Effects of Interruptible Load Program on Equilibrium Outcomes of Electricity Markets with Wind Power - Intelligent Computing for Sustainable Energy and Environment - page 413

The Cournot equilibrium model for the wholesale market with the IL contract
andwindpowercanbeobtainedbygathering n generators' optimization prob-
lems expressed by (5).

3 Solution Method

It can be noted from (2) that introduction of the IL contract will produce a
piecewise market demand, which makes this equilibrium model dicult to solve
using conventional analytic methods. In this paper, a novel solution method is
proposed to solve this equilibrium problem. In this method, according to the
relationships between the market price p and the trigger price k 0 , three cases
are considered as follows.
From (2) and (4), the corresponding demand faced by the conventional gen-
erators can be expressed as:

⎧
⎨

A−bp−q w , ifp< 0
( A−V ) −bp−q w ,ifp = k 0
( A−Q ) −bp−q w ,ifp>k 0

N

D c = q i =

(6)

⎩

i =1

The calculation process of this method can be described as:
Step 1: Assume that the market price p is less than k 0 ,thatis p<k 0 .
The demand faced by the conventional generators can be obtained from (6).
By solving the generators optimization problem, the corresponding equilibrium
overcomes can be calculated.
If the equilibrium market price is less than k 0 , that is, the market equilib-
rium satisfies the assumption that p<k 0 , then these equilibrium outcomes are
actually the solution of the equilibrium problems. Otherwise, if the equilibrium
market price is greater than k 0 ,thenturntostep2.
Step 2: Assume that the market price p is assumed to be greater than k 0 ,that
is p>k 0 . Following the step 1, the corresponding market equilibrium results
also can be obtained.
If the equilibrium market price is greater than k 0 , and satisfies the assumption
that p>k 0 , then these equilibrium outcomes are actually the solution of the
equilibrium problems. Otherwise, if the equilibrium market price is less than k 0 ,
then turn to step 1 again. If the equilibrium market price is less than k 0 when
the assumption of p>k 0 is used, while under the assumption of p<k 0 ,the
equilibrium market price is greater than k 0 , then turn to step 3.
Step 3: Assume that the market price p is assumed to be equal to k 0 ,andthe
IL contract can be partially exercised. Under the assumption of p = k 0 , following
the step 1, each generators equilibrium output can also be obtained.

4 Numerical Examples

Suppose that there are three conventional strategic generators in a wholesale
market. Each generator's cost parameters are listed in Tab.1. Consider that