Convexification Based Optimal Power-gas Flow Method Considering Power And Gas Losses

Optimal power-gas flow(OPGF)is a basic tool for research on coordinated operation and planning of an electricity-gas coupled system(EGCS),which is also the basis of further research on electricity-gas joint dispatch,joint market,risk assessment,and so on.The OPGF problem is essentially complex nonlinear and non-convex optimization problem.The solving methods cannot guarantee the either convergence,computational efficiency,or the global optimality.It is a great challenge to solve the OPGF problem.Most existing studies use a lossless and linear DC power flow model to approximate nonlinear AC power flow model and simplify the gas flow equations,which sacrifices the modeling accuracy to obtain an OPGF model that can be handled with less difficulty.For the purpose of pursuing both high computational accuracy and high efficiency,this dissertation focuses on the source of nonlinearity in OPGF,and conducts research based on approximation and convexify theory.The main work of this dissertation are summarized below:(1)Propose a low-nonlinearity OPGF model embedded power and gas losses.The nonlinear AC power flow equations and pipeline gas flow equations containing unknown gas flow directions are the important sources of computational complexity in an OPGF problem.In order to reduce the nonlinearity of OPGF and address the unknown gas flow directions,a low-nonlinearity OPGF model embedded power and gas losses is proposed.In the proposed low-nonlinearity OPGF model,a DC power flow model with power losses embedded is used to approximate the nonlinear AC power flow model,which can reduce the nonlinearity of AC power flow model but improve the modeling accuracy of the lossless DC power flow model.Then,employing the variable transformation and big-M methods reduce the nonlinearity of pipeline gas flow equations and address the unknown gas flow directions.An EGCS with the IEEE 14-bus system and a 12-node natural gas system is used to test the effectiveness of proposed OPGF model.Numerical results demonstrate that the proposed low-nonlinearity OPGF model effectively reduces the computational complexity of nonlinear OPGF model and still achieve a high approximation accuracy.(2)Propose a two-stage convexification OPGF method based on linearized loss.The low-nonlinearity OPGF model embedded power and gas losses is essentially a nonlinear programming problem.A two-stage convexification OPGF method based on linearized loss is proposed to address the nonlinearity in the proposed low-nonliearity OPGF model including power loss equations,pipeline gas flow equations,the compressors' gas consumption equations and gas-fired unit model.In the proposed method,power loss and the gas consumption equations are linearized by the first-order Taylor series expansion.The Weymouth equation is addressed by second-order cone(SOC)relaxation.To enhance the exactness of the relaxation,a penalty term is added to objective function.Gas-fired unit model is relaxed to a convex quadratic inequality constraint.To overcome the problem that the linearized starting points of power loss and gas consumption equations are difficult to obtain,a two-stage method is proposed to solve the problem.An EGCS with the IEEE 39-bus system and a 20-node natural gas system(E39-G20 EGCS)is used to investigate the effectiveness of the proposed method.Numerical results show that the proposed method has advantages of high accuracy and high speed.More importantly,the convergence of the proposed method can be guaranteed since the OPGF models of two stages are mixed-integer convex programming(MICP)and convex programming.(3)Propose a loss equivalence and iterative solution based OPGF method.On the basis of the proposed low-nonlinearity OPGF model,a loss equivalence and iterative solution based OPGF method is proposed.In the proposed method,power losses and gas consumptions are modeled as loss-equivalence loads and then solved by the iterative solution method.Two more penalty terms of compressors are introduced to further improve the estimation accuracy of gas loss-equivalent loads.A SOC relaxation method is proposed to address the pipeline gas flow equations,and the tightness of the SOC relaxation is guaranteed by introducing a penalty term and an iterative tightening procedure.Numerical results on E39-G20 EGCS show that the proposed OPGF method has advantages of high accuracy,rapid convergence and high efficiency.More importantly,the proposed method has decent adaptability to different EGCS operation conditions.