Integrated Resource Planning with PLEXOS

(1)

World Bank

Thirsty Energy - A Technical Workshop in Morocco

Dr. Randell M. Johnson, P.E.

[email protected]

Integrated Resource Planning with PLEXOS

March 24

th

& 25

th

, 2014

(2)

•

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

(3)

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)

Demand Duration Curves for Co-Optimized Expansion and

Operation of Water and Electricity Sectors

4 April, 2014 Energy Exemplar 4

C

oun

tr

y

W

at

er

Dem

an

d

(

MGD)

C

oun

tr

y

Elec

tric

ity

Dem

an

d

(

MW)

Percent Time

Country Electricity Demand Country Water Demand

- Multi Sector CapEx and OpEx

Least Cost Optimization

- Primary and Secondary

demand curve optimizations

(5)

Vol 1

Vol 2

Vol 3

Load

Water Use Water Use Water Use

C

pp1

C

tx pp1

C

pp2

C

pp3

C

tx pp2

C

tx pp3

C

tx Line 1

C

tx Line 2 Flow 1

Aqua Duct

C

ad 1

Flow

ad 1

Simplified Diagram of a Long Term Expansion Plan Optimization Problem

Thermal Plant 1 Thermal Plant 2 Thermal Plant 3

C

pp4 Thermal _{Plant 4}

C w2

C w4

C w3

C w1

Water Use

Flow 4 _{Flow 2} _{Flow 3}

C

tx 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

(6)

Coal Plant Cooling Water Requirement

(7)

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

(8)

Expansion with Stochastic Electric and Water Demands

4 April, 2014 8

1 7 ₁₃ ₁₉ ₂₅ ₃₁ ₃₇ ₄₃ ₄₉ ₅₅ ₆₁ ₆₇ ₇₃ ₇₉ ₈₅ ₉₁ ₉₇

103 109 115 121 127 133 139 145 151 157 163

Hours over a Week

Stochastic Electric Demand Paths

1 7 ₁₃ ₁₉ ₂₅ ₃₁ ₃₇ ₄₃ ₄₉ ₅₅ ₆₁ ₆₇ ₇₃ ₇₉ ₈₅ ₉₁ ₉₇

103 109 115 121 127 133 139 145 151 157 163

Hours over a Week

Stochastic Water Demand Paths

Stochastic

Decomposition

(9)

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

(10)

Illustrative Least Cost Optimization

10

Minimize 𝐵𝑢𝑖𝑙𝑑𝐶𝑜𝑠𝑡

_𝑖

× 𝐵𝑢𝑖𝑙𝑑

_𝑖,𝑦 𝐼 𝑖=1 𝑌 𝑦=1

+ 𝑃𝑟𝑜𝑑𝐶𝑜𝑠𝑡

_𝑖

× 𝑃𝑟𝑜𝑑

_𝑖,𝑡 𝐼 𝑖=1

+ 𝑆ℎ𝑜𝑟𝑡𝐶𝑜𝑠𝑡 × 𝑆ℎ𝑜𝑟𝑡𝑎𝑔𝑒

_𝑡 𝑇 𝑡=1 VOLL Unserved Energy Individual Unit Production Cost Individual Unit Production

subject to

Supply and Demand Balance: 𝑃𝑟𝑜𝑑

_𝑖,𝑡

𝐼 𝑖=1

+ 𝑆ℎ𝑜𝑟𝑡𝑎𝑔𝑒

_𝑡

= 𝐷𝑒𝑚𝑎𝑛𝑑

_𝑡

∀𝑡

Production Feasible: 𝑃𝑟𝑜𝑑

_𝑖,𝑡

≤ 𝑃𝑟𝑜𝑑𝑀𝑎𝑥

_𝑖

∀𝑖, 𝑡

Expansion Feasible: 𝐵𝑢𝑖𝑙𝑑

𝑖,𝑦

≤ 𝐵𝑢𝑖𝑙𝑑𝑀𝑎𝑥

𝑖,𝑦

∀𝑖, 𝑦

Integrality: 𝐵𝑢𝑖𝑙𝑑

_𝑖,𝑦

𝑖𝑛𝑡𝑒𝑔𝑒𝑟

Reliability: 𝐿𝑂𝐿𝐸(𝐵𝑢𝑖𝑙𝑑

_𝑖,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

(11)

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

(12)

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

(13)

Gas and Coal Gen Efficiency

MinCap 50% 65% 85% MaxCap In cr em en talHea tRa tes (b tu /k Wh ) A ve rag e He at Ra te (b tu /k Wh ) 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

(14)

PLEXOS Example:

Desalination

14

Seawater

Desalination

Freshwater

Heat

Electricity

(15)

Example of Desal Expansion

2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031

DE

SAL Elec

tr

ic

ity

Cons

umpt

ion

Desal Expansion

Existing Desal Capacity

Expanded Desal

Decision Option for

power plant expansion

simultaneous with a

desal expansion

(16)

Water Production Merit Order

1 5 9 ₁₃ ₁₇ ₂₁ ₂₅ ₂₉ ₃₃ ₃₇ ₄₁ ₄₅ ₄₉ ₅₃ ₅₇ ₆₁ ₆₅ ₆₉ ₇₃ ₇₇ ₈₁ ₈₅ ₈₉ ₉₃ ₉₇ 101 105 109 113 117 121 125 129 133 137 141 145 149 153 157 161 165

W

at

er

P

rodu

ction

Hours over Week

Unit A

(17)

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:

𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛

_𝑗

𝑗

+ 𝑈𝑆𝐸

_𝑖,𝑡

− 𝐷𝑢𝑚𝑝

_𝑖,𝑡

− 𝑁𝑒𝑡𝐼𝑛𝑗𝑒𝑐𝑡𝑖𝑜𝑛

_𝑖,𝑡

= 𝐿𝑜𝑎𝑑

_𝑖,𝑡

∀𝑖, 𝑡

•

Where

𝑈𝑆𝐸

_𝑖,𝑡

is unserved energy,

𝐷𝑢𝑚𝑝

_𝑖,𝑡

is over-generation and

𝑁𝑒𝑡𝐼𝑛𝑗𝑒𝑐𝑡𝑖𝑜𝑛

_𝑖,𝑡

is the net export from the transmission node

(18)

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

(19)

Production Cost with Desal

4 April 2014 Generic Decision Variables 19

1 5 9 ₁₃ ₁₇ ₂₁ ₂₅ ₂₉ ₃₃ ₃₇ ₄₁ ₄₅ ₄₉ ₅₃ ₅₇ ₆₁ ₆₅ ₆₉ ₇₃ ₇₇ ₈₁ ₈₅ ₈₉ ₉₃ ₉₇

101 105 109 113 117 121 125 129 133 137 141 145 149 153 157 161 165

(20)

Economic Generation Dispatch to meet Electrical Demand

and Water Demand

(21)

PLEXOS Example:

Co-Optimization of Generation and Transmission Expansion

(22)

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)

(23)

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

(24)

Generation and Transmission Expansion Results

24

(25)

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

(26)

PLEXOS Example:

Co-Optimization of Ancillary Services for Energy Storage to Balance

Renewables

(27)

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.

(28)

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

(29)

(30)

PLEXOS Example:

Sub-Hourly Energy and Ancillary Services Co-Optimization

(31)

31

PLEXOS Base Model Generation Result

•

Peaking plant in

orange operating at

morning peak

•

Some displacement of

hydro to allow for

ramping

(32)

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

(33)

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

(34)

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

(35)

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

(36)

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

(37)

PLEXOS Example:

Consideration of Adequacy of Supply for System Expansion Planning

(38)

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) Su m m er 2017 P eak Lo ad Forecas t Dis trib u tio n (MW) 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

(39)

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 $4,000,000,000 95 % 96 % 97 % 98 % 99 % 1 0 0 % 1 0 1 % 1 0 2 % 1 0 3 % 1 0 4 % 1 0 5 % 1 0 6 % 1 0 7 % 1 0 8 % 1 0 9 % 1 1 0 % LOLE (d ay s) Co st o f Lo st Lo ad ($ ) % NICR

Cost of Lost Load

Value of Lost Load LOLE Assumption: 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)

(40)

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

(41)

(42)

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

(43)

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

(44)

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

44

Illustrative DC-OPF LP Formation

s constraint other and group branch for limit flow line in limits flow ; line of resistance line ; line in flow power ) ( bus at load and generation , balance; energy system subject to minimize max , min max min , 2 i bg f bgf bg j f f f j r j l g PTDF f k l g f r l g g c i bg j j j i i j j j j k k k j k j k k j j j k k k k k k k i        





(45)

s Constraint Other and Emission s Constraint Fuel s Constraint on Transmissi s Constraint Energy Generator s Constraint Time Up/Down Min Generator s Constraint Rate Ramp Generator Limits) Capacity AS and n (Generatio k t, o g as g o g Limits) Capacity AS n (Generatio m k, t, o as as o as m) AS for constraint (AS m t, as as Balance) Energy (System t loss l g to subject as ac ) o (o sc g c Min t k MAX t, k m t k m, t k t k MIN t, k t k max t, k m, t k m, t k min t, k m, min t, m k t k m, j t j k t k k t k t k m t k m, t k m, 1 t k t k t k t k t k               









45

Illustrative Formulation of Energy/AS Co-optimization

(46)

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

(47)

•

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

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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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