# 基于蒙特卡罗方法的风电场潮流计算Wind Power Flow Calculation Based on Monte Carlo Method

DOI: 10.12677/JEE.2019.73018, PDF, HTML, XML, 下载: 304  浏览: 758  科研立项经费支持

Abstract: With the rapid development of wind energy, wind power can be integrated into the power grid on a large scale, which exacerbates the uncertainty of power system operation, making the power flow calculation of traditional power systems insufficient to adapt to many current uncertain factors. In view of this situation, this paper proposes the power flow calculation of uncertain power system based on Monte Carlo method. Firstly, based on the uncertainty characteristics of wind power, the mathematical model and probability distribution of wind power output are established, and then the wind power system with suitable power flow calculation is constructed. Secondly, according to the data sample, qualified injection nodes are found on the IEEE14 node power distribution system. Finally, the Newton-Raphson method is used to calculate the current of the system with wind power generation. The numerical results show that the method presented in this paper is more accurate in calculating the power flow of the system and can meet the engineering requirements.

1. 引言

2. 蒙特卡罗法

${X}_{N}=\frac{1}{N}\underset{n=1}{\overset{N}{\sum }}{x}_{n}$ (1)

$P\left(\underset{N\to \infty }{\mathrm{lim}}{X}_{N}=\omega \right)=1$ (2)

Figure 1. The basic idea of montecarlo

3. 风能模型

3.1. 风速概率模型

$f\left(v\right)=\left(\frac{k}{c}\right){\left(\frac{v}{c}\right)}^{k-1}\mathrm{exp}\left[-{\left(\frac{v}{c}\right)}^{k}\right]$ (3)

$F\left(v\right)=1-\mathrm{exp}\left[-{\left(\frac{v}{c}\right)}^{k}\right]$ (4)

3.2. 风力发电机输出模型

Figure 2. Wind turbine output power curve

$P=\left\{\begin{array}{ll}0\hfill & \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }V\le {V}_{i}\hfill \\ \frac{{P}_{r}}{{V}_{r}^{3}-{V}_{i}^{3}}\left({V}^{3}-{V}_{i}^{3}\right)\hfill & {V}_{i}{V}_{o}\hfill \end{array}$ (5)

4. 牛顿-拉夫逊法潮流计算

${U}_{i}={e}_{i}+j{f}_{i}$ (6)

${Y}_{ij}={G}_{ij}+j{B}_{ij}$ (7)

${P}_{i}={e}_{i}\underset{j=1}{\overset{n}{\sum }}\left({G}_{ij}{e}_{i}-{B}_{ij}{f}_{j}\right)+{f}_{j}\underset{j=1}{\overset{n}{\sum }}\left({G}_{ij}{f}_{j}+{B}_{ij}{e}_{j}\right)$ (8)

${Q}_{i}={f}_{i}\underset{j=1}{\overset{n}{\sum }}\left({G}_{ij}{e}_{i}-{B}_{ij}{f}_{j}\right)-{f}_{j}\underset{j=1}{\overset{n}{\sum }}\left({G}_{ij}{f}_{j}+{B}_{ij}{e}_{j}\right)$ (9)

$\Delta {P}_{i}={P}_{is}-{P}_{i}={P}_{i}{}_{s}-{e}_{i}\underset{j=1}{\overset{n}{\sum }}\left({G}_{ij}{e}_{i}-{B}_{ij}{f}_{j}\right)-{f}_{j}\underset{j=1}{\overset{n}{\sum }}\left({G}_{ij}{f}_{j}+{B}_{ij}{e}_{j}\right)=0$ (10)

$\Delta {Q}_{i}={Q}_{is}-{Q}_{i}={Q}_{i}{}_{s}-{f}_{i}\underset{j=1}{\overset{n}{\sum }}\left({G}_{ij}{e}_{i}-{B}_{ij}{f}_{j}\right)+{e}_{j}\underset{j=1}{\overset{n}{\sum }}\left({G}_{ij}{f}_{j}+{B}_{ij}{e}_{j}\right)=0$ (11)

$\Delta {P}_{i}={P}_{is}-{P}_{i}={P}_{i}{}_{s}-{e}_{i}\underset{j=1}{\overset{n}{\sum }}\left({G}_{ij}{e}_{i}-{B}_{ij}{f}_{j}\right)-{f}_{j}\underset{j=1}{\overset{n}{\sum }}\left({G}_{ij}{f}_{j}+{B}_{ij}{e}_{j}\right)=0$ (12)

$\Delta {U}_{i}^{2}={U}_{is}^{2}-{U}_{i}^{2}={U}_{is}^{2}-\left({e}_{i}^{2}+{f}_{i}^{2}\right)=0$ (13)

$\Delta W=-J\Delta U$ (14)

Figure 3. Flow calculation route

5. 算例分析

Figure 4. IEEE14 node system

Table 1. Single wind turbine parameters

Table 2. Expected value and standard deviation of wind speed and output power

Table 3. Power flow calculation results

6. 结论

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