Abstract
Considering a demand response (DR) based social welfare maximization model, a complementarity problem based on the Karush-Kuhn-Tuker condition is described, which is a non-dual method for determining real-time price for smart grids. The Lagrange multiplier in the dual method, which is used to determine the basic electricity price, is applied in the model. The proposed method computes the optimal electricity consumption, price and production. According to the electricity price, users can arrange their electricity equipment reasonably to reduce the consumption pressure at peak time. The model aims to encourage users to actively participate in the DR and realize peak cutting and valley filling. In addition, the model considers different utility functions representing three types of users. Finally, a Jacobian smoothing version of Newton method is used to solve the model. Statistical simulations of the model validate the rationality and feasibility of the proposed method.
Highlights
As our awareness about energy and the environment grows, the demand for a reliable and sustainable power grid and the need for high-quality and stable resources have led to the evolution of smart grids as novel means of electricity distribution [1, 2]
The proposed model is based on KKT conditions of the social welfare maximization problem, which computes the optimal electricity consumption for users, price and production for the electricity provider at the beginning of each time slot according to the electricity equipment information entered by users, and production and cost information provided by power companies
We consider three types of users in our model, which avoids the problem of a single utility function
Summary
As our awareness about energy and the environment grows, the demand for a reliable and sustainable power grid and the need for high-quality and stable resources have led to the evolution of smart grids as novel means of electricity distribution [1, 2]. Chai et al [12] studied the DR problem in systems with multiple utility companies and multiple residential customers, while Deng et al [13] proposed a distributed real-time DR algorithm that determines each user’s demand and each utility company’s supply These studies are concerned with DR programs and their role in the analysis of power system operations. The main work of the realtime pricing method based on the social welfare maximization model is to compute the shadow price (i.e., the Lagrange multiplier of an optimization problem). The dual method is used to solve the real-time pricing problem based on the social welfare maximization model. Based on the social welfare maximization model, a KarushKuhn-Tucker (KKT) condition is established This system is a complementarity problem, which contains the multiplier and the decision variables.
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