Determining the optimal bid direction of a generation company using the gradient vector of the profit function in the network constraints of the electricity market

One of the primary challenges faced by generation companies (GenCos), which operate multiple generation units within the electricity market, is the determination of the optimal bid price for these units to maximize profit. This paper proposes a novel approach to ascertain the optimal bid price direction for GenCos by leveraging the gradient vector of the profit function within the constraints of the electricity market. First, the Jacobian matrix of unit profits is computed using the electricity market structural decomposition method. This matrix highlights how the profit of generation units is affected by market input parameters, including the bid prices of the units. Then, the gradient vector of the GenCos' profit function and the optimal bid price direction are derived from the Jacobian matrix. The methodology is applied to a 24‐bus IEEE network, with results validated against those from a simulation method to confirm the efficacy of the proposed approach. The simulation results show that the highest and lowest profit changes with a step increase of 0.1$/MWh are observed for GenCo 4 and GenCo 6 with values of 60.28 and 2.20 $/h, respectively. The proposed approach can be effective in the changes of bid direction of the units of a GenCo to achieve the highest possible profit. The main innovation of this paper is to propose an analytical method combined with structural decomposition to maximize the profit of each GenCo in the network by using the gradient vector of the profit function of GenCos. In other words, the proposed method identifies that the marginal units placed in each GenCo with the least changes in the bid price in the optimal direction will achieve the highest profit for their GenCo by considering the transmission constraints. In general, the strategy of moving in the optimal direction of the bid prices by GenCos using the gradient vector of GenCos' profits has not been studied so far. Therefore, the most important innovation of this paper is to examine the optimal changes in the bid price of the generation units of each GenCo to achieve the maximum profit.