# Anti-Windup Load Frequency Controller Design for Multi-Area Power System with Generation Rate Constraint

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## Abstract

**:**

## 1. Introduction

## 2. Load Frequency Control Model

**Remark 1.**

## 3. Anti-Windup Load Frequency Controller Design

#### 3.1. Original ${H}_{\infty}$ Controller Design

#### 3.2. Anti-Windup Compensator Design

**Theorem 1.**

- Given any response of the modified closed-loop system Equations (3), (4) and (6) such that ${y}_{\overline{\text{c}}}=sa{t}_{\text{m}}\left({y}_{\overline{\text{c}}}\right)$ and ${y}_{\overline{\text{c}},\text{d}}=sa{t}_{\text{r}}\left({y}_{\overline{\text{c}},\text{d}}\right)$ for all t, then ${z}_{\ell}=z$ for all t, namely, the response of the anti-windup closed-loop system coincides with the response of the modified closed-loop system;
- The origin of the anti-windup closed-loop system is asymptotically stable.

**Remark 2.**

**Remark 3.**

## 4. Case Study

#### 4.1. Scenario 1: Simulations on Single-Area System

#### 4.2. Scenario 2: Simulations on a Two-Area System

#### 4.3. Scenario 3: Simulations on Three-Area Systems

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Load frequency control (LFC) diagram of Area i. ACE: area control error; GRC: generation rate constraint.

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**MDPI and ACS Style**

Huang, C.; Yue, D.; Xie, X.; Xie, J.
Anti-Windup Load Frequency Controller Design for Multi-Area Power System with Generation Rate Constraint. *Energies* **2016**, *9*, 330.
https://doi.org/10.3390/en9050330

**AMA Style**

Huang C, Yue D, Xie X, Xie J.
Anti-Windup Load Frequency Controller Design for Multi-Area Power System with Generation Rate Constraint. *Energies*. 2016; 9(5):330.
https://doi.org/10.3390/en9050330

**Chicago/Turabian Style**

Huang, Chongxin, Dong Yue, Xiangpeng Xie, and Jun Xie.
2016. "Anti-Windup Load Frequency Controller Design for Multi-Area Power System with Generation Rate Constraint" *Energies* 9, no. 5: 330.
https://doi.org/10.3390/en9050330