论文总字数：21203字

摘 要

在电力系统的日常运作中，有许多不确定性因素，例如负荷波动、电力设备故障等。正确评估这些不确定因素对电力系统的影响，对电力系统的规划和稳定运作至关重要。基于采样方法的蒙特卡罗模拟法(MCS)是分析电力系统不确定性的常用方法，因此完成电力系统状态的采样是分析电力系统的先决条件。然而蒙特卡罗采样效率低，计算量大。为克服蒙特卡罗法在此方面的缺陷，本文使用拉丁超立方抽样(Latin hypercube sampling，LHS)模拟电力系统的状态抽样，然后使用蒙特卡罗模拟分析不确定性的结果。

LHS方法通过有效地采样随机输入变量进行,能在较小采样规模达到计算精度的要求，大大提高计算效率，因此在电力系统不确定性问题的分析中得到了广泛的应用。此外LHS方法不仅能够用于数据的抽样，还可用于进行电力系统的可靠性评估和潮流计算，此两种方法是对电力系统不确定分析最常使用的方法。本文通过潮流计算达到电力系统不确定性分析。在系统存在不确定性的情况下，概率潮流计算无疑是最有效的方法。

概率潮流计算是评估电网稳定运行状况的有效工具，同时考虑到不确定性。通常使用与蒙特卡罗模拟和随机采样来执行此操作。尽管这种方法的应用是灵活的、而且计算精度很高，但它计算量太大,只能在大规模取样的情况下得以改进。使用LHS采样和Cholesky分解法的组合来进行概率潮流计算。LHS与Cholesky分解法相结合使用可以提高采样值相对于输入随机变量分布空间的覆盖范围、提高采样效率和减小采样规模，同时还可应用于蒙特卡罗模拟法中，具有广泛的应用可能性。

关键词：蒙特卡罗模拟法，拉丁超立方抽样，概率潮流计算，Cholesky分解法。

Abstract

There are many uncertain factors in the operation of power system, such as load fluctuation, power equipment failure and so on. How to properly evaluate the influence of these uncertain factors on the power system plays a vital role in the planning and stable operation of the power system. Monte Carlo Simulation (MCS), which is based on sampling method, is the most commonly used method in power system uncertainty analysis, so completing state sampling of power system is the first condition for power system analysis. However, Monte Carlo method has low sampling efficiency and large amount of calculation. In order to overcome the defects of Monte Carlo method in this aspect, this paper adopts Latin hypercube sampling (LHS) to sample the simulated state of power system, and then analyzes the uncertainty of sampling results by Monte Carlo simulation method.

Latin hypercube sampling method can effectively sample the input random variables, reduce the sampling scale required to achieve the specified accuracy, and greatly improve the calculation efficiency, so it has been widely used in the analysis of power system uncertainty. In addition, LHS method can be used not only for data sampling, but also for power system reliability evaluation and power flow calculation. These two methods are the most commonly used methods for power system uncertainty analysis. In this paper, the uncertainty analysis of power system will be completed by power flow calculation. Probabilistic power flow calculation is undoubtedly the most effective power flow calculation method for scenarios with uncertain factors.

The probabilistic load flow evaluation is an effective tool to evaluate the stable operation of power grid, taking into account the uncertainty. Monte Carlo simulation method combined with simple random sampling is usually used to calculate probabilistic load flow. Although this method is flexible in application and high in calculation accuracy, its calculation amount is too large, and the accuracy can be improved only in the case of large-scale sampling. The combination of LHS sampling and Cholesky decomposition method is used to calculate the probability power flow. The combination of Cholesky decomposition method can improve the coverage of sampling value relative to the distribution space of input random variables, improve the sampling efficiency and reduce the sampling scale, and can also be applied to Monte Carlo simulation method, which has wide application possibilities.

Key words: Monte Carlo simulation, Latin hypercube sampling, Probabilistic load flow calculation, Cholesky decomposition method.

目录

摘要Ⅰ

AbstractⅡ

第一章 绪论1

1.1 研究背景与意义1

1.2 电力系统概率潮流计算1

1.3 本文主要研究内容2

第二章 电力系统的状态抽样方法3

2.1蒙特卡罗模拟法3

2.2 LHS抽样法3

2.2.1 采样4

2.2.2 排列4

2.3 Cholesky分解法4

2.4 LHS抽样和蒙特卡罗抽样对比5

第三章 基于LHS抽样的电力系统概率潮流计算6

3.1输入随机变量相关性的处理方法6

3.2 CLMCS方法原理7

3.3 CLMCS和CSMCS的仿真对比9

第四章 结论与展望16

参考文献17

致谢19

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