计及机组启停的动态最优潮流问题研究
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摘要
随着我国节能减排政策的实施、温室气体减排清晰量化目标的出台、市场化改革的不断深入,众多基础产业(电力、航空、铁路等)在引入市场化竞争机制的同时,纷纷采取了提高能源效率、节能减排的措施,电力产业尤是如此。在保证电力系统安全稳定运行和可靠供电的前提下,改革和优化现行的发电调度模式,实现节能环保目标,具有显著现实意义。
本文以最优潮流、动态最优潮流、机组组合和计及机组启停的动态最优潮流问题为研究对象；采用离散域提升-投影紧松弛技术和连续域快速内点方法等数学方法,对研究对象展开理论与数值模拟研究工作。基于混合整数规划可行域的连续松弛构造其一个好的紧松弛来逼近其凸包,并通过求解紧松弛问题可很好逼近混合整数规划的解,而提升-投影技术可在高维空间构造混合整数集的紧松弛。内点算法是求解凸规划的多项式时间复杂度算法,各种内点算法及其相关算法在求解最优潮流和动态最优潮流问题上得到了广泛的应用。随着系统规模的增加以及计算速度要求的提高,并行内点算法也开始引入电力系统计算领域。
本文基于最优中心参数技术、改进多中心校正技术以及解耦技术,设计了新的快速内点算法,并将该方法应用于最优潮流和动态最优潮流问题的求解。再基于提升-投影技术,建立机组组合问题的紧混合整数规划模型,通过求解紧模型的连续松弛问题,实现机组组合问题求解。最后采用分层方式对计及机组启停的动态最优潮流问题进行求解,其中的核心子问题则采用本文所建立的新型快速内点算法和提升-投影紧松弛方法求解。全文共分为8章,归纳如下：
第1章主要对最优潮流、动态最优潮流、机组组合和计及机组启停的动态最优潮流问题进行介绍和分析,论述了研究计及机组启停的动态最优潮流问题的必要性和重要性,并简要回顾了以上几类问题的求解算法以及在实际中的应用情况,为后续章节的讨论奠定了基础。
第2章讨论本文使用的数学理论基础。讨论了内点算法基本理论与算法框架,并以线性规划内点算法为例,分析了内点算法的并行计算思想与方法。阐述了提升-投影的技术框架,并分析了其在混合整数规划中的推广应用。
第3章基于最优中心参数及改进多中心校正技术,提出一种求解最优潮流问题的新型内点算法。结合均衡距离-评价函数,给出了最优中心参数评价模型,采用线性化技术对模型近似,以降低模型计算量。利用线搜索技术实现近似模型求解以确定最优中心参数,该参数使得所提算法具有更多的优势步和更少的迭代次数。
第4章基于改进的多中心校正和解耦技术,提出一种求解动态最优潮流问题的并行算法。结合内点算法框架与动态最优潮流问题修正方程的分块箭形结构,给出修正方程的并行解耦-分解-回代解法。并结合这一解法特点,提出动态步长拉大技术及自适应最大校正次数技术,使得迭代步长增大,迭代点中心性提高,总迭代次数和计算时间显著减少。解耦技术的使用,使得所提算法的核心计算都可并行完成。
第5章基于凸包变换和提升-投影锥松弛技术,在超立方空间内构造了计及爬坡约束机组组合问题的紧连续松弛模型,提出一种通过求解紧松弛模型而获得UC问题次优解的新方法。
第6章基于凸包变换和提升-投影技术构造了计及爬坡约束机组组合问题的提升投影紧混合整数规划模型,通过逐次求解不断缩紧的连续松弛问题获得UC问题高质量的次优解,所提算法对爬坡约束的处理十分有效,计算速度快,可扩展性好。
第7章基于所提的新型快速内点算法以及提升-投影技术,实现了计及机组启停的动态最优潮流问题的分层求解。对分层后的两个连续子问题：动态最优潮流可行性子问题和确定机组启停后的动态最优潮流问题,采用新型快速内点算法实现并行计算。对分层后的离散子问题则采用提升-投影紧松弛技术求解。
第8章概括总结了本文的主要研究工作和成果,指出了今后有待进一步开展的研究工作。
With the emergence of policies in saving energy, quantitative goal in reducing greenhouse gas emissions and innovation in power markets, market competition mechanism and measures have been introduced for many basic industries, including power, aviation and railway etc., to improve the energy efficiency. Under this background, it is important in theoretical and practical to study the operation and dispatch of power system for energy saving and environment protection.
Based on the quickly interior point method in continuous domain and the lift-and-project in discrete domain, this thesis aims to study the optimal power flow, dynamic optimal power flow, unit commitment and dynamic optimal power flow with unit commitment in models and methods. A tight relaxation of a mixed integer programming feasible region can be gotten by using the relaxation of the feasible region, and the solutions of the tight relaxation problem are the good approximations of the solutions of the origin mixed integer programming. The tight relaxation of the mixed integer set can be constructed in high dimension space with lift-and-project. Interior point method is a polynomial time complexity algorithm for solving convex programming, and this method and many related algorithms have been widely used in power system. With the increasing in the size of problems and the demand for computing speed, parallel interior point methods have been introduced into power system computing.
This thesis proposes a new quickly interior point method based on the techniques of optimal centering parameter and improved multiple centrality corrections, and the optimal power flow, dynamic optimal power flow problems all can be solved with this new method. Then, several tight mixed integer programming models for the unit commitment problems are presented by using lift-and-project, and the continuous relaxations of these proposed models can be solved to achieve the sub-optimal solutions for the unit commitment problems. At last, the complicated dynamic optimal power flow with unit commitment problems can be solved in3steps; all the important sub problems can be solved with the aforementioned method. This thesis contains8chapters as follows:
In chapter1, the optimal power flow, dynamic optimal power flow, unit commitment and dynamic optimal power flow with unit commitment problems are discussed briefly at first. The necessity and importance of studying the dynamic optimal power flow problems with unit commitment problems are presented. Meanwhile, some methods, solving the aforementioned problems, are reviewed briefly for the following discussion.
Theory and practice of interior point method are discussed in chapter2, and parallel interior point method has been shown too. In this chapter, the procedure of life-and-project has been explained and extended to mixed integer programming problem.
In chapter3, a new quickly interior point algorithm was presented for solving optimal power flow problem based on the techniques of optimal centering parameter and improved multiple centrality corrections. The proposed method involves integrating equilibrium distance-quality function to establish a mathematical model for evaluating centering parameter, and the approximate expression of this model, which can be solved with fewer computations than the original one, was proposed using the linearization technique. After solving the approximate model with the line search technique, the optimal centering parameters can be obtained for the proposed method to own more dominant steps and less number of iterations than other interior point methods.
Chapter4presents a new parallel algorithm to solve dynamic optimal power flow based on the methods of improved multiple centrality corrections and decoupling. A parallel decoupling-factorization-substitution method for the correction equation of dynamic optimal power flow was proposed by integrating interior point method framework and the block arrow correction equation, and then, the methods of dynamic increasing step length and adaptive corrections were given. A longer iteration step length and a better central point, which can be obtained by the proposed algorithm, give on the reduction in the number of iterations and savings in computing time than other interior point methods. Most of operations in proposed method can be processed in parallel with decoupling.
In chapter5, a new tighter continuous relaxation model of the ramp rate constrained unit commitment problem is presented by integrating the techniques of convex hull transformation and lift-and-project cone relaxation. The proposed model can be solved directly to get the sub-optimal solutions of the unit commitment problem.
In chapter6, a novel method for the ramp rate constrained unit commitment problem is presented by solving a sequence of increasingly tight continuous relaxations based on the techniques of convex hull transformation and lift-and-project tight relaxation. The proposed method provides excellent performance and sub-optimal solutions.
A method with3steps based on proposed quickly interior point method and lift-and-project method for solving dynamic optimal power flow with unit commitment problem has been discussed in chapter7. The two continuous sub problems, feasible problem for dynamic optimal power flow and classic dynamic optimal power flow problem, can be solved using the parallel improved multiple center corrections interior point method, and the discrete sub problem can be solved with the lift-and-project method.
The conclusions and remained questions are given in chapter8.
本文以最优潮流、动态最优潮流、机组组合和计及机组启停的动态最优潮流问题为研究对象；采用离散域提升-投影紧松弛技术和连续域快速内点方法等数学方法,对研究对象展开理论与数值模拟研究工作。基于混合整数规划可行域的连续松弛构造其一个好的紧松弛来逼近其凸包,并通过求解紧松弛问题可很好逼近混合整数规划的解,而提升-投影技术可在高维空间构造混合整数集的紧松弛。内点算法是求解凸规划的多项式时间复杂度算法,各种内点算法及其相关算法在求解最优潮流和动态最优潮流问题上得到了广泛的应用。随着系统规模的增加以及计算速度要求的提高,并行内点算法也开始引入电力系统计算领域。
本文基于最优中心参数技术、改进多中心校正技术以及解耦技术,设计了新的快速内点算法,并将该方法应用于最优潮流和动态最优潮流问题的求解。再基于提升-投影技术,建立机组组合问题的紧混合整数规划模型,通过求解紧模型的连续松弛问题,实现机组组合问题求解。最后采用分层方式对计及机组启停的动态最优潮流问题进行求解,其中的核心子问题则采用本文所建立的新型快速内点算法和提升-投影紧松弛方法求解。全文共分为8章,归纳如下：
第1章主要对最优潮流、动态最优潮流、机组组合和计及机组启停的动态最优潮流问题进行介绍和分析,论述了研究计及机组启停的动态最优潮流问题的必要性和重要性,并简要回顾了以上几类问题的求解算法以及在实际中的应用情况,为后续章节的讨论奠定了基础。
第2章讨论本文使用的数学理论基础。讨论了内点算法基本理论与算法框架,并以线性规划内点算法为例,分析了内点算法的并行计算思想与方法。阐述了提升-投影的技术框架,并分析了其在混合整数规划中的推广应用。
第3章基于最优中心参数及改进多中心校正技术,提出一种求解最优潮流问题的新型内点算法。结合均衡距离-评价函数,给出了最优中心参数评价模型,采用线性化技术对模型近似,以降低模型计算量。利用线搜索技术实现近似模型求解以确定最优中心参数,该参数使得所提算法具有更多的优势步和更少的迭代次数。
第4章基于改进的多中心校正和解耦技术,提出一种求解动态最优潮流问题的并行算法。结合内点算法框架与动态最优潮流问题修正方程的分块箭形结构,给出修正方程的并行解耦-分解-回代解法。并结合这一解法特点,提出动态步长拉大技术及自适应最大校正次数技术,使得迭代步长增大,迭代点中心性提高,总迭代次数和计算时间显著减少。解耦技术的使用,使得所提算法的核心计算都可并行完成。
第5章基于凸包变换和提升-投影锥松弛技术,在超立方空间内构造了计及爬坡约束机组组合问题的紧连续松弛模型,提出一种通过求解紧松弛模型而获得UC问题次优解的新方法。
第6章基于凸包变换和提升-投影技术构造了计及爬坡约束机组组合问题的提升投影紧混合整数规划模型,通过逐次求解不断缩紧的连续松弛问题获得UC问题高质量的次优解,所提算法对爬坡约束的处理十分有效,计算速度快,可扩展性好。
第7章基于所提的新型快速内点算法以及提升-投影技术,实现了计及机组启停的动态最优潮流问题的分层求解。对分层后的两个连续子问题：动态最优潮流可行性子问题和确定机组启停后的动态最优潮流问题,采用新型快速内点算法实现并行计算。对分层后的离散子问题则采用提升-投影紧松弛技术求解。
第8章概括总结了本文的主要研究工作和成果,指出了今后有待进一步开展的研究工作。
With the emergence of policies in saving energy, quantitative goal in reducing greenhouse gas emissions and innovation in power markets, market competition mechanism and measures have been introduced for many basic industries, including power, aviation and railway etc., to improve the energy efficiency. Under this background, it is important in theoretical and practical to study the operation and dispatch of power system for energy saving and environment protection.
Based on the quickly interior point method in continuous domain and the lift-and-project in discrete domain, this thesis aims to study the optimal power flow, dynamic optimal power flow, unit commitment and dynamic optimal power flow with unit commitment in models and methods. A tight relaxation of a mixed integer programming feasible region can be gotten by using the relaxation of the feasible region, and the solutions of the tight relaxation problem are the good approximations of the solutions of the origin mixed integer programming. The tight relaxation of the mixed integer set can be constructed in high dimension space with lift-and-project. Interior point method is a polynomial time complexity algorithm for solving convex programming, and this method and many related algorithms have been widely used in power system. With the increasing in the size of problems and the demand for computing speed, parallel interior point methods have been introduced into power system computing.
This thesis proposes a new quickly interior point method based on the techniques of optimal centering parameter and improved multiple centrality corrections, and the optimal power flow, dynamic optimal power flow problems all can be solved with this new method. Then, several tight mixed integer programming models for the unit commitment problems are presented by using lift-and-project, and the continuous relaxations of these proposed models can be solved to achieve the sub-optimal solutions for the unit commitment problems. At last, the complicated dynamic optimal power flow with unit commitment problems can be solved in3steps; all the important sub problems can be solved with the aforementioned method. This thesis contains8chapters as follows:
In chapter1, the optimal power flow, dynamic optimal power flow, unit commitment and dynamic optimal power flow with unit commitment problems are discussed briefly at first. The necessity and importance of studying the dynamic optimal power flow problems with unit commitment problems are presented. Meanwhile, some methods, solving the aforementioned problems, are reviewed briefly for the following discussion.
Theory and practice of interior point method are discussed in chapter2, and parallel interior point method has been shown too. In this chapter, the procedure of life-and-project has been explained and extended to mixed integer programming problem.
In chapter3, a new quickly interior point algorithm was presented for solving optimal power flow problem based on the techniques of optimal centering parameter and improved multiple centrality corrections. The proposed method involves integrating equilibrium distance-quality function to establish a mathematical model for evaluating centering parameter, and the approximate expression of this model, which can be solved with fewer computations than the original one, was proposed using the linearization technique. After solving the approximate model with the line search technique, the optimal centering parameters can be obtained for the proposed method to own more dominant steps and less number of iterations than other interior point methods.
Chapter4presents a new parallel algorithm to solve dynamic optimal power flow based on the methods of improved multiple centrality corrections and decoupling. A parallel decoupling-factorization-substitution method for the correction equation of dynamic optimal power flow was proposed by integrating interior point method framework and the block arrow correction equation, and then, the methods of dynamic increasing step length and adaptive corrections were given. A longer iteration step length and a better central point, which can be obtained by the proposed algorithm, give on the reduction in the number of iterations and savings in computing time than other interior point methods. Most of operations in proposed method can be processed in parallel with decoupling.
In chapter5, a new tighter continuous relaxation model of the ramp rate constrained unit commitment problem is presented by integrating the techniques of convex hull transformation and lift-and-project cone relaxation. The proposed model can be solved directly to get the sub-optimal solutions of the unit commitment problem.
In chapter6, a novel method for the ramp rate constrained unit commitment problem is presented by solving a sequence of increasingly tight continuous relaxations based on the techniques of convex hull transformation and lift-and-project tight relaxation. The proposed method provides excellent performance and sub-optimal solutions.
A method with3steps based on proposed quickly interior point method and lift-and-project method for solving dynamic optimal power flow with unit commitment problem has been discussed in chapter7. The two continuous sub problems, feasible problem for dynamic optimal power flow and classic dynamic optimal power flow problem, can be solved using the parallel improved multiple center corrections interior point method, and the discrete sub problem can be solved with the lift-and-project method.
The conclusions and remained questions are given in chapter8.
引文
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