constraints, and over long horizons. Its weakness is in the way unit commit is decomposed so that units are dispatched individually. Thus if all units in the system were dispatched using dynamic programming it would be difficult to converge on a solution where system-wide demand was met exactly, and where any other system-wide or group constraint such as fuel or emission limits were obeyed. For certain classes of generator though DP can be fast and highly effective. The DP is most suited to units with a high capacity factor, and if applied to all units in the system is likely to produce significant under/over generation. Thus you must carefully select units for which the DP is applied e.g. high capacity factor plant with long min up time or min down time values are most suitable.

• Stochastic Programing - The goal of SO is to find some policy that is feasible for all (or almost all) of the possible data instances and maximize the expectation of some function of the decisions and the random variables

42 Multiple Optimization Methods Offer Advantages to Solving Planning Problems

Solving Unit Commitment and Economic Dispatch using MIP

Unit Commitment and Economical Dispatch can be formulated as a linear problem (after linearization) with integer variables of generator on-line status Minimize Cost = generator fuel and VOM cost + generator start cost + contract purchase cost – contract sale saving + transmission wheeling + energy / AS / fuel / capacity market purchase cost – energy / AS / fuel / capacity market sale revenue Subject to

– Energy balance constraints – Operation reserve constraints – Generator and contract chronological constraints: ramp, min up/down, min

capacity, etc. – Generator and contract energy limits: hourly / daily / weekly / … – Transmission limits – Fuel limits: pipeline, daily / weekly/ … – Emission limits: daily / weekly / … – Others

43

Where bgki,j = branch-group factor for line j in group i

44

Illustrative DC-OPF LP Formation

sconstraintother and

groupbranch for limit flow

linein limits flow

; line of resistance line ; linein flowpower )(

busat load and generation , balance;energy system

subject to

minimize

max

,

min

maxmin

,

2

ibgfbgfbg

jfff

jrjlgPTDFf

klgfrlg

gc

i

bgj

jjii

jjj

j

k

kkjkj

kk

j

jj

k

k

k

k

k

kk

i

PLEXOS Detailed Nodal Transmission Load Flows integrated with Optimization Algorithms

sConstraint Other and Emission

sConstraint Fuel

sConstraint onTransmissi

sConstraintEnergy Generator

sConstraint Time Up/Down MinGenerator

sConstraint Rate Ramp Generator

Limits)Capacity AS and n(Generatio kt, ogasgog

Limits)Capacity AS n(Generatio mk,t, oasasoas

m) AS for constraint (AS mt, asas

Balance)Energy (System t losslg

to subject

asac)o(oscgc Min

t

k

MAXt,

k

m

t

km,

t

k

t

k

MINt,

k

t

k

maxt,

km,

t

km,

t

k

mint,

km,

mint,

m

k

t

km,

j

t

j

k

t

k

k

t

k

t k m

t

km,

t

km,

1t

k

t

k

t

k

t

k

t

k

45

Illustrative Formulation of Energy/AS Co-optimization

Illustrative Formulation of Co-Optimization of Natural gas and Electricity Markets

• Objective:

– Co-Optimization of Natural Gas Electricity Markets

• Minimize:

– Electric Production Cost + Gas Production Cost + Electric Demand Shortage Cost + Natural Gas Demand Shortage Cost

• Subject to:

– [Electric Production] + [Electric Shortage] = [Electric Demand] + [Electric Losses]

– [Transmission Constraints]

– [Electric Production] and [Ancillary Services Provision] feasible

– [Gas Production] + [Gas Demand Shortage] = [Gas Demand] + [Gas Generator Demand]

– [Gas Production] feasible

– [Pipeline Constraints]

– others

46

• Fix perfect foresight issue

– Monte Carlo simulation can tell us what the optimal decision is for each of a number of possible outcomes assuming perfect foresight for each scenario independently;

– It cannot answer the question: what decision should I make now given the uncertainty in the inputs?

• Stochastic Programming

– The goal of SO is to find some policy that is feasible for all (or almost all) of the possible data instances and maximize the expectation of some function of the decisions and the random variables

• Scenario-wise decomposition

– The set of all outcomes is represented as “scenarios”, the set of scenarios can be reduced by grouping like scenarios together. The reduced sample size can be run more efficiently

47

Stochastic Optimization (SO)

Day-ahead Unit Commitment, Continued

Stochastic Optimisation:

Two stage scenario-wise decomposition Take the optimal

decision 2

Expected cost of

decisions 1+2

Is there a better

Decision 1?

Take Decision

1

Reveal the many

possible outcomes

Stage 1: Commit 1 or 2 or none of the generators Stage 2: There are hundreds of possible wind speeds. For each wind profile, decide the optimal commitment of the other units and dispatch of all units

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RESULT: Optimal unit commitment for generators

Integrated Resource Planning with PLEXOS - Energy...

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