# Optimization Strategy of SVC for Eliminating Electromagnetic Oscillation in Weak Networking Power Systems

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## Abstract

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## 1. Introduction

- (1)
- A quantitative method is provided for evaluating the influence of SVC on electromagnetic oscillation modes.
- (2)
- The contradiction between reactive power regulation ability and electromagnetic oscillation suppression ability of the SVC is revealed, which provides a basis for the definition of a comprehensive optimization objective function.
- (3)
- The performance criteria considering the damping characteristic and reactive performance of the SVC provides a new way to optimize PI parameters aiming at minimizing the negative effects of the SVC.
- (4)
- The process of SVC parameter optimization and the steps of multi-SVC parameter optimization in large power grid are proposed.

## 2. Problem Formulation

#### 2.1. A Brief Introduction of CTAIP

- (1)
- The length of the tie-line reaches 1497 km, and there is no power supply on the transmission lines.
- (2)
- The maximum short circuit current of 500 kV bus is only 5 kA. In substation LZ, it is only 3–4 kA.

#### 2.2. Electromagnetic Oscillation of CTAIP

## 3. Characteristics of Electromagnetic Oscillation Induced by SVCs

#### 3.1. Simplified Model

_{s}is the impedance of power supply. R, X and B are line resistance, reactance and admittance, respectively. L

_{h}is the high voltage shunt reactor, of which the compensation is considered within 70%. Transformer capacity is 750 MVA with rated voltage of 550/242/36 kV. The primary device parameters are shown in Table 1.

#### 3.2. Electromagnetic Oscillation Mode Calculation

_{d}, i

_{q}are the d axis and q axis components of the current, respectively. u

_{d}, u

_{q}are the d axis and q axis components of the voltage, respectively. ω

_{0}is reference frequency. X is inductance, B is admittance.

_{TCR}is the admittance of TCR. T

_{v}is time constant of inertial link. k

_{p}is proportional gain, k

_{i}is integral gain. U

_{ref}, U

_{l}are reference voltage and actual voltage of the SVC, respectively. s is the differential operator, x is the state variable.

_{0}is reference frequency. I

_{TCRd}, I

_{TCRq}are the d axis and q axis components of the TCR current respectively. U

_{ld}, U

_{lq}are the d axis and q axis components of the SVC voltage, respectively.

#### 3.3. Key Influence Factors of the Electromagnetic Oscillation

#### 3.4. Sensitivity of SVC Control Parameters to Electromagnetic Oscillation

_{p}, the eigenvalues of the electromagnetic mode move to the right side of the complex plane. K

_{p}has the greatest influence on the oscillation mode when ω is less than 314 rad/s (f < 50 Hz). When ω is greater than 1570 rad/s (f > 250 Hz), K

_{p}has almost no effect on the electromagnetic oscillation mode.

_{i}has almost no effect on electromagnetic oscillation mode. When ω is less than 314 rad/s (f < 50 Hz), with the increase of K

_{i}, the eigenvalues of the electromagnetic mode move to the right side of the complex plane.

_{p}. This is actually not true. The following part of this paper focuses on the oscillation modes with angular frequencies smaller than 314 rad/s, so this defect of this model does not affect this study.

#### 3.5. Effect of SVC Control Parameters on Reactive Power Regulation Performance

_{p}and k

_{i}. However, the reactive power and voltage regulation capability of the SVC will be weakened. As shown in Figure 10, the performance of electromagnetic oscillation damping levels and reactive power regulation are contradictory. Therefore, it is necessary to find an SVC control parameter optimization method which can suppress electromagnetic oscillation and maintain enough reactive power regulation performance of the SVC.

## 4. Parameter Optimization Strategy

#### 4.1. Reactive Power Regulation Performance index

_{1}(K) is proposed to indicate the reactive power regulation performance of SVC.

_{1}(K) is voltage regulation performance index function of SVC under PI parameters vector K = [k

_{p}, k

_{i}]. T

_{0.9}indicates the rise time from voltage differential exceeds voltage dead zone to SVC output reactive power or admittance reaches 90% target value. T

_{s}indicates the time from voltage differential exceeds voltage dead zone to SVC output reactive power or admittance reaches stability. k

_{1}represents the weight coefficient of rise time, and k

_{2}represents the weight coefficient of settling time. k

_{1}and k

_{2}can be set to 1. k

_{1}and k

_{2}can be set to 1.

#### 4.2. Electromagnetic Oscillation Suppression Capability Index

_{2}(K) is the electromagnetic oscillation suppression capability index. ξ

_{n}, f

_{n}is the damping ratio and the frequency of nth oscillation mode, respectively. f

_{max}is the highest oscillation frequency concerned. Because the TCR trigger frequency is 100 Hz, the frequency of oscillation caused by the SVC is lower than 50 Hz according to Shannon’s sample theorem. p

_{n}is the weight coefficient of each oscillation mode.

#### 4.3. Optimization Objective Function

_{1}, m

_{2}represent the weight of the reactive power regulation performance index and the weight of electromagnetic oscillation suppression index of the SVC, respectively. Considering the suppression of electromagnetic oscillation as the main factor, m

_{1}can be set to 1 and m

_{2}can be set to 2.

#### Optimization Process

## 5. Case Study

_{p}= 2, K

_{i}= 100, the system remains stable without any disturbance. When the equivalent impedance of the system increases from 60 to 80 Ω, an unstable electromagnetic oscillation occurs.

_{p}∈ [0.1,3], K

_{i}∈ (10,300]. The upper limit of oscillation frequency f

_{max}is 250 Hz. The weight coefficient of each oscillation mode p

_{i}= 1. The weight coefficient of rise time T

_{0.9}and settling time T

_{s}is 1. The weight coefficient of reactive power regulation performance index m

_{1}is 1, the weight coefficient of electromagnetic oscillation suppression capability index is 2. T

_{0.9}∈ [0.01,0.5], T

_{s}∈ [0.02,1]. After optimization, K

_{p}= 1.0751, and K

_{i}= 162.8425.

## 6. Application in CTAIP

#### 6.1. Parameter Optimization of CTAIP

_{p}decreased and k

_{i}increased.

_{0.9}decreased less than 0.07 s, T

_{s}decreased less than 0.13 s.

#### 6.2. Validation of Control Strategy

#### 6.2.1. Simulation with PSCAD/EMTDC

#### 6.2.2. Simulation with RTDS

#### 6.3. Engineering Verification

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 7.**Variation trend of eigenvalues of the main electromagnetic oscillation mode with transmission line length and equivalent impedance of power supply (with no SVC).

**Figure 8.**Variation trend of eigenvalues of the main electromagnetic oscillation mode with capacities of SVCs (1000 km transmission line).

**Figure 9.**Variation trend of eigenvalues of the electromagnetic oscillation mode with SVC PI parameters (1000 km transmission line).

**Figure 10.**Eigenvalue of the electromagnetic oscillation mode and admittance step response of the SVC under different PI parameters.

**Figure 14.**Dynamic response of the system under faults before and after SVC parameter optimization with PSCAD.

**Figure 16.**Dynamic response of the system under N-2 fault of the line BT-MK after SVC parameter optimization with RTDS.

X_{s} (Ω) | R (Ω/km) | X (Ω/km) | B (Siem/km) | Transformer (750 MVA) | ||
---|---|---|---|---|---|---|

60 | 0.0166 | 0.2968 | 4.24 × 10^{−6} | X_{12} (%) | X_{13} (%) | X_{23} (%) |

12 | 44 | 30 |

Parameter Source | LX | BM | MK | |||
---|---|---|---|---|---|---|

k_{p} | K_{i} | k_{p} | K_{i} | k_{p} | K_{i} | |

Before optimization | 4 | 100 | 4 | 100 | 4 | 100 |

After optimization | 1.1237 | 94.8621 | 1.9826 | 152.2815 | 2.0596 | 197.2081 |

Parameter Source | LX | BM | MK | |||
---|---|---|---|---|---|---|

T_{0.9} (s) | T_{s} (s) | T_{0.9} (s) | T_{s} (s) | T_{0.9} (s) | T_{s} (s) | |

Before optimization | 0.20 | 0.49 | 0.16 | 0.43 | 0.14 | 0.41 |

Parameters optimization | 0.27 | 0.62 | 0.19 | 0.54 | 0.16 | 0.49 |

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## Share and Cite

**MDPI and ACS Style**

Shi, H.; Sun, X.; Chen, G.; Zhang, H.; Tang, Y.; Xu, L.; Ding, L.; Fan, C.; Xu, Y.
Optimization Strategy of SVC for Eliminating Electromagnetic Oscillation in Weak Networking Power Systems. *Energies* **2019**, *12*, 3489.
https://doi.org/10.3390/en12183489

**AMA Style**

Shi H, Sun X, Chen G, Zhang H, Tang Y, Xu L, Ding L, Fan C, Xu Y.
Optimization Strategy of SVC for Eliminating Electromagnetic Oscillation in Weak Networking Power Systems. *Energies*. 2019; 12(18):3489.
https://doi.org/10.3390/en12183489

**Chicago/Turabian Style**

Shi, Huabo, Xinwei Sun, Gang Chen, Hua Zhang, Yonghong Tang, Lin Xu, Lijie Ding, Chengwei Fan, and Yin Xu.
2019. "Optimization Strategy of SVC for Eliminating Electromagnetic Oscillation in Weak Networking Power Systems" *Energies* 12, no. 18: 3489.
https://doi.org/10.3390/en12183489