Optimization Model And Algorithm For Real-Time Pricing Of Smart Grid Based On Demand Response

In the past few years,the rapid development of science and technology has brought great change to people’s lives,including fast modes of payment,convenient ways of travelling and intelligent modes of life.Therefore,people’s dependence on electronic products has become higher and higher,that is to say,people’s demand for electricity has also increased,resulting in more severe pressure on power companies.Further strengthening the rational and efficient use of power is an urgent problem to be solved in the market.Under the smart grid,the information exchange between the power supplier and the user is carried out through the two-way communication technology of information,so that the information can be updated in a timely and rapid manner,thereby increasing the user’s participation.Based on convex optimization,complementary optimization,duality theory,non-smoothing optimization,the smoothing approximation function and the smoothing Newton algorithm,this paper solves the real-time pricing problem of smart grid for various users.The main innovative research work is as follows:First,we consider a simple case,that is,the real-time electricity price problem of smart grid in a grid system that only includes one type of users(assumed to be commercial users)and one type of power supplier.Using the smoothing approximation function,the optimization problem is transformed into the problem of solving equations,and the error value between the smoothed approximation function and the minimum nonlinear complementary function is given.The simulation results show that the risk-averse commercial users are more affected by the electricity price.Obviously,it shows that the power supplier can adjust the electricity price to affect the user’s electricity consumption in various time periods.Secondly,the types of users are extended to consider a grid system with real-time pricing of smart grids including multiple types of users(residential users,commercial users and industrial users).The convex optimization problem is transformed into a nonlinear system of equations by using the smoothing Newton algorithm of the smoothing approximation function,and the non-singularity of the Jacobian matrix is proved.The simulation results compare three pricing mechanisms(time-of-use pricing,fixed pricing and real-time pricing),real-time pricing is superior to time-of-use pricing and fixed pricing in improving the utility of users,reducing the cost of power suppliers and improving the total social welfare value.Thirdly,in the previous literature on real-time pricing of smart grids,there are two types of user utility functions,one is quadratic function and the other is logarithmic function form.We construct a new utility function with the help of the logistic function,and satisfy the four properties of the utility function.The optimization model of smart grid real-time pricing is established by using the newly constructed utility function,which is transformed into the problem of solving nonlinear equations by using the smoothing approximation function and KKT condition,and the non-singularity of the Jacobian matrix is proved.The simulation results show that the new utility function is effective and feasible.Finally,with the help of the user utility function based on Logistic,an optimization model of real-time pricing of smart grid is established.In the process of transforming it into a nonlinear equation system,the approximation degree of the smoothing approximation function is used to solve the nonlinear equation.Therefore,a new smoothing approximation function constructed,and the approximation degree is higher than that of the previous smoothing approximation function.It is proved that the newly constructed smoothing approximation function is a nonlinear complementary function and the non-singularity of the Jacobian matrix.The simulation results show that by using the newly constructed smoothing approximation function to solve the smoothing Newton algorithm,the convergence times of electricity price and social welfare value are both lower,thus speeding up the convergence speed,which shows its effectiveness and feasibility.All in all,this paper uses the smoothing Newton method to study the real-time pricing of smart grid.The results of the paper show that the number of participants in the system,the selection of the utility function and the approximation degree of the smoothing approximation function can all affect the user’s electricity consumption and energy consumption.The cost of the power supplier has an impact.It can achieve the balance of energy supply and demand between users and suppliers,and achieve the purpose of cutting peaks and filling valleys and saving energy.The research made in this paper from several aspects can improve the social welfare value and speed up the convergence speed,and has strong feasibility.To a certain extent,it has certain guiding significance and practical value for the power development and smart grid infrastructure construction that are being reformed in our country.