1

David Gachiri Nderitu

SUFG, Purdue University

nderitu@purdue.edu

Quantifying the benefits of distributed generation in imperfectly competitive electricity markets

2

In this Presentation

• DG has a lot of benefitsMarket power mitigationReliabilitySecurity

• Especially when in oligopolistic marketsAverage cost models hide their value

• Spatial oligopoly model for Midwest

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Statement of Imperfect Competition

)()( qPQPP

Each firms decision variable is to maximize its profit

)()( ssss qTCqqP

Given a a market price

)( ss qTC

And the firms total cost function

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Profit Maximizing Conditions

0

sss

ss

s qMCq

PqP

q

And expanded further into

0.

sssk s

k

kss qMC

q

q

q

P

q

PqP

Conjectural variations model

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Alternative Assumptions/Models

• Cournot 0

s

skq

q 0

sqP

• Cartel

• Price leadership MRL = MCL on residual demand

• Quasi-competitive MCP

MCMR

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Relative Prices

Marginal Cost

Marginal Revenue

Quantity

Price

Car

tel

Bertland

Cournot

Cartel

Cou

rnot

Ber

tlan

d

Demand curve

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Suppliers in Electricity Market

i j

ijsijigsi

igsisi

iS FwhPGcqPMax ***

..TS s

isiii qbaP

j

jisj

ijsg

isis FFPGq

igsigs PGPG max

ijs

jiss

ijs FFF max

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KKT Optimality

g j jjisijsigsisss FFPGqL 1

s sjisijsisij FFqF max2

igsigs PGP max3

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Complementarity Problem

0

igs

s

PG

L0

ijs

s

F

L

0*

ijsijs

s FF

L0*

igsigs

s PGPG

L

Cournot Assumption

0

igs

igk

PG

PG0

ijs

ijk

F

F

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Case Study

PJM

AE

MAPP

CILC

CE

IPAMRN

SPIL

EEI

SIPCSIGECO

BREC

TVA

LG&EEKPC

HEREC

IPL

PSI

NIPSCO

CPC

DECO

FE

AEP

OVEC

VP

DPL

CG&E

DLCO

APS

OHY

SPP

AW

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Demand Response

-8.0%

-7.0%

-6.0%

-5.0%

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

% reduction in demand

% c

han

ge

in In

dia

na

pea

k p

rice