Transcript Document

Co-Optimizations for Electricity and Natural Gas Sectors
Introduction to Concepts, Theory, Working Examples
Dr. Randell M. Johnson, P.E.
October 28th & 29th, 2013
Co-Optimizations for Natural Gas and Electric Sectors
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Optimizations Methods
Co-Optimization Generation and Transmission Expansion
Co-Optimization of Energy and Ancillary Services
Co-Optimization Electric and Nat Gas Production Cost
Co-Optimization of Nat Gas and Electric Markets with Co-Optimization of Ancillary Services
Co-Optimization Electric and Nat Gas Capacity Expansion
Integrated Datasets
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Applications of Co-Optimization Tools
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Optimization Methods
PLEXOS Optimization Methods
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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). The unit
on/off decisions are optimized within criteria.
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
17 July, 2015
Energy Exemplar
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PLEXOS:
Stochastic Optimization
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Stochastic Optimization (SO)
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Fix perfect foresight issue
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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;
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It cannot answer the question: what decision should I make now given the uncertainty in the inputs?
Stochastic Programming
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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
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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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Stochastic Variables
• Set of uncertain inputs ω can contain any property that can be
made variable in PLEXOS:
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–
–
–
–
Load
Fuel prices
Electric prices
Ancillary services prices
Hydro inflows
Wind energy, etc
• 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
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20 Sample input distribution for variables
Wind
Solar
Night
Daily
Periods
Day
Morning
Load
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SO Theory
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, Continued
Where the first (or second) stage decisions must take integer values we have a stochastic integer
programming (SIP) problem
SIP problems are difficult to solve in general
Assuming integer first-stage decisions (e.g. “how many generators of type x to build” or “when do a
turn on/off this power plant”) we want to find a solution that minimises the total cost of the first
and second stage decisions
A number of solution approaches have been suggested in the literature
PLEXOS uses scenario-wise decomposition ...
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SO Theory




, Continued
𝑥 and 𝑦 represents the first and second-stage decisions resp.
𝜔 represents the uncertain data
𝑞, 𝑊, ℎ, 𝑇 are a realisation of the random data
R and Z denote reals and integers respectively
min 𝑐 𝑇 𝑥 + E 𝑄 𝑥, 𝜔
s.t. 𝐴𝑥 = 𝑏
𝑛 −𝑝
𝑝
𝑥 ∈ R+1 1 × Z+1
2-stage SIP
Formulation
where
𝑄 𝑥, 𝜔 ≔ min 𝑞 𝑇 𝑦
s.t. 𝑊𝑦 = ℎ − 𝑇𝑥
𝑛 −𝑝
𝑝
𝑦 ∈ R +2 2 × Z+2
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SO Theory
, Continued
 Assume the distribution 𝜔 of uncertain inputs can be evaluated as
discrete scenarios 𝜔1 , 𝜔1 , … , 𝜔𝑆 having probabilities 𝑝1 , 𝑝2 , … , 𝑝𝑆 the
two-stage SIP can be formulated:
𝑆
𝑝𝑠 𝑐 𝑇 𝑥𝑠 + 𝑞𝑠𝑇 𝑦𝑠
Minimise
𝑠=1
subject to
𝐴𝑥𝑠 = 𝑏 𝑠 = 1, … , 𝑆
𝑇𝑠 𝑥𝑠 + 𝑊𝑠 𝑦𝑠 = ℎ𝑠 𝑠 = 1, … , 𝑆
𝑛 −𝑝
𝑝
𝑥𝑠 ∈ R +1 1 × Z+1 𝑠 = 1, … , 𝑆
𝑛 −𝑝
𝑝
𝑦𝑠 ∈ R+2 2 × Z+2 𝑠 = 1, … , 𝑆
𝑥1 = 𝑥2 = ⋯ = 𝑥𝑆
Scenario wise
Decomposition
of
2-stage SIP
Formulation
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H1
H2
H3
H1
H2
M3
H1
M2
H3
H1
M2
M3
M3
H1
M2
L3
L3
M1
H2
H3
M1
H2
H3
P(1)
M1
H2
M3
M1
H2
M3
P(2)
M1
M2
H3
M1
M2
H3
P(3)
M1
M2
M3
M1
M2
M3
M1
M2
L3
M1
M2
L3
M3
M1
L2
M3
L1
M2
H3
L3
M1
L2
L3
L1
M2
M3
L1
M2
H3
L1
M2
L3
L1
M2
M3
L1
M2
M3
L1
M2
L3
L1
M2
M3
L1
L2
L3
H3
H2
M3
H1
H3
M2
Initial “high”
H3
H2
M3
H3
M1
M2
M3
L3
L2
Initial “mid”
H3
M2
L2
M3
L3
L2
Initial “low”
Initial Problem
M3
L3
Scenarios
Sample Reduction
p(9)
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Day-ahead Unit Commitment
, Continued
Stochastic Optimisation:
Two stage scenario-wise decomposition
Stage 1:
Commit 1 or 2 or none of the
“slow” 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
Reveal the
many
possible
outcomes
Take the
optimal
decision 2
Expected
cost of
decisions
1+2
Take
Decision
1
Is there a
better
Decision
1?
RESULT: Optimal unit commitment for “slow” generator
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Co-Optimization of Generation and Transmission Expansion
Overview: Generation Transmission Expansion Planning
• Focus on long-term studies with decision
variables spanning many years:
• Co-optimize generation new builds and
retirements with:
– Transmission line builds e.g. AC or DC lines; and
– Transmission interface upgrades;
– Physical contract purchases (generation or load)
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Objective Function
• Object function minimizes (expected value of) the
net present value (NPV):
– Cost of new builds:
• Generator, DC Line, AC Line, Interface, Physical Contract
• Cost of retirements:
• Generator, DC Line
– Fixed operating costs
– Variable operating (production) costs
– Net cost of external market trades
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Optimal Decisions under Uncertainty
• New investments:
– Where?
• Location
– When?
• Timing
– How much?
• Sizing
• Retirements…
– When?
• Timing
– How much?
• Number of units
• Uncertainties:
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Load
Fuel prices
Hydro inflows
Wind energy
Outages
etc
• Constraints:
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Reliability (LOLP)
Emissions
Fuels
etc
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Objective Function Components
• For any combination of expansion decisions x we
have two types of costs:
1. Capital costs C(x):
– Cost of new builds
– Cost/savings from retirements
2. Production costs P(x):
– Cost of operating the system with any given set of
existing and new builds and transmission network
– Notional cost of unserved energy
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Optimization
Cost $
Objective: Minimize net present value of
forward-looking costs (i.e. capital and
production costs)
Total Cost = C(x) + P(x)
Investment cost/
Capital cost C(x)
Production Cost P(x)
Minimum
cost plan x
Investment x
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Illustrative Formulation Generation Transmission Expansion
Co-Optimization
𝑌
𝐼
Minimize
𝑇
𝐼
𝐵𝑢𝑖𝑙𝑑𝐶𝑜𝑠𝑡𝑖 × 𝐵𝑢𝑖𝑙𝑑𝑖,𝑦 +
𝑦=1 𝑖=1
subject to
𝑃𝑟𝑜𝑑𝐶𝑜𝑠𝑡𝑖 × 𝑃𝑟𝑜𝑑𝑖,𝑡 + 𝑆ℎ𝑜𝑟𝑡𝐶𝑜𝑠𝑡 × 𝑆ℎ𝑜𝑟𝑡𝑎𝑔𝑒𝑡
𝑡=1
𝑖=1
𝐼
Supply and Demand Balance:
𝑃𝑟𝑜𝑑𝑖,𝑡 + 𝑆ℎ𝑜𝑟𝑡𝑎𝑔𝑒𝑡 = 𝐷𝑒𝑚𝑎𝑛𝑑𝑡
∀𝑡
𝑖=1
Production Feasible: 𝑃𝑟𝑜𝑑𝑖,𝑡 ≤ 𝑃𝑟𝑜𝑑𝑀𝑎𝑥𝑖 ∀𝑖, 𝑡
Expansion Feasible: 𝐵𝑢𝑖𝑙𝑑𝑖,𝑦 ≤ 𝐵𝑢𝑖𝑙𝑑𝑀𝑎𝑥𝑖,𝑦 ∀𝑖, 𝑦
Integrality: 𝐵𝑢𝑖𝑙𝑑𝑖,𝑦 𝑖𝑛𝑡𝑒𝑔𝑒𝑟
Reliability: 𝐿𝑂𝐿𝑃 𝐵𝑢𝑖𝑙𝑑𝑖,𝑦 ≤ 𝐿𝑂𝐿𝑃𝑇𝑎𝑟𝑔𝑒𝑡 ∀𝑦
This simplified illustration shows the essential elements of the mixed integer
programming formulation. Build decisions cover generation, and transmission
as does supply and demand balance and shortage terms. The entire problem is
solved simultaneously, yielding a true co-optimized solution.
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Algorithms
• Chronological or load duration curves
• Large-scale mixed integer programming
solution
• Deterministic, Monte Carlo; or
• Stochastic Optimization (optimal decisions
under uncertainty)
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Generation Expansion Capabilities
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Building new generating plant
Retiring existing generating plant
Multi-stage projects e.g. GT before CCGT
Thermal or hydro with storage
Multi-annual emission caps
Fuel-supply policies and constraints
Pumped storage
Other renewables:
– Wind, solar, wave, etc
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Transmission Expansion Capabilities
• Building new DC transmission lines
• Retiring existing DC transmission lines
• Building new AC transmission lines:
– Dynamic changes in impedance matrix
• Multi-stage transmission projects
• Transmission Interface expansion
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Energy and Ancillary Services Co-Optimization
Ancillary Services Products
• Integration of the intermittency of renewables requires study of CoOptimization of Ancillary Services and true co-optimization of Ancillary
services is done on a sub-hourly basis in real time markets
• More and more the last decade, it has been recognised that AS and Energy
markets 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 markets that differs from market to market
due to different regional reliability standards and operational practises.
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Co-Optimization
Ancillary Service Products in Wholesale Markets
Reliable and Secure System Operation requires the following product and
Services (not exhausted):
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)
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Solving SC UC/ED 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 + 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
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Illustrative Formulation of Energy/AS Co-optimization
Min  ckt g kt  sckt (okt  okt 1 )   acm,t k asm,t k
m
k
t
subject to
 g   l   loss
t
j
t
k
t
k
k
k
 as
t
m, k
t (System Energy Balance)
j
t, m (AS constraint for AS m )
 asmt,min
k
t,max t
t
t
asm,t,min
k ok  asm, k  asm, k ok
t, k,m (Generation AS Capacity Lim its)
g kt,MIN okt  g kt   asm,t k  g kt,MAX okt
t, k (Generation and AS Capacity Lim its)
m
GeneratorRam pRate Constraints
GeneratorMin Up/DownTim e Constraints
GeneratorEnergyConstraints
Transm ission Constraints
Fuel Constraints
Em issionand Other Constraints
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Security Constrained Unit Commit /Economic Dispatch
•
•
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.
Unit Commitment /
Economic Dispatch
(UC/ED)
Resource Schedules
in 24 hours
for DA simulations, or
in sub-hourly
Energy-AS Co-optimization using
for
RT simulations
Mixed Integer Programming (MIP)
enforces resource chronological
constraints, transmission
constraints passed from NA,
and others.
Network Applications
(NA)
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
Solutions include resource
on-line status, loading levels,
AS provisions, etc.
Violated Transmission
enforces nomograms
Constraints
Flow Diagram of Sequential DA/RT Modelling and Simulation
Sequential DA/RT is Optional Additional Feature for Simulation
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PLEXOS Example:
Sub-Hourly Energy and Ancillary Services Co-Optimization
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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
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Spinning Reserve Requirement
• 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
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PLEXOS higher resolution dispatch – 5 Minute Sub-Hourly Simulation
• Oil unit required at peak for
increased variability
• Increased displacement of
base load to cover for ramping
constraints
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Energy/AS Stochastic Co-optimisation!!!
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?
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Energy/AS Stochastic Co-optimisation
• 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
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Co-Optimization of Electric and Natural Gas Production Cost
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
•
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PLEXOS Example:
Co-Optimization of Natural Gas and Electricity Markets
for simplified northeast model
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New England and New York Markets
• Created a simple dataset to proxy the NY and
New England electricity and natural gas markets.
• Several simplifying assumptions:
– Assumed aggregation of gas production
– Simplified both the natural gas and electricity network
in New York State and New England.
– Simplified the complexity of generators and
interconnections.
Integrated Gas and Electric Model
Northeast Market Simplified Assumptions
•
Zonal electric market with limited transmission
– New York 3 zones: New York City and Long Island; Upstate NY and Western NY.
– New England 3 zones: North (ME, NH, VT); and West (MA, CT & RI); Central (eastern MA).
•
4 natural gas production regions:
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–
–
–
•
•
Alberta Canada with an interconnection at the Niagara Hub; Waddington and Montreal;
Gulf coast with an interconnection in New Jersey;
Shale Production in Mid-Western States with interconnection in Pennsylvania; and
A small natural gas production in upstate New York.
2 Natural Gas Markets: New York and New England.
5 adjoining electrical markets:
– PJM; NY, Ontario; Quebec and New England.
•
Daily natural gas load based on EIA monthly demand.
Integrated Gas and Electric Model
Simplified Combined Electric & Natural Gas Model
Gas
Montreal
Electric
Montreal
Wadding
ton
North
NE
To
Alberta
Niagara
Hub
North
NE
Upstate
West
Ontario
West
West
NE
Upstate
West
NE
PJM
West
NJ
Hub
Leidy
PJM
East
To Shale
To Gulf
NYC
NYC
Central
NE
Central
NE
Simplified Model Inputs/Results
NY and New England Gas Demand
Natural gas
demand (nongeneration)
provided by EIA.
Generation gas
demand
calculated by
PLEXOS.
Integrated Gas and Electric Model
Simplified Model Inputs/Results
Northeast Natural Gas Prices
Natural Gas
prices at Leidy,
Niagara Hub and
Transco Z6 are
used as the
production costs
for the natural
gas into NY and
New England.
Citygate prices
are calculated by
PLEXOS.
Integrated Gas and Electric Model
Simplified Model Results
Daily Pipeline Flows
Natural Gas
production
serving the
Northeast: NY,
Shale; Gulf; and
Canada
production.
Calculated by
PLEXOS.
Integrated Gas and Electric Model
Simplified Model Results
NY Electrical Load
Integrated Gas and Electric Model
Simplified Model Results
New England Electrical Load
Integrated Gas and Electric Model
Simplified Model Results
NY Electric LBMP
Nat Gas Network Constraints
Electrical Network Constraints
Electric Prices for
•
•
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NYC (Zones J-K);
Upstate (Zones F-I);
West (Zones A-E).
Prices in Winter
influenced by
natural gas
shortages. Summer
prices reflect
electric constraints
calculated by
PLEXOS.
Integrated Gas and Electric Model
Simplified Model Results
ISONE LMP
Electric Prices for
ISONE.
Nat Gas Network Constraints
Electrical Network Constraints
Prices in Winter
influenced by
natural gas
shortages. Summer
prices reflect
shortages
calculated by
PLEXOS.
Simplified Model Results
Northeast Fossil Fuel Consumption in MMBtu
Northeast fossil fuel
consumption
calculated by
PLEXOS.
Integrated Gas and Electric Model
Simplified Model Results
Northeast Fossil Fuel Generation in MWh
Northeast fossil fuel
consumption
calculated by
PLEXOS.
Integrated Gas and Electric Model
Co-Optimization of Natural Gas and Electric Markets with
Co-Optimization of Ancillary Services
Co-Optimization of Gas Electric Markets with Co-Optimization
of Ancillary Services
•
•
•
•
Electric: Security Constrained Unit Commitment and Economic Dispatch (Nodal or Zonal)
Gas: Production Cost Market Clearing Solved with LP (Nodal or Zonal)
Co-Optimization of Gas and Electric Clearing
Co-Optimization of Ancillary Services
•
Study Mode Capability:
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–
–
–
–
–
•
Impacts of Gas Constraints on Electricity Market
Increased electrical sector reliance on Natural Gas fired generation on Natural Gas Network
Impacts of renewable generation on Natural Gas Network
Impacts of electrical demand load ramping with Gas units on Natural Gas Network
Integration of Public Policy
Gas and or Electric Contingencies
Extensions:
–
–
–
–
–
–
Co-Optimization of Gas Electric Capacity Expansion
Flexibility Assessments
Demand Response
Evaluations of Energy Storage for Gas, Electric, storage of other fuels, and dual fuel
Integration of Renewables
Benefit Analysis to Gas and or Electric Rate Payers
Illustrative Formulation of Co-Optimization of Natural Gas and Electric Markets with
Co-Optimizations of Ancillary Services
•
Objective:
– Co-Optimization of Gas Electric Markets with Co-Optimization of Ancillary Services
•
Minimize:
– Electric Production Cost + Gas Production Cost + Electric Demand Shortage Cost + Natural Gas
Demand Shortage Cost + Ancillary Services Shortage Cost
•
Subject to:
– [Electric Production] + [Electric Shortage] = [Electric Demand] + [Electric Losses]
– [Ancillary Service Provision] >= [Ancillary Services Requirements]
– [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
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Ancillary Services
•
Contingency Reserves: Spinning reserve and Non-Spinning reserve
–
•
Regulation Reserve: Regulation up / down
–
•
Cover forced outages of generators or transmission lines
Cover load / renewable variability at second interval
Flexibility Reserve: Flexibility up / down
–
Cover load / renewable variability and uncertainty at the minute interval
•
For regulation and flexibility reserves, can define the reserve requirement based
on the load / renewable generation variability and uncertainty
•
The reserve provisions from generators are capped by the generator
dispatchable and un-used capacity, and the ramp rate
•
Co-optimization of the energy-AS mimic scheduling software to minimize the
total system cost
•
Shortage of generation capacity or ramp capacity will show in the reserve
provision shortfall (checking the ramp capacity adequacy)
Natural Gas Network
•
Natural Gas Demand
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–
•
Well Heads
–
–
•
Input well head production cost
Aggregate well heads in areas
Pipelines
–
–
–
•
Method calculates the gas demand required at natural gas pipeline location from generation based on the
generator heat rate.
Enter separate gas demands associated with a specific natural gas pipeline node of commercial, industrial and
residential gas.
Constraints
Flow
Line Pack
Gas Storage
–
–
Storage Capacity
Nat Gas Storage Inventory
Co-Optimization Electric and Nat Gas Capacity Expansion
Overview: Gas Electric Expansion Planning
• Focus on long-term studies with decision variables
spanning many years:
• Co-optimize generation new builds and retirements with:
–
–
–
–
–
Transmission line builds e.g. AC or DC lines; and
Transmission interface upgrades;
Physical contract purchases (generation or load)
Natural gas pipeline and storage expansion
And others such as ancillary services
59
Gas Expansion Capabilities
•
•
•
•
•
Develop new Gas Fields
Build new Gas Nodes and Pipelines
Build new Gas Storage
Retire Gas Node, Pipeline, Storage
Co-optimize electric production/expansion
with natural gas production/expansion
60
Objective Function
• Object function minimizes (expected value of) the
net present value (NPV):
– Cost of new builds:
• Generator, DC Line, AC Line, Interface, Physical Contract, Gas
Field, Pipeline, Storage
– Cost of retirements:
• Generator, DC Line
– Fixed operating costs
– Variable operating (production) costs
– Net cost of external market trades
61
Objective Function Components
• For any combination of expansion decisions x we
have two types of costs:
1. Capital costs C(x):
– Cost of new builds
– Cost/savings from retirements
2. Production costs P(x):
– Cost of operating the system with any given set of
existing and new builds and transmission network
– Notional cost of unserved energy
62
Optimization
Objective: Minimize net present value of
forward-looking costs (i.e. capital and
production costs for electric and gas sectors)
Cost $
Total Cost = Ce(x) + Pe(x) + Cg(x) + Pg(x)
Investment cost/
Capital cost Ce(x)+Cg(x)
Production Cost Pe(x) + Pg(x)
Minimum
cost plan x
Investment x
63
Illustrative Formulation Nat Gas Electric Expansion Planning
𝑌
𝐼
Minimize
𝑇
𝐼
𝐵𝑢𝑖𝑙𝑑𝐶𝑜𝑠𝑡𝑖 × 𝐵𝑢𝑖𝑙𝑑𝑖,𝑦 +
𝑦=1 𝑖=1
subject to
𝑃𝑟𝑜𝑑𝐶𝑜𝑠𝑡𝑖 × 𝑃𝑟𝑜𝑑𝑖,𝑡 + 𝑆ℎ𝑜𝑟𝑡𝐶𝑜𝑠𝑡 × 𝑆ℎ𝑜𝑟𝑡𝑎𝑔𝑒𝑡
𝑡=1
𝑖=1
𝐼
Supply and Demand Balance:
𝑃𝑟𝑜𝑑𝑖,𝑡 + 𝑆ℎ𝑜𝑟𝑡𝑎𝑔𝑒𝑡 = 𝐷𝑒𝑚𝑎𝑛𝑑𝑡
∀𝑡
𝑖=1
Production Feasible: 𝑃𝑟𝑜𝑑𝑖,𝑡 ≤ 𝑃𝑟𝑜𝑑𝑀𝑎𝑥𝑖 ∀𝑖, 𝑡
Expansion Feasible: 𝐵𝑢𝑖𝑙𝑑𝑖,𝑦 ≤ 𝐵𝑢𝑖𝑙𝑑𝑀𝑎𝑥𝑖,𝑦 ∀𝑖, 𝑦
Integrality: 𝐵𝑢𝑖𝑙𝑑𝑖,𝑦 𝑖𝑛𝑡𝑒𝑔𝑒𝑟
Reliability: 𝐿𝑂𝐿𝑃 𝐵𝑢𝑖𝑙𝑑𝑖,𝑦 ≤ 𝐿𝑂𝐿𝑃𝑇𝑎𝑟𝑔𝑒𝑡 ∀𝑦
This simplified illustration shows the essential elements of the mixed integer
programming formulation. Build decisions cover generation, transmission and
gas elements, as does supply and demand balance and shortage terms. The
entire problem is solved simultaneously, yielding a true co-optimized solution.
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Integrated Datasets
The landscape has changed for planning tools
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The US is seeing resource change driven by environmental policy and public policy where many areas of the US have minimal load
growth projections.
Although many organizations, regulators, ISO’s, federal departments, labs, consultants and others are engaged in a multitude of studies
for the future grid designs in America.
In the past few years there has been increased recognition that environmental policy and public policy in combination to the vast shale
gas developments will lead to increased reliance of the power sector on natural gas generation.
Gas Electric coordination has emerged as a complex topic for regulators and the gas and electric sectors to confront along with the
electrical system operators with concerns of present and future potential gas constraints that impact electric system operation and
reliability.
Many studies have been initiated for gas electric coordination in the major interconnects of the US.
As well integration of renewables have driven IRP managers and ISO’s to consider sub-hourly ancillary co-optimization analysis in
production cost models for major areas of the US.
In addition many regulators are interested in co-optimization of generation and transmission expansion to optimize resource change.
New strategies of co-optimization of electric and gas infrastructure are becoming of interest as much of the natural gas sector growth
may likely be driven by resource change and dependency of electrical sector on pipeline network and gas network operational issue.
This is all in the back drop of active demand response, energy efficiency, and renewable portfolio standard adoptions by state
governments as well as federal regulator orders such as FERC Order 1000 of considering public policy in transmission planning.
Thus the study process and the complexity of issues is driving the demand for integrated datasets and integrated models i.e. to handle
all the complexities of planning and operations and electric and gas sector analysis in the short, medium and long term.
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Integrated Datasets
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