# A Survey on Computational Intelligence Applications in Distribution Network Optimization

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## Abstract

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## 1. Introduction

## 2. Methodology

- Extraction of the presented mathematical model—In this step, a multi-member team took responsibility for extracting key information from each paper and, if necessary, filling in the gaps in the mathematical model.
- Synthesis of a defined mathematical model—If key parameters are missing in the first step, the paper is marked as incomplete and is temporarily not considered. However, it happened that some other work was based on the same laws as the one that was neglected, so one complements the other. In this step it is crucial to obtain the same or approximately the same starting point as the original authors.
- Development of an identical or similar solution—In this step, it has proved crucial to have a team of specialized experts and profiled researchers who can understand the principles to be set out in development in order to achieve greatest effect. Usually, rapid prototyping does not require more than a few days of work for a well-organized team, and as these are very similar methods based on common principles the testing time decreased exponentially throughout the research phase.
- Analysis of the obtained results—In this phase, the involvement of external domain experts proved to be crucial, who could intuitively, based on many years of experience, suggest measures for improvement if the results did not correspond to expectations. Moreover, they were able to explain some unexpected results and thus immediately conclude where the shortcomings of the basic observed model of some papers are. Analysis was conducted ad-hoc by the whole research team and most of the time heterogeneity of results was discussed.
- Brainstorming session—This is a key part of the whole process; in this step, there was an exchange of ideas, knowledge and solutions, and often with loud commenting a certain hypothesis or assumption was fiercely defended. After this session, the certainty of validity was ensured and the whole process was repeated as many times as necessary to process all the papers selected for processing.

## 3. DG and the Distribution Network

#### 3.1. SGAM Framework

- Universality—The proposed solutions must be vendor-agnostic and without preferences in existing architectures and solutions. Neutral and scientifically objective perspective is mandatory when evaluating the possible solutions for future power networks.
- Localization—Given the functional zones, the application of possible solution needs to be clearly stated for which zone it is intended. Systematic view of the whole framework is needed to clearly understand the level in the topology in which any solution can be applied to.
- Consistency—The use case must not violate the existing SGAM framework and in no case must single out one zone as dominant. Interdependence and reliable functioning with other zones must be respected.
- Flexibility—Alternative designs and implementation of use cases, functionalities and services to any SGAM layer or zone need to be covered. Methods and algorithms observed in this paper can be part of any SGAM layer or zone, with the best starting point in the third or fourth zone.
- Scalability—Once the proposed solution is part of one zone or a smaller part of the network, it must be able to successfully scale to other zones or to the whole network. Of course, the limiting factor here may be computational power, but this is not the subject of discussion in this paper and it can be solved by Cloud Computing [32].
- Extensibility—Solutions need to adapt to evolutionary changes in the Smart Grid environment.
- Interoperability—Interaction between multiple actors, applications and systems occurs via information exchange with defined protocols and data models. Chain of entities and connections define interfaces in which the consistency and interoperability become secured.

#### 3.2. DG Impact in ADN

## 4. Optimal DG Planning and Scheduling

#### 4.1. Optimization Methods

- Analytical methods;
- Heuristic and meta-heuristic methods;
- Artificial Intelligence–based methods;
- Evolutionary principles and biologically inspired methods;
- Distinct methods for specific purposes.

#### 4.2. Analytical Methods

_{i}is the real voltage of the i-th bus with the voltage angle,$\delta $.

#### 4.3. Computational Intelligence–Based Methods

- Conventional approaches.
- Approaches based on the artificial intelligence.
- Hybrid approaches based on multiple methods of artificial intelligence.

_{i}(DG), depending on consumer active power P

_{Di}and distributed generation active power P

_{DGi}.

#### 4.3.1. GA-Based Methods

_{DIST}, and the load distributed for the i-th fault, ${L}_{DIS{T}_{i}}$; the objective function of DG integration costs reduction (13), which is determined by financial units per kilowatt of installed DG power (KC) and observed as the objective of determining the least power of DG which will meet the previous two objectives [41]. The constraints of the proposed algorithm that the authors have defined, similarly to previous authors, are load-flow constraints through the specific branches, voltage constraints and limitations of the number of DG units.

#### 4.3.2. PSO-Based Approaches

_{1}represents the objective of real power losses reduction, the function f

_{2}represents the objective of the voltage profile improvement while the function f

_{3}is the radial feeder voltage stability index taken from the literature. Coefficients k

_{1}, k

_{2}, β

_{1}and β

_{2}represent the penalizing coefficients of the corresponding expressions. The presented objective function considers the values of the voltage (V

_{ni}) and the apparent power (S

_{ni}) on the observed radial feeder busbars.

#### 4.3.3. GA and PSO Comparison

## 5. Optimal Smart Grid Management

_{2}emissions Lamadrid et al. [129] proposed a novel optimization solution that favors RES in power dispatch and scheduling, if the technology permits planning. From the perspective of system operator and in compliance with network policies, authors present their optimization formulation respecting technical and economic limitations and prove the usefulness of their method by testing it on 279-bus transmission network in Texas, USA. The authors have taken into consideration a stochastic nature of some RES and gave them priority in dispatch schedule. Although modeling is complex, authors managed to perform it correctly by using mathematical correct workaround solutions. By proposed solution authors managed to simulate a future 24-hour period which is adequate for system schedule and operation in market conditions. For wind power modeling, authors used combination of historical and calculated data. This paper is very important due to the complexity of observed problem, and although the authors themselves say that improvements are needed, this paper presents state-of-the-art in operational management and DG scheduling.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Abbreviation | Description | Unit |
---|---|---|

${\alpha}_{ij}$ | Sensitivity factor of real power loss with respect to Real power injection from DG (Acharya et al., 2006) | MW |

${\alpha}_{ij}$ | The transmission coefficient of the real part of the complex power by Kansal et al. (2013) | $n$ |

${A}_{ij}$ | Quotient of product of voltage angle difference cosine and line resistance with voltage level (Biswas et al., 2012) | |

${\beta}_{ij}$ | Sensitivity factor of reactive power loss with respect to reactive power injection from DG (Acharya et al., 2006) | MVAr |

${\beta}_{ij}$ | The transmission coefficient of the reactive part of the complex power by Kansal et al. (2013) | $n$ |

${B}_{ij}$ | Quotient of product of voltage angle difference sinus and line resistance with voltage level (Biswas et al., 2012) | |

${\beta}_{1}$ | Penalty coefficient (${\mathsf{\beta}}_{1}=0.32)$ (Moradi and Abedini, 2012) | ${\beta}_{1}=0.32$ |

${\beta}_{2}$ | Penalty coefficient (${\mathsf{\beta}}_{2}=0.3)$ (Moradi and Abedini, 2012) | ${\beta}_{2}=0.3$ |

${C}_{i}^{a}$ | Active power prices with DG (Singh and Goswami, 2010) | US$/MWh |

${C}_{i}^{r}$ | Reactive power prices with DG (Singh and Goswami, 2010) | US$/MWh |

${C}_{DG}$ | Total cost associated with the DGs (Biswas et al., 2012) | US$ mil. |

${C}_{fc}$ | Cost of power generation from fuel cell (Niknam et al., 2011) | US$ |

${C}_{wind}$ | Cost of power generation from wind power (Niknam et al., 2011) | US$ |

${C}_{pv}$ | Cost of power generation from photovoltaic system (Niknam et al., 2011) | US$ |

$Cos{t}_{sub}$ | Cost of substation (Niknam et al., 2011) | US$ |

${\delta}_{ij}$ | Voltage angle difference between bus i and bus j (Alrashidi and Alhajri, 2011) | rad |

${E}_{{t}_{fc}}$ | Emission of atmospheric pollutants from fuel-cell power generation (Niknam et al., 2011) | kg/h |

${E}_{{t}_{wind}}$ | Emission of atmospheric pollutants from wind power generation (Niknam et al., 2011) | kg/h |

E_{tpv} | Emission of atmospheric pollutants from photovoltaic power generation (Niknam et al., 2011) | kg/h |

${I}_{i}$ | Actual current of the i-th branch (Niknam et al., 2011) | A |

$ILP$ | Real power losses after DG integration by El-Zonkoly (2014.) | % |

$ILQ$ | Reactive power losses after DG integration by El-Zonkoly (2014.) | % |

$IC$ | MVA capacity index regarding the power flows through conductors in paper by El-Zonkoly (2014.) | % |

$IVD$ | Voltage profile index, observed as voltage deviation from the nominal value by El-Zonkoly (2014.) | % |

$ISC$ | Short circuit level index, observed as DG impact on short circuit current increase in paper by El-Zonkoly (2014.) | % |

${k}_{1}$ | Penalty coefficient (Moradi and Abedini, 2012) | ${k}_{1}=0.6$ |

${k}_{2}$ | Penalty coefficient (Moradi and Abedini, 2012) | ${k}_{2}=0.35$ |

${K}_{C}$ | Is the cost of DG per KW (Biswas et al., 2012) | US$ |

$\mathsf{\lambda}$ | Electricity price at power supply point (Singh and Goswami, 2010) | US$/MWh |

$\mathrm{L}$ | Set of nodes in ADN by Lv and Ai (2016) | $n$ |

$LLR$ | Total line-loss reduction (Abou El-Ela et al., 2010) | % |

$L{L}_{wo/DG}$ | Line-loss without the DG (Abou El-Ela et al., 2010) | MW |

$L{L}_{w/DG}$ | Line-loss with the DG (Abou El-Ela et al., 2010) | MW |

${L}_{DIS{T}_{i}}$ | Load distributed for the i-th fault (Biswas et al., 2012) | MW |

$MBDG$ | Maximal composite benefits of DG (Abou El-Ela et al., 2010) | |

$MOF$ | PSO-based multi-objective function by El-Zonkoly (2014.) | |

$N$ | Number of buses in distribution system by Kansal et al. | N |

$NB$ | Number of radial distribution system buses (Alrashidi and Alhajri, 2011) | $n$ |

${N}_{br}$ | Number of the branches (Niknam et al., 2011) | $n$ |

${N}_{bus}$ | Total number of the buses (Niknam et al., 2011) | $n$ |

${N}_{d}$ | Number of years (Niknam et al., 2011) | $n$ |

${N}_{F}$ | Total number of faults within a specified time duration (Biswas et al., 2012) | |

N_{fc} | Number of fuel-cell units (Niknam et al., 2011) | $n$ |

${N}_{pv}$ | Number of photovoltaic units (Niknam et al., 2011) | $n$ |

${N}_{wind}$ | Number of wind units (Niknam et al., 2011) | $n$ |

$\mathsf{\theta}$ | Power exchange level by Lv and Ai (2016) | kW/t |

${P}_{\omega}^{t}$ | Inertial probability (Gomez-Gonzalez et al., 2012) | $Q\in \left[0,1\right]$ |

${p}_{\omega ,max}$ | Maximal inertia per population (Gomez-Gonzalez et al., 2012) | $Q\in \left[0,1\right]$ |

${p}_{\omega ,min}$ | Minimal inertia per population (Gomez-Gonzalez et al., 2012) | $Q\in \left[0,1\right]$ |

${P}_{Di}$ | Active power demand at any bus i (Singh and Goswami, 2010) | MW |

${P}_{DGi}$ | Real power injection at node i (Acharya et al., 2006) | MW |

${P}_{DGi}$ | Active power generated by DG (Singh and Goswami, 2010) | MW |

${P}_{D{G}_{i}}$ | Size of the i-th DG (Biswas et al., 2012) | MW |

${P}_{Di}$ | Load demand at node i (Acharya et al., 2006) | MW |

${P}_{i}^{\prime 2}$ | Real power flows at the receiving end of the forward-update procedure by Injeti el al. | MW |

${P}_{i},{P}_{j}$ | The active power injections at bus i and bus j by Kansal et al. | MW |

${P}_{fc}$ | Power generated from fuel cell (Niknam et al., 2011) | kWh |

${P}_{G}$ | Active power of distributed generation (Aman et al., 2012) | MW |

${\mathrm{P}}_{\mathrm{l},\mathrm{t}}^{\mathrm{PCC}}$ | PCC power exchange of MG n by Lv and Ai (2016) | kW |

${P}_{Loss}$ | Line losses (Injeti and Prema Kumar, 2013) | MW |

${P}_{T,Loss}$ | Total feeder losses (Injeti and Prema Kumar, 2013) | MW |

${\mathrm{P}}_{\mathrm{t}}^{\mathrm{LOSS}}$ | power loss of ADN in paper by Lv and Ai (2016) | kW |

${P}_{eleect}^{DG}$ | The price of electricity (Singh and Goswami, 2010) | US$/MWh |

$PFR$ | Power flow reduction in critical lines (Abou El-Ela et al., 2010) | % |

$P{F}_{k,wo/DG}$ | Power flow in line k without DG (Abou El-Ela et al., 2010) | MW |

$P{F}_{k,w/DG}$ | Power flow in line k with DG (Abou El-Ela et al., 2010) | MW |

${P}_{pv}$ | Power generated from photovoltaic system (Niknam et al., 2011) | kWh |

${P}_{wind}$ | Power generated from wind power (Niknam et al., 2011) | kWh |

${Q}_{i}^{\prime 2}$ | Reactive power flows at the receiving end of the forward-update procedure by Injeti el al. | MVAr |

${Q}_{Di}$ | Reactive power demand at any bus i (Singh and Goswami, 2010) | MVAr |

${Q}_{DGi}$ | Reactive power generated by DG (Singh and Goswami, 2010) | MVAr |

${Q}_{i},{Q}_{j}$ | The reactive power injections at bus i and bus j by Kansal et al. | MVAr |

${R}_{i}$ | Resistance of the i-th branch (Niknam et al., 2011) | $\mathsf{\Omega}$/km |

${r}_{ij}$ | Real part of line impedance (Aman et al., 2012) | $\mathsf{\Omega}$/km |

${R}_{1i}\left(j\right)$ | Equivalent resistance between bus 1 and bus i when DG is located at bus j (Wang and Nehrir, 2004) | p.u. |

$RPL$ | Real power loss (Biswas et al., 2012) | MW |

${\sigma}_{1},{\sigma}_{2},{\sigma}_{3},{\sigma}_{4},{\sigma}_{5}$ | Weights for corresponding importance of each DG impact index by El-Zonkoly (2014.) | ${\sigma}_{\mathrm{p}}\in \left[0,1\right]$ |

${S}_{DIST}$ | Total load distributed (Biswas et al., 2012) | |

$\left|{S}_{ni}\right|$ | Apparent power at bus ${\mathrm{n}}_{\mathrm{i}}$(Moradi and Abedini, 2012) | MVA |

$\left|{S}_{ni}^{max}\right|$ | Maximum apparent power at bus ${\mathrm{n}}_{\mathrm{i}}$(Moradi and Abedini, 2012) | MVA |

$S{R}_{w/DG}$ | Spinning reserve with DG [23] (Abou El-Ela et al., 2010) | p.u. |

$S{R}_{wo/DG}$ | Spinning reserve without DG (Abou El-Ela et al., 2010) | p.u. |

$SRI$ | Spinning reserve increasing (Abou El-Ela et al., 2010) | % |

$\mathrm{T}$ | The sum of scheduling period t in paper by Lv and Ai (2016) | $n$ |

$\Delta t$ | Time step (one year) (Niknam et al., 2011) | $n$ |

${\mathrm{U}}_{\mathrm{n}}$ | set of types of DGs in Microgrid n; u = 1, 2, 3, 4 and 5 denote fuel cell, microturbine, battery storage, Photovoltaic System and Wind turbine, respectively, by Lv and Ai (2016) | $n\in \left[0,5\right]$ |

${V}_{i}$ | The bus i voltage (Alrashidi and Alhajri, 2011) | p.u. |

${V}_{i}$ | Real voltage of the i-th bus (Niknam et al., 2011) | p.u. |

${\left|{V}_{i}\right|}^{2}$ | Voltage magnitude at the receiving end of the forward-update procedure Injeti el al. | p.u. |

${V}_{j}$ | The bus j voltage (Alrashidi and Alhajri, 2011) | p.u. |

${V}_{ni}$ | Voltage of bus ${\mathrm{n}}_{\mathrm{i}}$(Moradi and Abedini, 2012) | p.u. |

${V}_{ni}^{max}$ | Maximum voltage at bus ${\mathrm{n}}_{\mathrm{i}}$(Moradi and Abedini, 2012) | p.u. |

${V}_{ni}^{min}$ | Minimum voltage at bus ${\mathrm{n}}_{\mathrm{i}}$ [(Moradi and Abedini, 2012) | p.u. |

${V}_{Rating},{V}_{rate}$ | Nominal voltage of the i-th bus (Niknam et al., 2011) | p.u. |

$VPI$ | Voltage profile improvement (Abou El-Ela et al., 2010) | % |

$V{P}_{w/DG}$ | Voltage profile index of the system with DG (Abou El-Ela et al., 2010) | p.u. |

$V{P}_{wo/DG}$ | Voltage profile index without DG (Abou El-Ela et al., 2010) | p.u. |

${w}_{1},{w}_{2}$ | Weight factors, ${\mathrm{w}}_{1}+{\mathrm{w}}_{2}=1$(Yang and Chen, 2011) | |

${w}_{1},{w}_{2},{w}_{3},{w}_{4}$ | Benefit weighting factors (Abou El-Ela et al., 2010) |

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**Figure 9.**Simplified model of microgrid used for validation in this paper, inspired by Reference [109].

Reference | Optimization Method | Merits | Limitations |
---|---|---|---|

Acharya et al. [25] | Analytical approach based on mathematical expression | Simple analytical solution for determining size and position of DG | If DG is already installed there is a need for significant amount of power flow calculations |

Gözel et al. [26] | Bus-injection to branch-current and branch-current to bus-voltage matrices. | One power-flow calculation, simple matrix algebra and faster performance | Does not take into account the interaction of nodes in the network when first DG is placed |

Wang et al. [37] | Analytical approach | For radial feeders multiple DG can be taken into account; consideration of time varying DG | Only overhead lines with uniformly distributed loads are considered |

Aman et al. [38] | Power Stability Index and Golden Section Search algorithm | Reduced computation time when compared to Golden Section Search Algorithm | Only radial networks are simulated and tested |

Injeti et al. [27] | Simulated annealing | Comparison of meta-heuristic methods, including genetic algorithm, Particle Swarm algorithm and Loss Sensitivity Factor Simulated algorithm | Only radial networks are simulated and tested |

Singh et al. [39] | GA | Pricing problem addressed instead of power losses | DG is considered as negative load, not simulated independently |

Abou El-Ela et al. [40] | Modified GA | Consideration of voltage profile improvement, spinning reserve and line power flow reduction; exceptional mathematical overview of main DG impact indicators; tested on real Egyptian network | Time variability of generation and consumption not considered |

Biswas et al. [41] | GA | Technical and economical optimization performed; visual representation of losses variation as DG location and size changes; essential problem formulation | Time variability of generation and consumption not considered |

AlRashidi et al. [42] | PSO | Multiple DG planning and consideration in single run; fitness function development; backward/forward sweep approach; experimental design of custom PSO | Only time-independent loads and generation considered |

Gomes-Gonzales [43] | PSO | Total power generation covers total demand and real power losses what makes foundation for island operation | DG units have fixed power factors; time-independent loads and DG considered |

Moradi et al. [44] | GA + PSO | Hybrid method development; different algorithms benchmark | Time-independent loads and DG considered |

Soares et al. [45] | Signaled Particle Swarm Optimization | Identification of active distribution network management; achieving a balance between production and consumption; hourly optimization; fast execution | Missing emphasis on island operation possibility and justification of that possibility |

Saif et el. [46] | Double-layer Particle Swarm Optimization | Possibility of island operation and connected operation in which energy is sold to superior network; simulation-based optimization with considering stochastic behavior of distribution network; supply reliability considered | Sensitivity analysis of Particle Swarm Optimization model not emphasized |

Kansal et al. [47] | PSO | Different types of distributed generation considered with Particle Swarm and analytical approach | Demonstration of Particle Swarm performance for various types of distributed generation is not clear |

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Vukobratović, M.; Marić, P.; Horvat, G.; Balkić, Z.; Sučić, S. A Survey on Computational Intelligence Applications in Distribution Network Optimization. *Electronics* **2021**, *10*, 1247.
https://doi.org/10.3390/electronics10111247

**AMA Style**

Vukobratović M, Marić P, Horvat G, Balkić Z, Sučić S. A Survey on Computational Intelligence Applications in Distribution Network Optimization. *Electronics*. 2021; 10(11):1247.
https://doi.org/10.3390/electronics10111247

**Chicago/Turabian Style**

Vukobratović, Marko, Predrag Marić, Goran Horvat, Zoran Balkić, and Stjepan Sučić. 2021. "A Survey on Computational Intelligence Applications in Distribution Network Optimization" *Electronics* 10, no. 11: 1247.
https://doi.org/10.3390/electronics10111247