# A Multi-Rate Simulation Strategy Based on the Modified Time-Domain Simulation Method and Multi-Area Data Exchange Method of Power Systems

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^{2}

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## Abstract

**:**

## 1. Introduction

- (1)
- To ensure the accuracy of multi-rate simulation, this paper proposes a modified TDS method. The proposed method modifies the built-in algorithm of the traditional TDS method, which is not applicable for multi-rate simulation. Without any approximation, this modification enables initial data of subsequent simulation to be obtained from information exchange between different subsystems after the first process. Therefore, high accuracy can be achieved in completing multi-rate simulations.
- (2)
- To verify the versatility of the multi-rate interface, this paper proposes a multi-area data exchange method. It allows the interface data to be transferred between different subsystems, while maintaining high applicability and superiority of the original dynamic simulation algorithm. Furthermore, this method adopts interpolation technique to solve the numerical stability issues caused by varying tolerance levels of different systems for different exchanged data.

## 2. Multi-Rate Interface Strategy

#### 2.1. The Modified TDS Method

_{1}and Δt

_{2}are the time steps for Subsystem 1 and Subsystem 2, respectively. Typically, in the multi-rate simulation method applied to power system analysis, this simulation software offers the functionality to customize the simulation step size for each subsystem. Therefore, the step size for integrating the differential equations can be selected based on the dynamic characteristics of each subsystem, thereby enhancing the simulation efficiency.

#### 2.2. Efficiency Improvement Analysis and Interpolation Correction

^{2}is divided into two subsystems with orders of (0.5n)

^{2}and (1.5n)

^{2}, respectively, the overall efficiency, due to the serial process being entirely dependent on the 2.25n

^{2}system, shows a remarkable improvement in simulation efficiency.

#### 2.3. Multi-Area Data Exchange Method

- (1)
- The fast-dynamic system operates a dynamic simulation with a large step size of 10 ms. Assume a short-circuit fault is applied at 1.0 s and it lasts until 1.01 s, resulting in an output file. The amplitude and phase angle of the voltage are extracted from this output file and inputted as the injected power at the Slack bus in the slow dynamic system’s input file. The slow dynamic system then runs a dynamic simulation with a small step size of 1 ms using this input file. This input file contains a minor disturbance to simulate the impact from Subsystem 1. Similarly, another output file is obtained, which provides the active and reactive power of the bus.
- (2)
- In general simulation software, the dynamic simulation program is called the TDS. The power-based modified TDS program for Subsystem 1 is designated as TDS1, and for Subsystem 2, it is designated as TDS2. The power from the bus in the previous step’s output file is injected into Subsystem 1, while other variables remain unchanged from the previous step. On this basis, all variables are used in TDS1 for the second step of dynamic simulation. The output includes the amplitude and phase angle of the interface bus voltage, with interpolation processing and consideration of numerical stability issues during the exchange process.
- (3)
- Subsystem 2 receives the bus voltage transmitted by subsystem 1 and then runs TDS2 for subsequent simulations.
- (4)
- By continuously repeating steps (2) and (3), a complete cycle of multi-rate simulation can be achieved.

## 3. Case Studies

#### 3.1. Case Study of the Integrated System of IEEE 14-Bus and 33-Bus Systems

#### 3.1.1. Simulation Setup Description

#### 3.1.2. Simulation Results Analysis

#### 3.2. Case Study of a Power System in the Guangxi Power Grid

#### 3.2.1. Simulation Setup Description

#### 3.2.2. Simulation Results Analysis

^{2}to (0.85n)

^{2}and (1.15n)

^{2}. Therefore, based on theoretical analysis, the efficiency of this system can be theoretically improved by 67.5%. It is noteworthy that the multi-rate method exhibits a more significant improvement in simulation efficiency for large-scale power systems. As indicated in Table 2, the uniform small timestep simulation takes a considerable amount of time, totaling 248.2992 s. However, while maintaining simulation accuracy, the multi-rate method substantially enhances the efficiency by 66.83%, ultimately reducing the simulation time to 82.3734 s. It is evident that the multi-rate interface strategy improves the efficiency of large-scale power systems more obviously.

## 4. Conclusions and Outlook

- (1)
- The paper introduces a modified TDS method. This method addresses inherent limitations encountered in traditional simulation software when applied to the multi-rate simulation. The proposed method eliminates the initialization process, allowing electric data to be directly exchanged within the system from the first exchange. This facilitates subsequent simulations to incrementally build upon initial results.
- (2)
- The proposed multi-area data exchange method significantly simplifies exchange between different subsystems. Interpolation techniques are employed during the exchange process to correct numerical stability issues. Furthermore, the proposed method suggests a theoretical possibility by envisioning a general interface for different simulation software.
- (3)
- The advantages of the proposed multi-rate interface strategy have been verified through a standard case study and a real-world power system in the Guangxi Power Grid in China. The standard case study shows that the simulation efficiency in the IEEE 14-bus and 33-bus system is improved by 53.03% compared with that of the integrated system, and is improved by 66.83% in the real-world system. Meanwhile, the simulation accuracy of the simulation is ensured.

- (1)
- Abstracting the multi-rate simulation interface to meet the needs of the simulation framework, thereby enabling adaptation to other simulation software. This aims to reduce the need for custom modifications by users and enhance the scalability of the framework.
- (2)
- Building upon the foundation of multi-rate simulation, incorporating dynamic partitioning strategies and parallel simulation techniques. This would better reflect the distribution of distributed energy devices in real power systems and further enhance the efficiency of the simulation process.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Table A1.**The static active power (PL0), static reactive power (QL0) of the loads in IEEE 14 and 33-bus integrated system.

Bus | P_{L0} (pu) | Q_{L0} (pu) |
---|---|---|

2 | 0.217 | 0.127 |

3 | 0.5 | 0.25 |

4 | 0.478 | 0.1 |

5 | 0.076 | 0.016 |

6 | 0.15 | 0.075 |

9 | 0.295 | 0.166 |

10 | 0.09 | 0.058 |

11 | 0.035 | 0.018 |

12 | 0.061 | 0.016 |

13 | 0.135 | 0.058 |

14 | 0.2 | 0.07 |

16 | 0.001 | 0.0006 |

17 | 0.0009 | 0.0004 |

18 | 0.0012 | 0.0008 |

19 | 0.0006 | 0.0003 |

20 | 0.0006 | 0.0002 |

21 | 0.002 | 0.001 |

22 | 0.002 | 0.001 |

23 | 0.0006 | 0.0002 |

24 | 0.0006 | 0.0002 |

25 | 0.00045 | 0.0003 |

26 | 0.0006 | 0.00035 |

27 | 0.0006 | 0.00035 |

28 | 0.0012 | 0.0008 |

29 | 0.0006 | 0.0001 |

30 | 0.0006 | 0.0002 |

31 | 0.0006 | 0.0002 |

32 | 0.0009 | 0.0004 |

33 | 0.0009 | 0.0004 |

34 | 0.0009 | 0.0004 |

35 | 0.0009 | 0.0004 |

36 | 0.0009 | 0.0004 |

37 | 0.0009 | 0.0005 |

38 | 0.0042 | 0.002 |

39 | 0.0042 | 0.002 |

40 | 0.0006 | 0.00025 |

41 | 0.0006 | 0.00025 |

42 | 0.0006 | 0.0002 |

43 | 0.0012 | 0.0007 |

44 | 0.002 | 0.006 |

45 | 0.0015 | 0.0007 |

46 | 0.0021 | 0.001 |

47 | 0.0006 | 0.0004 |

**Table A2.**The static active power (PG0), static reactive power (QG0) of the generators in IEEE 14 + 33-bus system.

Bus | P_{G0} (pu) | Q_{G0} (pu) |
---|---|---|

2 | 0.4 | 0.15 |

3 | 0.4 | 0.15 |

6 | 0.3 | 0.1 |

8 | 0.35 | 0.1 |

27 | 0.008 | 0.006 |

33 | 0.002 | 0.008 |

37 | 0.004 | 0.004 |

40 | 0.008 | 0.004 |

idx | D | M | ra | xl | xq | xd | xd1 | xd2 | xq1 | xq2 | Td10 | Td20 | Tq10 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 13 | 0 | 0.06 | 1.7 | 1.8 | 0.3 | 0.25 | 0.55 | 0.25 | 8 | 0.03 | 0.4 |

2 | 0 | 13 | 0 | 0.054 | 1.66 | 1.66 | 0.25 | 0.25 | 0.55 | 0.25 | 8 | 0.03 | 0.4 |

3 | 0 | 10 | 0 | 0.06 | 1.7 | 1.8 | 0.3 | 0.25 | 0.55 | 0.25 | 8 | 0.03 | 0.4 |

4 | 0 | 10 | 0 | 0.054 | 1.66 | 1.66 | 0.25 | 0.25 | 0.55 | 0.25 | 8 | 0.03 | 0.4 |

5 | 0 | 10 | 0 | 0.06 | 1.7 | 1.8 | 0.3 | 0.25 | 0.55 | 0.25 | 8 | 0.03 | 0.4 |

**Table A4.**Symbol description of dynamic parameters of the synchronous generator in IEEE 14 + 33-bus system.

Symbol | Description |
---|---|

D | damping coefficient |

M | machine start-up time |

ra | armature resistance |

xl | leakage reactance |

xq | d-axis transient reactance |

xd | d-axis synchronous reactance |

xd1 | q-axis synchronous reactance |

xd2 | d-axis sub-transient reactance |

xq1 | q-axis transient reactance |

xq2 | q-axis sub-transient reactance |

Td10 | d-axis transient time constant |

Td20 | d-axis sub-transient time constant |

Tq10 | q-axis transient time constant |

idx | Bus | Sn | dqdv | fdbd | ddn | ialim | vt0 | vt1 | vt2 | vt3 | ft0 | ft1 | ft2 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 27 | 1 | 0 | 0.06 | −1 | −0.017 | 5 | 1.2 | 0.88 | 0.9 | 49.5 | 49.7 | 50.3 |

2 | 33 | 1 | 0 | 0.06 | −1 | −0.017 | 5 | 1.2 | 0.88 | 0.9 | 49.5 | 49.7 | 50.3 |

3 | 37 | 1 | 0 | 0.06 | −1 | −0.017 | 5 | 1.2 | 0.88 | 0.9 | 49.5 | 49.7 | 50.3 |

4 | 40 | 1 | 0 | 0.06 | −1 | −0.017 | 5 | 1.2 | 0.88 | 0.9 | 49.5 | 49.7 | 50.3 |

**Table A6.**Symbol description of dynamic parameters of the distributed PV in IEEE 14 + 33-bus system.

Symbol | Description |
---|---|

dqdv | Q-V droop characteristics |

fdbd | Frequency deviation deadband |

ddn | Gain after f deadband |

ialim | Apparent power limit |

vt0 | Voltage tripping response curve point 0 |

vt1 | Voltage tripping response curve point 1 |

vt2 | Voltage tripping response curve point 2 |

vt3 | Voltage tripping response curve point 3 |

ft0 | Frequency tripping response curve point 1 |

ft1 | Frequency tripping response curve point 2 |

ft2 | Frequency tripping response curve point 3 |

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**Figure 9.**The relative error about variables in integrated and multi-rate simulations in IEEE 14-bus and 33-bus system.

**Figure 11.**The output active power of the distributed energy storage device at Bus 174 in the integrated and multi-rate simulations.

**Figure 12.**The output reactive power of the distributed energy storage device at Bus 174 in the integrated and multi-rate simulations.

Scenarios | T/s |
---|---|

Large step size | 3.4051 |

Small step size | 142.0161 |

Multi-rate | 66.7128 |

Scenarios | T/s |
---|---|

Large step size | 5.3975 |

Small step size | 248.2992 |

Multi-rate | 82.3734 |

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**MDPI and ACS Style**

Yao, R.; Chen, Q.; Bai, H.; Liu, C.; Liu, T.; Luo, Y.; Yang, W.
A Multi-Rate Simulation Strategy Based on the Modified Time-Domain Simulation Method and Multi-Area Data Exchange Method of Power Systems. *Electronics* **2024**, *13*, 884.
https://doi.org/10.3390/electronics13050884

**AMA Style**

Yao R, Chen Q, Bai H, Liu C, Liu T, Luo Y, Yang W.
A Multi-Rate Simulation Strategy Based on the Modified Time-Domain Simulation Method and Multi-Area Data Exchange Method of Power Systems. *Electronics*. 2024; 13(5):884.
https://doi.org/10.3390/electronics13050884

**Chicago/Turabian Style**

Yao, Ruotian, Qi Chen, Hao Bai, Chengxi Liu, Tong Liu, Yongjian Luo, and Weichen Yang.
2024. "A Multi-Rate Simulation Strategy Based on the Modified Time-Domain Simulation Method and Multi-Area Data Exchange Method of Power Systems" *Electronics* 13, no. 5: 884.
https://doi.org/10.3390/electronics13050884