# Jaya based Optimization Method with High Dispatchable Distributed Generation for Residential Microgrid

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. Energy Management Using Deterministic and Chance-Constrained Optimization Approaches

#### 2.2. Energy Management Using Heuristic Optimization Approaches

- A scenario is given to allow MG operators to include the actions of energy trading with the main grid. This depends on ToU, CPP, and the conditions of trading to achieve multiple objectives, including the minimization of production and fuel cost along with the maximization of sales revenue.
- An efficient algorithm is proposed to perform optimal energy management, and an objective function is formulated as a multi-objective scheduling problem, (i.e., MG is considered for two cases: standalone and grid-connected operation modes).
- The mechanism of CPP is also incorporated because it influences more power supply during critical pricing hours announced by the utility. This pricing mechanism also helps in reducing cost during other hours of the day.
- We also considered microturbines (MTs), WTs, PVs, and diesel generators as dispatchable DGs and ESSs.

## 3. Problem Formulation

#### 3.1. Formulation of Objective Function

- 24-h ToU or CPP hourly load demand forecast
- 24-h WT energy forecast
- 24-h MT energy forecast
- 24-h PV energy forecast
- The utility price forecast or a pre-specified utility price.

#### 3.1.1. Case I: Standalone Mode

#### 3.1.2. Case II: Grid-Connected Mode

#### 3.1.3. Formulation of the Multi-Objective Scheduling Problem

## 4. Proposed System Model

#### 4.1. Jaya Algorithm

- Step 1
- Obtain the hourly power rating of the individual dispatchable DGs, the hourly selling and buying prices (i.e., ToU and CPP), load demand, P are taken as 30 individual solutions, n as 6 decision variables (i.e., the dispatchable DGs), and 125 iterations are used as the stopping criterion.
- Step 2
- Generate the initial population randomly within the range of values that corresponds to $h\left(x\right)$ (i.e., using the upper and lower limits). After the population generation, a counter is set to the maximum iterations.
- Step 3
- Step 4
- Update the population based upon the fitness comparison at the end of each iteration. Perform a local search to ascertain if the solution satisfies the objective constraints. Apply mutation strategy to maintain and introduce diversity in the population. In addition, a global solution is obtained if the new solution gives a better objective value.
- Step 5
- Transform the updated population into binary that denotes the ON and OFF status of dispatchable DGs.
- Step 6
- Run the EMS for each individual and compute their corresponding objective values at each iteration.
- Step 7
- Consider the energy storage if it is empty, then turn ON standby dispatchable DG, otherwise turn OFF dispatchable DG.
- Step 8
- If the load demand at a particular time slot t is high and the utility price is also high, then the power stored is dispatched to satisfy the load demand at that particular time slot t, a control signal is sent to other dispatchable DGs, and EMS memory is updated. This process continues for 24-h.
- Step 9
- Identify the ideal and worst solutions and modify the solution using Equation (14) and execute the dispatch after considering the modified solution, obtain the objective value for each individual solution, and update the solution if it provides the ideal solution.
- Step 10
- Stop execution if termination criteria are reached.

Algorithm 1: Jaya optimization technique |

#### 4.2. SBA

#### 4.3. EDE

## 5. Simulations and Discussions

#### 5.1. Operation in Standalone MG Mode

#### Operation in Grid-Connected Mode

#### 5.2. Performance Trade-Off

## 6. Conclusions and Future Work

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

$Min$ & $Max$ | Minimum and maximum population bound |

$h\left(x\right)$ | Objective function |

n | Index of decision variables |

p | Number of individual solution |

$MaxItr$ | Maximum number of iteration |

${V}_{j,ideal,t}$ | ${j}^{th}$ individual with the ideal value during the ${t}^{th}$ iteration |

${V}_{j,worst,t}$ | ${j}^{th}$ individual with the worse value during the ${t}^{th}$ iteration |

${r}_{1,j,l}$ & ${r}_{2,j,l}$ | Two random numbers for ${l}^{th}$ variable during ${t}^{th}$ iteration |

P | Population size |

T | Total of time period |

k | Number of dispatchable DGs |

${D}_{k}^{unit}\left(t\right)$ | Decision variables at time period t |

$ESU$ | Number of batteries within MG |

${P}_{power}^{output}\left(t\right)$ | The power output of the ${k}^{th}$ dispatchable DG at time t |

${S}_{k}^{cost}$ | Startup cost of the ${k}^{th}$ dispatchable DG |

$Fue{l}_{k}^{cost}\left(t\right)$ | Fuel cost at any given time t |

a, b & c | Parameters of the fuel cost function |

$O{M}_{k}\left(t\right)$ | Operation and Maintenance cost at any given time t |

$O{M}^{wind}\left(t\right)$ | Operation and Maintenance cost for WT at any given time t |

$O{M}^{MT}\left(t\right)$ | Operation and Maintenance cost for MT at any given time t |

$O{M}^{PV}\left(t\right)$ | Operation and Maintenance cost for PV at any given time t |

${P}^{wind}\left(t\right)$ | Forecast power generation for WT at any given time t |

${P}^{MT}\left(t\right)$ | Forecast power generation for MT at any given time t |

${P}^{PV}\left(t\right)$ | Forecast power generation for PV at any given time t |

$es{u}^{th}$ | Index of energy storage unit |

$O{M}_{esu}^{ES}\left(t\right)$ | Operation and Maintenance cost for energy storage unit at any given time t |

${G}_{buy}\left(t\right)$ | Electricity buying price at any given time t |

${P}^{grid}\left(t\right)$ | Power bought from the utility at any given time t |

${G}_{sell}\left(t\right)$ | Electricity selling price at any given time t |

${P}^{grid}\left(t\right)$ | Power sold to the utility at any given time t |

${E}_{grid}^{p}\left(t\right)$ | Power exchange at any given time t |

${E}_{grid}^{pmin}\left(t\right)$ | Minimum limit of power exchange at any given time t |

${E}_{grid}^{pmax}$ | Maximum limit of power exchange |

$E{S}_{esu}^{pmin}\left(t\right)$ | Minimum battery charging limit at any given time t |

$E{S}_{esu}^{pmax}\left(t\right)$ | Maximum battery charging limit at any given time t |

${\vartheta}_{esu}^{es}\left(t\right)$ | Battery charging efficiency at any given time t |

${\xi}_{esu}^{es}$ | Rated storage capacity |

${P}_{load}^{forecast}\left(t\right)$ | Forecast demand load requirement at any given time t |

${P}_{esu}^{ES}\left(t\right)$ | Charging and discharging power at any given time t |

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**Figure 1.**Proposed system model. EMS: energy management system; PCC: point of common coupling; PV: photovoltaic; WT: wind turbine.

**Figure 4.**Power stored using the battery-1: (

**a**) Standalone MG using ToU; (

**b**) Grid-connected MG-1 using ToU; (

**c**) Grid-connected MG-2 using ToU; (

**d**) Standalone MG using CPP; (

**e**) Grid-connected MG-1 using CPP; (

**f**) Grid-connected MG-2 using CPP.

**Figure 5.**(

**a**) Power stored using battery-2 in standalone MG using ToU; (

**b**) Power stored using battery-2 in grid-connected MG-1 using ToU; (

**c**) Power stored using battery-2 in grid-connected MG-2 using ToU; (

**d**) Power generation using the diesel generator in standalone MG using ToU; (

**e**) Power generation using the diesel generator in grid-connected MG-1 using ToU; (

**f**) Power generation using the diesel generator in grid-connected MG-2 using ToU.

**Figure 6.**(

**a**) SOC in standalone MG using ToU; (

**b**) SOC in grid-connected MG-1 using ToU; (

**c**) SOC in grid-connected MG-2 using ToU; (

**d**) SOC in standalone MG using CPP; (

**e**) SOC in grid-connected MG-1 using CPP; (

**f**) SOC in grid-connected MG-2 using CPP.

**Figure 7.**(

**a**) Power generation for MT in standalone MG using ToU; (

**b**) Power generation for MT in grid-connected MG-1 using ToU; (

**c**) Power generation for MT in grid-connected MG-2 using ToU; (

**d**) Power generation for MT in standalone MG using CPP; (

**e**) Power generation for MT in grid-connected MG-1 using CPP; (

**f**) Power generation for MT in grid-connected MG-2 using CPP.

**Figure 8.**(

**a**) Power generation for WT in standalone MG using ToU; (

**b**) Power generation for WT in grid-connected MG-1 using ToU; (

**c**) Power generation for WT in grid-connected MG-2 using ToU; (

**d**) Power generation for PV in standalone MG using ToU; (

**e**) Power generation for PV in grid-connected MG-1 using ToU; (

**f**) Power generation for PV in grid-connected MG-2 using ToU.

**Figure 9.**(

**a**) Diesel fuel consumption cost in standalone MG using CPP; (

**b**) Diesel fuel consumption cost in grid-connected MG-1 using CPP; (

**c**) Diesel fuel consumption cost in grid-connected MG-2 using CPP; (

**d**) Diesel fuel consumption cost in standalone MG using ToU; (

**e**) Diesel fuel consumption cost in grid-connected MG-1 using ToU; (

**f**) Diesel fuel consumption cost in grid-connected MG-2 using ToU.

**Figure 10.**(

**a**) Operation and maintenance cost using ToU; (

**b**) Production cost using ToU; (

**c**) Selling revenue using ToU; (

**d**) Operation and maintenance using CPP; (

**e**) Production cost using CPP; (

**f**) Selling revenue using CPP.

**Figure 11.**(

**a**) Demand and supply in standalone MG using ToU; (

**b**) Demand and supply in grid-connected MG-1 using ToU; (

**c**) Demand and supply in grid-connected MG-2 using ToU; (

**d**) Demand and supply in standalone MG using CPP; (

**e**) Demand and supply in grid-connected MG-1 using CPP; (

**f**) Demand and supply in grid-connected MG-2 using CPP.

Technique(s) | Achievement(s) | Limitation(s) |
---|---|---|

RegPSO [1] | Addresses the single energy storage problem, incorporates the isolated and nonisolated microgrid operation modes, minimizes the operation and maintenance cost, maximizes sales revenue. | Time-of-use (ToU), critical peak price (CPP), and microturbines (MTs) are not considered. |

Deterministic and chance-constrained [2] | Reduces burden, operational cost, and enhances energy exchange commitment. | Sales revenue is not considered in their energy exchange plan. |

ROA [3] | Reduces procurement energy cost to bid day-ahead, RTP, and ToU. | CPP is not considered. |

Probabilistic programming models [12,13] | Residential and industrial MG. | Requires extra computational power. |

Dynamic programming models [14,15] | Residential and industrial MG. | Inefficient for large decision variables. |

MILP [27] | Provide cost-saving for residential MG. | MTs are not considered. |

MILP [28] | Minimizes net electricity cost of MG. | Production, purchasing, and fuel cost are not considered in their objective function. |

MILP [29] | Short-term load scheduling, minimizes operational cost and conserves user’s unique PSI. | Energy exchanged with main grid is not considered. |

Benders decomposition [30] | Minimizes total operation, generation, and spinning reserve cost of local resources as well as purchasing cost of energy. | Ignored possibility of CPP circumstances. |

MMEP [31] | Maximizes the level of distributed energy resource (DER), satisfying operational constraints with high probability. | Energy exchange with main grid is not considered. |

Fuzzy decision-making, GA [32] | Resolves conflicting requirements of MG operations. | MTs and electricity market tariff are not considered. |

coalitional game theory [33] | Minimizes electricity cost and load consumption. | Fuel cost and production cost are not considered. |

MODMG [34] | Reduces economic costs and voltage deviation. | MTs are not considered. |

AIA and DRA [35] | Maximizes net benefits and social welfare of the customers, and reduces generation cost. | ToU, CPP, energy exchange, and consumer privacy are not considered. |

Novel inverter [36,37] | Minimize the burden on MG | Energy exchange is not considered |

FF, PSO, DE, GA, TLBO [38] | MG operation cost minimization. | Energy exchange is not considered. |

Coordinated load scheduling and controlling algorithm [39] | Minimizes peak load consumption. | Dispatchable distributed generators (DGs) are not considered. |

PSO [40] | Addresses the impact of demand response on networked MG. | PSO may not escape local optimum solution because of premature convergence. |

Jaya Algorithm [41] | Determines the best operating levels, reduces the real power losses, stabilizes voltage, and optimizes generation cost. | CPP, ToU, standalone, and grid-connected not specified, energy exchange, sales revenue maximization, and market prices are not considered. |

**Table 2.**Proposed algorithms mapping on EMS. EDE: enhanced differential evolution; SBA: strawberry algorithm.

Jaya-Parameters | EDE-Parameters | SBA-Parameters | EMS Parameters | Values |
---|---|---|---|---|

P | P | P | Individual Solution | 30 |

Modified function | Mutant vector | Growth | Initial DGs states | 2 |

n | Trial vectors | NRunner | Number of dispatchabe DGs | 6 |

Selection | Selection | Droot | Schedule/Time slots | 24 |

Fitness function | Fitness function | Fitness function | Design objective function | 1 |

Hour(s) | Load Demand (kWh) | ToU (c$/kWh) | CPP (c$/kWh) | Selling Price (c$/kWh) |
---|---|---|---|---|

1 | 720 | 8.7 | 11.4 | 12 |

2 | 960 | 8.7 | 11.4 | 12 |

3 | 640 | 8.7 | 11.4 | 12 |

4 | 180 | 8.7 | 11.4 | 12 |

5 | 480 | 8.7 | 11.4 | 12 |

6 | 720 | 8.7 | 11.4 | 12 |

7 | 260 | 13.2 | 11.4 | 12 |

8 | 1720 | 13.2 | 11.4 | 12 |

9 | 2120 | 13.2 | 11.4 | 12 |

10 | 1400 | 13.2 | 11.4 | 12 |

11 | 680 | 18 | 123.4 | 12 |

12 | 1160 | 18 | 123.4 | 12 |

13 | 640 | 18 | 123.4 | 12 |

14 | 320 | 18 | 123.4 | 12 |

15 | 180 | 18 | 123.4 | 12 |

16 | 720 | 18 | 123.4 | 12 |

17 | 720 | 13.2 | 11.4 | 12 |

18 | 200 | 13.2 | 11.4 | 12 |

19 | 220 | 8.7 | 11.4 | 12 |

20 | 680 | 8.7 | 11.4 | 12 |

21 | 780 | 8.7 | 11.4 | 12 |

22 | 640 | 8.7 | 11.4 | 12 |

23 | 500 | 8.7 | 11.4 | 12 |

24 | 160 | 8.7 | 11.4 | 12 |

Unit Types | Min Power (kW) | Max Power (kW) | O and M Cost (c$/kW) | Start Up Cost (c$/kW) |
---|---|---|---|---|

WT | 0 | 2500 | 0.3767 | 900 |

PV | 0 | 480 | 0.2169 | 1200 |

**Table 5.**Parameters of the energy storage devices [1].

Unit Types | Min Power (kW) | Max Power (kW) | OM Cost (c$/kW) | Efficiency |
---|---|---|---|---|

Battery 1 | 240 | 4 h × 300 | 23.4 | 0.95 |

Battery 2 | 160 | 4 h × 200 | 35.0 | 0.85 |

**Table 6.**Battery specifications [1]. SOC: state of charge.

Capacity | 20 kWh |
---|---|

Upper bound of SOC | 100 |

Lower bound of SOC | 20 |

Upper bound of power | 30 kW |

Lower bound of power | −30 kW |

Unit Types | Min Power (kW) | Max Power (kW) | O and M Cost (c$/kW) | Startup Cost (c$/kW) | a | b | c |
---|---|---|---|---|---|---|---|

Diesel | 10 | 500 | 175.2 | 3.0 | 1.30 | 0.0304 | 0.00104 |

MT | 10 | 200 | 262.8 | 2.0 | 0.40 | 0.0397 | 0.00051 |

Standalone Grid | ||||
---|---|---|---|---|

Optim. Model | Total Daily Fuel Cost (c$/kWh) | Daily Energy Selling Profit (c$/kWh) | Total Daily Production Cost (c$/kWh) | Computational Time (s) |

Without EMS | 403,850 | 13,325,000 | 4,2495,000 | - |

Jaya | 327,280 | 31,027,000 | 2,600,500 | 0.4505 |

EDE | 152,800 | 31,125,000 | 3,015,600 | 0.8126 |

SBA | 334,610 | −60,302,000 | 2,686,000 | 0.5172 |

Grid-connected MG-1 | ||||

Jaya | 249,840 | 23,023,000 | 2,600,500 | 0.0488 |

EDE | 838,520 | −18,478,000 | 3,015,600 | 0.3275 |

SBA | 381,320 | −65,229,000 | 2,686,000 | 0.2598 |

Grid-connected MG-2 | ||||

Jaya | 230,240 | 31,503,000 | 2,593,600 | 0.0575 |

EDE | 789,070 | −11,099,000 | 3,015,400 | 0.3371 |

SBA | 162,600 | −51,486,000 | 2,616,500 | 0.2316 |

Standalone Grid | ||||
---|---|---|---|---|

Optim. Model | Total Hourly Fuel Cost (c$/kWh) | Total Hourly Energy Selling Profit (c$/kWh) | Total Daily Production Cost (c$/kWh) | Computational Time (s) |

Without EMS | 403,850 | 13,611,000 | 42,593,000 | - |

Jaya | 401,380 | 22,376,000 | 24,998,000 | 0.4253 |

EDE | 524,930 | −7,369,700 | 27,972,000 | 0.6791 |

SBA | 111,560 | −45,810,000 | 24,157,000 | 0.5479 |

Grid-connected MG-1 | ||||

Jaya | 537,750 | 15,945,000 | 3,255,200 | 0.0977 |

EDE | 552,070 | 17,002,000 | 3,244,600 | 0.3641 |

SBA | 191,690 | −5,992,000 | 3,056,600 | 0.2736 |

Grid-connected MG-2 | ||||

Jaya | 436,290 | 19,398,000 | 2,691,000 | 0.0551 |

EDE | 326,570 | 23,644,000 | 2,652,800 | 0.3725 |

SBA | 376,930 | −61,490,000 | 2,697,000 | 0.3507 |

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Samuel, O.; Javaid, N.; Ashraf, M.; Ishmanov, F.; Afzal, M.K.; Khan, Z.A.
Jaya based Optimization Method with High Dispatchable Distributed Generation for Residential Microgrid. *Energies* **2018**, *11*, 1513.
https://doi.org/10.3390/en11061513

**AMA Style**

Samuel O, Javaid N, Ashraf M, Ishmanov F, Afzal MK, Khan ZA.
Jaya based Optimization Method with High Dispatchable Distributed Generation for Residential Microgrid. *Energies*. 2018; 11(6):1513.
https://doi.org/10.3390/en11061513

**Chicago/Turabian Style**

Samuel, Omaji, Nadeem Javaid, Mahmood Ashraf, Farruh Ishmanov, Muhammad Khalil Afzal, and Zahoor Ali Khan.
2018. "Jaya based Optimization Method with High Dispatchable Distributed Generation for Residential Microgrid" *Energies* 11, no. 6: 1513.
https://doi.org/10.3390/en11061513