# A Bi-Layer Multi-Objective Techno-Economical Optimization Model for Optimal Integration of Distributed Energy Resources into Smart/Micro Grids

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## Abstract

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## 1. Introduction

- A multi-objective optimization problem is formulated for the grid-connected microgrid to realize the appropriate grid-integration of renewable resources, EV charging stations, and energy storage systems.
- A two-layer optimization framework is developed to obtain optimal site and size of DERs, simultaneously, and coordinate DERs operation with the grid.
- A Fuzzy-based ICM is developed for optimal scheduling of charging and discharging of EVs and ESS.
- A time-of-use based demand response program is implemented to investigate how customers behave in response to changes in electricity prices.
- A comprehensive comparison between our proposed algorithm with other algorithms reported in the literature has been reported in this work.

## 2. Modeling System Components

#### 2.1. Solar Cell

#### 2.2. Wind Turbine

#### 2.3. Energy Storage System

#### 2.4. Probabilistic Model of Parking Lot Hourly Electricity Demand

## 3. The Formulation and Solution

#### 3.1. Objective Function

#### 3.1.1. Power Losses $\left({\mathrm{f}}_{1}\right)$

#### 3.1.2. Voltage Fluctuations $\left({\mathrm{f}}_{2}\right)$

#### 3.1.3. Electricity Supply Costs $\left({\mathrm{f}}_{3}\right)$

#### 3.2. Constraints

#### 3.2.1. Demand-Supply Balance

#### 3.2.2. Bus Voltage Limitations

#### 3.2.3. Line Current Constraint

#### 3.2.4. Pricing Constraints

#### 3.3. Methodology

#### 3.3.1. GA

#### 3.3.2. PSO

#### 3.3.3. GA-PSO Optimization Algorithm

#### 3.3.4. Fuzzy Membership Rule

#### 3.3.5. Demand Response Program

#### 3.3.6. ICM

#### Set Rules

#### Fuzzifier

#### Inference Engine

#### Defuzzifier

#### 3.3.7. Backward-Forward Sweep Power Flow

- Calculating the apparent power for each bus based on the input parameters;
- Calculating the current of each bus using Equation (48), assuming that the voltage and phase angle at each bus is equal to one and zero, respectively;$${I}_{i}={\left({S}_{i}/{V}_{i}\text{}\right)}^{*}.$$
- Calculating the line currents based on Equation (49) considering the values obtained for the current of each bus moving from the end nodes to the slack bus:$${I}_{\left(i,i-1\right)}={I}_{i}+{{\displaystyle \sum}}^{\text{}}currents\text{}in\text{}branches\text{}emanating\text{}from\text{}bus\text{}number\text{}\left(i\right).$$

- Calculating the bus voltages according to Equation (50), taking into account the voltage drop moving from the first bus to the last bus. It has to be mentioned that for 1st bus as it is a slack bus, the voltage magnitude and phase angle are considered to be one and zero, respectively:$${V}_{i}={V}_{i-1}+{I}_{\left(i-1,i\right)}\times {Z}_{\left(i-1,i\right)}.$$
- Controlling the convergence criteria (continue if the difference between the newly calculated value for the voltage amount and the previous one is higher than the convergence condition. Otherwise, stop the load flow calculation);
- Calculating the bus currents using new values obtained for the bus voltages;
- Return to the first step of the backward sweep stage.

## 4. Results and Discussion

#### Sample Case Study

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

VL, L, M, H | Very low, low, medium, high |

FC, QC, SC | Fast, quick, slow charging |

NOCT | Nominal operating cell temperature ($\xb0$C) |

TUP | Time-of-use price |

SOC | State of charge |

FD, QD, SD | Fast, quick, slow discharging |

NOP | No operation |

NOFE | Number of function evaluation |

CRL | Calculated remaining load |

DOD | Depth of discharge |

${P}_{D}$ | Aggregated demand in response to price changes (MWh) |

${P}_{g/d}$ | Active power generated/demand (MW) |

${P}_{sub}$ | Active power supplied by centralized power plant (MW) |

${S}_{ij}$ | Apparent power flow (MVA) |

${t}_{arr/dep}$ | Arrival/Departure time of EVs to/from parking (h) |

${f}_{chr/dch}$ | Cost of charging/Benefit of discharging ($/MWh) |

${t}_{dur}$ | Duration of the EV availability in the parking (h) |

${E}_{\mathrm{ESS}}$ | Energy stored in ESS (MWh) |

$SO{C}_{\mathrm{ESS}}$ | ESS level of charge (%) |

${D}_{\mathrm{EV}}^{avg}$ | EV average demand (MW) |

${P}_{D0}$ | Aggregated demand in response to fixed pricing (MWh) |

$Dis{t}^{max}$ | Max distance traveled by EVs (mile) |

${f}_{r}^{max/min}$ | Max/Min value of objective function |

$Dist$ | Distance traveled by EVs (mile) |

${\pi}^{\mathrm{TOU}}$ | Time-of-use price of electricity ($/MWh) |

${P}_{\mathrm{pv}}$ | Output power of solar cell (MW) |

${P}_{\mathrm{Parking}}$ | Output power of parking lot (MW) |

${P}_{\mathrm{wind}}$ | Output power of wind plant (MW) |

${\delta}_{i}$ | Phase angle of voltage at bus $i$-th |

$\theta $ | Phase angle of the $ij$-th element of admittance matrix |

${Q}_{g/d}$ | Reactive power generated/demand (MVar) |

${D}_{\mathrm{EV}}$ | Total EV demand (MW) |

${P}_{\mathrm{Loss}}$ | System power losses (MW) |

${V}_{i}$ | Voltage magnitude at bus $i$-th (kV) |

${P}_{\mathrm{ESS}}^{chr/dch}$ | Charging/Discharging power of ESS (MW) |

${f}_{i}$ | Objective function of optimization process |

${T}_{amb}$ | Ambient temperature ($\xb0$C) |

$A$ | Area covered by the wind turbine blades (m^{2}) |

${\eta}_{conv}$ | AC/DC converter efficiency (%) |

$\alpha $,$\beta $ | Beta distribution parameters |

${P}_{\mathrm{EV}}^{chr/dch}$ | Charging/discharging power of EVs (MW) |

$w$ | Coefficient of inertia |

$\pi $ | Base price of electricity ($/MWh) |

${\eta}_{\mathrm{ESS}}$ | ESS efficiency (%) |

${\propto}_{dch}$ | ESS Self-discharge rate (%energy/day) |

$BCAD$ | EV battery capacity (kWh) |

${E}_{c}$ | EV energy consumption per mile (kWh/mile) |

$\gamma $ | Fuzzy membership value |

$G\mathrm{best}$ | Global best position of PSO particles |

${Y}_{ij}$ | $ij$^{th} element of admittance matrix |

Z | Impedance of transmission line |

$SO{C}_{\mathrm{EV}}^{init}$ | EV Initial level of charge (kWh) |

$K{E}_{\mathrm{air}}$ | Kinetic energy of the air |

${C}_{1,2}$ | Learning coefficients |

${V}^{max/min}$ | Max/Min of bus voltage (kV) |

$L$ | Length of the wind turbine blade (m) |

$m,v,\text{}\rho $ | Mass, speed and bulk density of the air |

${S}_{ij}^{max}$ | Max apparent power flow (MVA) |

$\mu .\text{}\sigma $ | Mean and standard deviation of statistical data |

${N}_{ST}$ | Number of charging stations |

${N}_{\mathrm{EV}}$ | Number of EVs at each time interval |

$NB$ | Number of network buses |

${N}_{OF}$ | Number of objective functions |

${N}_{PP}$ | Number of Pareto front points |

${P}_{N\mathrm{pv}}$ | Nominal output power of solar cell (MW) |

$\tau $ | Payment factor |

$P\mathrm{best}$ | Personal best position of each PSO particle |

$U$ | Position vector of PSO particles |

$X,r$ | Random variables |

${\eta}_{\mathrm{pv}}$ | Solar cell efficiency (%) |

${T}_{C}$ | Solar cell temperature ($\xb0$C) |

$Sun$ | Solar radiation (W/m^{2}) |

$O$ | Velocity vector of PSO particles |

$\lambda $, $k$ | Weibull distribution parameters |

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**Figure 3.**Membership function of input variables on the weight of (

**a**) EV state of charge, (

**b**) ESS state of charge, (

**c**) calculated remaining load and (

**d**) time-of-use price.

**Figure 4.**Membership function of output variables on weight of (

**a**) EV charging/discharging power and (

**b**) ESS charging/discharging power.

SOC^{1} Upper Limit (%) | SOC Lower Limit (%) | Self-discharge Rate (%Energy/month) | Efficiency (%) |
---|---|---|---|

90 | 20 | 5 | 95 |

^{1}State of charge.

EV Type | Battery Cap (kWh) | Energy Consumption (kWh/mile) | Market Share (%) | |||
---|---|---|---|---|---|---|

Road | City | Freeway | High Traffic | |||

A | 35 | 0.14 | 0.182 | 0.210 | 0.213 | 38 |

B | 16 | 0.13 | 0.168 | 0.194 | 0.196 | 9 |

C | 18 | 0.16 | 0.210 | 0.242 | 0.245 | 25.5 |

D | 12 | 0.16 | 0.210 | 0.242 | 0.245 | 27.5 |

Mean value | 18.54 | 0.1397 | 0.1945 | 0.2245 | 0.2274 |

Charging/Discharging Power (kW) | Charging Mode |
---|---|

0.1 | Slow charging |

0.3 | Quick charging |

1.0 | Fast charging |

Load Type | IMP |
---|---|

Domestic | 0.1 |

Industrial | 0.5 |

INP-1 | $\mathit{S}\mathit{O}{\mathit{C}}_{\mathbf{ESS}}$ | VL | VL | VL | VL | VL | VL | VL | VL | VL |

INP-2 | $SO{C}_{\mathrm{EV}}$ | VL | VL | VL | VL | VL | VL | VL | VL | VL |

INP-3 | CRL | L | L | L | M | M | M | H | H | H |

INP-4 | TUP | L | M | H | L | M | H | L | M | H |

OUT-1 | ESS C/D | C | C | C | C | C | C | C | C | C |

OUT-2 | EV C/D | FC | FC | FC | FC | QC | QC | FC | QC | SC |

INP-1 | $SO{C}_{\mathrm{ESS}}$ | L | L | L | L | L | L | L | L | L |

INP-2 | $SO{C}_{\mathrm{EV}}$ | L | L | L | L | L | L | L | L | L |

INP-3 | CRL | L | L | L | M | M | M | H | H | H |

INP-4 | TUP | L | M | H | L | M | H | L | M | H |

OUT-1 | ESS C/D | C | C | C | C | C | NOP | C | C | NOP |

OUT-2 | EV C/D | FC | QC | QC | QC | SC | NOP | QC | SC | NOP |

INP-1 | $SO{C}_{\mathrm{ESS}}$ | M | M | M | M | M | M | M | M | M |

INP-2 | $SO{C}_{\mathrm{EV}}$ | M | M | M | M | M | M | M | M | M |

INP-3 | CRL | L | L | L | M | M | M | H | H | H |

INP-4 | TUP | L | M | H | L | M | H | L | M | H |

OUT-1 | ESS C/D | C | C | D | C | NOP | SD | NOP | D | D |

OUT-2 | EV C/D | SC | SC | SD | SC | NOP | SD | NOP | SD | QD |

INP-1 | $SO{C}_{\mathrm{ESS}}$ | H | H | H | H | H | H | H | H | H |

INP-2 | $SO{C}_{\mathrm{EV}}$ | H | H | H | H | H | H | H | H | H |

INP-3 | CRL | L | L | L | M | M | M | H | H | H |

INP-4 | TUP | L | M | H | L | M | H | L | M | H |

OUT-1 | ESS C/D | NOP | D | D | D | D | D | D | D | D |

OUT-2 | EV C/D | NOP | SD | QD | QD | QD | FD | QD | FD | FD |

Scenario | Description | Scenario | Description |
---|---|---|---|

1 | Base case | 2 | Only RES |

3 | Only ESS | 4 | RES and ESS |

5 | Only parking lot | 6 | RES and Parking lot |

7 | ESS and Parking lot | 8 | RES and ESS and Parking lot |

Target Variables | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

PV loc. | − | 29 | − | 12 | − | 33 | − | 12 |

PV cap. | − | 715.26 | − | 603.99 | − | 868.19 | 704.5 | |

Wind loc. | − | 11 | − | 31 | − | 22 | 29 | |

Wind cap. | − | 956.26 | − | 1196.01 | − | 1108.72 | − | 1308.4 |

ESS loc. | − | − | 11 24 | 25 22 | − | − | 10 31 | 10 25 |

ESS cap. | − | − | 350.04 271.88 | 314.62 388.27 | − | − | 295.65 403.04 | 375 625 |

Parking loc. | − | − | − | − | 6 30 | 23 12 | 22 25 | 4 27 |

Parking cap. | − | − | − | − | 847.91 515.37 | 881.26 1004.79 | 756.21 843.79 | 1200.32 1254.58 |

Scenario | Processing Time (sec) | ${\mathit{f}}_{1}\left(\mathbf{M}\mathbf{W}\right)$ | ${\mathit{f}}_{2}\left(\mathbf{p}\mathbf{u}\right)$ | ${\mathit{f}}_{3}\left(\mathbf{\$}\right)$ |
---|---|---|---|---|

1 | 82 | 4.04 | 38.05 | 16,431,256.00 |

2 | 149 | 3.01 | 29.2 | 09,416,752.81 |

3 | 125 | 3.75 | 36.98 | 16,209,434.04 |

4 | 199 | 2.79 | 27.77 | 08,743,071.31 |

5 | 187 | 3.27 | 34.16 | 16,027,047.10 |

6 | 263 | 2.44 | 24.99 | 07,952,727.90 |

7 | 240 | 3.35 | 33.67 | 15,843,017.04 |

8 | 317 | 1.98 | 22.54 | 07,360,217.66 |

Demand Supplied by Other Resources (%) | |||||
---|---|---|---|---|---|

Scenario | Total System Load (MW) | RES | V2G | ESS | CPP (%) |

1 | 66.280 | − | − | − | 100 |

2 | 66.280 | 40.65 | − | − | 59.35 |

3 | 67.190 | − | − | 1.27 | 98.73 |

4 | 67.309 | 43.57 | − | 1.44 | 54.99 |

5 | 68.133 | − | 2.46 | − | 97.54 |

6 | 68.166 | 47.91 | 2.50 | − | 49.59 |

7 | 68.902 | − | 2.10 | 1.39 | 96.51 |

8 | 70.238 | 49.27 | 3.42 | 1.63 | 45.68 |

Scenario | Total DSO Profit ($) | Peak Hours Profit ($) | Low Load Hours Profit ($) |
---|---|---|---|

2 | 6,926,503.47 | 3,869,185.11 | 3,057,318.36 |

3 | 0311,911.95 | 0276,199.37 | 0035,712.58 |

4 | 7,185,884.93 | 4791,212.64 | 3,946,720.29 |

5 | 0394,297.27 | 0244,049.55 | 0150,247.72 |

6 | 8,378,418.19 | 5,570,857.10 | 2,807,561.09 |

7 | 0683,438.52 | 0295,294.17 | 0388,144.35 |

8 | 9,071,038.34 | 6,170,581.26 | 2,900,457.08 |

Scenario | Total System Loss (MW) | Total System Load (MW) | Peak Shaving (MW) | Peak to Valley Distance (MW) | Load Factor (%) |
---|---|---|---|---|---|

Base case | 4.04 | 66.280 | − | 2.326 | 85.1 |

Fixed pricing | 2.11 | 70.238 | −0.1 | 1.997 | 88.5 |

Online pricing | 1.98 | 65.248 | 0.295 | 1.506 | 90.2 |

**Table 12.**Comparison of the proposed genetic algorithm (GA)-particle swarm optimization (PSO) algorithm with literature (scenario 8).

Algorithm | Iteration | Pop Size | NOFE | Processing Time (sec) | ${\mathit{f}}_{1}\left(\mathbf{MW}\right)$ | ${\mathit{f}}_{2}\left(\mathbf{pu}\right)$ | ${\mathit{f}}_{3}\left(\mathbf{\$}\right)$ |
---|---|---|---|---|---|---|---|

Adaptive GA-PSO | 200 | 50 | 72,480 | 317 | 1.98 | 22.54 | 07,360,217.66 |

NSGA-II | 200 | 50 | 99,667 | 436 | 3.00 | 23.81 | 10,109,490.86 |

DE | 200 | 50 | 83,516 | 374 | − | − | − |

GA | 200 | 50 | 96,860 | 428 | − | − | − |

E-PSO | 200 | 50 | 114,127 | 495 | 2.09 | 22.90 | 07,582,571.10 |

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## Share and Cite

**MDPI and ACS Style**

Rezaeimozafar, M.; Eskandari, M.; Amini, M.H.; Moradi, M.H.; Siano, P.
A Bi-Layer Multi-Objective Techno-Economical Optimization Model for Optimal Integration of Distributed Energy Resources into Smart/Micro Grids. *Energies* **2020**, *13*, 1706.
https://doi.org/10.3390/en13071706

**AMA Style**

Rezaeimozafar M, Eskandari M, Amini MH, Moradi MH, Siano P.
A Bi-Layer Multi-Objective Techno-Economical Optimization Model for Optimal Integration of Distributed Energy Resources into Smart/Micro Grids. *Energies*. 2020; 13(7):1706.
https://doi.org/10.3390/en13071706

**Chicago/Turabian Style**

Rezaeimozafar, Mostafa, Mohsen Eskandari, Mohammad Hadi Amini, Mohammad Hasan Moradi, and Pierluigi Siano.
2020. "A Bi-Layer Multi-Objective Techno-Economical Optimization Model for Optimal Integration of Distributed Energy Resources into Smart/Micro Grids" *Energies* 13, no. 7: 1706.
https://doi.org/10.3390/en13071706