# Appropriate Volt–Var Curve Settings for PV Inverters Based on Distribution Network Characteristics Using Match Rate of Operating Point

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background and Related Works

#### 1.2. Motivation and Contribution

#### 1.3. Outline

## 2. Specifications in Volt–Var Curve for PV Inverter

#### 2.1. Volt–Var Characterictic

_{ref}, dead zone, slope, and maximum reactive power Q

_{max}. Because a large number of PV inverters are interconnected in a distribution feeder, it is necessary to individually determine the optimal volt–var curve for each inverter to obtain the ultimate optimization of supply voltage and distribution power loss. However, setting up an optimal volt–var curve for every inverter is difficult from the technical aspects of obtaining all the necessary voltages and impedances, as well as the huge amount of work involved. Therefore, from the realistic workload of distribution-system operation and planning, the volt–var curves of all the PV inverters installed in a distribution feeder were assumed to be the same, and the effects of the four parameters shown in Figure 1 on the voltage control and distribution line losses of the distribution system were investigated.

#### 2.2. Capacity Restriction of Inverter

#### 2.3. Calculation of Operating Point on Volt–Var Curve

_{INV}

^{(n − 1)}is applied to the (n − 1) th calculation and the voltage V

_{INV}

^{(n − 1)}is obtained. From the volt–var curve, the reactive power of next time step is represented by Q

_{INV}(V

_{INV}

^{(n − 1)}). However, if the difference between Q

_{INV}

^{(n − 1)}and Q

_{INV}(V

_{INV}

^{(n − 1)}) is large, the voltage at the next time step varies considerably; thus, the voltage convergence may be poor. Therefore, the volt–var curve in the (n − 1)th calculation is proportionally divided by a factor α. The reactive power applied to the n th calculation is expressed by the following equation.

## 3. Dependence of Effect of Volt–Var Curve on Distribution System Configuration

#### 3.1. Residential Area 1

#### 3.1.1. Simulation Model

#### 3.1.2. Simulation Results

_{ref}, deadband, and slope are set to 202 V, 12 V, and 6 V, respectively, which are the parameters that determine the volt–var curve. Volt–var control improves the voltage deviation during the daytime, and the voltage is controlled within the proper range. The time variation of the reactive-power output of each PV inverter is shown in Figure 8. The time variation of the reactive power output is the result of following the volt–var curve and the capacity constraint of the inverter.

#### 3.1.3. Control Characteristics

_{ref}and the dead band are small, reactive power output is required by the volt–var curve even if the voltage at PV inverter is not high enough to violate the voltage constraint. However, owing to the power factor constraint of the inverter, it may not be possible to output the commanded reactive power according to the volt–var curve. As a result, the match rate is reduced as shown in Table 2. The 360 patterns of volt–var curves can be narrowed down to 128 patterns if we select those with a match rate of 99% or higher.

#### 3.2. Rural Area 1

#### 3.2.1. Simulation Model

#### 3.2.2. Control Characteristics

#### 3.3. Dependence on PV Capacity and Line Length

## 4. Selection of Volt–Var Curve

## 5. Discussion

_{ref}, dead zone, and slope, and cover almost all the volt–var curves that may be applied in practice. As another solution, the volt–var curve can be determined by solving the volt–var curve optimization problem [24,25,26,27], which is one of state-of-the-art counterparts to determine the volt–var curve. However, the solution obtained should be equal to or very close to one of the 360 patterns. As shown in Table 5, all of the 23 selected volt–var curves can provide excellent effects on the distribution system.

## 6. Conclusions

- From the simulation results for the 360 patterns of the volt–var curve, the reactive-power-output accumulation of the PV inverters, distribution loss, and the number of tap operations of LRT are plotted in a three-dimensional graph, and the response of the volt–var curve can be characterized visually.
- The three-dimensional graph indicates that as the lagged reactive power accumulation increases, the distribution line loss also increases; however, the increase or decrease in the number of tap operations depends on the characteristics of the distribution line.
- Owing to the power factor constraint of the inverter, it is not possible to output the commanded reactive power according to the volt–var curve. By calculating the match rate to evaluate this, we can narrow down the volt–var curve that can effectively utilize the reactive power of the PV inverter for voltage control.
- Furthermore, by selecting the volt–var curve that can control the voltage within the appropriate range, we were able to narrow down the 360 patterns of volt–var curves to 23 patterns. When the volt–var curve that minimizes the reactive power output is selected and compared with the standard volt–var curve of the Hawaii Power Company, it was found that the volt–var curve selected using the proposed method is superior to that of the Hawaii Power Company from the viewpoint of distribution loss, voltage violation, and match rate.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 4.**Distribution-network model (residential area 1): (

**a**) medium-voltage distribution network; (

**b**) low-voltage distribution network.

**Figure 7.**Time variation in voltage of low-voltage customers with volt–var control (V

_{ref}= 202 [V], dead band = 12 [V], and slope = 6 [V]).

**Figure 8.**Time variation in reactive power of PV inverters with volt–var control (V

_{ref}= 202 [V], dead band = 12 [V], and slope = 6 [V]).

**Figure 9.**Time variation in LRT tap with volt–var control (V

_{ref}= 202 [V], dead band = 12 [V], and slope = 6 [V]).

**Figure 10.**Time variation in power loss of distribution network with volt–var control (V

_{ref}= 202 [V], dead band = 12 [V], and slope = 6 [V]).

**Figure 12.**Relationship between cumulative reactive power, network loss, and the number of LRT tap operations when 360 patterns of volt–var curves are applied to the distribution system model (residential area 1).

**Figure 14.**Relationship between cumulative reactive power, network loss, and the number of LRT tap operations when 360 patterns of volt–var curves are applied to distribution system model (rural area 1).

**Figure 15.**Relationship between the number of volt–var curves satisfying all the conditions listed in Table 4 and the installed PV capacity.

**Figure 16.**Candidates of volt–var curve by taking the logical product of the extracted volt–var curves for each distribution system model.

**Figure 17.**Selected volt–var curve that the reactive power output is the minimum necessary to minimize the distribution losses. The standard volt–var curve in the grid interconnection rules of the Hawaii Power company is also shown.

Parameter | List of Values |
---|---|

Center voltage V_{ref} [V] | 202, 204, 206, 208, 210, 212, 214, 216, 218 |

deadband [V] | 0, 4, 8, 12, 16, 20, 24, 28 |

slope [V] | 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 |

Maximum reactive power Q_{max} [%] | 53 (Value dependent on power factor constraint) |

V_{ref}(V) | Slope (V) | Dead Band (V) | |||||||
---|---|---|---|---|---|---|---|---|---|

0 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | ||

202 | 2 | 26.0 | 27.7 | 43.4 | 59.2 | 71.2 | 82.9 | 88.6 | 100.0 |

4 | 26.1 | 33.7 | 50.2 | 70.5 | 96.3 | 100.0 | 100.0 | 100.0 | |

6 | 29.1 | 40.1 | 61.2 | 83.8 | 97.2 | 100.0 | 100.0 | 100.0 | |

8 | 33.5 | 51.7 | 73.1 | 87.3 | 97.5 | 100.0 | 100.0 | 100.0 | |

10 | 43.3 | 64.2 | 77.5 | 88.5 | 97.7 | 100.0 | 100.0 | 100.0 | |

204 | 2 | 27.0 | 43.4 | 59.2 | 71.2 | 82.9 | 88.6 | 100.0 | 100.0 |

4 | 33.0 | 50.2 | 70.5 | 96.3 | 100.0 | 100.0 | 100.0 | 100.0 | |

6 | 39.8 | 61.2 | 83.8 | 97.2 | 100.0 | 100.0 | 100.0 | 100.0 | |

8 | 51.4 | 73.1 | 87.3 | 97.5 | 100.0 | 100.0 | 100.0 | 100.0 | |

10 | 63.9 | 77.5 | 88.5 | 97.7 | 100.0 | 100.0 | 100.0 | 100.0 | |

206 | 2 | 38.4 | 58.7 | 70.9 | 82.9 | 88.6 | 100.0 | 100.0 | 100.0 |

4 | 46.0 | 70.1 | 96.1 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | |

6 | 57.7 | 83.4 | 97.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | |

8 | 70.0 | 86.8 | 97.3 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | |

10 | 74.8 | 88.1 | 97.6 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | |

208 | 2 | 47.4 | 66.2 | 81.5 | 88.2 | 100.0 | 100.0 | 100.0 | 100.0 |

4 | 59.6 | 91.8 | 98.7 | 99.7 | 100.0 | 100.0 | 100.0 | 100.0 | |

6 | 73.6 | 93.1 | 98.7 | 99.7 | 100.0 | 100.0 | 100.0 | 100.0 | |

8 | 77.0 | 93.7 | 98.7 | 99.8 | 100.0 | 100.0 | 100.0 | 100.0 | |

10 | 79.9 | 94.1 | 98.8 | 99.8 | 100.0 | 100.0 | 100.0 | 100.0 | |

210 | 2 | 47.4 | 67.6 | 83.4 | 98.6 | 99.6 | 100.0 | 100.0 | 100.0 |

4 | 73.3 | 86.4 | 95.5 | 98.7 | 99.7 | 100.0 | 100.0 | 100.0 | |

6 | 75.1 | 88.1 | 95.8 | 98.7 | 99.7 | 100.0 | 100.0 | 100.0 | |

8 | 76.5 | 88.9 | 96.2 | 98.7 | 99.8 | 100.0 | 100.0 | 100.0 | |

10 | 77.3 | 90.3 | 96.3 | 98.8 | 99.8 | 100.0 | 100.0 | 100.0 | |

212 | 2 | 39.5 | 57.0 | 83.5 | 94.9 | 98.6 | 99.6 | 100.0 | 100.0 |

4 | 63.3 | 74.9 | 85.4 | 95.5 | 98.7 | 99.7 | 100.0 | 100.0 | |

6 | 65.7 | 76.6 | 88.1 | 95.8 | 98.7 | 99.7 | 100.0 | 100.0 | |

8 | 67.7 | 77.9 | 88.9 | 96.2 | 98.7 | 99.8 | 100.0 | 100.0 | |

10 | 68.8 | 79.4 | 90.3 | 96.3 | 98.8 | 99.8 | 100.0 | 100.0 | |

214 | 2 | 42.5 | 57.9 | 68.5 | 82.8 | 94.9 | 98.6 | 99.6 | 100.0 |

4 | 52.3 | 60.9 | 73.5 | 85.1 | 95.5 | 98.7 | 99.7 | 100.0 | |

6 | 57.5 | 63.4 | 76.2 | 88.1 | 95.8 | 98.7 | 99.7 | 100.0 | |

8 | 59.4 | 65.8 | 77.9 | 88.9 | 96.2 | 98.7 | 99.8 | 100.0 | |

10 | 61.4 | 67.8 | 79.4 | 90.3 | 96.3 | 98.8 | 99.8 | 100.0 | |

216 | 2 | 44.7 | 48.9 | 57.4 | 68.0 | 82.4 | 94.9 | 98.6 | 99.6 |

4 | 47.6 | 51.2 | 60.2 | 72.9 | 84.8 | 95.5 | 98.7 | 99.7 | |

6 | 49.7 | 56.4 | 62.7 | 76.0 | 88.1 | 95.8 | 98.7 | 99.7 | |

8 | 52.3 | 58.8 | 65.5 | 77.9 | 88.9 | 96.2 | 98.7 | 99.8 | |

10 | 55.6 | 60.8 | 67.8 | 79.4 | 90.3 | 96.3 | 98.8 | 99.8 | |

218 | 2 | 38.9 | 44.3 | 48.3 | 57.4 | 68.0 | 82.4 | 94.9 | 98.6 |

4 | 43.3 | 47.2 | 51.0 | 60.2 | 72.9 | 84.8 | 95.5 | 98.7 | |

6 | 46.4 | 49.3 | 56.2 | 62.7 | 76.0 | 88.1 | 95.8 | 98.7 | |

8 | 48.5 | 52.2 | 58.8 | 65.5 | 77.9 | 88.9 | 96.2 | 98.7 | |

10 | 50.6 | 55.6 | 60.8 | 67.8 | 79.4 | 90.3 | 96.3 | 98.8 |

Model | PV Capacity (MW) | Main Line Length (km) |
---|---|---|

Residential area 1 | 6.3 | 4.2 |

Rural area 1 | 9.5 | 4.4 |

Rural area 2 | 5.5 | 7.5 |

Industrial area 1 | 4.5 | 3.6 |

Industrial area 2 | 6.8 | 4.7 |

Parameter | Evaluation Condition |
---|---|

Voltage of low-voltage customer V (pu) | 0.9 ≤ V≤ 1.1 |

Match rate P_{M} (%) | 99 ≤ P_{M} |

LRT tap operation N per day | N ≤ 15 |

V_{ref}(V) | Deadband (V) | Slope (V) | Line Loss (kWh) | Curtailment (kWh) | Match Rate(%) | Voltage Violation (kV^{2}s) | LRT Tap Operation |
---|---|---|---|---|---|---|---|

202 | 28 | 4 | 2620 | 122 | 99.9 | 0 | 5.2 |

202 | 28 | 6 | 2582 | 58 | 99.9 | 0 | 5.6 |

202 | 28 | 8 | 2570 | 39 | 99.9 | 0 | 5.6 |

204 | 24 | 4 | 2620 | 122 | 99.9 | 0 | 5.2 |

204 | 24 | 6 | 2582 | 58 | 99.9 | 0 | 5.6 |

204 | 24 | 8 | 2570 | 39 | 99.9 | 0 | 5.6 |

204 | 28 | 2 | 2546 | 74 | 100.0 | 0 | 6.4 |

204 | 28 | 4 | 2537 | 40 | 100.0 | 0 | 6.4 |

206 | 20 | 4 | 2620 | 122 | 99.9 | 0 | 5.2 |

206 | 20 | 6 | 2582 | 58 | 99.9 | 0 | 5.6 |

206 | 20 | 8 | 2570 | 39 | 99.9 | 0 | 5.6 |

206 | 24 | 2 | 2546 | 74 | 100.0 | 0 | 6.4 |

206 | 24 | 4 | 2537 | 40 | 100.0 | 0 | 6.4 |

206 | 28 | 2 | 2521 | 25 | 100.0 | 0 | 7.6 |

208 | 16 | 4 | 2620 | 122 | 99.9 | 0 | 5.2 |

208 | 16 | 6 | 2582 | 58 | 99.9 | 0 | 5.6 |

208 | 16 | 8 | 2570 | 39 | 99.9 | 0 | 5.6 |

208 | 20 | 2 | 2546 | 74 | 100.0 | 0 | 6.4 |

208 | 20 | 4 | 2537 | 40 | 100.0 | 0 | 6.4 |

208 | 24 | 2 | 2521 | 25 | 100.0 | 0 | 7.6 |

210 | 16 | 2 | 2546 | 74 | 99.9 | 0 | 6.4 |

210 | 16 | 4 | 2537 | 40 | 99.9 | 0 | 6.4 |

210 | 20 | 2 | 2521 | 25 | 100.0 | 0 | 7.6 |

**Table 6.**Comparison of the effect of volt–var curves: (a) volt–var curve of the Hawaii power company; (b) volt–var curve, shown in Figure 17, proposed in this study.

Volt-Var Curve | Model | Line Loss (kWh) | Curtailment (kWh) | Match Rate (%) | Voltage Violation (kV^{2}s) | LRT Tap Operation |
---|---|---|---|---|---|---|

(a) | Residential area 1 | 4482 | 1801 | 61.2 | 0 | 3 |

Rural area 1 | 5505 | 3867 | 26.0 | 0 | 9 | |

Rural area 2 | 3038 | 1560 | 50.9 | 0 | 6 | |

Industrial area 1 | 1998 | 1722 | 34.3 | 5.9 | 8 | |

Industrial area 2 | 3448 | 2321 | 45.1 | 0 | 10 | |

(b) | Residential area 1 | 2906 | 12 | 100 | 0 | 13 |

Rural area 1 | 3875 | 113 | 99.7 | 0 | 5 | |

Rural area 2 | 2400 | 59 | 100 | 0 | 4 | |

Industrial area 1 | 1278 | 0 | 100 | 0 | 4 | |

Industrial area 2 | 2392 | 11 | 100 | 0 | 2 |

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**MDPI and ACS Style**

Iioka, D.; Kusano, K.; Matsuura, T.; Hamada, H.; Miyazaki, T.
Appropriate Volt–Var Curve Settings for PV Inverters Based on Distribution Network Characteristics Using Match Rate of Operating Point. *Energies* **2022**, *15*, 1375.
https://doi.org/10.3390/en15041375

**AMA Style**

Iioka D, Kusano K, Matsuura T, Hamada H, Miyazaki T.
Appropriate Volt–Var Curve Settings for PV Inverters Based on Distribution Network Characteristics Using Match Rate of Operating Point. *Energies*. 2022; 15(4):1375.
https://doi.org/10.3390/en15041375

**Chicago/Turabian Style**

Iioka, Daisuke, Kenichi Kusano, Takahiro Matsuura, Hiromu Hamada, and Teru Miyazaki.
2022. "Appropriate Volt–Var Curve Settings for PV Inverters Based on Distribution Network Characteristics Using Match Rate of Operating Point" *Energies* 15, no. 4: 1375.
https://doi.org/10.3390/en15041375