Generation Companies’ Behaviors in Bilateral Electricity Market

market environment and mathematical formulations have been provided to model oligopolistic electricity market in order to find out the output of generation companies in imperfect bilateral electricity market.

4.5.1 Generation Companies’ Behaviors in Bilateral Electricity Market

The main goal of each generation company (GenCo) in electricity market is to maximize its profit in bilateral trading far ahead of Gate Closure, in order to reduce the exposure to price volatility risks.

Generation companies, as sellers, are a group of market participants in the market that produce the commodity, which is electricity in this case, and provide several services to the buyers or supply companies (SupplyCos). The strategies of the

GenCos are very much related to the volume of electricity they are going to generate, market price and specifically demand side, SupplyCos, behaviors.

As described in Chapter 3, in bilateral electricity markets like BETTA, the GenCos and SupplyCos will enter into bilateral negotiations in order to establish an agreement to trade electricity and fulfill the end-users requirements.

There are a few factors that determine the behavior of SupplyCos as buyers in the market, which affect the demand for electricity. Among the main factors are price and quantity. Assuming that other non-price factors are correctly defined, the demand behavior is very much dependent on the price of the generated electricity.

The quantity of electricity purchased by SupplyCos normally increases with the decrease in the price and vice versa. This relationship is given by the inverse demand function graph as illustrated in Figure 4.3.

Figure 4.3 determines the relationship between the price of electricity and the quantity of the demand. According to inverse demand function this relationship can be seen from two aspects. The first aspect sees how the electricity price can affect the quantity of the demand. As mentioned earlier, the demand decreases as the price increases. This is the case when the SupplyCos have alternatives.

Figure 4.3:The Relationship between Price of Electricity and the Quantity of Demand

Price

MW £ / MW

Quantity

Moreover, the second aspect demonstrates that the SupplyCos are willing to pay to have a small additional amount of electricity. It also indicates how much money these consumers would want to receive as a compensation for a reduced consumption [3]. According to the second aspect, the SupplyCos are willing to pay a high price for additional electricity if they have only purchased a small amount of it.

In contrast, their marginal willingness to pay for this commodity decreases when their consumption increases. The change in demand resulted from the change in price shows that the demand is elastic. On the other hand, if the relative change in demand is smaller than the relative change in price then the demand is inelastic to the price. Generally, the inverse demand curve in oligopolistic electricity market is inelastic. Therefore, inverse demand function plays an important role in oligopolistic electricity markets and generation companies’ behaviors and strategies.

4.5.2 CVE Applications and Formulations in an Oligopolistic Electricity Market

A small number of GenCos dominate the whole industry and these companies try to maximize their incomes.

For each GenCos in the market the main objective is to maximize its profit:

Where:

: Number of GenCos

:GenCo profit

: Output of GenCo

: Cost function of GenCo

It is noticeable that the sub-index in this research refers to the generation side of the bilateral electricity market.

Also, is an initial inverse demand function and represents the price that each generation company will sell electricity to the supply companies. In this research a novel hierarchical algorithm has been introduced and applied in order to find the equilibrium point of the bilateral market and in the proposed algorithm, which will be introduced in Chapter 6, an initial value can be identified for inverse demand function in order to perform the algorithm. More details will be provided in Chapter 6.

The purpose of introducing is that it is not possible to obtain the inverse demand function based on historical data in the bilateral electricity market and use it for all GenCos, as the amount of traded electricity in bilateral trading is not disclosed. In such electricity markets, a GenCo and a SupplyCo participate in a forward contract;

therefore it is not applicable to use one inverse demand function for each contract.

On the other hand in most research, e.g. [89], it is suggested to use a residual demand function (RDC), which can be computed for GenCo :

Where:

: Demand curve

: Aggregation of generation functions of all GenCos except GenCo .

In this case, estimating the generation function of all rivals is inevitable which is computationally costly; also it requires access to a suitable historical database.

Furthermore, it would be challenging in terms of investigating the specifications of other rivals’ generation functions, since based on the CVE method, rivals’ reactions should be considered, whereas in bilateral markets such as BETTA the major share of trading is forward and future contracts.

However, by introducing an initial inverse demand function there is no need to estimate the rivals’ supply function and calculate the RDC directly. In this case, an

initial inverse demand function is assumed to be a simple linear 45 degree curve to have a feasible flat start and via an iterative method, which will be covered in Chapter 6, this curve will be updated in terms of intercept and slope to obtain an accurate and realistic shape and will result in calculating the output of each GenCo in the bilateral electricity market. It is noticeable that this initial value does not have any effect on the results [90].

To maximize the profit, the optimal solution of Equation 4.10 for GenCos is:

The optimal solution of above equation should meet the following condition:

Where:

: Marginal revenue of GenCo : Marginal cost of GenCo

Since is a function of and (the output of other GenCos expect GenCo ) is an implicit function of , therefore the marginal revenue will be:

Furthermore, the cost function of GenCos can be defined as follow:

Where:

: Fixed cost of GenCo

: Linear co-efficient of GenCo cost function : Quadratic co-efficient of GenCo cost function Thus, the marginal cost will be:

Thus, according to Equation 4.13:

Based on Equation 4.17, the Conjectural Variation (CV) for generation companies in oligopolistic market can be defined as follow:

Where:

: Output of other generation companies except GenCo

The CV is the belief or any expectation of any market participant in the market about other rivals’ reactions according to any changes in the strategy of that firm. The value of CV for GenCos in oligopoly models results from hypothesizing how

GenCos make its decision in order to maximize their profits. In order to achieve to this goal, a significant question should be answered: how does one GenCo simulate other GenCos reaction to its decisions?

CV is such an index to estimate the reactions in which the output of each GenCos is used as the decision variable. In this approach, the estimations or conjectures of generation companies in an imperfect bilateral electricity market will be changed, in terms of the possibility of competitors’ future reactions and that is the reason why term has appeared in CV formulations (Equation 4.18).

It is notable that diverse strategies, like different CV values, can result in different oligopoly models. Further discussion will be provided in Chapter 5.

Equation 4.17 can be transformed to:

Additionally, as introduced above, is the initial inverse demand function in the novel algorithm, which will be discussed in Chapter 6. Since this research attempts to find a cross-over-point of both sides of the market (oligopolistic and oligopsonistic markets), and that point is the equilibrium point of the market as well, the inverse demand function can be formulated as a linear curve to simplify the calculations:

Where:

: Intercept of inverse demand curve : Slope of inverse demand curve

Also, is the total supply and should be equal to total demand, .

Figure 4.4 illustrates the initial inverse demand function. This curve represents the changes in price respect to any changes in the output.

Figure 4.4: Initial Inverse Demand Curve

According to the figure above, the derivative of the inverse demand curve is to be negative.

Assuming all GenCos are playing rationally in oligopolistic electricity market, the Equation 4.10 will be transformed to:

Where:

In order to optimize the profit of each GenCo the first derivative of Equation 4.22 will be:

£ / MW

Slope:

MW

According to Equation 4.21, the above equation will be: other rivals’ reactions can be derived as follows:

market. In order to simply the above equation the aggregation of other competitors’

output can be simplified as follow:

cost functions [86]. By aggregating all rivals into one pseudo-competitor denoted as the new variable can be defined as follow:

Therefore, by using Equations 4.26 and 4.27, Equation 4.25 can be transformed and simplified as follow:

Consequently, the output of GenCo will be a function of slope and intercept of inverse demand function, its own cost function’s coefficients and its estimation about other rivals reactions in the market. More details will be provided in Chapters 5 and 6 in order to demonstrate how GenCos will learn about their rivals behavior and how other competitors reactions affect the output of each generation company while the hierarchical algorithm considers both sides of the market aiming to cope with oligopolistic and oligopsonistic electricity markets to find out the equilibrium point of the whole bilateral market.