Research On Optimal Scheduling Method Of Electric Power And Energy Systems With 0-1 Variables

The development of electric power and energy systems shows a trend of both sides: the further development of large-scale power systems on the generation and transmission side and the gradual development of multi-carrier energy systems on the distribution side.The optimal scheduling problems of power systems on the generation and transmission side and multi-carrier energy systems on the distribution side are the basic content of optimal operation and energy management of power and energy systems,which are also key difficult problems worth being explored in depth.In this research field,the large-scale power system unit commitment problems and the multi-carrier energy system optimal scheduling problems are two key technical problems,and their modeling based on AC power flow constraints will be more accurate.In mathematics,they have similar characteristics.They are both a class of mixed integer nonlinear programming(MINLP)problems with 0-1 variables,and their efficient solution methods face major challenges.Therefore,this thesis has carried out research on the optimal scheduling of power and energy systems.A new decomposition algorithm is proposed to reduce the complexity of the MINLP problem and improve the computational efficiency.The classical branch-and-bound(B&B)algorithm for solving the MINLP problems with 0-1 variables is applied to the optimal scheduling problem in a new manner to accelerate the solution.Moreover,the nonlinear AC power flow constraints are considered to make the model more accurate.And the dynamic modeling idea is applied to the optimal scheduling problem considering the continuous load trajectory,and a fast solution method is utilized.The specific research content and achievements of this thesis are summarized as follows:First,a partial surrogate cuts(PSC)method for the AC power flow constrained unit commitment(ACUC)problem is proposed,and the parallel computing is implemented to speed up the calculation.By constructing an ACUC model with separable binary variables,the PSC method divides the continuous variables into linear and nonlinear subsets,and decomposes the original problem into mixed integer linear programming master problems and nonlinear subproblems,which are solved iteratively.To improve the efficiency of the solution,the linearized AC power flow constraints are incorporated into the master problem,leading to the modified PSC method for ACUC.The idea is to guide the searching in the master problem by adding more cuts into it,resulting a tighter feasible region and eventually benefiting the reduction of iterations.For large-scale problems,the parallel computing is further implemented to save the computational time through the block bordered diagonal frame of the correction equation derived by the interior point method.Through the numerical simulations of two IEEE test systems and a practical 739-bus system,the effectiveness of the proposed modified PSC method for solving ACUC problems is verified.Combined with parallel computing,the efficiency of solving large-scale problems is significantly improved.Second,the modeling of ACUC problems through semi-continuous variables is proposed,in order to accelerate the solution through B&B method.Instead of using auxiliary binary variables that indicate the on/off states of generating units,the new formulation directly utilizes the semi-continuous variables,i.e.,the active power output of units,to describe the operation levels of units,and the overall problem is reformulated without changing the original logical relation except few and close approximations.Therefore,it reduces the number of variables and simplifies the search space compared with the commonly used binary paradigm.As an important result,it can improve the computational performance of ACUC through B&B method.In the case studies of two IEEE test systems and a practical 739-bus system,the binary-variable-based ACUC model is compared to verify the effectiveness of the semi-continuous-variable-based ACUC model,which can significantly reduce the calculation time and improve the efficiency.Third,a dynamic model and its fast solution method for ACUC problems considering continuous load trajectory are proposed.The differences of UC problems with and without consideration of the load trajectory are illustrated.Then,from the perspective of dynamic optimization,differential equations are introduced.Thus,the ACUC problem considering load trajectory is formulated as a mixed integer dynamic optimization model,which can provide a smooth curve for the output of the unit.To solve this problem,a convex reformulation and relaxation method for dealing with the binary variables is utilized,thus converting the problem into a continuous dynamic optimization and reducing the calculation complexity.Afterwards,it is solved as a nonlinear programming problem through the Radau collocation method.In the numerical simulations of three IEEE test systems,the scheduling results for the model based on stepped load curve are compared.The unit output curve obtained by the dynamic optimization model has no sudden rise and fall,which is smoother.The simulation results show that the proposed algorithm has higher computational efficiency and good applicability in systems with larger scale.Last,considering the network constraints,a mixed-integer second-order cone model and the PSC method for the optimal scheduling of multi-carrier energy systems with demand response are proposed.The optimal scheduling model of the system considering the influences of the electrical and heating sub-networks is formulated,and the detailed constraints for energy storage systems such as the maximum number of switching operations are taken into account,in order to save the lifetime of the devices and reach a sustainable operation.The overall formulation is a mixed integer nonlinear programming problem.To solve this problem,the second-order cone relaxation is performed on the power flow model of the distribution network,and the constraint with absolute value calculation is linearized.Hence,the model is transformed into a mixed integer second-order cone programming model,which can guarantee convergence and directly leverage the solver.Accordingly,a PSC method for this problem is proposed,which can further improve the computational efficiency,especially for large-scale problems.Numerical simulations on two modified practical multi-carrier energy systems are conducted,and the influences of network constraints on the optimal scheduling problem are analyzed.The effectiveness of the PSC method for this problem is verified.It can provide a solution in shorter computing time,and its advantage is remarkable in the large-scale test system.