# An Effective Bi-Stage Method for Renewable Energy Sources Integration into Unbalanced Distribution Systems Considering Uncertainty

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## Abstract

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## 1. Introduction

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- The impact of the RES (PV and wind) penetration levels on distribution systems are studied;
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- A bi-stage procedure is proposed to improve the system performance and reduce the system voltage fluctuation due to RES;
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- The proposed method aims to determine the optimal placement and sizing of RES and the optimal setting of the system voltage control devices in order to maximize the benefits of the RES penetration and minimize the variation in the system voltage;
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- The MO-CSO algorithm is combined with an unbalanced power flow method in order to analyze the system and solve the optimal placement and sizing problem.

## 2. Voltage Control Devices

#### 2.1. Static VAR Compensator (SVC)

#### 2.2. Transformer Tap Changer (TTC)

#### 2.3. Distribution Voltage Regulators (DVRs)

## 3. Cat Swarm Optimization (CSO) Algorithm

## 4. Impact of RES Penetration Level on Voltage Profile

#### 4.1. RES Uncertainty Representation

#### 4.2. Influence of RES Penetration on System Voltage

- RES penetration in the distribution system causes voltage variation in the system buses due to the uncertainty operation of RES;
- Voltage variation does not only depend on the RES penetration level, but also the placement of DG units may have a significant effect on the voltage variation percentage.

## 5. The Proposed Bi-Stage Method

#### 5.1. Method Description

#### 5.2. Application of Proposed Two-Stage Method to IEEE 34-Bus Distribution System

#### 5.2.1. First Stage

#### 5.2.2. Second Stage

## 6. Simulation Results and Discussion

#### 6.1. First Stage Results

#### 6.2. Second Stage Results

## 7. Conclusions

- RES uncertainty causes voltage variation to the distribution system voltage profile and makes the voltage profile exceed the limits;
- Voltage variation depends not only on the RES penetration level but also on the placement of DG units;
- The paper proposed a bi-stage method based on the CSO algorithm for minimizing voltage variation and power loss, and improves the system voltage profile considering the uncertainty of RES units;
- The first stage was concerned with the placement and sizing of RES units. It succeeded in reducing the power loss by 15.9% and minimizing the voltage fluctuation index to be 0.0437;
- In the second stage, the voltage control devices including voltage regulators and SVC were adjusted by the optimization technique for improving the voltage profile. It succeeded in reducing the voltage profile index to be 1.6663, with a 94.2% reduction from the first stage, while the improvements achieved in the first stage were maintained;
- The proposed RES integration method was tested on unbalanced IEEE 34-bus radial system networks under uncertainty conditions, which provided satisfactory results for increasing the RES penetration level.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CVV | Control variable value |

D-FACTS | Distributed flexible AC transmission system |

DG | Distributed generation |

SVC | Static VAR compensator |

WT | Wind turbine |

PV | Photovoltaic |

FF | Fitness function |

OF | Objective function |

r | Random number between 0 and 1 |

v_{new} | New cat speed |

v_{old} | Old cat speed |

VF | Voltage variation between the highest and lowest voltage profiles |

w | Weighting factor |

PG | Generated power |

P_{D} | Demand load power |

P_{loss} | Power loss |

${P}_{i}^{in}$ | Input active power of section i |

${P}_{i}^{out}$ | Output active power of section i |

S_{load} | Total demand load |

n_{pop} | Number of populations |

n_{bus} | Number of buses |

VR | Voltage regulator device |

V_{highi} | Highest voltage at bus i |

V_{lowi} | Lowest voltage at bus i |

ΔV | Voltage difference between highest and lowest voltage profiles |

VR_{TAP} | Voltage regulator taps setting. |

Q_{svc} | SVC reactive power. |

G | Solar insolation (kW/m^{2}) |

G_{std} | Standard solar insolation (1 kW/m^{2}) |

G_{C} | Certain irradiance point (0.12 kW/m^{2}) |

P_{rated} | Rated power |

V_{W} | Wind speed(m/s) |

V_{r} | Rated wind speed |

V_{ci} | Cut-in wind speed |

V_{co} | Cut-out wind speed |

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Penetration Level | Case 1 (25%) | Case 2 (50%) | Case 3 (75%) |
---|---|---|---|

Output power from each unit | 147.485 kW | 294.970 kW | 442.467 kW |

Penetration Level | Cases | First RES Bus | Second RES Bus | Third RES Bus |
---|---|---|---|---|

0% | Case 0 | No output from any RES | ||

75% | Case 1 | 4 | 20 | 27 |

Case 2 | 9 | 23 | 31 | |

Case 3 | 2 | 3 | 4 | |

Case 4 | 25 | 30 | 31 |

Bus Number | 3 | 27 | 20 | 2 |
---|---|---|---|---|

DG Generation at Best Condition (kW) | 176.09 | 83.43 | 94.98 | 962.09 |

Device | Adjustment |
---|---|

Substation transformer | 1.023 p.u. |

VR1 tap | 9 |

VR2 tap | 14 |

SVC bus | 21 |

QSVC | 200 KVar |

Stage | First Stage | Second Stage |
---|---|---|

P_{loss} of the lowest voltage profile (kW) | 285.47 | 296.11 |

P_{loss} of the highest voltage profile (kW) | 239.93 | 246.93 |

voltage fluctuation index (OF1) | 0.0437 | 0.0481 |

voltage profile index (FF) | 28.7646 | 1.6663 |

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**MDPI and ACS Style**

Ali, E.S.; El-Sehiemy, R.A.; Abou El-Ela, A.A.; Mahmoud, K.; Lehtonen, M.; Darwish, M.M.F.
An Effective Bi-Stage Method for Renewable Energy Sources Integration into Unbalanced Distribution Systems Considering Uncertainty. *Processes* **2021**, *9*, 471.
https://doi.org/10.3390/pr9030471

**AMA Style**

Ali ES, El-Sehiemy RA, Abou El-Ela AA, Mahmoud K, Lehtonen M, Darwish MMF.
An Effective Bi-Stage Method for Renewable Energy Sources Integration into Unbalanced Distribution Systems Considering Uncertainty. *Processes*. 2021; 9(3):471.
https://doi.org/10.3390/pr9030471

**Chicago/Turabian Style**

Ali, Eman S., Ragab A. El-Sehiemy, Adel A. Abou El-Ela, Karar Mahmoud, Matti Lehtonen, and Mohamed M. F. Darwish.
2021. "An Effective Bi-Stage Method for Renewable Energy Sources Integration into Unbalanced Distribution Systems Considering Uncertainty" *Processes* 9, no. 3: 471.
https://doi.org/10.3390/pr9030471