# Quantification and Mitigation of Unfairness in Active Power Curtailment of Rooftop Photovoltaic Systems Using Sensitivity Based Coordinated Control

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Problem Formulation

_{1}and u

_{2}are source and line end voltage, respectively, and Φ is the phase angle between the two voltages.

_{cri}inverter output follows maximum power point tracking (mppt). The active power is curtailed linearly once the voltage at the bus exceeds the critical voltage. If the voltage at PCC exceeds the upper voltage limit u

_{thr}the active power output of the inverter is reduced to the minimum permissible value P

_{min}.

#### Voltage Sensitivity Estimation

^{cal}is greater than a critical value P

^{cri}, the inverter set point is switched to zero temporarily. The change in voltage is then recorded and du/dp is estimated using finite difference. The process is repeated to and the results are filtered to minimize estimation errors. For this work, P

^{cri}has been set to 70% of the rated power. P

^{cri}is intentionally set high so that a significant change in the voltage can be recorded and the impact of other inverters and the load present in the system can be neglected. The main thought process behind estimation of voltage sensitivity is to provide a truly plug-and-play solution for voltage control. Figure 1 presents a graphical overview of the PV inverter.

## 3. Formulation of Key Performance Indices

#### 3.1. Total Curtailed Energy

#### 3.2. Unfairness in Active Power Curtailment

## 4. Proposed Algorithm

^{lb}, no energy is curtailed. In distressed mode, the controller generates set points for every inverter. This section details the working of the proposed controller.

#### 4.1. Calculation of Sensitivity Matrix

_{ij}is the minimum electrical distance from the transformer to the ith node. In case i ≠ j, L

_{ij}is the maximum overlap of the paths formed from the transformer to the ith and jth node. r

_{ij}is the average resistance per kilometer of the branches belonging to L

_{ij}. For i > j or j > i, if overlapping path length is much greater than non-overlapping path lengths the off-diagonal elements of the sensitivity matrix can be approximated as the diagonal elements of the matrix.

#### 4.2. Active Power Reduction Calculation

_{ij}and the rated powers ${P}_{i}^{\mathrm{rated}}$.

#### 4.2.1. Equal Loss of Revenue for Each Photovoltaic Owner

#### 4.2.2. Equal Percentage Reduction in Revenue

^{max}is k × l matrix. In the final step, S function is used to reduce excessive curtailment.

## 5. Test Case and Simulation Setup

#### 5.1. Network Model

#### 5.2. PowerFactory Python Interfacing

^{++}library. A C

^{++}library has been used to implement sockets to communicate with Python. In this work, socket based communication approach has been preferred as it can easily be extended to incorporate a network simulator such as OMNET

^{++}to study the impact of communication on voltage control for future work. Figure 4 is a graphical illustration of coupling scheme used.

## 6. Results and Discussion

#### 6.1. Local Voltage Regulation

_{min}) is 50% of the rated power. The critical (u

^{cri}) and threshold voltages (u

^{thr}) have been set at 1.02 p.u. and 1.05 p.u. respectively for every inverter on the residential feeder. Voltage profiles for the inverters are presented in Figure 8a.

#### 6.2. Coordinated Voltage Regulation

^{ub}and lower u

^{lb}limits of the voltage regulation band for the coordinating controller have been set at 1.02 and 1.05, respectively.

#### 6.2.1. Equal Loss of Revenue for Each Photovoltaic Owner

^{cri}in p.u. and the reduction in active power ΔP in kW. Figure 9a shows the plot of the critical voltages calculated for each PV inverter. u

^{cri}is calculated only when u

^{max}is greater than u

^{lb}, otherwise, u

^{cri}is set to 1.05 which means no APC. Figure 9b is the plot for maximum expected over voltage (∆u). It is import to note that even though u

^{max}is greater than u

^{lb}between the time 2 a.m. and 7 a.m., maximum expected voltage rise is ∆u which is less than zero for the duration, hence no power is curtailed during the above mentioned period.

^{max}), maximum voltage in the network (u

^{max}) and the upper and lower voltage limits. Figure 10 shows the impact of the S function used in Equations (24) and (25) on APC. As u

^{max}approaches u

^{ub}, ∆P approaches ∆P

^{max}. This improves efficiency by minimizing unnecessary APC. It is important to note that variable A in Equation (25) can be used to adjust the slope of the S function. In this study, the value of A is 5 for all the experiments. The value of ∆P calculated by CC1 is the same for all PV inverters which ensures equal curtailment for every PV system. The use of S function reduces curtailment set point for PV installed at Res01 and reduces E

^{cur}from 221 kWh (theoretical maximum) to 148 kWh a reduction of 32.6% (the grey shaded region in Figure 10).

#### 6.2.2. Equal Percentage Reduction in Revenue

^{cri}in p.u. and the reduction in active power $\Delta P$ in kW. In this case however, ∆P is matrix and the set point for each inverter is a function of its rated power. Figure 12a shows critical voltages calculated for each PV inverter. Figure 12b shows maximum reduction in active power calculated for each inverter to ensure voltage remains within bounds.

## 7. Conclusions

## Author Contributions

## Conflicts of Interest

## Abbreviations

MV/HV/LV | Medium voltage/high voltage/low voltage |

PV | Photovoltaic |

DG | Distributed generator |

PCC | Point of common coupling |

OLTC | On-load tap changer |

D-STATCOM | Distribution static synchronous compensator |

RPC | Reactive power compensation |

APC | Active power curtailment |

LVN | Low voltage network |

DSO | Distribution system operator |

KPI | Key performance indices |

DSL | DigSILENT simulation language |

CCx | Coordinating controller x |

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**Figure 5.**(

**a**) PV-Res03 inverter output; (

**b**) voltage at point of common coupling (PCC); and (

**c**) du/dp estimation results.

**Figure 8.**(

**a**) Voltage profiles at PCC of each inverter with local voltage controller; and (

**b**) curtailed power from each inverter.

**Figure 11.**(

**a**) Voltage profiles at PCC of each inverter with CC1; and (

**b**) curtailed energy from each inverter.

**Figure 12.**(

**a**) Critical voltages calculated for each PV and (

**b**) maximum curtailment for each inverter.

**Figure 14.**(

**a**) Voltage profiles at PCC of each inverter with CC2 and (

**b**) curtailed energy from each inverter.

Type | Inverter ID | Rating-KVA |
---|---|---|

PV | PV-Res01 | 45 |

PV | PV-Res02 | 33 |

PV | PV-Res03 | 27 |

PV | PV-Res04 | 41 |

PV | PV-Res05 | 50 |

**Table 2.**Calculated key performance indices (KPI) for the implemented control schemes. CUI: curtailment unfairness index.

KPI | Local | CC1 | CC2 |
---|---|---|---|

TEC-kWh | 610.15 | 752.42 | 712.88 |

CUI1-kWh | 77.99 | 11.24 | 33.58 |

CUI2-h | 1.49 | 1.27 | 0.001 |

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**MDPI and ACS Style**

Latif, A.; Gawlik, W.; Palensky, P. Quantification and Mitigation of Unfairness in Active Power Curtailment of Rooftop Photovoltaic Systems Using Sensitivity Based Coordinated Control. *Energies* **2016**, *9*, 436.
https://doi.org/10.3390/en9060436

**AMA Style**

Latif A, Gawlik W, Palensky P. Quantification and Mitigation of Unfairness in Active Power Curtailment of Rooftop Photovoltaic Systems Using Sensitivity Based Coordinated Control. *Energies*. 2016; 9(6):436.
https://doi.org/10.3390/en9060436

**Chicago/Turabian Style**

Latif, Aadil, Wolfgang Gawlik, and Peter Palensky. 2016. "Quantification and Mitigation of Unfairness in Active Power Curtailment of Rooftop Photovoltaic Systems Using Sensitivity Based Coordinated Control" *Energies* 9, no. 6: 436.
https://doi.org/10.3390/en9060436