An important goal of China's electric power system reform is to create a double-side day-ahead wholesale electricity market in the future, where the suppliers (represented by GenCOs) and demanders (represented by DisCOs) compete simultaneously with each other in one market. Therefore, modeling and simulating the dynamic bidding process and the equilibrium in the double-side day-ahead electricity market scientifically is not only important to some developed countries, but also to China to provide a bidding decision-making tool to help GenCOs and DisCOs obtain more profits in market competition. Meanwhile, it can also provide an economic analysis tool to help government officials design the proper market mechanisms and policies. The traditional dynamic game model and table-based reinforcement learning algorithm have already been employed in the day-ahead electricity market modeling. However, those models are based on some assumptions, such as taking the probability distribution function of market clearing price (MCP) and each rival's bidding strategy as common knowledge (in dynamic game market models), and assuming the discrete state and action sets of every agent (in table-based reinforcement learning market models), which are no longer applicable in a realistic situation. In this paper, a modified reinforcement learning method, called gradient descent continuous Actor-Critic (GDCAC) algorithm was employed in the double-side day-ahead electricity market modeling and simulation. This algorithm can not only get rid of the abovementioned unrealistic assumptions, but also cope with the Markov decision-making process with continuous state and action sets just like the real electricity market. Meanwhile, the time complexity of our proposed model is only O(n). The simulation result of employing the proposed model in the double-side day-ahead electricity market shows the superiority of our approach in terms of participant's profit or social welfare compared with traditional reinforcement learning methods.

In this paper, the electromagnetic scattering from a rectangular large open cavity embedded in an infinite ground plane is studied. By introducing a nonlocal artificial boundary condition, the scattering problem from the open cavity is reduced to a bounded domain problem. A compact fourth order finite difference scheme is then proposed to discrete the cavity scattering model in the rectangular domain, and a special treatment is enforced to approximate the boundary condition, which makes truncation errors reach O(h 4 ) in the whole computational domain. A fast algorithm, exploiting the discrete Fourier transformation in the horizontal and a Gaussian elimination in the vertical direction, is employed, which reduces the discrete system to a much smaller interface system. An effective preconditioner is presented for the BICGstab iterative solver to solve this interface system. Numerical results demonstrate the remarkable accuracy and efficiency of the proposed method. In particular, it can be used to solve the cavity model for the large wave number up to 600π.Mathematics subject classification: 65N06, 78M20.

The enantioselectivity of the photoisomerization of (Z)-cyclooctene sensitized by the linear maltodextrin-based nanosponges are critically dependent on the phase properties.

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