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 智能系统学报  2020, Vol. 15 Issue (1): 41-49  DOI: 10.11992/tis.201906026 0

### 引用本文

CHEN Zengqiang, HUANG Zhaoyang, SUN Mingwei, et al. Active disturbance rejection control of load frequency based on big probability variation’s genetic algorithm for parameter optimization[J]. CAAI Transactions on Intelligent Systems, 2020, 15(1): 41-49. DOI: 10.11992/tis.201906026.

### 文章历史

1. 南开大学 人工智能学院，天津 300350;
2. 天津市智能机器人重点实验室，天津 300350

Active disturbance rejection control of load frequency based on big probability variation’s genetic algorithm for parameter optimization
CHEN Zengqiang 1,2, HUANG Zhaoyang 1, SUN Mingwei 1, SUN Qinglin 1
1. College of Artificial Intelligence, Nankai University, Tianjin 300350, China;
2. Key Laboratory of Intelligent Robotics of Tianjin, Tianjin 300350, China
Abstract: In this paper, the active disturbance rejection control (ADRC) is applied to the load frequency control (LFC) of the two-zone interconnected power system, which is extended from a power system model with non-reheating steam turbines to other models, one with turbines, and another consists of reheating turbines with consideration of power generation rate constraints and governor dead zones, involving three control objects of linear, nonlinear and non-minimum phase characteristics. The model is used to adjust the parameters of the controller utilizing the big probability variation’s genetic algorithm. The simulation is compared with the PI control based on the big probability variation’s genetic algorithm. The simulation shows that ADRC based on big probability variation’s genetic algorithm possesses fast dynamic response, small deviation, good robustness, strong anti-interference characteristics, which is more effective for the LFC system.
Key words: active disturbance rejection control    load frequency control    big probability variation’s genetic algorithm    two-area interconnected power system    turbine    generation rate constraint    governor’s dead zone    nonlinear    non-minimum phase characteristics

1 自抗扰控制的基本原理

TD模型：

 $\left\{ \begin{array}{l} {v_1} = {v_1} + h{v_2} \\ {v_2} = {v_2} + h{v_3} \\ {v_3} = {v_3} + h{\rm{fh}} \\ {\rm{fh}} = {\rm{ - }}{r_0}{\rm{(}}{r_0}{\rm{(}}{r_0}{\rm{(}}{v_1}{\rm{) + 3}}{v_2}{\rm{) + 3}}{v_3}{\rm{)}} \\ \end{array} \right.$

ESO模型：

 $\left\{ \begin{array}{l} e = {z_1} - y \\ {z_1} = {z_1} + h({z_2} - {\beta _{01}}e) \\ {z_2} = {z_2} + h({z_3} - {\beta _{02}}\;{\rm{fal}}\;(e,0.5,\delta )) \\ {z_3} = {z_3} + h({z_4} - {\beta _{03}}\;{\rm{fal}}\;(e,0.25,\delta ) + {b_0}u) \\ {z_4} = {z_4} + h( - {\beta _{04}}\;{\rm{fal}}\;(e,0.125,\delta )) \\ \end{array} \right.$

NLSEF模型：

 $\left\{ \begin{array}{l} {e_1} = {v_1} - {z_1},{e_2} = {v_2} - {z_2},{e_3} = {v_3} - {z_3} \\ {u_0} = \displaystyle\sum\limits_{i = 1}^3 {{\beta _i}\;{\rm{fal}}\;({e_i},{\alpha _i},{\delta _0})} \\ u = \dfrac{{{u_0} - {z_4}}}{{{b_0}}} \\ \end{array} \right.$

 ${\rm{fal}}(e,\alpha ,\delta ) = \left\{ \begin{array}{l} \dfrac{e}{{{\delta ^{\alpha - 1}}}},\;\;\;\;\;\;\;\;{\rm{ }}\left| e \right| \leqslant \delta \\ {\left| e \right|^\alpha }\;{\rm{sign}}\;(e),\;\;\;\;{\rm{ }}\left| e \right| > \delta \\ \end{array} \right.$

2 基于大变异遗传算法的自抗扰控制器

1)初始种群选取。首先初始化种群规模和交叉及原始变异概率，确定自抗扰控制器需要整定的参数对应的二进制编码，选取初始染色体种群，解码得到控制器参数，运行系统仿真，并计算每个染色体的适应值。其中，ADRC参数编码描述如下：固定参数 ${r_0} = 4$ , $\delta = {\delta _0} = 0.05$ , ${\alpha _1} = 0.3$ , ${\alpha _2} = 0.8$ , ${\alpha _3} = 1.1$ 。然后剩余参数在如下范围内随机初始化取多组初值参与优化： $\;{\beta _{01}} \in [0,400],$ $\;{\beta _{02}} \in$ $[0,4\;000],$ $\;{\beta _{03}} \in [0,40\;000],$ $\;{\beta _{04}} \in [0,800\;000],$ $\;{\beta _1} \in [0,1\;000],$ $\;{\beta _2} \in$ $[0,1\;500],$ $\;\;{\beta _3} \in [0,500],$ $\;{b_0} \in [1,500]$

2)种群进化。根据适应值选择父母染色体，进行复制、交叉操作，判断是否满足大变异操作条件以确定变异概率，进行变异操作得到新的染色体种群，解码得到控制器参数，重新运行系统仿真，计算新种群中每个染色体的适应值。

3)种群优化。判断是否满足结束条件，不满足时重复操作2)直到满足为止。

 Download: 图 2 基于大变异遗传算法的自抗扰控制参数整定流程图 Fig. 2 Flow chart of active disturbance rejection control parameter tuning based on big probability variation's genetic algorithm
3 负荷频率自抗扰控制 3.1 电力系统线性模型

 ${G_g}(s) = \frac{1}{{{T_g}s + 1}}$

 ${G_t}(s) = \frac{1}{{{T_t}s + 1}}$

 ${G_p}(s) = \frac{{{K_p}}}{{{T_p}s + 1}}$

 $G(s) = \frac{{{K_p}}}{{({T_p}s + 1)({T_g}s + 1)({T_t}s + 1) + {K_p}/R}}$

3.2 两区域频率控制系统

 $\begin{array}{l} {K_{\rm{p}} } = 120,{T_p} = 20,{T_t} = 0.3,{T_{12}} = 0.3, \\ {a_{12}} = - 1,{T_g} = 0.08,R = 2.4,B = 0.425 \\ \end{array}$

 $J = {\rm{ITAE}} = \int_0^\infty {((\left| {\Delta {f_1}} \right| + \left| {\Delta {f_2}} \right| + \left| {\Delta {P_{{\rm{tie}}}}} \right|)} \cdot t){\rm{d}}t$

 Download: 图 5 非再热式两区域响应 Fig. 5 Response of non-reheated two-connected area with turbine

 Download: 图 6 模型参数的蒙特卡洛实验 Fig. 6 Monte Carlo test of model parameters

 Download: 图 7 模型参数摄动时闭环系统响应 Fig. 7 Response of the closed-loop systems under parametric perturbations

4 推广模型

4.1 水轮机

 $\begin{array}{l} {G_t}(s) = \dfrac{{{a_{23}} + ({a_{23}}{a_{11}} - {a_{21}}{a_{12}}){T_w}s}}{{1 + {a_{11}}s}} \end{array}$

 $\begin{array}{l} {K_{\rm{p}}} = 120,{T_{p1}} = 20,{T_w} = 1.5,\\ {T_g} = 0.1,{R_1} = {R_2} = 2.4,{T_{12}} = 0.545,\\ {B_1} = {B_2} = 0.425,{a_{11}} = 0.491,\\ {a_{12}} = 0.789,{a_{21}} = 1.46,{a_{23}} = 0.74 \end{array}$

t=0时在区域1加入阶跃负荷扰动 $\Delta {P_{d1}} =$ $0.01$ ，性能指标数值比较见表5。自抗扰控制器下的系统响应如图8实线所示。

 Download: 图 8 具有水轮机的两区域响应 Fig. 8 Response of two-connected area with turbine

4.2 再热汽轮机、发电速率约束与调速器死区

 ${G_t}(s) = \frac{{{K_r}{T_r}s + 1}}{{({T_t}s + 1)({T_r}s + 1)}}$