Real-time Pricing Based On Social Welfare Maximization Model In Smart Grid

Demand side management(DSM)is one of the most important factors in smart grid.Its main purpose is to realize the balance of supply and demand in the short term,and to cut the peak and fill the valley in the long term.The real-time pricing(RTP)mechanism based on demand response is an ideal method to adjust the power balance between supply and demand and then to realize the goal of cutting peak and filling valley.Its implementation has a profound impact on users' behavior,and on operation and management of the power grid.The social welfare maximization model is built from the perspective of the whole society,which maximizes user's utility function and minimizes the cost of energy supplier,it fully reflects the interests of both sides.In this paper,the optimization theory is used to research the RTP mechanism under the social welfare maximization model.From single time slot and multi-time slots two angles,we set up models for different situations,discuss the characteristics of the models,and design proper algorithms to solve these models.The main work and contributions are as follows:First of all,we conduct an extended discussion of a single time slot social welfare maximization model and give a theoretical analysis of the existence and uniqueness of the Lagrangian multiplier.A distributed optimization method based on alternating direction method of multipliers algorithm with Gaussian back substitution is proposed in this study.On one hand,the proposed algorithm takes abundant advantage of the separability among variables in the model.On the other hand,the proposed algorithm can not only speed up the convergence rate to enhance the efficiency of computing,but also overcome the deficiency of distributed dual sub-gradient method,the possibility of nonconvergence in iteration process.In addition,we give the theoretical proof of the convergence of the proposed algorithm.Furthermore,the interdependent relationship between variables has been discussed in depth during numerical simulations in the study.Secondly,aiming at maximizing social welfare,the dynamic change of users' aggregate demand is analyzed,which corrects the electricity risk items in online real-time risk model in the way of changing the individual user's power fluctuations to all the users' demand power fluctuations,and optimization model is rebuilt.An algorithm is presented to overcome the existing online one without computing the overall power consumption by equivalently converting the optimization problem through dual method.The algorithm will help to get real-time electricity price.Thirdly,the general type piecewise linear function is introduced as the users' utility function.Considering the relationship between the two stages of users' power demand,a periodic social welfare maximization model based on Markov chain is presented to solve real-time pricing strategy.It can help users to formulate their power demand more rationally and closer to the actual.At the same time,studying on the correlation between the same type of user's power demand,and different types of users with different price discrimination,a periodic real-time pricing strategy is given on the users' categories.Finally,we propose an expectation social welfare maximization model,considering the classification of the smart home appliances(SHA)and the correlation of power consumption of multi-time slots.Users can arrange their appliances more profitably and more closely to reality with the advantage of multi-time slots RTP strategy.The constraint condition reflects the fluctuation(uncertainty)of power consumption caused by operating continuity of the SHA.By introducing probabilistic constraints,the uncertainty optimization model is transformed into a convex optimization problem.The existence and uniqueness of the optimal solution are shown,and its properties are further analyzed.Considering the convex optimization problem is separable in dual domain,we propose a decentralized online RTP algorithm to determine each user's demand and the energy supplier's supply simultaneously.By utilizing Armijo line search to replace the fixed step size of the dual sub-gradient method,the decentralized online RTP algorithm proposed can overcome the defects of slow convergence and even no convergence of the original dual sub-gradient method.The research results show that the real-time pricing strategy in smart grid can better mobilize the enthusiasm of users to participate in power management,then achieve the goal of peak shaving and valley filling in DSM.The single time slot RTP strategy can reflect real-time information of supply and demand in time,reach the balance of supply and demand,then realize the short-term goal of demand side;the multi-time slots RTP mechanism can better regulate the user's consumption mode in a period.The designed distributed algorithm has better convergence speed under the premise of ensuring user's privacy.When the number of users is large-scale,the proposed algorithms are quite practical.