Research On Convex-Relaxation Based Optimal Power Flow In Power Systems Under The Background Of Energy Interconnection

Optimal power flow,which has been a concern for power system analysis,is facing new challenges as energy interconnection develops rapidly.On the one hand,the topology of the power system is becoming increasingly complex,and different energy systems are intercon-nected,which requires the establishment of a more comprehensive optimization model? On the other hand,in order to improve the optimization efficiency and the solving reliability,it is nec-essary to design a suitable optimization algorithm which can guarantee the global optimality.Convex relaxation method,which is good at dealing with nonlinear constraints and has high solving efficiency,is popular in the field of optimization.In view of this,this thesis follows the research ideas of network topology ranging from simple to complex,carries out research on the convex relaxation method of power flow optimization from the three aspects of radial power network,meshed power network,and integrated electricity-gas system.Focus on the establish-ment of convex relaxation models and the algorithm to reduce the relaxation gap,a series of optimization models and solving algorithms are proposed.Firstly,to meet the requirement of enough safety margins in power systems under the back-ground of energy interconnection,a second-order cone relaxation based optimization model considering current margins is proposed for optimal power flow.A sufficient condition to guarantee the exactness of the relaxation is proposed and proved with mathematical analysis in radial networks.Different from the traditional optimal power flow model,this model can make the transmission lines have closer current margins after optimization.Secondly,to address the issue of inexact angle relaxation in the relaxed model used for meshed networks power flow optimization,a quadratic voltage relaxation model is proposed.Different from the common relaxation based models,the proposed model uses the real and imaginary parts of the voltage variables directly,so the requirements of meshed network closure can be met without additional constraints.The objective function is modified with a specific penalty term so that the exactness of the relaxation can be guaranteed for the meshed networks with maximum phase angle differences between buses less than 90?.The selection criteria of the penalty factor considering the network parameters is illustrated by self-contained mathematical analysis.Thirdly,an enhanced and modified model based on the quadratic voltage model is proposed to solve the optimal power flow for the meshed power network.In this model,two sets of inequality constraints are used to replace the equality constraints.Besides,an iterated concave-convex procedure is imposed to convexify the non-convex constraints,which is regarded as the enhanced model.The convergence of the iterative method is proved with the sufficient theoretical analysis,which thus ensures that the optimal solution must be located in the feasible solution region.At the same time,by introducing a penalty concave-convex procedure,the proposed model is improved from the aspect of reducing demand for iterative initial value.Finally,an optimized model with a dynamic tightened approach is presented to achieve the power flow optimiza tion in meshed power -gas system by utilizing the quadratic voltage model proposed above.Based on the second-order cone and convex hull relaxations,the optimal power flow problem is totally convexified.Different from regular power flow optimization models,the model proposed in this paper considers the line-pack and gas direction constraints of natural gas system.Besides,the meshed topology of the integrated system is concluded in the constraints.The solving process of the proposed dynamic tightened approach can be divided into two steps.The first step is to reconstruct the solution domain dynamically by solving the linear programming.And the other is to tighten the feasible region of the relaxed model with a mixed integer second-order cone programming.As a result,the power flow optimization of meshed electricity-gas system can be solved with smaller relaxation gap.