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Optimal Investment for Retail Company in Electricity Market

机译：电力市场中零售公司的最优投资

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摘要

Considering an optimal investment problem for a retailer in electricity market, the objective is to seek the optimal investment decision that maximizes the weighted sum of the expected return and the variance of wealth. Unlike existing works, the price fluctuation of both the wholesale and retail side of electricity market is considered, and the retailer can invest its wealth in electricity market and traditional financial market simultaneously. Hence, there is a complicated wealth dynamic, which is the main challenge in our work. In this paper, by utilizing the method of Lagrange multiplier and the classical Tchebycheff inequality, we first show that the investment problem is a quadratic programming problem in terms of the decision variable, and thus has a unique optimal solution. Then, a closed-form optimal solution is derived by solving the stationary equation and comparing the feasible solution interval. Based on the optimal solution, we find the key price, which will affect the investment is the wholesale price rather than the retail price. Moreover, with a similar analysis approach, we also provide the optimal solution considering a more general model, which allows the retailer to purchase the electricity temporarily to avoid the supply shortage. Extensive simulations demonstrate the better performance of the proposed solution over the Kelly strategy widely used in the financial market.
机译：考虑到电力市场中零售商的最佳投资问题，目标是寻求使预期收益和财富方差的加权总和最大化的最佳投资决策。与现有作品不同，电力市场的批发和零售方面都考虑了价格波动，零售商可以同时将其财富投资于电力市场和传统金融市场。因此，财富动态复杂，这是我们工作中的主要挑战。本文利用拉格朗日乘数法和经典的Tchebycheff不等式，首先证明了投资问题在决策变量方面是二次规划问题，因此具有唯一的最优解。然后，通过求解平稳方程并比较可行的求解区间，得出闭式最优解。根据最佳解决方案，我们找到关键价格，它将影响投资的是批发价而不是零售价。此外，通过类似的分析方法，我们还考虑了更通用的模型，从而提供了最佳解决方案，该模型允许零售商临时购买电力以避免供应短缺。广泛的仿真表明，与金融市场中广泛使用的Kelly策略相比，所提出的解决方案具有更好的性能。

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