# Scenario-Based Stochastic Framework for Optimal Planning of Distribution Systems Including Renewable-Based DG Units

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Problem Statement

#### 1.2. Literature Survey

#### 1.3. Contribution of Paper

- Proposing an efficient framework for the optimal planning of distribution systems considering the uncertainties of load and the output powers of renewable based DGs.
- The application of scenario-based methods for modeling the uncertainties in the electrical systems.
- The application of an efficient algorithm, called the EO, for solving the planning problem.
- The developed algorithms are applied for optimal integration of the renewable-based DGs for loss reduction, voltage improvements, system voltage deviation, the total cost, and the total emissions of the IEEE 69-bus and 94-bus distribution networks.
- A comparison is presented between the EO and other well know techniques for solving the planning problem.

#### 1.4. Paper Layout

## 2. Problem Formulation

#### 2.1. The Objective Functions

#### 2.1.1. Minimization of the Expected Power Loss ($E{P}_{Loss}$)

#### 2.1.2. Minimization of the Expected Voltage Deviations ($ETVD$)

#### 2.1.3. Enhancement of the Expected Voltage Stability ($ETVSI$)

#### 2.1.4. Minimization of the Expected Total Cost ($ETCost$)

#### 2.1.5. Minimization of the Expected Total Emissions ($ETEmission$)

_{2,}and SO

_{2}are 2.2952 kg/MWh, 921.25 kg/MWh and 3.5834 kg/MWh, respectively [15].

#### 2.1.6. The Multi-Objective Function

#### 2.2. The System Constraints

#### 2.2.1. Equality Constraints

#### 2.2.2. Inequality Constraints

## 3. Uncertainty Modeling

#### 3.1. Modeling of Load Demand

#### 3.2. Modeling of Wind Speed

#### 3.3. Modeling of Solar Irradiance

#### 3.4. The Combined Load-Generation Model

## 4. Equilibrium Optimizer

#### The Steps of EO

## 5. Results and Discussion

#### 5.1. The IEEE 69-Bus System

^{3}$\mathrm{kg}/\mathrm{MWh}$, respectively. As mentioned, in Section 3, by combining the load demand, wind speed, and solar irradiance uncertainties, 27 scenarios have been generated to model the uncertainties of the system as depicted in Table 2. By application of the EO, the optimal sites for PV and wind turbine-based DGs are at buses number 26 and 62, respectively, while the optimal rating of the PV and wind turbine-based DGs are 177.5 kW and 1151 kW, respectively. Table 6 and Figure 4 provide the output power of the PV and wind turbine-based DGs for each scenario, as well as the corresponding ${P}_{Loss}\left(\mathrm{MW}\right)$, $VD\left(\mathrm{pu}\right)$, $VSI\left(\mathrm{pu}\right)$, $Cost\left(\mathrm{USD}\right)$, and $Emision\left(\mathrm{kg}/\mathrm{MWh}\right).$ As solar irradiance, wind speed, and load demand have different values in each scenario, the yielded result will also be different. At a high probability value which occurred in scenario 13, according to Table 2 the output power of the wind turbine and PV systems is 394.2 kW and 108.4228 kW, respectively. Table 7 provides the expected values for each scenario with optimal integration of RERs. According to Table 7, the summation of the expected values including $ET{P}_{Loss}$, $ETVD$, $ETVSI$, $ETCost$ and $ETEmission$ are enhanced to be 56.2394 kW, 0.8816 p.u, 64.6087 p.u, 1,248,050 USD, and 4,677.936 × 10

^{3}$\mathrm{kg}/\mathrm{MWh}$, respectively.

#### 5.2. The IEEE 94-Bus System

^{3}$\mathrm{kg}/\mathrm{MWh}$, respectively. In other words, the enhancement in the summation of the expected values with optimal integration of the RERs including $E{P}_{Loss}$, $EVD$, $ETVSI$, $ETCost$, and $\mathit{EEmission}$ are 48.38, 39.73%, 11.99%, 57.06%, and 76.42%, respectively. Figure 7 shows the voltage profile for the obtained scenarios.

## 6. Conclusions

- -
- The effectiveness of the proposed framework for solving the optimal planning problem for distribution systems.
- -
- The superiority of the EO for assigning the optimal placement and sizes of the DGs compared to SCA, PSO, and ALO techniques.
- -
- The inclusion of solar PV and wind turbine-based DGs using the proposed method in the IEEE 69-bus system can reduce the expected power losses, voltage deviations, cost, and emissions rate and enhance the voltage stability compared to the base case by 60.95%, 37.09%, 2.91%, 70.66%, and 48.73%, respectively.
- -
- The inclusion of solar PV and wind turbine-based DGs using the proposed method in a 94-bus system can reduce the expected power losses, voltage deviations, cost, and emissions rate and enhance the voltage stability compared to the base case by 48.38%, 39.73%, 57.06%, 76.42%, and 11.99%, respectively.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Acronyms | |

DGs | Distributed Generators |

DSs | Distribution Systems |

PV | Photovoltaic |

WT | Wind Turbine |

RERs | Renewable Energy Resources |

Probability Distribution Function | |

RDN | Radial Distribution Network |

EO | Equilibrium Optimizer |

SCA | Sine Cosine Algorithm |

ALO | Ant-Lion Optimizer |

PSO | Particle Swarm Optimization |

IAGA | Improved Adaptive Genetic Algorithm |

MFO | Moth Flame Optimization |

GA | Genetic-Algorithm |

GA-MCS | Genetic-Algorithm with Monte Carlo simulation |

CSA | Cuckoo Search Algorithm |

CSO-MCS | Crisscross Optimization Algorithm and Monte Carlo Simulation |

IALO | Improved Antlion Optimization Algorithm |

SGA | Specialized Genetic Algorithm |

ACO | Ant Colony Optimizer |

MDEA | Modified Differential Evolution Algorithm |

SOA | Seeker Optimization Algorithm |

Indices and Sets | |

${P}_{loss}$ | Loss power |

${P}_{Total\_Loss}$ | The total active power loss |

$ET{P}_{Loss}$ | Expected Total Loss Power |

${R}_{k,k+1}$ | The resistance of the line between buses $k$ and $k+1$, |

${P}_{k}$ | Real power |

${Q}_{k}$ | Reactive powers |

${P}_{L}$ | The active load demand |

${Q}_{L}$ | The reactive load demand |

${V}_{k}$ | Nominal voltage |

$E{P}_{Loss,k}$ | Expected power loss for scenario k |

$ET{P}_{Loss}$ | Expected total power loss |

$VD$ | Voltage Deviations |

$EV{D}_{k}$ | Expected voltage deviation for scenario k |

$ETVD$ | Expected total voltage deviation |

VSI | Voltage Stability Index |

$EVS{I}_{k}$ | Expected Voltage Stability Index for scenario k |

$ETVSI$ | Expected total Voltage Stability Index |

$EEmissio{n}_{k}$ | Expected emission for scenario k |

$ETEmission$ | Expected total emission |

$NB$ | Number of buses |

Kt | Kilotons |

$PF$ | Power Factor |

$ECos{t}_{Grid,k}$ | Expected cost grid for scenario k |

$ETCos{t}_{Grid}$ | Expected total cost grid |

$ECos{t}_{Loss,k}$ | Expected cost loss for scenario k |

$ETCos{t}_{Loss}$ | Expected total cost loss |

$ECos{t}_{wind,k}$ | Expected cost wind for scenario k |

$ETCos{t}_{wind}$ | Expected total cost wind |

$ECos{t}_{PV,k}$ | Expected cost solar for scenario k |

$ETCos{t}_{PV}$ | Expected total cost solar |

$TVSI$ | Total Voltage Stability Index |

$ETVSI$ | Expected Total Voltage Stability Index |

$ETCost$ | The expected total annual cost |

$ECos{t}_{loss}$ | The expected annual energy loss cost |

$Cos{t}_{Grid}$ | Cost of the power injection at substation |

$ECos{t}_{Grid}$ | The expected cost of the power injection at substation |

$ECos{t}_{PV}$ | The expected PV units cost |

${P}_{Grid}$ | Power of the grid |

${K}_{Grid}$ | Cost of electricity in USD/kW h |

$Cos{t}_{Loss}$ | Cost of the losses |

${K}_{Loss}$ | The energy loss cost |

${P}_{Total\_loss}$ | The total power losses |

$ECos{t}_{Loss}$ | The expected loss cost |

${\pi}_{S}$ | The Combined probabilities |

${\pi}_{d,i}$ | The portability of load demand of i-th interval |

${\pi}_{wind,z}$ | The probability of the wind speed of z-th interval |

${\pi}_{Solar,m}$ | The probability of the solar irradiance of m-th interval |

$ECos{t}_{wind}$ | The expected WT cost |

$CF$ | The capital recovery factor |

${P}_{wr}$ | Rated output power of the WT |

$ECos{t}_{PV}$ | The expected PV cost |

${\mathit{CSDG}}_{\mathit{PV}}$ | Installation cost of the PV |

${P}_{sr}$ | The rated power of PV unit |

${P}_{s}$ | The output power of PV unit |

${P}_{wr}$ | The rated power of WT |

${P}_{w}$ | The output power of WT |

$Cost\_P{V}_{O\&M}$ | Operation and maintenance costs of the PV unit |

${\mathit{CSDG}}_{\mathit{wind}}$ | Installation cost of the WT |

$Cost\_W{T}_{O\&M}$ | Operation and maintenance costs of the WT |

$E{R}_{\mathit{Grid}}$ | The emission rate of grid |

$LF$ | Load factor |

$ET{P}_{Los{s}_{base}}$ | Expected Total power loss of base case |

$ETV{D}_{base}$ | Expected voltage deviation of base case |

$ETCos{t}_{base}$ | Expected total cost of base case |

$ETEmissio{n}_{base}$ | Expected emission rate of base case |

${f}_{d}$ | The normal PDF of load demand |

${f}_{v}$ | The Weibull PDF of wind speed |

${f}_{G}$ | The Beta PDF of solar irradiance |

${v}_{\omega i}$ | The cut in wind speed of WT |

${v}_{\omega r}$ | The rated wind speed of WT |

${v}_{\omega o}$ | The cut out wind speed of WT |

$k$, $c$ | Shape and scale parameters of Weibull function |

${\sigma}_{d}$ | The standard deviation of the load demand |

${\mu}_{d}$ | The mean deviation of the load demand |

${\propto}_{1}$, ${\propto}_{2},{\propto}_{3},{\propto}_{4},{\propto}_{5}$ | The weight factors |

$\rho $ | Rate of interest on DG capital investment |

${T}_{max}$ | Number of iterations |

$NP$ | Lifetime of the PV unit or the WT |

$NT$ | Number of branches |

${I}_{max}$ | Maximum Allowable current in branches |

${Q}_{WT}$ | Injected reactive power by wind turbine |

$NWT$ | Number of wind turbine |

${V}_{min}$ | Minimum allowable voltage limit |

${V}_{max}$ | Maximum allowable voltage limit |

${Q}_{Grid}$ | Reactive power injected at slack bus |

$NPV$ | Number of PV units |

${P}_{d,i}^{max}$ | The maximum limit of the selected interval i |

${P}_{d,i}^{min}$ | The minimum limit of the selected interval i |

${v}_{z}^{max}$ | The ending point of wind speed’s interval at z-th scenario |

${v}_{z}^{min}$ | The starting point of wind speed’s interval at z-th scenario |

${G}_{m}^{max}$ | The ending point of solar irradiance’s interval at m-th scenario |

${G}_{m}^{min}$ | The starting point of solar irradiance’s interval at m-th scenario |

Parameters and Constants | |

$\mathrm{G}$ | Solar Irradiance |

${X}_{c}$ | A certain irradiance point |

${G}_{STD}$ | Standard environment solar irradiance (1000 W/m2) |

${V}_{n}$ | Voltage of the n-th bus |

$\mathrm{\Gamma}$ | Gamma function |

α, β | Parameters of the beta PDF |

${\mu}_{s}$ | Mean deviation of the solar irradiance for each time segment |

Variables and Functions | |

$F$ | Multi-objective function |

${f}_{1}$ | The objective function representing the normalized active total power losses |

${f}_{2}$ | The objective function representing the normalized total voltage deviations |

${f}_{3}$ | The objective function representing the normalized voltage stability index |

${f}_{4}$ | The objective function representing the normalized total cost |

${f}_{5}$ | The objective function representing the normalized total emission |

## References

- Ganguly, S.; Sahoo, N.; Das, D. Recent advances on power distribution system planning: A state-of-the-art survey. Energy Syst.
**2013**, 4, 165–193. [Google Scholar] [CrossRef] - Sims, R.E.; Rogner, H.-H.; Gregory, K. Carbon emission and mitigation cost comparisons between fossil fuel, nuclear and renewable energy resources for electricity generation. Energy Policy
**2003**, 31, 1315–1326. [Google Scholar] [CrossRef] - Ehsan, A.; Yang, Q. Active distribution system reinforcement planning with EV charging stations—Part I: Uncertainty modeling and problem formulation. IEEE Trans. Sustain. Energy
**2019**, 11, 970–978. [Google Scholar] [CrossRef] - Cervantes, J.; Choobineh, F. Optimal sizing of a nonutility-scale solar power system and its battery storage. Appl. Energy
**2018**, 216, 105–115. [Google Scholar] [CrossRef] - Lai, C.S.; Jia, Y.; Lai, L.L.; Xu, Z.; McCulloch, M.D.; Wong, K.P. A comprehensive review on large-scale photovoltaic system with applications of electrical energy storage. Renew. Sustain. Energy Rev.
**2017**, 78, 439–451. [Google Scholar] [CrossRef] - Xavier, G.A.; Martins, J.H.; Monteiro, P.M.d.B.; Diniz, A.S.A.C.; Diniz, A.C. Simulation of distributed generation with photovoltaic microgrids—Case study in Brazil. Energies
**2015**, 8, 4003–4023. [Google Scholar] [CrossRef] - Weckx, S.; D’hulst, R.; Driesen, J. Locational pricing to mitigate voltage problems caused by high PV penetration. Energies
**2015**, 8, 4607–4628. [Google Scholar] [CrossRef] [Green Version] - Georgilakis, P.S.; Hatziargyriou, N.D. A review of power distribution planning in the modern power systems era: Models, methods and future research. Electr. Power Syst. Res.
**2015**, 121, 89–100. [Google Scholar] [CrossRef] - Gao, Y.; Liu, J.; Yang, J.; Liang, H.; Zhang, J. Multi-objective planning of multi-type distributed generation considering timing characteristics and environmental benefits. Energies
**2014**, 7, 6242–6257. [Google Scholar] [CrossRef] - El-Khattam, W.; Hegazy, Y.; Salama, M. An integrated distributed generation optimization model for distribution system planning. IEEE Trans. Power Syst.
**2005**, 20, 1158–1165. [Google Scholar] [CrossRef] - Liu, Z.; Wen, F.; Ledwich, G. Optimal siting and sizing of distributed generators in distribution systems considering uncertainties. IEEE Trans. Power Deliv.
**2011**, 26, 2541–2551. [Google Scholar] [CrossRef] - Shaaban, M.F.; El-Saadany, E. Accommodating high penetrations of PEVs and renewable DG considering uncertainties in distribution systems. IEEE Trans. Power Syst.
**2013**, 29, 259–270. [Google Scholar] [CrossRef] - Zeng, B.; Zhang, J.; Zhang, Y.; Yang, X.; Dong, J.; Liu, W. Active distribution system planning for low-carbon objective using cuckoo search algorithm. J. Electr. Eng. Technol.
**2014**, 9, 433–440. [Google Scholar] [CrossRef] [Green Version] - Peng, X.; Lin, L.; Zheng, W.; Liu, Y. Crisscross optimization algorithm and Monte Carlo simulation for solving optimal distributed generation allocation problem. Energies
**2015**, 8, 13641–13659. [Google Scholar] [CrossRef] [Green Version] - Esmaeili, M.; Sedighizadeh, M.; Esmaili, M. Multi-objective optimal reconfiguration and DG (Distributed Generation) power allocation in distribution networks using Big Bang-Big Crunch algorithm considering load uncertainty. Energy
**2016**, 103, 86–99. [Google Scholar] [CrossRef] - Santos, S.F.; Fitiwi, D.Z.; Bizuayehu, A.W.; Shafie-Khah, M.; Asensio, M.; Contreras, J.; Cabrita, C.M.P.; Catalao, J.P. Novel multi-stage stochastic DG investment planning with recourse. IEEE Trans. Sustain. Energy
**2016**, 8, 164–178. [Google Scholar] [CrossRef] - Kroposki, B.; Sen, P.K.; Malmedal, K. Optimum sizing and placement of distributed and renewable energy sources in electric power distribution systems. IEEE Trans. Ind. Appl.
**2013**, 49, 2741–2752. [Google Scholar] [CrossRef] - Baghaee, H.; Mirsalim, M.; Gharehpetian, G.; Talebi, H. Reliability/cost-based multi-objective Pareto optimal design of stand-alone wind/PV/FC generation microgrid system. Energy
**2016**, 115, 1022–1041. [Google Scholar] [CrossRef] - Saric, M.; Hivziefendic, J.; Konjic, T.; Ktena, A. Distributed generation allocation considering uncertainties. Int. Trans. Electr. Energy Syst.
**2018**, 28, e2585. [Google Scholar] [CrossRef] - Zhao, B.; Guo, C.; Cao, Y. A multiagent-based particle swarm optimization approach for optimal reactive power dispatch. IEEE Trans. Power Syst.
**2005**, 20, 1070–1078. [Google Scholar] [CrossRef] - Abdel-Fatah, S.; Ebeed, M.; Kamel, S. Optimal Reactive Power Dispatch Using Modified Sine Cosine Algorithm. In Proceedings of the 2019 International Conference on Innovative Trends in Computer Engineering (ITCE), Aswan, Egypt, 2–4 February 2019; pp. 510–514. [Google Scholar]
- Sulaiman, M.; Rashid, M.M.; Aliman, O.; Mohamed, M.; Ahmad, A.; Bakar, M. Loss minimisation by optimal reactive power dispatch using cuckoo search algorithm. In Proceedings of the 3rd IET International Conference on Clean Energy and Technology (CEAT) 2014, Kuching, Malaysia, 24–26 November 2014. [Google Scholar]
- Heidari, A.A.; Abbaspour, R.A.; Jordehi, A.R. Gaussian bare-bones water cycle algorithm for optimal reactive power dispatch in electrical power systems. Appl. Soft Comput.
**2017**, 57, 657–671. [Google Scholar] [CrossRef] - Li, Z.; Cao, Y.; Dai, L.V.; Yang, X.; Nguyen, T.T. Finding solutions for optimal reactive power dispatch problem by a novel improved antlion optimization algorithm. Energies
**2019**, 12, 2968. [Google Scholar] [CrossRef] [Green Version] - Villa-Acevedo, W.M.; López-Lezama, J.M.; Valencia-Velásquez, J.A. A novel constraint handling approach for the optimal reactive power dispatch problem. Energies
**2018**, 11, 2352. [Google Scholar] [CrossRef] [Green Version] - Abou El-Ela, A.; Kinawy, A.; El-Sehiemy, R.; Mouwafi, M. Optimal reactive power dispatch using ant colony optimization algorithm. Electr. Eng.
**2011**, 93, 103–116. [Google Scholar] [CrossRef] - Sakr, W.S.; El-Sehiemy, R.A.; Azmy, A.M. Adaptive differential evolution algorithm for efficient reactive power management. Appl. Soft Comput.
**2017**, 53, 336–351. [Google Scholar] [CrossRef] - Khazali, A.; Kalantar, M. Optimal reactive power dispatch based on harmony search algorithm. Int. J. Electr. Power Energy Syst.
**2011**, 33, 684–692. [Google Scholar] [CrossRef] - Dai, C.; Chen, W.; Zhu, Y.; Zhang, X. Seeker optimization algorithm for optimal reactive power dispatch. IEEE Trans. Power Syst.
**2009**, 24, 1218–1231. [Google Scholar] - Mandal, B.; Roy, P.K. Optimal reactive power dispatch using quasi-oppositional teaching learning based optimization. Int. J. Electr. Power Energy Syst.
**2013**, 53, 123–134. [Google Scholar] [CrossRef] - Faramarzi, A.; Heidarinejad, M.; Stephens, B.; Mirjalili, S. Equilibrium optimizer: A novel optimization algorithm. Knowl.-Based Syst.
**2020**, 191, 105190. [Google Scholar] [CrossRef] - Ramadan, A.; Ebeed, M.; Kamel, S.; Nasrat, L. Optimal power flow for distribution systems with uncertainty. In Uncertainties in Modern Power Systems; Elsvier: Amsterdam, The Netherlands, 2020; pp. 145–162. [Google Scholar]
- Bastawy, M.; Ebeed, M.; Rashad, A.; Alghamdi, A.S.; Kamel, S. Micro-Grid Dynamic Economic Dispatch with Renewable Energy Resources Using Equilibrium Optimizer. In Proceedings of the 2020 IEEE Electric Power and Energy Conference (EPEC), Edmonton, AB, Canada, 9–10 November 2020; pp. 1–5. [Google Scholar]
- Özkaya, H.; Yıldız, M.; Yıldız, A.R.; Bureerat, S.; Yıldız, B.S.; Sait, S.M. The equilibrium optimization algorithm and the response surface-based metamodel for optimal structural design of vehicle components. Mater. Test.
**2020**, 62, 492–496. [Google Scholar] [CrossRef] - Abdel-Basset, M.; Mohamed, R.; Mirjalili, S.; Chakrabortty, R.K.; Ryan, M.J. Solar photovoltaic parameter estimation using an improved equilibrium optimizer. Sol. Energy
**2020**, 209, 694–708. [Google Scholar] [CrossRef] - Gampa, S.R.; Das, D. Optimum placement and sizing of DGs considering average hourly variations of load. Int. J. Electr. Power Energy Syst.
**2015**, 66, 25–40. [Google Scholar] [CrossRef] - Soroudi, A.; Aien, M.; Ehsan, M. A probabilistic modeling of photo voltaic modules and wind power generation impact on distribution networks. IEEE Syst. J.
**2011**, 6, 254–259. [Google Scholar] [CrossRef] [Green Version] - Mohseni-Bonab, S.M.; Rabiee, A. Optimal reactive power dispatch: A review, and a new stochastic voltage stability constrained multi-objective model at the presence of uncertain wind power generation. IET Gener. Transm. Distrib.
**2017**, 11, 815–829. [Google Scholar] [CrossRef] - Ebeed, M.; Alhejji, A.; Kamel, S.; Jurado, F. Solving the Optimal Reactive Power Dispatch Using Marine Predators Algorithm Considering the Uncertainties in Load and Wind-Solar Generation Systems. Energies
**2020**, 13, 4316. [Google Scholar] [CrossRef] - Hetzer, J.; David, C.Y.; Bhattarai, K. An economic dispatch model incorporating wind power. IEEE Trans. Energy Convers.
**2008**, 23, 603–611. [Google Scholar] [CrossRef] - Biswas, P.P.; Suganthan, P.N.; Mallipeddi, R.; Amaratunga, G.A.J. Optimal reactive power dispatch with uncertainties in load demand and renewable energy sources adopting scenario-based approach. Appl. Soft Comput.
**2019**, 75, 616–632. [Google Scholar] [CrossRef] - Atwa, Y.; El-Saadany, E.; Salama, M.; Seethapathy, R. Optimal renewable resources mix for distribution system energy loss minimization. IEEE Trans. Power Syst.
**2009**, 25, 360–370. [Google Scholar] [CrossRef] - Salameh, Z.M.; Borowy, B.S.; Amin, A.R. Photovoltaic module-site matching based on the capacity factors. IEEE Trans. Energy Convers.
**1995**, 10, 326–332. [Google Scholar] [CrossRef] - Liang, R.-H.; Liao, J.-H. A fuzzy-optimization approach for generation scheduling with wind and solar energy systems. IEEE Trans. Power Syst.
**2007**, 22, 1665–1674. [Google Scholar] [CrossRef] - Reddy, S.S.; Bijwe, P.; Abhyankar, A.R. Real-time economic dispatch considering renewable power generation variability and uncertainty over scheduling period. IEEE Syst. J.
**2014**, 9, 1440–1451. [Google Scholar] [CrossRef] - Mirjalili, S. SCA: A sine cosine algorithm for solving optimization problems. Knowl.-Based Syst.
**2016**, 96, 120–133. [Google Scholar] [CrossRef] - Eberhart, R.; Kennedy, J. A New Optimizer Using Particle Swarm Theory. In Proceedings of the Sixth International Symposium on Micro Machine and Human Science (MHS’95), Nagoya, Japan, 4–6 October 1995; pp. 39–43. [Google Scholar]
- Mirjalili, S. The ant lion optimizer. Adv. Eng. Softw.
**2015**, 83, 80–98. [Google Scholar] [CrossRef] - Chandramohan, S.; Atturulu, N.; Devi, R.K.; Venkatesh, B. Operating cost minimization of a radial distribution system in a deregulated electricity market through reconfiguration using NSGA method. Int. J. Electr. Power Energy Syst.
**2010**, 32, 126–132. [Google Scholar] [CrossRef] - Pires, D.F.; Antunes, C.H.; Martins, A.G. NSGA-II with local search for a multi-objective reactive power compensation problem. Int. J. Electr. Power Energy Syst.
**2012**, 43, 313–324. [Google Scholar] [CrossRef]

**Figure 4.**The outcomes for each scenario of the IEEE 69-bus system: (

**a**) the photovoltaic (PV) power, (

**b**) the wind turbine (WT) power, (

**c**) the voltage deviations, (

**d**) the voltage stability index, (

**e**) the total cost, (

**f**) the total emission rate, (

**g**) the power loss, and (

**h**) the probability.

**Figure 6.**The outcomes for each scenario of the 94-bus system: (

**a**) the PV power, (

**b**) the WT power, (

**c**) the voltage deviations, (

**d**) the voltage stability index, (

**e**) the total cost, (

**f**) the total emission rate, (

**g**) the power loss, and (

**h**) the probability.

Load Scenario | ${\mathit{\pi}}_{\mathit{d},\mathit{i}}$ | Loading % |
---|---|---|

1 | 0.1587 | 54.7486 |

2 | 0.6827 | 70.0000 |

3 | 0.1587 | 85.2514 |

Wind Scenario | ${\pi}_{wind,z}$ | Wind Speed (m/s) |

1 | 0.7902 | 7.4518 |

2 | 0.1694 | 13.6153 |

3 | 0.0404 | 17.7289 |

Irradiance Scenario | ${\pi}_{Solar,m}$ | Solar Irradiance (W/m^{2}) |

1 | 0.1605 | 416.0627 |

2 | 0.4412 | 609.1166 |

3 | 0.3983 | 790.4621 |

Scenario | Loading % | Wind Speed (m/s) | Solar Irradiance (W/m^{2}) | ${\mathit{\pi}}_{\mathit{d},\mathit{i}}$ | ${\mathit{\pi}}_{\mathit{Solar},\mathit{m}}$ | ${\mathit{\pi}}_{\mathit{wind},\mathit{z}}$ | ${\mathit{\pi}}_{\mathit{S}}$ |
---|---|---|---|---|---|---|---|

$\mathrm{S}1$ | 54.7486 | 7.4518 | 416.0627 | 0.1587 | 0.1605 | 0.7902 | 0.0201 |

$\mathrm{S}2$ | 54.7486 | 13.6153 | 416.0627 | 0.1587 | 0.1605 | 0.1694 | 0.0043 |

$\mathrm{S}3$ | 54.7486 | 17.7289 | 416.0627 | 0.1587 | 0.1605 | 0.0404 | 0.0010 |

$\mathrm{S}4$ | 54.7486 | 7.4518 | 609.1166 | 0.1587 | 0.4412 | 0.7902 | 0.0553 |

$\mathrm{S}5$ | 54.7486 | 13.6153 | 609.1166 | 0.1587 | 0.4412 | 0.1694 | 0.0119 |

$\mathrm{S}6$ | 54.7486 | 17.7289 | 609.1166 | 0.1587 | 0.4412 | 0.0404 | 0.0028 |

$\mathrm{S}7$ | 54.7486 | 7.4518 | 790.4621 | 0.1587 | 0.3983 | 0.7902 | 0.0499 |

$\mathrm{S}8$ | 54.7486 | 13.6153 | 790.4621 | 0.1587 | 0.3983 | 0.1694 | 0.0107 |

$\mathrm{S}9$ | 54.7486 | 17.7289 | 790.4621 | 0.1587 | 0.3983 | 0.0404 | 0.0026 |

$\mathrm{S}10$ | 70.0000 | 7.4518 | 416.0627 | 0.6827 | 0.1605 | 0.7902 | 0.0866 |

$\mathrm{S}11$ | 70.0000 | 13.6153 | 416.0627 | 0.6827 | 0.1605 | 0.1694 | 0.0186 |

$\mathrm{S}12$ | 70.0000 | 17.7289 | 416.0627 | 0.6827 | 0.1605 | 0.0404 | 0.0044 |

$\mathrm{S}13$ | 70.0000 | 7.4518 | 609.1166 | 0.6827 | 0.4412 | 0.7902 | 0.2380 |

$\mathrm{S}14$ | 70.0000 | 13.6153 | 609.1166 | 0.6827 | 0.4412 | 0.1694 | 0.0510 |

$\mathrm{S}15$ | 70.0000 | 17.7289 | 609.1166 | 0.6827 | 0.4412 | 0.0404 | 0.0122 |

$\mathrm{S}16$ | 70.0000 | 7.4518 | 790.4621 | 0.6827 | 0.3983 | 0.7902 | 0.2149 |

$\mathrm{S}17$ | 70.0000 | 13.6153 | 790.4621 | 0.6827 | 0.3983 | 0.1694 | 0.0461 |

$\mathrm{S}18$ | 70.0000 | 17.7289 | 790.4621 | 0.6827 | 0.3983 | 0.0404 | 0.0110 |

$\mathrm{S}19$ | 85.2514 | 7.4518 | 416.0627 | 0.1587 | 0.1605 | 0.7902 | 0.0201 |

$\mathrm{S}20$ | 85.2514 | 13.6153 | 416.0627 | 0.1587 | 0.1605 | 0.1694 | 0.0043 |

$\mathrm{S}21$ | 85.2514 | 17.7289 | 416.0627 | 0.1587 | 0.1605 | 0.0404 | 0.0010 |

$\mathrm{S}22$ | 85.2514 | 7.4518 | 609.1166 | 0.1587 | 0.4412 | 0.7902 | 0.0553 |

$\mathrm{S}23$ | 85.2514 | 13.6153 | 609.1166 | 0.1587 | 0.4412 | 0.1694 | 0.0119 |

$\mathrm{S}24$ | 85.2514 | 17.7289 | 609.1166 | 0.1587 | 0.4412 | 0.0404 | 0.0028 |

$\mathrm{S}25$ | 85.2514 | 7.4518 | 790.4621 | 0.1587 | 0.3983 | 0.7902 | 0.0499 |

$\mathrm{S}26$ | 85.2514 | 13.6153 | 790.4621 | 0.1587 | 0.3983 | 0.1694 | 0.0107 |

$\mathrm{S}27$ | 85.2514 | 17.7289 | 790.4621 | 0.1587 | 0.3983 | 0.0404 | 0.0026 |

Item | 69-Bus | 94-Bus |
---|---|---|

System voltage | 12.66 KV | 15KV |

${V}_{min}$ (p.u) | 0.90919 @ bus 65 | 0.84749 @ bus 92 |

${V}_{max}$ (p.u) excluding the slack bus | 0.99997 @ bus 2 | 0.99508 @ bus 2 |

Total active load demand (KW) | 3801.490 | 4797.000 |

Total reactive load demand (KVAR) | 2694.600 | 2323.900 |

Total active loss (KW) | 224.975 | 365.173 |

Total reactive loss (KVAR) | 102.187 | 505.785 |

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

Voltage limits | $0.90\le {\mathrm{V}}_{\mathrm{i}}\le 1.05\mathrm{p}.\mathrm{u}$ |

PV sizing limits for the 69-bus system | $0\le {\mathrm{P}}_{\mathrm{PV}}\le 3801.490\mathrm{kW}$ |

WT sizing limits for the 69-bus system | $0\le {\mathrm{P}}_{\mathrm{WT}}\le 3801.490\mathrm{kW}$ |

Power factor limits | $0.65\le {\mathrm{PF}}_{\mathrm{i}}\le 1$ |

PV sizing limits for the 94-bus system | $0\le {\mathrm{P}}_{\mathrm{PV}}\le $4797 $\mathrm{kW}$ |

WT sizing limits for the 94-bus system | $0\le {\mathrm{P}}_{\mathrm{WT}}\le 4797\mathrm{kW}$ |

Algorithm | Parameter Settings |
---|---|

EO | ${T}_{max}$ = 100, Search agents No. = 25, L1 = 2, L2 = 1, GP = 0.5 |

PSO | ${T}_{max}$ = 100, Search agents No. = 25, |

ALO | ${T}_{max}$ = 100, Search agents No. = 25 |

SCA | ${T}_{max}$ = 100, Search agents No. = 25 |

**Table 6.**The output powers of renewable energy resources (RERs), the power losses, Voltage Deviations (VD), Voltage Stability Index (VSI), cost, and emission rates for each scenario of IEEE 69-bus system.

Scenario | ${\mathit{P}}_{\mathit{w}}\left(kW\right)$ | $\mathit{P}{5}_{\mathit{s}}\left(kW\right)$ | ${\mathit{P}}_{\mathit{L}\mathit{o}\mathit{s}\mathit{s}}\left(MW\right)$ | ${\mathit{\pi}}_{\mathit{S}}$ | $\mathit{V}\mathit{D}\left(pu\right)$ | $\mathit{V}\mathit{S}\mathit{I}\left(pu\right)$ | $\mathit{C}\mathit{o}\mathit{s}\mathit{t}\left(USD\right)$ | $\mathit{E}\mathit{E}\mathit{m}\mathit{i}\mathit{s}\mathit{i}\mathit{o}\mathit{n}$ $\left(kg/MWh\right)$ |
---|---|---|---|---|---|---|---|---|

$\mathrm{S}1$ | 394.2 | 74.0592 | 48.4097 | 0.0201 | 0.8028 | 64.8894 | 1,071,600 | 345.9392 |

$\mathrm{S}2$ | 939.9 | 74.0592 | 12.7234 | 0.0043 | 0.3889 | 66.4681 | 1,589,600 | 723.2575 |

$\mathrm{S}3$ | 1151 | 74.0592 | 12.7201 | 0.0010 | 0.318 | 67.0724 | 1,785,600 | 860.2859 |

$\mathrm{S}4$ | 394.2 | 108.4228 | 47.6489 | 0.0553 | 0.7733 | 65.0009 | 1,103,800 | 368.7346 |

$\mathrm{S}5$ | 939.9 | 108.4228 | 12.2143 | 0.0119 | 0.3597 | 66.581 | 1,621,700 | 745.8896 |

$\mathrm{S}6$ | 1151 | 108.4228 | 12.2965 | 0.0028 | 0.2924 | 67.1859 | 1,817,700 | 882.8625 |

$\mathrm{S}7$ | 394.2 | 140.7023 | 47.0604 | 0.0499 | 0.7456 | 65.1057 | 1,133,900 | 390.0656 |

$\mathrm{S}8$ | 939.9 | 140.7023 | 11.8596 | 0.0107 | 0.3323 | 66.687 | 1,651,700 | 767.0688 |

$\mathrm{S}9$ | 1151 | 140.7023 | 12.0212 | 0.0026 | 0.2684 | 67.2924 | 1,847,700 | 903.9902 |

$\mathrm{S}10$ | 394.2 | 74.0592 | 66.5655 | 0.0866 | 1.0111 | 64.119 | 1,090,700 | 353.3142 |

$\mathrm{S}11$ | 939.9 | 74.0592 | 18.8061 | 0.0186 | 0.5899 | 65.6923 | 1,612,500 | 738.4678 |

$\mathrm{S}12$ | 1151 | 74.0592 | 14.7628 | 0.0044 | 0.4346 | 66.2941 | 1,809,800 | 878.1181 |

$\mathrm{S}13$ | 394.2 | 108.4228 | 65.433 | 0.2380 | 0.9813 | 64.23 | 1,123,000 | 376.3508 |

$\mathrm{S}14$ | 939.9 | 108.4228 | 17.9418 | 0.0510 | 0.5603 | 65.8046 | 1,644,700 | 761.3304 |

$\mathrm{S}15$ | 1151 | 108.4228 | 13.9894 | 0.0122 | 0.4051 | 66.407 | 1,842,000 | 900.9217 |

$\mathrm{S}16$ | 394.2 | 140.7023 | 64.4987 | 0.2149 | 0.9534 | 64.3342 | 1,153,200 | 397.9062 |

$\mathrm{S}17$ | 939.9 | 140.7023 | 17.2566 | 0.0461 | 0.5327 | 65.9101 | 1,674,900 | 782.7241 |

$\mathrm{S}18$ | 1151 | 140.7023 | 13.3886 | 0.0110 | 0.3775 | 66.513 | 1,872,100 | 922.2607 |

$\mathrm{S}19$ | 394.2 | 74.0592 | 91.9413 | 0.0201 | 1.2233 | 63.3491 | 1,114,300 | 361.2603 |

$\mathrm{S}20$ | 939.9 | 74.0592 | 31.2589 | 0.0043 | 0.7942 | 64.9174 | 1,640,200 | 754.8008 |

$\mathrm{S}21$ | 1151 | 74.0592 | 22.9091 | 0.0010 | 0.6363 | 65.5169 | 1,838,900 | 897.2459 |

$\mathrm{S}22$ | 394.2 | 108.4228 | 90.4229 | 0.0553 | 1.1932 | 63.4595 | 1,146,700 | 384.5473 |

$\mathrm{S}23$ | 939.9 | 108.4228 | 30.0269 | 0.0119 | 0.7644 | 65.0292 | 1,672,500 | 777.902 |

$\mathrm{S}24$ | 1151 | 108.4228 | 21.7739 | 0.0028 | 0.6065 | 65.6292 | 1,871,200 | 920.2843 |

$\mathrm{S}25$ | 394.2 | 140.7023 | 89.1295 | 0.0499 | 1.165 | 63.5631 | 1,177,100 | 406.3358 |

$\mathrm{S}26$ | 939.9 | 140.7023 | 28.9996 | 0.0107 | 0.7365 | 65.1342 | 1,702,800 | 799.5178 |

$\mathrm{S}27$ | 1151 | 140.7023 | 20.8364 | 0.0026 | 0.5787 | 65.7347 | 1,901,400 | 941.8418 |

Scenario | ${\mathit{\pi}}_{\mathit{S}}$ | $\mathit{E}\mathit{T}{\mathit{P}}_{\mathit{L}\mathit{o}\mathit{s}\mathit{s}}\left(pu\right)$ | $\mathit{E}\mathit{T}\mathit{V}\mathit{D}\left(pu\right)$ | $\mathit{E}\mathit{T}\mathit{V}\mathit{S}\mathit{I}\left(pu\right)$ | $\mathit{E}\mathit{T}\mathit{C}\mathit{o}\mathit{s}\mathit{t}\left(USD\right)$ | $\mathit{E}\mathit{T}\mathit{E}\mathit{m}\mathit{i}\mathit{s}\mathit{s}\mathit{i}\mathit{o}\mathit{n}$ $\left(kg/MWh\right)$ |
---|---|---|---|---|---|---|

$\mathrm{S}1$ | 0.0201 | 0.973 | 0.0161 | 1.3043 | 21,540 | 6.9534 |

$\mathrm{S}2$ | 0.0043 | 0.0547 | 0.0017 | 0.2858 | 6840 | 3.1100 |

$\mathrm{S}3$ | 0.0010 | 0.0127 | 0.0003 | 0.0671 | 1790 | 0.8603 |

$\mathrm{S}4$ | 0.0553 | 2.635 | 0.0428 | 3.5946 | 61,040 | 20.3910 |

$\mathrm{S}5$ | 0.0119 | 0.1453 | 0.0043 | 0.7923 | 19,300 | 8.8761 |

$\mathrm{S}6$ | 0.0028 | 0.0344 | 0.0008 | 0.1881 | 5090 | 2.4720 |

$\mathrm{S}7$ | 0.0499 | 2.3483 | 0.0372 | 3.2488 | 56,580 | 19.4643 |

$\mathrm{S}8$ | 0.0107 | 0.1269 | 0.0036 | 0.7136 | 17,670 | 8.2076 |

$\mathrm{S}9$ | 0.0026 | 0.0313 | 0.0007 | 0.175 | 4800 | 2.3504 |

$\mathrm{S}10$ | 0.0866 | 5.7646 | 0.0876 | 5.5527 | 94,460 | 30.5970 |

$\mathrm{S}11$ | 0.0186 | 0.3498 | 0.011 | 1.2219 | 29,990 | 13.7355 |

$\mathrm{S}12$ | 0.0044 | 0.065 | 0.0019 | 0.2917 | 7960 | 3.8637 |

$\mathrm{S}13$ | 0.2380 | 15.573 | 0.2335 | 15.2867 | 267,270 | 89.5715 |

$\mathrm{S}14$ | 0.0510 | 0.915 | 0.0286 | 3.356 | 83,880 | 38.8278 |

$\mathrm{S}15$ | 0.0122 | 0.1707 | 0.0049 | 0.8102 | 22,470 | 10.9912 |

$\mathrm{S}16$ | 0.2149 | 13.8608 | 0.2049 | 13.8254 | 247,830 | 85.5101 |

$\mathrm{S}17$ | 0.0461 | 0.7955 | 0.0246 | 3.0385 | 77,210 | 36.0836 |

$\mathrm{S}18$ | 0.0110 | 0.1473 | 0.0042 | 0.7316 | 20,590 | 10.1449 |

$\mathrm{S}19$ | 0.0201 | 1.848 | 0.0246 | 1.2733 | 22,400 | 7.2613 |

$\mathrm{S}20$ | 0.0043 | 0.1344 | 0.0034 | 0.2791 | 7050 | 3.2456 |

$\mathrm{S}21$ | 0.0010 | 0.0229 | 0.0006 | 0.0655 | 1840 | 0.8972 |

$\mathrm{S}22$ | 0.0553 | 5.0004 | 0.066 | 3.5093 | 63,410 | 21.2655 |

$\mathrm{S}23$ | 0.0119 | 0.3573 | 0.0091 | 0.7738 | 19,900 | 9.2570 |

$\mathrm{S}24$ | 0.0028 | 0.061 | 0.0017 | 0.1838 | 5240 | 2.5768 |

$\mathrm{S}25$ | 0.0499 | 4.4476 | 0.0581 | 3.1718 | 58,740 | 20.2762 |

$\mathrm{S}26$ | 0.0107 | 0.3103 | 0.0079 | 0.6969 | 18,220 | 8.5548 |

$\mathrm{S}27$ | 0.0026 | 0.0542 | 0.0015 | 0.1709 | 4940 | 2.4488 |

Summation | 1 | 56.2394 | 0.8816 | 64.6087 | 1,248,050 | 467.7936 |

**Table 8.**A comparison of the obtained results by the application of the investigated algorithms for the IEEE 69-bus system.

Algorithm | Average | Best Solution | Worst Solution | Standard Deviation |
---|---|---|---|---|

SCA | 0.3660 | 0.3621 | 0.3851 | 0.0077 |

PSO | 0.3934 | 0.3617 | 0.4505 | 0.0290 |

ALO | 0.3928 | 0.3636 | 0.4147 | 0.0194 |

EO | 0.3616 | 0.3609 | 0.3624 | 0.0006 |

**Table 9.**The output powers of RERs, the power losses, Voltage Deviations (VD), Voltage Stability Index (VSI), cost, and emission rates for each scenario of the IEEE 94-bus system.

Scenario | ${\mathit{P}}_{\mathit{w}}\left(kW\right)$ | ${\mathit{P}}_{\mathit{s}}\left(kW\right)$ | ${\mathit{P}}_{\mathit{L}\mathit{o}\mathit{s}\mathit{s}}\left(MW\right)$ | ${\mathit{\pi}}_{\mathit{S}}$ | $\mathit{V}\mathit{D}\left(pu\right)$ | $\mathit{V}\mathit{S}\mathit{I}\left(pu\right)$ | $\mathit{C}\mathit{o}\mathit{s}\mathit{t}\left(USD\right)$ | $\mathit{E}\mathit{E}\mathit{m}\mathit{i}\mathit{s}\mathit{s}\mathit{i}\mathit{o}\mathit{n}$ $\left(kg/MWh\right)$ |
---|---|---|---|---|---|---|---|---|

$\mathrm{S}1$ | 432.2 | 44.5187 | 74.0228 | 0.0201 | 4.1453 | 77.6061 | 1,144,200 | 355.6937 |

$\mathrm{S}2$ | 1030.5 | 44.5187 | 52.827 | 0.0043 | 1.5785 | 86.8996 | 1,706,500 | 757.7621 |

$\mathrm{S}3$ | 1262 | 44.5187 | 62.2786 | 0.0010 | 1.2001 | 90.5301 | 1,918,400 | 901.8688 |

$\mathrm{S}4$ | 432.2 | 65.1755 | 72.9507 | 0.0553 | 4.0964 | 77.7732 | 1,163,700 | 369.7955 |

$\mathrm{S}5$ | 1030.5 | 65.1755 | 52.801 | 0.0119 | 1.5339 | 87.0723 | 1,725,600 | 771.1849 |

$\mathrm{S}6$ | 1262 | 65.1755 | 62.5802 | 0.0028 | 1.207 | 90.705 | 1,937,500 | 915.0791 |

$\mathrm{S}7$ | 432.2 | 84.5794 | 72.0738 | 0.0499 | 4.0507 | 77.9294 | 1,182,000 | 382.9575 |

$\mathrm{S}8$ | 1030.5 | 84.5794 | 52.8868 | 0.0107 | 1.5015 | 87.2339 | 1,743,600 | 783.7222 |

$\mathrm{S}9$ | 1262 | 84.5794 | 62.9677 | 0.0026 | 1.2138 | 90.8688 | 1,955,400 | 927.4206 |

$\mathrm{S}10$ | 432.2 | 44.5187 | 112.9715 | 0.0866 | 4.987 | 74.7688 | 1,179,600 | 367.2078 |

$\mathrm{S}11$ | 1030.5 | 44.5187 | 75.2483 | 0.0186 | 2.3577 | 83.974 | 1,747,100 | 780.0024 |

$\mathrm{S}12$ | 1262 | 44.5187 | 79.4775 | 0.0044 | 1.453 | 87.5682 | 1,960,700 | 927.4984 |

$\mathrm{S}13$ | 432.2 | 65.1755 | 111.2094 | 0.2380 | 4.9359 | 74.9366 | 1,199,300 | 381.7574 |

$\mathrm{S}14$ | 1030.5 | 65.1755 | 74.644 | 0.0510 | 2.3114 | 84.1472 | 1,766,400 | 793.8006 |

$\mathrm{S}15$ | 1262 | 65.1755 | 79.2327 | 0.0122 | 1.4557 | 87.7437 | 1,979,900 | 941.0633 |

$\mathrm{S}16$ | 432.2 | 84.5794 | 109.6941 | 0.2149 | 4.8884 | 75.0935 | 1,217,800 | 395.3338 |

$\mathrm{S}17$ | 1030.5 | 84.5794 | 74.1937 | 0.0461 | 2.2683 | 84.3093 | 1,784,600 | 806.6858 |

$\mathrm{S}18$ | 1262 | 84.5794 | 79.1134 | 0.0110 | 1.4596 | 87.9079 | 1,998,000 | 953.7337 |

$\mathrm{S}19$ | 432.2 | 44.5187 | 166.2304 | 0.0201 | 5.8647 | 71.9096 | 1,224,200 | 380.0133 |

$\mathrm{S}20$ | 1030.5 | 44.5187 | 110.2486 | 0.0043 | 3.1668 | 81.0279 | 1,797,400 | 804.6575 |

$\mathrm{S}21$ | 1262 | 44.5187 | 108.7544 | 0.0010 | 2.1969 | 84.586 | 2,012,800 | 955.8679 |

$\mathrm{S}22$ | 432.2 | 65.1755 | 163.7147 | 0.0553 | 5.8113 | 72.0782 | 1,244,100 | 395.052 |

$\mathrm{S}23$ | 1030.5 | 65.1755 | 109.0211 | 0.0119 | 3.1187 | 81.2017 | 1,817,000 | 818.8602 |

$\mathrm{S}24$ | 1262 | 65.1755 | 107.9232 | 0.0028 | 2.1504 | 84.762 | 2,032,300 | 969.8134 |

$\mathrm{S}25$ | 432.2 | 84.5794 | 161.5027 | 0.0499 | 5.7616 | 72.2358 | 1,262,900 | 409.0805 |

$\mathrm{S}26$ | 1030.5 | 84.5794 | 107.9934 | 0.0107 | 3.0738 | 81.3643 | 1,835,300 | 832.1201 |

$\mathrm{S}27$ | 1262 | 84.5794 | 107.2602 | 0.0026 | 2.107 | 84.9267 | 2,050,500 | 982.8367 |

Scenario | ${\mathit{\pi}}_{\mathit{S}}$ | $\mathit{E}\mathit{T}{\mathit{P}}_{\mathit{L}\mathit{o}\mathit{s}\mathit{s}}\left(kW\right)$ | $\mathit{E}\mathit{T}\mathit{V}\mathit{D}\left(pu\right)$ | $\mathit{E}\mathit{T}\mathit{V}\mathit{S}\mathit{I}\left(pu\right)$ | $\mathit{E}\mathit{T}\mathit{C}\mathit{o}\mathit{s}\mathit{t}\left(USD\right)$ | $\mathit{E}\mathit{T}\mathit{E}\mathit{m}\mathit{i}\mathit{s}\mathit{s}\mathit{i}\mathit{o}\mathit{n}$ $\left(kg/MWh\right)$ |
---|---|---|---|---|---|---|

$\mathrm{S}1$ | 0.0201 | 1.4879 | 0.0833 | 1.5599 | 23,000 | 71,494 |

$\mathrm{S}2$ | 0.0043 | 0.2272 | 0.0068 | 0.3737 | 7340 | 32,584 |

$\mathrm{S}3$ | 0.0010 | 0.0623 | 0.0012 | 0.0905 | 1920 | 9019 |

$\mathrm{S}4$ | 0.0553 | 4.0342 | 0.2265 | 4.3009 | 64,350 | 204,497 |

$\mathrm{S}5$ | 0.0119 | 0.6283 | 0.0183 | 1.0362 | 20,540 | 91,771 |

$\mathrm{S}6$ | 0.0028 | 0.1752 | 0.0034 | 0.254 | 5430 | 25,622 |

$\mathrm{S}7$ | 0.0499 | 3.5965 | 0.2021 | 3.8887 | 58,980 | 191,096 |

$\mathrm{S}8$ | 0.0107 | 0.5659 | 0.0161 | 0.9334 | 18,660 | 83,858 |

$\mathrm{S}9$ | 0.0026 | 0.1637 | 0.0032 | 0.2363 | 5080 | 24,113 |

$\mathrm{S}10$ | 0.0866 | 9.7833 | 0.4319 | 6.475 | 102,150 | 318,002 |

$\mathrm{S}11$ | 0.0186 | 1.3996 | 0.0439 | 1.5619 | 3,2500 | 145,080 |

$\mathrm{S}12$ | 0.0044 | 0.3497 | 0.0064 | 0.3853 | 8630 | 40,810 |

$\mathrm{S}13$ | 0.2380 | 26.4678 | 1.1748 | 17.8349 | 285,440 | 908,583 |

$\mathrm{S}14$ | 0.0510 | 3.8068 | 0.1179 | 4.2915 | 90,090 | 404,838 |

$\mathrm{S}15$ | 0.0122 | 0.9666 | 0.0178 | 1.0705 | 24,160 | 114,810 |

$\mathrm{S}16$ | 0.2149 | 23.5733 | 1.0505 | 16.1376 | 261,710 | 849,572 |

$\mathrm{S}17$ | 0.0461 | 3.4203 | 0.1046 | 3.8867 | 82,270 | 371,882 |

$\mathrm{S}18$ | 0.0110 | 0.8702 | 0.0161 | 0.967 | 21,980 | 104,911 |

$\mathrm{S}19$ | 0.0201 | 3.3412 | 0.1179 | 1.4454 | 24,610 | 76,383 |

$\mathrm{S}20$ | 0.0043 | 0.4741 | 0.0136 | 0.3484 | 7730 | 34,600 |

$\mathrm{S}21$ | 0.0010 | 0.1088 | 0.0022 | 0.0846 | 2010 | 9559 |

$\mathrm{S}22$ | 0.0553 | 9.0534 | 0.3214 | 3.9859 | 68,800 | 218,464 |

$\mathrm{S}23$ | 0.0119 | 1.2974 | 0.0371 | 0.9663 | 21,620 | 97,444 |

$\mathrm{S}24$ | 0.0028 | 0.3022 | 0.006 | 0.2373 | 5690 | 27,155 |

$\mathrm{S}25$ | 0.0499 | 8.059 | 0.2875 | 3.6046 | 63,020 | 204,131 |

$\mathrm{S}26$ | 0.0107 | 1.1555 | 0.0329 | 0.8706 | 19,640 | 89,037 |

$\mathrm{S}27$ | 0.0026 | 0.2789 | 0.0055 | 0.2208 | 5330 | 25,554 |

Summation | 1 | 105.6493 | 4.3489 | 77.0479 | 1,332,680 | 4,774,869 |

**Table 11.**A comparison of the obtained results by the application of the investigated algorithms on the 94-bus system.

Algorithm | Average | Best Solution | Worst Solution | SD |
---|---|---|---|---|

SCA | 0.3546 | 0.3543 | 0.3562 | 0.0005 |

PSO | 0.3738 | 0.3621 | 0.4141 | 0.0160 |

ALO | 0.3898 | 0.3544 | 0.4879 | 0.0424 |

EO | 0.3543 | 0.3535 | 0.3564 | 0.0008 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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/).

## Share and Cite

**MDPI and ACS Style**

Ramadan, A.; Ebeed, M.; Kamel, S.; Abdelaziz, A.Y.; Haes Alhelou, H.
Scenario-Based Stochastic Framework for Optimal Planning of Distribution Systems Including Renewable-Based DG Units. *Sustainability* **2021**, *13*, 3566.
https://doi.org/10.3390/su13063566

**AMA Style**

Ramadan A, Ebeed M, Kamel S, Abdelaziz AY, Haes Alhelou H.
Scenario-Based Stochastic Framework for Optimal Planning of Distribution Systems Including Renewable-Based DG Units. *Sustainability*. 2021; 13(6):3566.
https://doi.org/10.3390/su13063566

**Chicago/Turabian Style**

Ramadan, Ashraf, Mohamed Ebeed, Salah Kamel, Almoataz Y. Abdelaziz, and Hassan Haes Alhelou.
2021. "Scenario-Based Stochastic Framework for Optimal Planning of Distribution Systems Including Renewable-Based DG Units" *Sustainability* 13, no. 6: 3566.
https://doi.org/10.3390/su13063566