# A Study on the Power Reserve of Distributed Generators Based on Power Sensitivity Analysis in a Large-Scale Power System

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. VMS Power Flow Analysis

#### 2.1. Concept of the Proposed Power System Operation with VMS Droop Control

#### 2.2. VMS Power Flow Analysis

**J**($\in {\mathbb{R}}^{2(n-1)\times 2(n-1)}$), is defined as

**K**. Then, the voltage and power mismatches in only the virtual slack buses can be calculated as:

**K**in (3). As shown in (5), ${K}^{VMS}$ includes the data of only the bases to which the CBGs under the VMS droop control are connected. ${K}^{Net}$ includes the data of all buses except the actual slack bus and is given as (6).

## 3. Calculating the Power Reserve for Each CBG

## 4. Simulation Results

#### 4.1. The Load Changes in the Representative Bus

#### 4.2. Case Study 1: Results Based on the CBG Control Mode Differences

#### 4.3. Case Study 2: Results of the Difference in the Amount of Power Reserves of CBGs

_{A}

_{1}in FPR was lower than that of APR and the initial powers of CBG

_{A}

_{2}and CBG

_{A}

_{3}in FPR were higher than those of APR.

_{A}

_{2}and CBG

_{A}

_{3}, respectively. In FPR, the additional power from CBG

_{A}

_{3}was limited to 26.4 MW because of the limited size of the CBG.

_{A}

_{3}greatly reduced frequency stability at 240 s.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The Korean 2030 power system plan with high renewable penetration. CBGs, converter-based generators; MPPT, maximum power point tracking; VMS, virtual multi-slack.

**Figure 4.**Real power responses of the representative CBGs with (

**a**) MPPT, (

**b**) VMS droop control, and (

**c**) balanced response (BR).

**Figure 5.**Total real power changes in (

**a**) Area 1, (

**b**) Area 2, (

**c**) Area 3, and (

**d**) the other areas, including Metro Area.

**Figure 6.**Total real (

**a**) and reactive (

**b**) power loss changes of the power system according to the CBG’s control mode.

**Figure 8.**The comparison of output power of CBG according to its power reserve: (

**a**) Area 1 (

**b**) Area 2, and (

**c**) Area 3. APR, appropriate power reserve; FPR, fixed power reserve.

Year | PV | Wind | Hydro | Offshore | Bio | Wastes | Byproduct Gas | Fuel Cell | IGCC | Total |
---|---|---|---|---|---|---|---|---|---|---|

2017 | 5030 | 1174 | 1795 | 255 | 725 | 323 | 1377 | 291 | 346 | 11,316 |

2020 | 9330 | 2724 | 1850 | 255 | 1025 | 323 | 1377 | 531 | 346 | 17,761 |

2025 | 19,530 | 8474 | 1960 | 255 | 1405 | 323 | 1377 | 691 | 746 | 34,761 |

2030 | 33,530 | 17,674 | 2105 | 255 | 1705 | 323 | 1377 | 746 | 746 | 58,461 |

${\mathit{P}}_{\mathit{H}\mathit{S}}^{\mathit{r}\mathit{e}\mathit{s}}$ | ${\mathit{P}}_{\mathit{H}\mathit{L}}^{\mathit{r}\mathit{e}\mathit{s}}$ | ${\mathit{P}}_{\mathit{C}\mathit{L}}^{\mathit{r}\mathit{e}\mathit{s}}$ | ${\mathit{P}}_{}^{\mathit{r}\mathit{e}\mathit{s}}$ | ${\mathit{P}}_{}^{\mathit{i}\mathit{n}\mathit{i}}$ | |
---|---|---|---|---|---|

$CB{G}_{A1}$ | 8.7 | 9 | 50.1 | 50.1 | 309.9 |

$CB{G}_{A2}$ | 12.6 | 50 | 36.3 | 62.6 | 297.4 |

$CB{G}_{A3}$ | 7.2 | 69.3 | 39 | 76.5 | 283.5 |

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**MDPI and ACS Style**

Kim, D.; Park, J.-W.; Lee, S.H.
A Study on the Power Reserve of Distributed Generators Based on Power Sensitivity Analysis in a Large-Scale Power System. *Electronics* **2021**, *10*, 769.
https://doi.org/10.3390/electronics10070769

**AMA Style**

Kim D, Park J-W, Lee SH.
A Study on the Power Reserve of Distributed Generators Based on Power Sensitivity Analysis in a Large-Scale Power System. *Electronics*. 2021; 10(7):769.
https://doi.org/10.3390/electronics10070769

**Chicago/Turabian Style**

Kim, Dongmin, Jung-Wook Park, and Soo Hyoung Lee.
2021. "A Study on the Power Reserve of Distributed Generators Based on Power Sensitivity Analysis in a Large-Scale Power System" *Electronics* 10, no. 7: 769.
https://doi.org/10.3390/electronics10070769