Optimal Generation Scheduling in

a Carbon Dioxide Allowance

Market Environment

Project M21 Part III

Wei Sun Iowa State University

Chen-Ching Liu University College Dublin

PSERC Webinar, April 5, 2011

New Generation Scheduling

Problem (GSP)

GENCOs

Electricity

Market

CO2 Allowance

Market

Unit Commitment

Generation Output

Maintenance

Scheduling

CO2 Allowance

Amount and Price

Enough Allowances

to Cover Emitted CO2

Traditional GSP New GSP 2

Outline

Motivation

Carbon Dioxide (CO2) Allowance Market

New Generation Scheduling Problem

considering CO2 Cap-And-Trade

Conclusions

3

Greenhouse Gas (GHG)

4 * U.S. Energy Information Administration

Motivation

5

European Power Prices Pre- and Post-CO2 Regulation

* Source: JPMorgan Energy Strategy, Bloomberg

CO2 Emission Regulation

• Carbon Capture and Storage

/Sequestration (CCS)

• Non-CO2 or Low-CO2 Emission

Power Sources (hydroelectric,

nuclear, renewable energy

resources)

• Market-based and least-cost

Mechanisms: Emission

Trading

6

CO2 Emission Cap-and-Trade

CO2 Emission Cap-And-Trade

7

A Cap Set on CO2

Emissions

Permits are

Divided Up

Polluters Buy or Get Free

Permits

Permits Decrease Over

Time

A Trading Market

Reasons to Sell Permits

Reasons to Buy Permits

Trading Permits

Creates Profit

The buyer is paying a charge for polluting, while the seller is being

rewarded for having reduced emissions

To encourage polluters to shift away from CO2-emitting fossil fuels

and toward clean, renewable energy sources

Cap

+

Trade

Providing economic incentives to achieve

reductions in the emissions of pollutants

Carbon Trading Markets

8

1. Kyoto Protocol

2. New Zealand

Emissions Trading

Scheme (NZ ETS)

3. European Union

Emission Trading

Scheme (EU ETS)

4. United States

• Chicago Climate Exchange (CCX)

starting from 2003;

• Western Climate Initiative (WCI)

starting from 2007;

• Regional Greenhouse Gas

Initiative (RGGI) starting from 2009.

RGGI CO2 Allowance Market

Ten Northeastern and Mid-Atlantic

states, starting from Jan. 1, 2009

Reduce 10% of CO2 emissions by

2018

Primary and secondary market

Quarterly auction in the format of

single-round, uniform-price, sealed-bid

Three-year compliance period

Reserved price

Using offsets

Cost-effective emission reductions 9

Market Equilibrium Model

• To investigate the ability of generation

companies (GENCOs) to manipulate prices

(market power)

• Derived a nonlinear complementarity problem

(NCP) formulation based on the equivalence

between the KKT conditions and strong

stationarity

• Transformed to a nonlinear programming

problem (NLP) and solve it by AMPL/MINOS commercial solver

10

GENCO Bidding Model

2

2 2

, , , ,

max

max

. . 0

0.033

0

COi i i i

e CO

i i i i i i i iP q OS A

i i i i

i i

i i

P a P b P A h OS

s t k P A OS

OS A

P P

2CO

2COq

1

2

3

3q2q1q

(λ, q) GENCO’ bid

11

GENCO Bidding Model

2

2 2

, , , ,

max

max

. . 0

0.033

0

COi i i i

e CO

i i i i i i i iP q OS A

i i i i

i i

i i

P a P b P A h OS

s t k P A OS

OS A

P P

2CO

2COq

1

2

3

3q2q1q

(λ, q)

Revenue from

electricity market Generation

cost

Emission

allowance cost

Offset

cost

Emission regulation constraints

Offset usage constraints

Generation capacity constraints

GENCO’ bid

12

Market Clearing Model

13

2

1

2 1 2

1

2

3 2

0

0 0

0 01,

0 0

0 0.25 0

nCO

j

j

CO

j j j j

j j j

j j

CO

j j

A CAP

A w w

w q Aj n

w A

w CAP A

1

2

1

2

max

. .

0.25

0

i

n

j jA

j

nCO

j

j

CO

j

j j

A

s t A CAP

A CAP

A q

2CO

2COq

2CO

2COq2

A1A

(λCO2*, Ai)

RGGI’s rule

Allowance price and

cleared demand

2

1 2 3

2 2

, , , ,

, , ,

max

2

1

2 1 2

1

2

3 2

max ( )

. . 0

0.033

0

0

0 0

0 0

0 0

0 0.25 0

COi i i

i i i i

e CO

i i i i i i i iP q OS

A w w w

i i i i

i i

i i

nCO

j

j

CO

j j j j

j j j

j j

CO

j j

P a P b P A h OS

s t k P A OS

OS A

P P

A CAP

A w w

w q A

w A

w CAP A

1,j n

CO2 Allowance Market Model

14

Mathematical

Programs

with

Equilibrium

Constraints

(MPEC)

Equilibrium

Problems

with

Equilibrium

Constraints

(EPEC) (λ, q)

GENCO’ bid

(λCO2*, Ai)

Allowance price &

cleared demand

EPEC Formulation

15

0, ,max ,

. . , 0

01,

0 0

i

ix y s

i

j j

j j

f x y

s t g x y

H sj n

y s

2 1 2 3

2 2

, , ,

, , , ,

max

2

1

2 1 2

1

2

3 2

max ( )

. . 0

0.03

0

0

0 0

0 0

0 0

0 0.25 0

i i i

COi i i i

e CO

i i i i i i i iP q OS

A w w w

i i i i

i i

i i

nCO

j

j

CO

j j j j

j j j

j j

CO

j j

P a P b P A h OS

s t k P A OS

OS A

P P

A CAP

A w w

w q A

w A

w CAP A

1,j n

Equilibrium Point

, ,x y s

NCP Formulation

, , , 0

, , , 0

0

0 , 0

, 0

0 0

0 0

0 0

0 0

i i ix i x i i x i i i

y i y i i y i i i i

i i i

i i

i i

i i

i i

i

i i i

f x y g x y h x y

f x y g x y h x y s

y

g x y

h x y s

x

s y

y s

, , , , , , , ,x y s Strongly Stationary Point

multipliers

Theorem 1: If there is an equilibrium point of EPEC and every MPEC

satisfies an MPEC-LICQ, then there exist multipliers to get a strongly

stationary point of the NCP. 16

NLP Formulation

, , , , , , ,1

min :

. . , , , 0

, , , 0

0

,

,

0, 0

0, 0, 0, 0, 0

0, 0

i i i

nT T T T T

pen i i i i i ix y s

i

x i x i i x i i i

y i y i i y i i i i i

i i i

i i

i i

i i i i i

i i

C x t y s y s

s t f x y g x y h x y

f x y g x y h x y s

y

g x y t

h x y s

y s

x t

Theorem 2: If there is an local solution , , , , , , , , , ,x y s t

then is a strongly stationary point of the EPEC. , ,x y s with Cpen=0, 17

Sensitivity Analysis

GENCO a b λe

($/MW)

Pmax

(MW)

Bidding

Price λ ($/p.u.)

k

(ton/MW)

h

($/p.u.)

1 15 0.005 20 500 2 1 10

2 18 0.004 20 800 1.5 1 10

3 10 0.005 20 800 2.5 1 10

4 15 0.004 20 800 2.3 1 10

GEN. P(MW) A

(p.u.) q (p.u.)

Profit

($)

λCO2

($/p.u.)

1 262.5 262.5 262.5 574.2

1.5 2 0 0 594 0

3 800 800 800 3600

4 437.5 437.5 437.5 765.6

Base case

18

Sensitivity Analysis

GENCO a b λe

($/MW)

Pmax

(MW)

Bidding

Price λ ($/p.u.)

k

(ton/MW)

h

($/p.u.)

1 15 0.005 20 500 2 1 10

2 18 0.004 20 800 1.5 1 10

3 10 0.005 20 800 2.5 1 10

4 15 0.004 20 800 2.3 1 10

GEN. P(MW) A

(p.u.) q (p.u.)

Profit

($)

λCO2

($/p.u.)

1 262.5 262.5 262.5 574.2

1.5 2 0 0 594 0

3 800 800 800 3600

4 437.5 437.5 437.5 765.6

Base case

GEN. P(MW) A

(p.u.) q (p.u.)

Profit

($)

λCO2

($/p.u.)

1 310 310 310 480.5

1.9 2 2.5 2.5 313.3 0.225

3 800 800 800 3280

4 387.5 387.5 387.5 600.625

λ2=1.9

19

Sensitivity Analysis

GENCO a b λe

($/MW)

Pmax

(MW)

Bidding

Price λ ($/p.u.)

k

(ton/MW)

h

($/p.u.)

1 15 0.005 20 500 2 1 10

2 18 0.004 20 800 1.5 1 10

3 10 0.005 20 800 2.5 1 10

4 15 0.004 20 800 2.3 1 10

GEN. P(MW) A

(p.u.) q (p.u.)

Profit

($)

λCO2

($/p.u.)

1 262.5 262.5 262.5 574.2

1.5 2 0 0 594 0

3 800 800 800 3600

4 437.5 437.5 437.5 765.6

Base case

GEN. P(MW) A

(p.u.) q (p.u.)

Profit

($)

λCO2

($/p.u.)

1 310 310 310 480.5

1.9 2 2.5 2.5 313.3 0.225

3 800 800 800 3280

4 387.5 387.5 387.5 600.625

λ2=1.9

Need to consider both electricity

market and CO2 allowance market 20

GENCOs Interactions in Two

Markets

21

Day 1

E-Market

Day t

E-Market

Day T

E-Market

GENCOs in Electricity Market (daily)

GENCOs in CO2 Allowance

Market (quarterly)

LMP,

Output LMP,

Output

LMP,

Output

LMP and

Output

CO2 Allowance

Price and Cleared

Demand

Time Horizon of New GSP

Quarter 1 Quarter i Quarter 12

First Three-Year Compliance Period Next Period

Week1 Week j Week 12

Day 1 Day k Day 7

Quarterly CO2

Allowance Market

Weekly Generation

Maintenance

Scheduling

Daily Unit

Commitment and

Hourly Economic

Dispatch

dt

qt

wt

qitA

witX

ditu

ditg

22

GENCO's Maximization Problem

23

Max Total Profit during Time Period T

subject to

Generation Maintenance Scheduling Constraints

UC and OPF Operation Constraints

CO2 Allowance Market Constraints

GENCO’s

Decision

Variables:

ftq

ftOS

itX

Allowances bid by firm f in interval t’

Offsets used by firm f in interval t’

Maintenance schedule of generation i in period t

where Profit = Revenue - Cost

selling power to the electricity market

maintenance, fuel production, startup, shutdown and CO2 allowance

Structure of New GSP

Max GENCO’s Profit

s.t. Generation Maintenance

Scheduling Constraint

CO2 Allowance Market Constraint

Traditional

Generation

Scheduling

New Emission

Regulation

Environment

New Generation

Scheduling Model

Upper Level

Problem

Lower Level

Problem

Mixed Integer

Bi-level Linear

Programming

New Solution

Method

Optimal Generation Scheduling

Considering CO2 Allowance Market

ISO Maintenance Clearing Subproblem

ISO Unit Commitment Subproblem

ISO Economic Dispatch Subproblem

CO2 Allowance Market Clearing Subproblem

24

2

, , ,

1

1 1 1

max

. . , ,

1, ,

1 ,

, ,

,

d d d d d d w q q q

d w q q d w qit it it it

d d w

w d

w

w

w w wi

w w

E P SU SD M CO OS

iit it it it it it it t it itg x q OSt t t

d w

it it it

d w

it it

iitt

w

it it it T

it ti

p g C g C C C p A C OS

s t u u x i t t

x u i t t

x T i

x x x i t

x NM t

2

,

2

,

, hydroelectric

1 , ,

1 , ,

,

0.033 ,

, , , 0

d d

d d

w d

d w

d q q q

d q

q d

d q

d w q q

w

MAX

iit itt t

MIN d w

i it it

MAX d w

iit it

CO IA q

i it it it iti t t

CO q

iit iti t t

it it it it

g G HE i

G x g i t t

g G x i t t

R g A OS A t

OS R g t

g x q OS

Upper-Level Optimization Problem

Generation

Maintenance

Scheduling

CO2

Allowance

Market

Revenue Cost

25

Lower-Level Optimization Problem

,

,

min

. . ,

w w

d wit

d w w

d w

M UE

it itgit

w

it it itii t t

C C UE

s t g UE D t

2

max

1min

2

. . 0,

,

0

d d

dit

d d d

d d d

d d d

d

i iit itgi

it it ti i

k i kit it kti

MIN MAX

i iit it it

it

g g

s t g D

GSF g D F k

G u g G u

g

d d d d

d d

E energy cong

it it it it

k it kti

p LMP LMP LMP

GSF

2

2 2

2

max

. . 0,

0.25 , ,

0 , ,

q q

qit

q q q

q q

q q

CO

it itAi

CO q CO

it t ti

CO q

it t

q

it it

B A

s t A CAP t p

A CAP i t

A q i t

where:

I. ISO Maintenance

Clearing

Subproblem II. ISO Unit

Commitment

Subproblem

III. ISO Economic

Dispatch

Subproblem

IV. CO2 Allowance

Market Clearing

Subproblem 26

1

min

. . ,

,

,

, ,

, ,

, ,

, ,

d d d d

d dit

d d

d d

d d

d d

d d d d

d d d

d d d

d d

P SU SD

it it it itgi t

d

it iti i

S S d

it ti

O O d

it ti

MIN d

i it it

S O MAX d

iit it it it

S S d

it t it

O O d

it t it

it it

C g C C

s t g D t

r R t

r R t

G u g i t

g r r G u i t

r R u i t

r R u i t

g g MaxI

1

1 1

1 1

, ,

, ,

0, ,

0, ,

, ,

d d

d d d

d d d

d d

d

i

d

iit it

ON ON d

iit it it

OFF OFF d

iit it it

d

ki kit iti

nc i t

g g MaxDec i t

Y T u u i t

Y T u u i t

PTDF g D MaxFlow i t

,max 1* 1*

. . 1* 1* 1

arg max 2* 2*

. . 2* 2* 2

0 integer

0 integer

x y

w

I

J

C x d y

s t A x B y b

y C x d w

s t A x B w b

w w

x x

Mixed Integer Bilevel Linear

Programming Problem (MIBLP)

Upper Level

Problem

Lower Level

Problem

27

• Benders Decomposition

• Linear Problem with Complementarity Constraints (LPCC)

• Branch-and-Cut

Solution Methodology

Step 1: Decompose MIBLP to slave problems (SPs) and restricted master problem (RMP)

28

fix the binary variables and get the BLP - UB

eliminate the constraints

and the lower objective

function - LB

Step 2: Transform SP to LPCC, and solve LPCC using “θ-free” algorithm

Step 3: From the solution, construct the LP, which provides an UB (in Min problem)

Step 4: Using the optimal dual values of LP to add a cut back to RMP

Feasibility cut (dual LP unbounded)

Optimality cut (dual LP bounded and restrict RMP)

Integer Exclusion cut (dual LP bounded but not

restrict RMP)

Step 5: Solve the augmented RMP to get a new LB

Step 6: If not satisfy convergence criterion, using RMP

solutions to construct a new SP to iterate. Otherwise,

Stop.

Numerical Example

PJM 5-Bus System

1-Auction with

3 Bidding Strategies 7-Week

Generation

Maintenance

Scheduling

Daily Unit

Commitment &

Hourly Economic

Dispatch

Strategy Quantity Price

1 Small Low

2 Medium Medium

3 Large High

+ +

29

Simulation Results

30

I II

III IV

Simulation Results

31

I II

III IV

Simulation Results

32

Bidding

Strategy Optimal

Maintenance

Scheduling

Conclusions • Optimal generation maintenance scheduling will be changed when

GENCOs participate in both electricity market and CO2 allowance

market.

• Neither the conservative (small quantity) nor the aggressive

(large quantity) bidding strategy will bring the optimal profit.

• GENCOs need to consider the maintenance scheduling and CO2

allowance bidding together in order to maximize their profits.

• Based on the proposed model, GENCOs will be able to determine

their optimal mid-term generation maintenance scheduling and

CO2 allowance bidding strategy participating in both markets.

33

Questions