# Coordinated Control and Dynamic Optimal Dispatch of Islanded Microgrid System Based on GWO

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Modeling

#### 2.1. Model of Wind Turbine

_{ci}, rated wind speed V

_{r}, and cut-out wind speed V

_{co}are often used. Three physical quantities are measured, and then the fan output power characteristic equation is obtained by curve fitting. All wind turbines have roughly the same wind speed power curve shape. Total extracted power from the wind turbines P

_{wt}at any time can be calculated as follows [22]:

_{wt−rate}is the rated power of the WT. Generally, in the standard test case, the wind speed power characteristic curve of the wind turbine is drawn, and then the wind speed power expression shown in the above formula is obtained by curve fitting, but there are certain errors in the actual environment, so the standard test environment is correct the wind speed power characteristic curve obtained below.

#### 2.2. Model of PV Array

_{pv}is the output power of PV arrays, N

_{pv}is numbers of PV arrays, the maximum output power of the photovoltaic array is expressed in P

_{rate−pv}. This value is the rated output power obtained by measuring the output of the PV array in a standard environment with a solar radiation intensity (S

_{ref}) of 1 kW/m

^{2}and a temperature (T

_{ref}) of 25 °C under no wind conditions. S is solar radiation intensity and T

_{c}is the PV cell temperature.

_{a}is the ambient temperature and NOCT is the temperature of the battery under standard operation.

#### 2.3. Model of Energy Storage System (ess)

_{b}(t) and E

_{b}(t−1) are the power stored in the battery at times t and t−1, P

_{ch,t}represents the battery charging power, ${\eta}_{b}^{ch}$ represents the battery charging efficiency, generally take 95%.

_{dch,t}represents the battery discharging power.

_{batt}is the number of battery, E

_{bma}and E

_{bmin}are the maximum and minimum storage capacity, and E

_{rate−batt}is the battery pack rate (kWh), and DOD is the depth of discharge, which is taken 80% in this study.

#### 2.4. Model of Diesel Engine

_{de−rate}and P

_{de}represent the rated power value and actual output power value of the diesel engine, respectively, F

_{0}and F

_{1}represent the two fitting coefficients of the fuel-power curve of the diesel generator, which can generally be measured according to the actual measurement of the diesel generator.

## 3. Objective Function Formulation

#### 3.1. Cost Analysis of Distributed Power

_{m−pv}, c

_{m−wt}and c

_{om−de}represent the unit power maintenance costs of photovoltaic power generation units, wind turbines and diesel generators, respectively, c

_{om−de}, P

_{wt,t}and P

_{de,t}represent photovoltaic power generation units, the rated power output of the generator and the diesel generator at time t, a, b, and c respectively represent the power generation fitting coefficients of the diesel generators.

#### 3.2. Analysis of Operating Cost of Energy Storage System

_{m−ess}·R

_{r−ess}represents a fixed part of the operation and maintenance cost of the energy storage system, c

_{m−ess}and R

_{r−ess}represent the unit operation and maintenance cost and rated capacity of the ess, c

_{me−ess}·E

_{a}represents the variable operation and maintenance of the energy storage system cost [27]. In addition to the operation and maintenance costs of the ess, the depreciation cost C

_{b−ess}of the ess and the power loss C

_{lo-ess}are also considered.

#### 3.3. Analysis of Emissions

_{2}, SO

_{2}, NO

_{X}, etc.

_{pol}represents environmental protection costs; n indicates the type of harmful gas emitted, such as CO

_{2}, SO

_{2}, etc.; φ

_{n}represents the unit treatment cost of a certain harmful gas; V

_{n}indicates harmful gas n emissions; ${V}_{n}^{\prime}$ means diesel generator exhaust gas per unit power. For the purpose of calculation, the emissions from the operation of diesel generators are linearly closed.

_{2}, SO

_{2}and nitrogen oxides. For detailed parameter settings, see the analysis of examples in this paper. In summary, the objective function established in this part is:

## 4. Constraints

_{pv,t}and P

_{wt,t}represent the output power of the WT and photovoltaic at time t, P

_{l,t}represent the load power at t, and P

_{de,t}represent the output power of the diesel generator at t.

## 5. Formulation of the Optimization Strategy

#### Optimal Sizing of Microgrid Using GWO

_{p}represents the position vector of the prey; X(t) represents the current grey wolf’s position vector; a linearly decreases from 2 to 0 during the entire iteration process; r

_{1}and r

_{2}are the random vector in [0, 1].

_{α}, X

_{β}, X

_{δ}represent the position vector of α, β, δ in the current population; X represent the position vector of the grey wolf; D

_{α}, D

_{β}, D

_{δ}represent the distance between the current search agent and the best three wolves; when the |A>1|, the gray wolf searches for prey in different areas as much as possible. When |A<1|, grey wolves focused on searching for prey within a certain area.

## 6. Case Study and Simulation Results

#### 6.1. Case Study

#### 6.2. Description of the System

_{2}, NOx and SO

_{2}[31]. The corresponding emissions and environmental treatment costs are shown in Table 3.

#### 6.3. Simulation Results

#### 6.4. Analysis of Optimal Dispatching Results of Microgrid

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A, C | synergy coefficients |

C_{om−pv} | photovoltaic maintenance cost |

C_{om−wt} | wind turbine maintenance cost |

C_{de} | diesel generator cost |

C_{om−ess} | battery cost |

C_{pol} | environmental governance cost |

E_{b} | energy stored in the battery [kWh] |

E_{bma} | maximum storage capacity [kWh] |

E_{bmin} | minimum storage capacity [kWh] |

E_{rate−batt} | battery bank rate [kWh] |

F | Generator’s fuel consumption [L] |

F_{0} | fitting coefficients |

F_{1} | fitting coefficients |

N_{pv} | number of photovoltaics |

P_{wt} | total power of the wind turbines [kW] |

P_{wt−rate} | rated power of wind turbines [kW] |

P_{pv} | output power of photovoltaics [kW] |

P_{rate−pv} | rated power of photovoltaics [kW] |

P_{ch,t} | battery charging power [kW] |

P_{dch,t} | battery discharging power [kW] |

r_{1}, r_{2} | random vectors [0, 1] |

S_{ref} | maximal solar radiation [kW/m2] |

S | solar radiation intensity [kW/m^{2}] |

T_{c} | PV cell temperature [°C] |

T_{ref} | reference temperature [°C] |

T_{a} | ambient temperature [°C] |

## Greek Symbols

α, β, δ, ω | wolfs in GWO algorithm |

${\eta}_{b}^{ch}$ | battery charge efficiency [%] |

${\eta}_{b}^{dch}$ | battery discharge efficiency [%] |

## Abbreviations

ANN | artificial neural network |

DOD | depth of discharge |

ess | energy storage systems |

GA | genetic algorithm |

GWO | grey wolf optimizer |

PSO | particle swarm optimization |

PV | photovoltaics |

WT | Wind turbine |

T_{ref} | reference temperature [°C] |

T_{a} | ambient temperature [°C] |

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Components | Installed Capacity (kW) | UP Cost ($/kW) | UP Operation and Maintenance Cost ($/kW) | Power Generation Cost ($/kW) | ||
---|---|---|---|---|---|---|

a | b | c | ||||

WT | 100 | 112 | 0.0042 | 0 | ||

PV | 150 | 24 | 0.0013 | 0 | ||

DG | 100 | 12 | 0.0245 | 0 | 0.24 | 0.0035 |

Parameter | Value | Parameter | Value |
---|---|---|---|

type | ess | Max charge & discharge power/kW | 50 |

Capacity/kWh | 50 × 5 | Initial capacity/kW | 50 |

Max allowable state of charge | 95% | Charging efficiency | 15 |

Min allowable state of charge | 15% | Discharging efficiency | 95% |

Pollution | CO_{2} | NOx | SO_{2} |
---|---|---|---|

Emissions (g/kWh) | 649.05 | 9.33 | 0.46 |

Value ($/KG) | 0.0288 | 8.9747 | 2.1328 |

GWO | PSO | |||
---|---|---|---|---|

Ave | Std | Ave | Std | |

S1 | −10.086523 | 12.233906 | 0.000136 | 0.000202 |

S2 | 2.517264 | 0.029014 | 0.042144 | 0.045421 |

S3 | 2.943147 | 79.14958 | 70.12562 | 22.11924 |

S4 | 8.249561 | 1.315088 | 1.086481 | 0.317039 |

S5 | 0.816579 | 0.000126 | 0.000102 | 17.50737 |

S6 | 0.002213 | 0.100286 | 0.122854 | 0.044957 |

Dispatching Results | Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | Scenario 5 | Scenario 6 |
---|---|---|---|---|---|---|

Total power (kWh) | 122,998 | 123,072 | 123,524 | 124,207 | 124,524 | 124,632 |

Total emissions (kg) | 61,755 | 62,157 | 64,625 | 71,070 | 70,251 | 81,439 |

Total cost ($) | 50,441 | 50,577 | 63,077 | 64,961 | 64,736 | 65,046 |

wind power (kWh) | 10,941 | 10,941 | 10,941 | 36,327 | 36,327 | 36,327 |

PV power (kWh) | 1330 | 1330 | 1330 | 6549 | 6549 | 6549 |

wind power utilization (%) | 70.73 | 70.12 | 60.66 | 86.40 | 82.33 | 87.15 |

PV power utilization (%) | 78.63 | 70.26 | 74.68 | 98.76 | 99.16 | 98.76 |

Renewable energy utilizaition rate (%) | 74.68 | 70.19 | 67.67 | 92.58 | 90.75 | 92.96 |

Renewable energy output fuluctuations | 26,891.16 | 28,121.92 | 4225.39 | 9859.25 | 15,568.06 | 10,322.18 |

Residual power generation capacity of WT and PV (kWh) | 3486.65 | 3664.71 | 4640.95 | 5021.68 | 6473.99 | 4749.23 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Wang, Y.; Li, C.; Yang, K.
Coordinated Control and Dynamic Optimal Dispatch of Islanded Microgrid System Based on GWO. *Symmetry* **2020**, *12*, 1366.
https://doi.org/10.3390/sym12081366

**AMA Style**

Wang Y, Li C, Yang K.
Coordinated Control and Dynamic Optimal Dispatch of Islanded Microgrid System Based on GWO. *Symmetry*. 2020; 12(8):1366.
https://doi.org/10.3390/sym12081366

**Chicago/Turabian Style**

Wang, Yuting, Chunhua Li, and Kang Yang.
2020. "Coordinated Control and Dynamic Optimal Dispatch of Islanded Microgrid System Based on GWO" *Symmetry* 12, no. 8: 1366.
https://doi.org/10.3390/sym12081366