Proposition 6. The optimal solution in the two-stage game where the cooperative is the only player in the market is:
(i) The demand served by a large consumer is qi∗ =
pn2(4φc(β1+αi−nαi) +n2((β0−ψ)2−4β1φc)) +n2(β0−ψ)
2n2(αi+β1+nβ1) , (49)
(ii) The market price is p∗ =β0− β1(p
n2(4φc(β1+αi−nαi) +n2((β0−ψ)2−4β1φc)) +n2(β0−ψ))
2n2(αi+β1+nβ1) , (50)
(iii) The profit for a large consumer is πi∗ = 1
4n2(αi+β1 +nβ1)2(−2α2iφc−2n(α2i + 6αiβ1+ 4β12)φc+
n2(2β1((β0−ψ)2−4β1φc) +α1((β0−ψ)2−2β1φc))−αi2β1φc+
pn2(4φc(β1+αi−nαi) +n2((β0−ψ)2−4β1φc))(β0−ψ)(αi+ 2β1)). (51)
Since in this scenario the aggregator is forced out of the market, the flexible load of small consumers is not used and and the consumers follow their initial consumption schedule.
Their capacity is too small to bid at the market directly, therefore, they will no longer participate in flexibility trading.
and Scenario 1. This fixed cost does not influence the chosen quantity and price, but it affects the market participants’ profit, i.e. the profit is reduced by the amount of the fixed cost. This is not the case in Scenario 3, though, where the members of the cooperative share the fixed intraday market access and flexible demand coordination cost φ depending on their traded quantity. This means that their and the aggregator’s (in Scenario 3a) offered quantities, as well as the market price, depend on the cooperative’s fixed cost φc.
The second insight is that larger variable cost of placing a bid at the intraday market ψ reduces the quantity offered by the aggregator and the large consumers and the price increases in all scenarios. The profit of all players becomes lower and the consumer surplus diminishes too.
The third insight is that larger number of large consumers n reduces individually offered quantities by the aggregator and large consumers, even though the total quantity at the mar-ket increases. The price falls due to increased competition and consumer surplus increases in all scenarios.
The fourth insight reveals that larger large consumer’s cost of shifting the first MW of electricity αi reduces the quantity offered to the market. Even though the aggregator is increasing the quantity, the total amount in the market is lower and the price goes up. This leads to a lower consumer surplus. An interesting observation here is that, up to a certain point, the profit of the large consumers increases with increasing αi due to a higher market price. Thus, increasing large consumers’ cost does not harm the large consumers. On the contrary, it increases the profit on the expense of the final consumers. However, when αi becomes even higher, then the profit starts shrinking. Similarly, the aggregator’s payment to small consumers for shifting the first MW of electricity wa reduces its offered quantity, increases the quantities offered by the large consumers, the total quantity in the market decreases and the market price goes up. This harms the final consumers, as the consumer surplus shrinks. However, in this situation, the aggregator does not yield a larger profit. Its profit is lower because of the smaller quantity traded in the market, and the large consumers increase their profits on the expense of final consumers.
Finally, the aggregator could leave the market and stop trading small consumers’ flexibility
in Scenario 1 and Scenario 3. When the aggregator’s profit becomes negative, the aggregator would exit the market in the long run. The only variable that does not affect the aggregator’s profit in both scenarios is the large consumer’s fixed intraday market access and flexible demand coordination cost φi. All other variables influence the aggregator’s profit at a different rate. From the sensitivity analysis one can see that a few variables have a higher impact to the aggregator’s decision to leave the market, i.e. larger number of large consumers n, higher aggregator’s payment to small consumers for shifting the first MW of electricitywa, higher aggregator’s fixed intraday market access and flexible demand coordination costφa, higher slope of the inverse demand functionβ1, and lower large consumer’s cost of shifting the first MW of electricityαi, as well as lower intercept of the inverse demand curveβ0 would lead to a situation where the aggregator leaves the market in the long run. Naturally, higher competition, increasing cost, decreasing competitors’ cost and lower consumers’ willingness to pay negatively affects the aggregator’s profit and may lead to exiting the market. With decreasing β0, αi, and increasing β1, n, wa, φa the aggregator exits the market sooner in Scenario 1, where it has to compete with large consumers bidding at the market individually.
A more detailed analysis of different scenarios is provided in sections 5.2 Results and 5.3 Sensitivity analysis.
The equilibrium outcomes of all scenarios also depend on the market size. For example, a larger market could lead to the equilibrium where the large consumers would be able to cover their cost when bidding individually; or, due to increased traded quantities, the aggregator would be able to stay in the market and compete with the cooperative. However, the rating of all analysed scenarios would not change much, except the Scenario 2b, where the large consumers are compensated according to their potential profits when bidding individually.
This would make the Scenario 2b more attractive to the large consumers than the Scenario 2a, where the large consumers profit is equal to zero. Furthermore, Scenario 2c might become less attractive to the large consumers, if the aggregator does not need to leave the market in Scenario 3, as their compensations would be equal to those where the aggregator competes with the cooperative.