基于马尔可夫链的蒸汽动力系统两阶段随机规划

现有的解决蒸汽动力系统蒸汽需求不确定性的优化方法有随机规划和鲁棒优化，但二者不能同时兼顾稳定性和经济性。本文提出一种基于马尔可夫链的两阶段随机规划去解决这个问题。第一阶段基于空间距离表达划分不确定变量，通过聚类算法划分成不同工况。第二阶段基于状态切换概率构建马尔可夫链，通过场景生成和削减的方法预测蒸汽的需求值。以某煤制气企业蒸汽动力系统为实例建立相应的优化模型，将预测的蒸汽值带入优化模型求解，得出的最优操作方案与随机规划和鲁棒优化法进行对比和分析。结果表明，本优化方法综合了随机规划经济性高和鲁棒优化稳定性高的优点，稳定性和经济性都介于随机规划和鲁棒优化的中间，为解决蒸汽动力系统的不确定优化问题提供了新思路。

Two-stage stochastic programming of steam power system based on Markov chain

The existing optimization methods to solve the uncertainty of steam demand in steam power system include stochastic programming and robust optimization. However, these methods can not trade off the stability and economy at the same time. This paper proposes a two-stage stochastic programming based on Markov chain to solve this problem. In the first stage, uncertain variables are divided based on spatial distance expression and divided into different working conditions by clustering algorithm. In the second stage, the Markov chain is constructed based on the state transition probability, and the demand value of steam is predicted by the method of scenario generation and reduction. The steam power system of a coal-to-gas enterprise is taken as an example to establish the corresponding optimization model, and the predicted steam value is brought into the optimization model to solve. The optimal operation scheme obtained is compared and analyzed with stochastic programming and robust optimization. The results show that the proposed optimization method combines the advantages of high economy of stochastic programming and high stability of robust optimization, both stability and economy are intermediate between stochastic programming and robust optimization, and provides a new idea for solving uncertain optimization problems of steam power system.