Kriging-based value function approximation for the strategic bidding problem of virtual power plant in the electricity market

• A novel bi-level algorithm based on value function approximation (VFA) is proposed. • A novel kriging-based VFA technique is proposed to achieve accurate approximation. • The proposed algorithm delivers high computational accuracy and efficiency. • The adaptability of the proposed algorithm is verified on three different systems. In this paper, the strategic bidding problem of virtual power plant is described as a bi-level optimization model, and a Kriging-based value function approximation (VFA) algorithm is proposed for the solution. Unlike traditional bi-level optimization algorithms that introduce a large number of integer variables and thus reduce the computational efficiency, the proposed algorithm decouples the nested bi-level model into tractable single-level optimization model based on value functions, while no integer variables are introduced. This helps to greatly improve the computational efficiency while ensuring the near optimality. A Kriging-based VFA technique is further proposed to establish the approximate value function. Different from traditional approximation techniques that only use sample points to approximate the value function while ignoring the deviation, the proposed technique can adaptively correct the deviation of approximate value function based on the spatial correlation between unknown points and sample points. In this way, the accuracy of approximate value function can be enhanced accordingly. Numerical simulations show that the proposed algorithm maintains a relative error of only 0.03%, while achieving a speed advantage of more than twice compared to other algorithms on different systems.