# Optimal Operation Method for Distribution Systems Considering Distributed Generators Imparted with Reactive Power Incentive

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## Abstract

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## Featured Application

**The incentive method with flexible contribution functions can be applied to demand response by the reactive power market and distribution company, which has the possibility to reduce the additional installation of distribution control equipment and battery capacity. It also leads to the reduction of total electricity purchase cost of consumers, and the power system can achieve high mixing of renewable energy in the grid with the reactive power incentive demand response and the IoT development. Furthermore, reliability assessment of cooperative control with the participation rate will give an important contribution to the robust design of the system.**

## Abstract

## 1. Introduction

- Technical issues related to high penetration of RES (voltage deviation and reverse power flow)
- Cost increase due to increased controllers and storage battery for voltage control and surplus power absorption.
- Issues for the DR program; increase in dissatisfaction with small demand response due to price change and compulsory DR.

#### Contributions and Structure of This Paper

^{®}simulations. Not only does this paper provide a detailed technical assessment, but it also shows the economic benefits of both of the DisCo and customers. In addition, optimal operation is calculated by using the particle swarm optimization (PSO) algorithm, and the solution is provided as optimal one-day scheduling. In order to avoid over-control, a modified scheduling method is proposed in this paper.

## 2. Demand Response

#### 2.1. Price Elasticity

#### 2.2. Reactive Power Market

## 3. Modeling and Formulation for the Optimization Problem

#### 3.1. Objective Function and Constraints for Optimal Scheduling

**Objective function:**

#### 3.2. Constraints

**Robust voltage range for PV installation:**

**Power flow constraints regarding reverse power flow and the power factor:**

**BESS configuration and operation:**

## 4. Reactive Power Incentive Method

#### 4.1. Calculation of Reactive Power Incentive Unit Price

#### 4.2. Contribution Factor

#### 4.3. Profit Obtained by Customers

## 5. Optimization Algorithm

#### 5.1. Particle Swarm Optimization

**Step****1:**- Generate an initial searching point for each swarm.
**Step****2:**- Evaluate the objective function using each swarm’s searching point.
**Step****3:**- Finish searching if stopping conditions are satisfied. If not, go to Step 4.
**Step****4:**- Search the next point considering the best of the current swarm’s searching point and every swarm’s best searching point. Go to Step 2.

${V}_{k+1}\left(i\right)$: | i-th particle velocity in the ($k+1$)-th search |

$ran{d}_{1}$: | uniform random numbers from 0–1 |

${S}_{k+1}$: | search position of the i-th particle in the k-th search |

w: | weighting of inertia |

${c}_{1}$: | weighting for the best position of the self-particle |

${c}_{2}$: | weighting for the best position of the particle swarm |

$pbest$: | best position of the self-particle |

$gbest$: | best position of the particle swarm. |

#### 5.2. Modified Particle Swarm Optimization for Scheduling

## 6. Simulation Results

#### 6.1. Optimal Scheduling for Voltage Control

- Case 1: Without optimization impact evaluation for massive penetration of RESs.
- Case 2: Conventional control method by DisCo; the distribution system consists of BESS, OLTCs (LRT, three SVRs), SVCs at each node, DGs (PV and its interfaced inverters) and loads.
- Case 3: Coordinated operation under the DR program; DisCo verifies the maximum amount of control equipment reduction.
- Case 4: Although this case concludes the coordinated operation of the DR program, unlike Case 3, distribution loss reduction is the main point of view.

#### 6.2. Economic Assessment with the DR Program

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Objective function and constraints: | |

${F}_{com}$ | Objective function for the conventional problem |

${F}_{inc}$ | Objective function for the proposed incentive method |

${N}_{node}$ | Node number of the distribution system |

${P}_{f}$ | Active power flow at the interconnection point |

${P}_{f}^{min},{P}_{f}^{max}$ | Lower and upper limit of active power flow at the interconnection point |

${P}_{Loss,i}$ | Active power loss of node i |

${Q}_{f}$ | Reactive power flow at the interconnection point |

${Q}_{f}^{min},{Q}_{f}^{max}$ | Lower and upper limit of reactive power flow at the interconnection point |

t | Time step at optimization |

${T}_{k}$ | Tap positions of LRT and SVR |

${T}_{k}^{min},{T}_{k}^{max}$ | Lower and upper tap limit of LRT and SVRs |

${V}_{min},{V}_{max}$ | Minimum and maximum voltage constraints |

${V}_{m}$ | Node voltage at node m |

BESS: | |

$\eta $ | Charging and discharging efficiency of large BESS |

${\zeta}_{LB}$ | State of charge of large BESS |

${C}_{LB}$ | Capacity of large BESS |

${P}_{LBinv}$ | Active power output of BESS from DisCo |

${P}_{LBinv}$ | Active power output of large BESS |

${P}_{LBinv}^{min},{P}_{LBinv}^{max}$ | Lower and upper limit of active power of a large BESS inverter |

${Q}_{LBinv}$ | Reactive power output of large BESS |

${Q}_{LBinv}^{min},{Q}_{LBinv}^{max}$ | Lower and upper limit of reactive power output of a large BESS inverter |

${S}_{LBinv}$ | Inverter capacity of large BESS |

Photovoltaic system: | |

${P}_{PVinv}$ | Active power output from the PV generator system |

${P}_{PV}$ | Active power output from the PV panel |

${Q}_{PVinv}$ | Reactive power output of inverters interfaced with PV |

${Q}_{PVinv}^{\ast}$ | Order value of reactive power |

${Q}_{PVinv}^{min},{Q}_{PVinv}^{max}$ | Lower and upper limit of the PV inverter regarding reactive power output |

${S}_{PVinv}$ | Inverter capacity of the PV inverter |

Reactive power incentive | |

$\kappa $ | Contribution factor of reactive power |

${\kappa}_{lin}$ | Linear contribution function |

${\kappa}_{sig}$ | Sigmoid contribution function |

${A}_{lin}$ | Slope of the linear contribution function |

${A}_{sig}$ | Coefficient value for the sigmoid contribution function |

${C}_{Q}$ | Total cost regarding voltage regulation devices |

${C}_{SVC}$ | Introduction cost of SVC |

${C}_{SVR}$ | Introduction cost of SVR |

${N}_{SVR}$ | Total number of SVR |

${P}_{base}$ | Rated power in the distribution system |

${Q}_{PV}^{\prime}$ | Contribution of the customer for DisCo with reactive power output |

v | Customer profit of the reactive power incentive |

${v}_{q}$ | Reactive power incentive unit price |

${Y}_{D,SVC}$ | Depreciation term of SVC |

$\pi $ | Price elasticity of demand |

$\pi (i,j)$ | Price elasticity at time i corresponding to j |

D | Load demand |

${p}_{l}$ | Price of goods |

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**Figure 1.**DR menu and its behavior. (

**a**) Several DR menus regarding pricing based and others [35] and (

**b**) an example of net load demand behavior under the DR program.

**Figure 2.**Distribution system model. LRT, load ratio transformer; SVR, step voltage regulator; SVC, static VAR compensator.

**Figure 3.**Active and reactive power control system. (

**a**) Interfaced inverter of the PV system and (

**b**) inverter of BESS at the interconnection point.

**Figure 5.**Sigmoid contribution factor of reactive power incentive. (

**a**) Sigmoid contribution function for hourly powerand each node and (

**b**) contribution region of the sigmoid and linear function.

**Figure 8.**Simulation results without optimization (Case 1). (

**a**) Voltage profile without control, (

**b**) active power flow at the interconnection point and (

**c**) reactive power flow at the interconnection point.

**Figure 9.**Simulation results of the comparison method (Case 2). (

**a**) Voltage profile without control, (

**b**) active power flow at the interconnection point and (

**c**) reactive power flow at the interconnection point. (

**d**) Active power output of large BESS. (

**e**) Reactive power output of large BESS. (

**f**) SOC of large BESS. (

**g**) SVC output. (

**h**) Tap position of on-load tap changers (OLTCs) (LRT and SVRs). (

**i**) Distribution losses of each node over time.

**Figure 10.**Simulation results of the comparison method (Case 3). (

**a**) Voltage profile without control, (

**b**) active power flow at the interconnection point and (

**c**) reactive power flow at the interconnection point. (

**d**) Active power output of large BESS. (

**e**) Reactive power output of large BESS, (

**f**) SOC of large BESS. (

**g**) Reactive power compensation from the interfaced inverter of end-users. (

**h**) Tap position of OLTC (LRT). (

**i**) Distribution losses of each node over time.

**Figure 11.**Simulation results of proposed method (Case 4). (

**a**) Voltage profile without control, (

**b**) active power flow at the interconnection point and (

**c**) reactive power flow at the interconnection point. (

**d**) Active power output of large BESS. (

**e**) Reactive power output of large BESS. (

**f**) SOC of large BESS. (

**g**) Reactive power compensation from the interfaced inverter of the end users. (

**h**) Tap position of OLTCs (LRT and SVRs). (

**i**) Distribution losses of each node over time.

**Figure 13.**Profit of the customer from reactive power incentive (Case 3). (

**a**) Hourly profits of each node and (

**b**) end-of-day profit for customers at each node.

**Figure 14.**Profit of the customer from reactive power incentive (Case 4). (

**a**) Hourly profits of each node and (

**b**) end-of-day profit for customers at each node.

**Figure 15.**Profit comparison for the case study (Case 3 and 4) with the participation rate of customers.

**Figure 16.**A comparison of hourly profit with contribution functions (=${\kappa}_{sig}-{\kappa}_{lin}$) in the cooperative condition (participation rate is 100%).

Line impedance at each section | $0.04+\mathit{j}0.04$ pu |

Rated capacity of PV node | $0.08$ pu (400 kW) |

Rated capacity of PV-interfaced inverter ${S}_{PV}$ | $0.08$ pu (400 kW) |

Large BESS capacity ${C}_{LB}$ | 20.0 pu (100 MWh) |

Rated capacity of BESS-interfaced inverter ${S}_{LB}$ | 1.0 pu (5 MW) |

Rated Capacity of SVC ${S}_{SVC}$ | 0.05 pu (250 kVar) |

Variable | Cost (JPY) & Capacity (kVar) |
---|---|

${C}_{SVC}$ | 1.5 $\times {10}^{8}$ (JPY) |

${C}_{SVR}$ | 3.0 $\times {10}^{8}$ (JPY) |

${C}_{Q}$ | 3.15 $\times {10}^{9}$ (JPY) |

${S}_{SVC}$ | 250 (kVar) |

${\upsilon}_{q}$ | 4.8 or 3.4 (JPY/kVarh) |

Comparison Method | Proposed Method | Reduction Status | ||
---|---|---|---|---|

case 2 | case 3 | case 4 | case 3 | case 4 |

LRT | LRT | LRT | - | - |

(Substation) | (Substation) | (Substation) | ||

Three SVRs | - | Three SVRs | √ (three SVRs) | - |

(nodes 2–7,3–4,4–11) | (nodes 2–7,3–4,4–11) | |||

Fifteen SVCs | - | - | √ (fifteen SVCs) | √ (fifteen SVCs) |

(all nodes installed) | ||||

PV output | PV output | PV output | - | - |

(${P}_{PVinv}$) | (${P}_{PVinv},{Q}_{PVinv}$) | (${P}_{PVinv},{Q}_{PVinv}$) | ||

BESS | BESS | BESS | √ (capacity 7 pu) | √ (capacity 7 pu) |

(${P}_{LBinv},{Q}_{LBinv}$) | (${P}_{LBinv},{Q}_{LBinv}$) | (${P}_{LBinv},{Q}_{LBinv}$) | ||

BESS inverter | BESS inverter | BESS inverter | √ (capacity 0.2 pu) | √ (capacity 0.2 pu) |

(${S}_{LB}$ 1.0 pu) | (${S}_{LB}$ 0.8 pu) | (${S}_{LB}$ 0.8 pu) |

Distribution Loss | |
---|---|

Without optimization (Case 1) | 7513 kWh |

Comparison method (Case 2) | 3743 kWh ($-50.2\%$) |

Proposed method (Case 3) | 4258 kWh ($-43.3\%$) |

Proposed method (Case 4) | 3718 kWh ($-50.5\%$) |

Comparison Method (Case 2) | Proposed Method (Case 3) | Proposed Method (Case 4) | |
---|---|---|---|

SC1 | 1,2,5–24 (h) | 1,6–24 (h) | 1,8–21,24 (h) |

SC2 | 3–4 (h), | 2–3,4–5 (h) | 2–3,4–5,6–7,22–23 (h) |

Simulation time | +20 % | +18 % | +21 % |

Loss reduction | 3.2 % | 5.1% | 6.5 % |

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## Share and Cite

**MDPI and ACS Style**

Shigenobu, R.; Kinjo, M.; Mandal, P.; Howlader, A.M.; Senjyu, T. Optimal Operation Method for Distribution Systems Considering Distributed Generators Imparted with Reactive Power Incentive. *Appl. Sci.* **2018**, *8*, 1411.
https://doi.org/10.3390/app8081411

**AMA Style**

Shigenobu R, Kinjo M, Mandal P, Howlader AM, Senjyu T. Optimal Operation Method for Distribution Systems Considering Distributed Generators Imparted with Reactive Power Incentive. *Applied Sciences*. 2018; 8(8):1411.
https://doi.org/10.3390/app8081411

**Chicago/Turabian Style**

Shigenobu, Ryuto, Mitsunaga Kinjo, Paras Mandal, Abdul Motin Howlader, and Tomonobu Senjyu. 2018. "Optimal Operation Method for Distribution Systems Considering Distributed Generators Imparted with Reactive Power Incentive" *Applied Sciences* 8, no. 8: 1411.
https://doi.org/10.3390/app8081411