基于改进交替方向乘子法的电-气综合能源系统优化调度

Optimal Dispatch of Integrated Electricity and Gas System Based on Modified Alternating Direction Method of Multipliers

在电-气综合能源系统分布式优化调度中,非线性非凸的Weymouth方程给问题求解带来了巨大挑战。一方面,目前许多研究采用二阶锥松弛Weymouth方程,较为复杂;另一方面,主流分布式算法即交替方向乘子法(ADMM)的计算效率并不高。对此,该文提出一种精确近似的Weymouth方程线性化模型和多参数规划改进ADMM算法以解决上述两个问题。Weymouth方程线性化模型基于泰勒展开,利用一簇切线松弛Weymouth方程。特别地,增加了惩罚项以收紧松弛间隙,通过变量替换的方法减少切线的数量,并给出了一种有效的切线选取方法。对于多参数规划改进ADMM算法,其通过多参数规划得到子问题最优解的解析式。迭代过程中,若参数落在临界域内,可直接将参数代入最优解解析式获得子问题的最优解,无需求解子问题,提高了迭代速度。此外,该文还对多参数规划中难以避免的退化问题进行了处理,提升了算法的通用性。最后在两个不同规模的系统中验证了Weymouth方程线性化模型的精确性和多参数规划改进ADMM算法的高效性。

It is challenging for distributed optimal dispatch of integrated electricity and gas systems due to the nonlinear and nonconvex Weymouth equation.At present,many studies use the second-order cone to relax the Weymouth equation,which is relatively complicated.On the other hand,the mainstream distributed algorithm alternating direction method of multipliers(ADMM)is not computationally efficient.In this paper,an exact approximate Weymouth equation linearization model and a multi-parameter programming modified ADMM algorithm are proposed to address the aforementioned two concerns.The Weymouth equation linearization model is based on Taylor expansion,which uses a cluster of tangents to relax the Weymouth equation and replaces the curve with tangents approximately.In particular,a penalty term is added to tighten the slack gap,and the number of tangents is reduced by variable substitution.Then an effective tangent selection method is given to obtain an accurate approximation of the Weymouth equation linearization model.The multi-parameter programming modified ADMM algorithm improves ADMM by multi-parameter programming,to improve the computational efficiency of distributed optimal dispatch.In the ADMM subproblem,the analytical expression of the optimal solution of the subproblem is obtained by multi-parameter programming.During the iteration,as long as the parameters fall in the critical regions,the parameters can be directly substituted into the analytic equation of the optimal solution to obtain the optimal solution of the subproblem without solving the subproblem,to improve the iteration speed.In addition,this paper also deals with the unavoidable degradation problem in multi-parameter programming by the method based on QR decomposition,which enhances the generality of the multi-parameter programming modified ADMM algorithm.The simulation results of the small-scale system show that the average relative error of the Weymouth equation linearization model is 0.49%,and the maximum relative error is 2.75%,which achieves a good approximation effect.Compared with the piecewise linearization method,the proposed linearization method has higher accuracy and computational efficiency.In the distributed optimal dispatch,the number of iterations of the multi-parameter programming modified ADMM algorithm and classic ADMM is the same,but the time consumption of the proposed algorithm is only 63.43%of classic ADMM,which is equivalent to a 57.66%increase in computational efficiency.For the varying penalty parameter ADMM,although the number of iterations of the varying penalty parameter ADMM is one less than that of the proposed algorithm,the time consumption of the proposed algorithm is still less than that of the varying penalty parameter ADMM,and the computational efficiency can also be improved by 44.53%.In addition,the simulation results of the large-scale system also verify the accuracy of the Weymouth equation linearization model and the efficiency of the multi-parameter programming modified ADMM algorithm.Through simulation analysis,the following conclusions can be drawn:(1)The Weymouth equation linearization model can accurately describe the pipeline gas flow,and it has advantages in computational efficiency.(2)The multi-parameter programming modified ADMM algorithm improves the efficiency of distributed optimal dispatch of the integrated electricity and gas system,which is conducive to real-time dynamic economic dispatch.