#### 期刊菜单

Optimal Configuration Strategy of Under-Frequency Load Shedding for Power Grid Based on Correlation Degree under High Penetration Level of Clean Energy
DOI: 10.12677/SG.2022.124015, PDF, HTML, XML, 下载: 56  浏览: 99

Abstract: The under-frequency load shedding (UFLS) in the third line of defense of power system is one of the significant measures to prevent the rapid and continuous decline of the system frequency and ultimately maintain the stability of system frequency after disturbance. Meanwhile, when a large amount of clean energy is connected to the power grid, the frequency characteristics of the power system become worse. How to explore and exploit the optimal configuration strategy of UFLS under high penetration level of clean energy is a key issue to be solved urgently. Therefore, under the background of large-scale grid-connected clean energy, this paper deduces the correlation degree index which can effectively realize load shedding. On this basis, the improved scenario-based method is utilized to describe the uncertainty of clean energy. Further, the setting process of UFLS solution based on the adjustment power and steady-state frequency is proposed. Finally, taking the IEEE standard test system as an example, the validity of the proposed optimal configuration strategy of UFLS is verified by simulations and comparative analysis.

1. 引言

2. 关联度指标

2.1. 机组出力与负荷消耗功率关系

${I}_{\text{N}}\text{=}{Y}_{\text{N}}{U}_{\text{N}}$ (1)

${I}_{\text{B}}\text{=}{Y}_{\text{B}}{A}^{\text{T}}{U}_{\text{N}}$ (2)

${I}_{\text{B}}\text{=}{Y}_{\text{B}}{A}^{\text{T}}{Y}_{\text{N}}^{\text{-1}}{I}_{\text{N}}\text{=}{Y}_{\text{B}}C{Z}_{\text{N}}{I}_{\text{N}}=\left[\begin{array}{ccc}{y}_{1}& & \\ & \ddots & \\ & & {y}_{m}\end{array}\right]\left[\begin{array}{ccc}{c}_{11}& \cdots & {c}_{1n}\\ ⋮& & ⋮\\ {c}_{m1}& \cdots & {c}_{mn}\end{array}\right]\left[\begin{array}{ccc}{z}_{11}& \cdots & {z}_{1n}\\ ⋮& & ⋮\\ {z}_{n1}& \cdots & {z}_{nn}\end{array}\right]\left[\begin{array}{c}{\stackrel{˙}{I}}_{n1}\\ ⋮\\ {\stackrel{˙}{I}}_{nn}\end{array}\right]$ (3)

${\stackrel{˙}{I}}_{ab}={\sum }_{j=1}^{n}{y}_{g}\left[{\sum }_{l=1}^{n}{c}_{gl}{z}_{lj}\right]{\stackrel{˙}{I}}_{nj}={\sum }_{j=1}^{n}{\mu }_{j}{\stackrel{˙}{I}}_{nj}$ (4)

${\mu }_{j}={y}_{g}{\sum }_{l=1}^{n}{c}_{gl}{z}_{lj}$ (5)

Figure 1. Diagram of a simplified power grid

$\frac{{\stackrel{˜}{I}}_{ab}{\stackrel{˙}{U}}_{a}}{{\stackrel{˙}{U}}_{a}}={\sum }_{j=1}^{n}{\mu }_{j}\frac{{\stackrel{˜}{I}}_{nj}{\stackrel{˙}{U}}_{j}}{{\stackrel{˙}{U}}_{j}}$ (6)

${P}_{ab}+j{Q}_{ab}={\sum }_{j=1}^{n}{\mu }_{j}\frac{\left({P}_{j}+j{Q}_{j}\right){\stackrel{˙}{U}}_{a}}{{\stackrel{˙}{U}}_{j}}$ (7)

${P}_{ab}={\sum }_{j=1}^{n}{\mu }_{j}\left[\mathrm{cos}\left({\delta }_{a}-{\delta }_{j}\right)-\mathrm{tan}{\phi }_{j}\mathrm{sin}\left({\delta }_{a}-{\delta }_{j}\right)\right]{P}_{j}$ (8)

2.2. 不平衡功率关联度优先级指标

${\lambda }_{ri}=\frac{{\mu }_{i}\left[\mathrm{cos}\left({\delta }_{a}-{\delta }_{i}\right)-\mathrm{tan}{\phi }_{i}\mathrm{sin}\left({\delta }_{a}-{\delta }_{i}\right)\right]}{{\sum }_{j\in L}{\mu }_{j}\left[\mathrm{cos}\left({\delta }_{a}-{\delta }_{j}\right)-\mathrm{tan}{\phi }_{j}\mathrm{sin}\left({\delta }_{a}-{\delta }_{j}\right)\right]}$ (9)

${R}_{i}={\sum }_{r\in F}{\sum }_{w\in r}{p}_{r}×{P}_{fw}×{\lambda }_{wi}$ (10)

3. 基于改进场景法的清洁能源不确定性建模

3.1. 改进K-means算法

1) 场景聚类：在这里将采用改进的最大最小距离算法来确定初始聚类中心，具体过程为：

a) 计算初始场景集N中任意两个场景si，sj间的Euclidean距离：

$d\left({s}_{i},{s}_{j}\right)=‖{s}_{i}-{s}_{j}‖,\text{\hspace{0.17em}}{s}_{i},{s}_{j}\in N$ (11)

b) 找到Euclidean距离中最小的两个场景 ${{s}^{\prime }}_{i}$${{s}^{\prime }}_{j}$，并使用这两个场景的平均值 来替代它们：

$\stackrel{¯}{s}=\frac{{{s}^{\prime }}_{i}+{{s}^{\prime }}_{j}}{2},\text{\hspace{0.17em}}{{s}^{\prime }}_{i},{{s}^{\prime }}_{j}\in N$ (12)

c) 重复上述过程(a)和过程(b)，直到剩余场景数目为事先设定的数目k，即为生成的初始聚类中心。在确定了初始聚类中心后，场景聚类的剩余过程都与常规K-means场景缩减方法一样。

2) 场景选择：在上述场景聚类步骤完成后，需在每个子集内选择最有代表性的场景作为典型的场景来代表整个子集。本研究中将引入一种典型度的思想来选择典型的场景，其具体计算过程描述如下：

a) 对于一个特定的子集cu，利用下式计算表示其内部相似性的归一化因子Zru和表示外部不相似性的归一化因子Zd

$\left\{\begin{array}{l}diam\left({c}_{u}\right)={\mathrm{max}}_{{s}_{a},{s}_{b}\in {c}_{u}}‖{s}_{a}-{s}_{b}‖\\ {Z}_{ru}={\mathrm{max}}_{{c}_{u}}diam\left({c}_{u}\right)\\ {Z}_{d}={\mathrm{max}}_{{s}_{i},{s}_{j}\in N}‖{s}_{i}-{s}_{j}‖\end{array},\text{\hspace{0.17em}}\text{\hspace{0.17em}}u=1,2,\cdots ,k$ (13)

b) 对于特定子集cu中的任何一个场景s，定义相同子集内的其他场景作为其“朋友”场景，记作 $F=f{r}_{1},f{r}_{2},\cdots ,f{r}_{i},\cdots ,f{r}_{n}$，则该特定子集内中每个场景s的内部相似性R(s)可表示为：

$R\left(s\right)=\frac{{\sum }_{i=1}^{n}\left(1-‖s-f{r}_{i}‖\right)/{Z}_{ru}}{n},\text{\hspace{0.17em}}s\in {c}_{u}$ (14)

c) 将特定子集cu外部的所有其他场景看作为场景s的“反对者”场景，记作 $E={e}_{1},{e}_{2},\cdots ,{e}_{i},\cdots ,{e}_{m}$，则该特定子集内中每个场景s的外部不相似性D(s)可表示为：

$D\left(s\right)=\frac{{\sum }_{i=1}^{n}‖s-{e}_{i}‖/{Z}_{d}}{m},\text{\hspace{0.17em}}s\in {c}_{u}$ (15)

d) 根据公式(14)和公式(15)定义的内部相似性R(s)和外部不相似性D(s)，则可利用下式来计算特定子集内中每个场景s的典型度T(s)为：

$T\left(s\right)=\frac{R\left(s\right)\cdot D\left(s\right)}{R\left(s\right)\cdot D\left(s\right)+\left(1-R\left(s\right)\right)\cdot \left(1-D\left(s\right)\right)},\text{\hspace{0.17em}}\text{\hspace{0.17em}}s\in {c}_{u}$ (16)

e) 根据公式(16)选择典型度值最大的场景su来代表整个特定子集cu，并利用下式来计算其概率 $p\left({s}_{u}\right)$ 为：

$p\left({s}_{u}\right)=\frac{U}{{N}_{m}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}u=1,2,\cdots$ (17)

3.2. 风电场出力

${P}_{WF}=\left\{\begin{array}{l}0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}v<\frac{{v}_{ci}}{\sqrt[3]{\zeta }}\text{\hspace{0.17em}}\text{ }\text{or}\text{\hspace{0.17em}}\text{ }\text{ }v>{v}_{co}\\ \frac{{v}^{3}\cdot \zeta -{v}_{ci}^{3}}{{v}_{r}{}^{3}-{v}_{ci}^{3}}\cdot {P}_{wfr}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{{v}_{ci}}{\sqrt[3]{\zeta }}\le v<\frac{{v}_{r}}{\sqrt[3]{\zeta }}\\ {P}_{wfr}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{{v}_{r}}{\sqrt[3]{\zeta }}\le v<{v}_{co}\end{array}$ (18)

${P}_{wfr}={n}_{row}\cdot {n}_{col}\cdot {P}_{wt}$ (19)

${R}_{i}={\sum }_{s=1}^{k}p\left(s\right)\cdot {R}_{is}$ (20)

4. 含高占比清洁能源的低周减载方案优化配置

4.1. 定义调节功率

4.2. 两步骤法低周减载方案优化配置流程

4.2.1. 步骤1：获取甩负荷容量近似解

${P}_{tr}={P}_{f}-{P}_{re}$ (21)

$\left\{\begin{array}{l}{t}_{l}\ge \Delta t\\ {t}_{l+1}<\Delta t\end{array}$ (22)

4.2.2. 步骤2：获取甩负荷容量精确解

$49.8\text{\hspace{0.17em}}\text{Hz}\le {f}_{\infty }\le 50.2\text{\hspace{0.17em}}\text{Hz}$ (23)

Figure 2. Flowchart of optimal configuration strategy of under-frequency load shedding for power grid based on correlation degree under high penetration level of clean energy

5. 算例仿真分析

Figure 3. Wiring diagram of modified IEEE 39-bus test system

5.1. 验证关联度指标

Figure 4. Frequency curves after shedding different loads with the same capacity

5.2. 验证关联度优先级指标

Table 1. System simulation result data of IEEE 39-bus test system

Figure 5. Frequency curve after UFLS is triggered for the most extreme fault

Figure 6. Comparisons of the transient frequency

5.3. 高占比清洁能源对低周减载策略的影响

Table 2. Comparisons of the simulation results after UFLS with high penetration level of clean energy (32.9%)

Table 3. Comparisons of the simulation results after UFLS with high penetration level of clean energy (46.4%)

6. 结论

1) 当电网受到扰动产生不平衡功率时，切除与此不平衡功率关联度指标较高的负荷，可以在相同甩负荷容量的基础上相较于其他负荷得到更好的动作效果，相对地减少了减载容量，故应优先切除。

2) 本文所提出的基于关联度的低周减载优化配置策略可以有效地减小电网暂态频率的变化范围，更有利于电网稳定。

3) 对高占比清洁能源对低周减载带来的影响展开研究，发现损失常规机组出力给高新能源渗透率电网带来的波动更大，对低周减载方案的要求更高，当系统新能源渗透率进一步增加后尤其明显。

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