# Political-Optimizer-Based Energy-Management System for Microgrids

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## Abstract

**:**

## 1. Introduction

- The examples provided above used different optimization algorithms in order to carry out the ED or energy management in diverse microgrids. In fact, new optimization algorithms are always being developed and it is not clear which optimization algorithm would serve as the best for the EMSs of microgrids. The question is quite relevant given the rapid adoption and development of microgrids. In this regard, the contributions of this paper are summarized as follows:
- The investigation of two recently developed optimization algorithms for carrying out Optimal-Power-Flow (OPF) studies in electrical networks. This step is essential since it is important to test any new approach on a standard, well-known system before it is used for energy management in highly localized and diverse microgrids. The tested algorithms include the Political Optimizer (PO) and the Lichtenberg Algorithm (LA). The OPF studies were carried out by the cost minimization of the IEEE 30-bus system.
- The comparison of the performance of the newly developed approaches with existing conventional approaches. In this regard, a comprehensive comparison of the values of all the decision variables as a result of applying the PO and LA were compared with the results from applying the Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). Furthermore, a small comparison of the results taken from the well-known literature was also made.
- The best performing optimization algorithm was then selected to carry out ED studies in a microgrid that consisted of numerous sources of energy such as Li-ion storage systems, fuel cells (FCs), solar PV panels, micro-hydro power plants and diesel generators (DGs). The LCOE of all the sources of energy were calculated and it was found to be minimized during the operation of the microgrid. The microgrid was connected and hourly grid prices were used in the study.
- Finally, in order to understand the cost implications year round, clustering was used to identify representative days of the year with which comparisons were made regarding the microgrid operation. The microgrid model was based on the existing elements present at Wroclaw University of Science and Technology.
- The novelty of the study comes from the fact that the Political Optimizer and the Lichtenberg Algorithm have not yet been used for OPF studies. Moreover, the study shows that the Political Optimizer is an effective option for an energy-management system of microgrids, which, to the best of our knowledge, has not yet been explored. The study presents an energy-management approach that analyzes the behavior of the microgrid and the LCOE cost for an entire year, which is valuable to microgrid planners in the region.

## 2. Investigated Optimization Algorithms

#### 2.1. Political Optimizer

#### 2.2. Lichtenberg Algorithm

#### 2.3. Performance Evaluation of the Investigated Algorithms

## 3. Microgrid Layout, Mathematical Model and LCOE Calculations

#### 3.1. Microgrid Layout

#### 3.2. Mathematical Model

_{c}is the overall cost function that is minimized during the microgrid operation. P

_{i}is the generated power of every generator i in the microgrid and their corresponding LCOE is represented using C

_{i}. The power exchange with the main grid is represented by P

_{EX}and the cost for doing so is represented by C

_{EX}. n

_{g}represents the total generators present within the microgrid.

_{gi}, Q

_{gi}, P

_{di}and Q

_{di}represent the active power generated, reactive power generated, active power demand and reactive power demand, respectively, in each node i. The voltages at any two nodes i and k are represented by V

_{i}and V

_{k}. They are useful in calculating the active and reactive power losses according to Equations (2) and (3). Y

_{ik}represents the admittance between two nodes i and k and ${\theta}_{ik}$ represents the admittance angle between them, whereas the voltage angles at the nodes i and k are represented by ${\delta}_{i}$ and ${\delta}_{k}$. In general, the two equality constraints (2) and (3) are responsible for balancing the power within the microgrid. Equation (4) represents the limits of the active power of every generator within the minimum ${P}_{gi}^{min}$ and maximum ${P}_{gi}^{max}$. Equation (5) represents similar limits for the reactive power between minimum ${Q}_{gi}^{min}$ and maximum ${Q}_{gi}^{max}$ for every generator. Equation (6) represents the voltage magnitude limit at every node i between minimum ${V}_{i}^{min}$ and maximum ${V}_{i}^{max}$. Equation (7) represents the voltage angle limit at every node i between minimum ${\delta}_{i}^{min}$ and maximum ${\delta}_{i}^{max}$.

#### 3.3. LCOE Calculations

_{t}represents the yearly total costs and E

_{t}represents the yearly total energy outputs. Both the terms are discounted over the generator lifetime by ${\left(1+r\right)}^{t}$ where, r is the discounted rate and t is the year under consideration. The total lifetime is T. A more comprehensive version of (8) is shown in (9).

- C
_{c}: Initial capital cost (assumed as a single payment in the study) - I
_{c}: Installation costs - F
_{c}: Fuel costs - $O\&{M}_{c}$: Operation and maintenance costs discounted by ${\left(1+r\right)}^{t}.$

## 4. Generator Models

#### 4.1. Solar PV Panels

_{cpv}, the cost of one solar panel is C

_{pv}and the total number of such panels is N

_{pv}. For the purposes of the calculation of the LCOE, the cost of installation was set at 20% of the capital cost [24]. The lifetime of the panels is around 25 years, which is equal to the project lifetime in this study; therefore, it was decided that no replacement would be involved. The yearly maintenance associated with the panels, which includes both cleaning and inspection, was set at $6.5/yr [24]. The inverters, which typically last around 10–11 years, had to be replaced two times during the project lifetime. All of the costs associated with the LCOE calculations are summarized in Table 3 at the end of the section.

#### 4.2. Li-Ion Storage System (BESS)

_{s}(t) and at step t−1 it is represented by E

_{s}(t − 1). The self-discharge rate of the BESS is represented by $\sigma $. E

_{g}(t) and E

_{l}(t) represent the energy produced and the load demand in the microgrid at the time step t, whereas ${\mathsf{\eta}}_{\mathrm{conv}}$, ${\mathsf{\eta}}_{\mathrm{cc}}{\mathrm{and}\text{}\mathsf{\eta}}_{\mathrm{rbat}}$ represent the converter efficiency, charge controller efficiency and round-trip efficiency, respectively.

_{cbss}) associated with the BESS is presented in (13) where the capital cost associated with each unit is represented by C

_{bss}and the total number of such units is represented by N

_{bss}.

_{cbss}[24]. The O&M costs were not considered for this energy source since it needs little to no maintenance and has no moving parts. A standard Li-ion battery system has a lifespan of 5,000 cycles. Based on simulations of the microgrid model that was run on data from the past 5 years, it was found that the average cycles per year are 671.5. This puts the lifespan of the BESS in this project at 7.4 years, which indicates that it has to be replaced three times over the entire project lifespan. This replacement cost has been included in the LCOE calculations in a discounted fashion. Furthermore, the fuel costs for the BESS were calculated based on the energy consumed during charging.

#### 4.3. Fuel Cell + Hydrogen Storage Tank

_{hs}(t) is the energy equivalent of the hydrogen stored during time step t and E

_{hs}(t − 1) represents the same during time step t − 1. E

_{g}, E

_{l}and ${\mathsf{\eta}}_{\mathrm{conv}}$ have the same definitions as before, whereas ${\mathsf{\eta}}_{\mathrm{FC}}$ is the fuel-cell efficiency. The process of excess-energy conversion to hydrogen within the microgrid is represented by Equation (15), in which case the electrolyzer utilized this energy to split water into hydrogen and oxygen and the hydrogen was stored in the tanks.

#### 4.4. Diesel Generators (DGs)

_{DG}(t) is the total consumed fuel, a

_{DG}and b

_{DG}are consumption coefficients, P

_{DGgen}is the power produced by the DG and its rated power is represented by P

_{DGrat}. The total capital cost is calculated by (17),

_{cdg}, the cost per DG unit is C

_{dg}and the total number of units is N

_{dg}. The installation cost in this study was set at 3.5% of the Ccdg. The O&M costs were set at $510/kW/yr. The DG units had lifespans close to 20,000 h and since they operated regularly throughout the project lifespan, they were replaced every two years. The costs associated with the replacement were accounted for in the LCOE after being appropriately discounted.

#### 4.5. Micro-Hydro Power Plant

^{3}. g has a value of 9.8 m/s

^{2}and represents the acceleration associated with gravity. The head of the water source feeding the power plant is represented by h with a value of 12 m in this study. The water discharge represented by Q is calculated using Equation (19) and the units are m

^{3}/s. The stream is characterized by its velocity (V) in m/s and cross-sectional area (A) in m

^{2}. For this study, it was assumed that the plant was controllable and that the discharge was kept within a range of 0.7 m

^{3}/s and 0.11 m

^{3}/s.

## 5. Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 7.**Clustered seasonal load variations (

**a**) and clustered seasonal variations in microgrid output (

**b**).

Control Variable Values | GA | PSO | PO | LA |
---|---|---|---|---|

* P_{G1} (MW) | 176.45 | 176.76 | 177.39 | 180.45 |

P_{G2} (MW) | 48.75 | 49.36 | 48.84 | 47.59 |

P_{G5} (MW) | 21.09 | 21.76 | 21.40 | 22.99 |

P_{G8} (MW) | 23.20 | 25.73 | 21.69 | 18.30 |

P_{G11} (MW) | 12.21 | 11.12 | 12.19 | 12.86 |

P_{G13} (MW) | 10.95 | 13.81 | 11.20 | 10.98 |

V_{1} (p.u.) | 1.06 | 1.06 | 1.06 | 1.06 |

V_{2} (p.u.) | 1.04 | 1.04 | 1.04 | 1.05 |

V_{5} (p.u.) | 1.01 | 1.01 | 1.01 | 1.01 |

V_{8} (p.u.) | 1.01 | 1.01 | 1.01 | 1.01 |

V_{11} (p.u.) | 1.08 | 1.08 | 1.08 | 1.08 |

V_{13} (p.u.) | 1.07 | 1.07 | 1.07 | 1.07 |

T_{11} | 0.94 | 1.03 | 1.01 | 0.95 |

T_{12} | 1.07 | 0.96 | 0.93 | 1.01 |

T_{15} | 0.97 | 0.96 | 0.94 | 1.09 |

T_{36} | 0.94 | 0.95 | 0.93 | 1.00 |

Q_{c10} (MVAr) | 3.26 | 4.77 | 4.61 | 0.23 |

Q_{c12} (MVAr) | 4.30 | 4.10 | 5.00 | 3.39 |

Q_{c15} (MVAr) | 4.00 | 0.13 | 4.32 | 2.97 |

Q_{c17} (MVAr) | 4.85 | 0.04 | 4.92 | 3.55 |

Q_{c20} (MVAr) | 4.58 | 3.23 | 4.56 | 4.56 |

Q_{c21} (MVAr) | 4.65 | 4.26 | 5.00 | 2.56 |

Q_{c23} (MVAr) | 3.27 | 0.28 | 2.71 | 0.81 |

Q_{c24} (MVAr) | 1.39 | 4.27 | 3.65 | 3.75 |

Q_{c29} (MVAr) | 3.06 | 1.37 | 2.72 | 3.89 |

Run time (s) | 34.20 | 7.89 | 4.09 | 54.15 |

Cost ($/h) | 801.6 | 801.7 | 801.6 | 802.8 |

From | To | Distance (m) | r + jx (Ω) (10^{−1}) |
---|---|---|---|

node 1 | node 2 | 180 | 0.455 + 0.147j |

node 2 | node 3 | 130 | 0.329 + 0.106j |

node 3 | node 4 | 145 | 0.367 + 0.118j |

node 4 | node 5 | 195 | 0.493 + 0.159j |

node 5 | node 1 | 140 | 0.354 + 0.114j |

node 2 | node 5 | 190 | 0.481 + 0.155j |

Parameters | Value | Parameters | Value |
---|---|---|---|

Capital cost of PV panels | 0.6 $/kW | Annual O&M for entire installation | 141 $ |

Annual O&M costs of PV | 6.5 $/module | Erection cost of FC + HST + electrolyzer | 5% of capital cost of entire FC installation |

Total installed capacity | 48.9 kW | Fuel cost of FC + HST | ^{1} 0.033 times the energy consumed |

Erection cost PV system | 20% of capital cost of PV system | Electrolyzer replacement cost | Cost of replacement at capital cost at discounted rate |

Capital cost of BSS | 1500 $ | Capital cost of DG | 2099 $/unit |

Erection cost of BSS | 5% of capital cost of BSS | Total number of units | 2 |

Fuel cost of BSS | ^{1} 0.033 time the energy consumed | Replacement cost | Cost of replacement at capital cost at discounted rate |

O&M costs of BSS | Cost of replacement at capital cost at discounted rate | O&M cost for DGs | 1020 $ |

Capacity of BSS | 9.8 kWh | Fuel Cost of DG | Calculated based on yearly fuel consumption |

Capital cost of FC | 2400 $/kW | Capital cost of Francis turbine | 15,200 $ |

Installed capacity of FC | 3 kW | Total installed capacity | 11.6 kW |

Capital cost of electrolyzer | 800 $/kW | Erection cost for Francis turbine | 20% of capital cost of turbine |

Installed rating of electrolyzer | 3 kW | Annual O&M costs | 1216 $ |

Capital cost of HST | 600 $ | Replacement cost | No replacement, life > 25 years |

^{1}coefficient obtained based on the charging process of the HST which is done only when there is excess power produced in the microgrid.

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**MDPI and ACS Style**

Suresh, V.; Jasinski, M.; Leonowicz, Z.; Kaczorowska, D.; J., J.; Reddy K., H.
Political-Optimizer-Based Energy-Management System for Microgrids. *Electronics* **2021**, *10*, 3119.
https://doi.org/10.3390/electronics10243119

**AMA Style**

Suresh V, Jasinski M, Leonowicz Z, Kaczorowska D, J. J, Reddy K. H.
Political-Optimizer-Based Energy-Management System for Microgrids. *Electronics*. 2021; 10(24):3119.
https://doi.org/10.3390/electronics10243119

**Chicago/Turabian Style**

Suresh, Vishnu, Michal Jasinski, Zbigniew Leonowicz, Dominika Kaczorowska, Jithendranath J., and Hemachandra Reddy K.
2021. "Political-Optimizer-Based Energy-Management System for Microgrids" *Electronics* 10, no. 24: 3119.
https://doi.org/10.3390/electronics10243119