Capacity‐based optimization using whale optimization technique of a power distribution network

In the power distribution network, real power loss and voltage profile management are critical issues. By providing active and reactive power support, both of these issues can be managed. Distributed generation (DG) and capacitor bank (QG) can be utilized to solve these issues. Therefore, this paper utilized optimally placed and sized DG and capacitor (QG) to minimize losses and improve the voltage profile. The overall problem is optimized using an upgraded method of the fitness assignment and solution chasing based on the aggregate approach called multi‐objective whale optimization algorithm (MWOA). Wind and solar photovoltaic sources with biomass are utilized as the DG sources with their probabilistic outputs. The developed method is tested using two practical feeders of Bahir Dar city distribution network, Ethiopia. The results of loss minimization and voltage profile enhancement with MWOA are compared with multi‐objective particle swam optimization (MPSO) with an equal number of iterations to show the superiority of the developed method.

type of DG sources, site selection and resource assessment are performed. Further feasibility analyses of the selected DG sources are performed for the better utilization of these sources. Optimal placement and sizing of DG sources are the critical issues in the smart power system as these will critically minimized the system losses as well enhanced the voltage profile of the system. Different optimization techniques are utilized by the various researchers to optimally place and size the DG sources. Further, load flow techniques are required to generate the input data for the optimal placement of DG sources. Recent improved load flow techniques 3,4 can be utilized to obtain input data for performing the optimal placement problem of DG sources.

Related work
For a decade various power flow techniques with different optimization methods are utilized to perform the optimal placement and sizing of the DG sources in the power system. From these recent technologies, some of them are critically reviewed. In Reference

Research gap
After detailed and critically analyzed the various research, different techniques are missing to incorporate the following issues: • Various literatures did not utilize the practical system implementation of the proposed work.
• Different research missed a detailed cost analysis in terms of the DG sources incorporation cost.
• Much literature did not use the total feeders' carrying capacity as a constraint to get the least power loss

Contribution of the work
This work performed the placement of the DG and capacitors (QG) units to support the unbalanced reactive power and for the maximum active power loss reduction. Therefore, this study presented the total real power loss reduction with voltage profile improvement of the two critical practical feeders of the Bahir Dar distribution network by optimally quantifying and locating the DG and capacitors (QG). So, this work incorporated the practical network to find possible minimum power loss by considering the maximum network capacity limits (upper limit constraint). To perform this research, a recent and powerful optimization technique called whale optimization algorithm (WOA) 29 is used as it has a fast convergence, large input carrying capacity and multi direction searching capability. Incorrect size of DG and QG may increase the system losses as compared to the base case condition. WOA is utilized for the proper site and size of the DG. Further, it is applied to locate and size of the capacitors. Therefore, in this work, MWOA is used for optimal sizing and siting of DG and QG. Hence, this work used a mechanism called feeder carrying capacity limit under the constraint condition for distribution network optimization. It is mentioned that DG and QG size can be less than the total power required by the system. Therefore, for the purpose of network security, in this work, 80% of the total power demand is taken as the upper limit of DG and QG. The significant contributions of this work are as follows: • Two practical feeders of the Bahir Dar distribution network are considered and modeled to know the performance of the real system.
• Multi-objective WOA is utilized to perform the optimal placement and sizing of the DG and QG sources in the system.
• Actual local metrological solar irradiation and wind speed data are considered to assess the energy outputs from the DG sources.
• Total feeders' carrying capacity is considered as limits to get the maximum possible least power loss. It is optimally quantifying and locating the DG and QG within the network carrying capacity limit and a way of searching the possible minimum loss from the all buses instead of searching the relative weakest bus. Here the maximum size or upper limit of DG/QG will be decided from the limit of network carrying capacity and the program will keep the performance.
• A detailed comparative analysis of the developed MWOA method is performed using multi-objective particle swam optimization (MPSO), 30 which shows the superiority of the MWOA.

Organization
The paper is organized as follows: Section 2 discussed the background of the performed research. Section 3 presented methodology and problem formulation. Section 4 presented the results and comparative analysis, followed by the conclusion.

BACKGROUND
This section discussed the background of the study area, with selection and assessment of the DG and reactive power supply sources for the study area is presented in this section.

SPV system
This work used the SPV system to generate active power as DG source.

Power output of PV array
The out power of photo voltaic (PV) array is presented as 31,32 where, P pv represents the output of PV array, A C is the array area, MP is the maximum power point efficiency of the array (≈14%), E is the efficiency of power-conditioning equipment (≈90%), and G T is the incident solar radiation on the array.

Solar radiation estimations
Solar declination angle ( ) is the angle between the earth's equatorial plane and the earth sun line. The solar hour angle is the angle Earth has rotated since solar noon. The relation between these angles is given by 31,32 : where, represents solar declination angle ( • ), n d is day number of the year starting at January 1st as 1, is (t s − 12 h).
where, s represents the solar altitude ( • ) and is latitude ( • ). 31,32 where, s represents the solar azimuz ( • ). The sunset/sunrise angle is given by 31,32 The solar angle of incident θ i is the angle between the solar beam and normal to the solar panel, which is given by: cos( i ) = [sin sin cos − sin cos sin cos + cos cos cos cos + sin sin cos cos + cos sin sin sin ] The solar constant (G sc ) is equals to1367 W/m 2 . The extraterrestrial irradiance on a surface at normal incidence (G on ) can be expressed as 31,32 : The extraterrestrial irradiance incident on a horizontal plane at an arbitrary angle of incidence is expressed as. 33 where, z is the zenith angle between the solar beam and the vertical. z and are not in the same plane.
Integrating the solar constant (extraterrestrial irradiance) over the day length gives us daily solar radiation on the horizontal surface. 31 where, is declination angle ( • ),and s is sunset hour angle ( • ). For Bahir Dar city the computed solar irradiance is as follows:

Solar energy resource in Bahir Dar
Bahir Dar is located near the equator; its solar resource is of significant potential. The annual average daily radiation in Bahir Dar reaching the ground is estimated to be 6 kWh/m 2 /day, which varies from a minimum of 5.26 kWh/m 2 /day in July to a maximum value of 6.86 kWh/m 2 /day in February. 34 An indirect estimation of solar radiation is performed by ground level measurement. Table 1 presented the estimated monthly solar radiation for Bahir Dar district. For the renewable hybrid power system design of Bahir Dar, the estimated monthly average global solar radiation from the ground measured sunshine hour data from National Meteorological Service Agency, Ethiopia summarized and listed in Table 2 and uses for the feasibility study of the proposed hybrid renewable energy system using HOMER.

Wind turbine
The second distributed energy source used in this work is the wind turbine.

Speed and power relations
The kinetic energy of wind in joules is presented by 31 : where, m represents mass, V is the wind speed. The power generated in watts is given by 31 : where, P represents mechanical power in the moving air (watts), is air density (kg/m 3 ), A is area swept by the rotor blades (m 2 ), and V represents the velocity of the air (m/s). The mechanical power output from the upstream wind is presented by, where, AV represents the volumetric flow rate, and AV represents the mass flow rate of the air in kilograms per second. The power density of the selected area is used to compare two potential wind sites in watts per square meter and presented by:

Wind speed distribution
The mean wind velocity is given by, The variation in wind speed is the best described by Weibull probability distribution function f with two parameters, the shape parameter k, and the scale parameter c. The following equation gives the probability of wind speed being v during any time interval 31 : The cumulative distribution F(u) is given by, where, u is the wind speed, k(> 0) is the shape parameter, and c(> 0) is the scale parameter of the distribution. The value of the shape factor is varying from 1 to 4.
For k = 2; Average wind speed and scale factor in the equation are used to find the probability distribution using HOMER software.
The annual average wind speed for that hour is represented by each of the 24 values of the average diurnal profile. 31

Wind power density distributions and mean power density
The average power density is given by 31 : is the gamma function and given as: The air density varies with altitude and therefore the formula that governs is Finally, power density for each month is given by: The wind power density values for each month for Bahir Dar city are calculated and listed in Table 3 below, where equals to 1.225 kg/m 3 .
The energy density characteristics at a height of 50 m are presented in Table 4 below. Observing Table 4, the power density category of Bahir Dar city is on the seventh category, which indicates the region, has great potential for electric power generation. The technical data of Vestas V82 wind turbine according to the manufacturer data sheet are presented in Table 5. 33

2.2.4
Wind speed-height correction The average wind speed increases with the height is approximately 1/7th of the power for the ideal smooth plane. 31 where, V(z 2 ) is the wind speed at the desired height of z 2 ; v(z 1 ) is the wind speed measured at a known height z 1 , and is a coefficient known as the wind shear exponent. A modified formula is best suited for estimating the wind speed at hub height. v

Wind power generation
As the power generated for wind turbine is given by, The air density ratio is provided by, The air density under standard conditions, that is, at sea level and 15 • C is 1.22 kg/m 3 . The hourly generation from wind turbine is given by, The coefficients a and b is given by: Annual wind energy production and capacity factor The capacity factor of wind turbine is given as 31 : By using U c = 3 m∕s, U R = 13 m∕s, U F = 20 m∕s, and C = 10.43 m∕s, the computed value of the capacity factor is 0.466. Therefore, the annual energy production of a single wind turbine is 6,602,587.2 kWh by taking nominal rated power as 1650 kW. 31 The minimum output power from the cut in speed (i.e., 3 m/s) is 26.27 kW power. The estimated capacity factor and annual energy production from a single Vestas V82 wind turbine are summarized in Table 6.
The estimated capacity factor indicates that all values and annual energy production are within the acceptable range from a single Vestas V82 wind turbine. TA B L E 6 V82 wind turbine-estimated capacity factor and annual energy production 31

District
Scale factor (C)

Biomass energy
The third distributed energy source used in this work is the biomass energy source as it is widely available in Bahir Dar, Ethiopia. Bahir Dar is located in the northwest of Ethiopia, where most of the country's agricultural crops are cultivated. Apart from huge availability of Corn, beans, teff, barley and wheat in Gojjam and Gonder cities, which are near Bahir Dar, the forest around the city, municipal solid waste, biosolids, industrial waste, animal manures, forestry residual, landscaping and tree clipping can be used as biomass resources. Figure 1 presents the Crop residue biomass resource in Gojjam, Bahir Dar, Ethiopia. Table 7 presented the Crop cultivation areas in the parts of Amhara region, near Bahir Dar, Ethiopia.

Physical properties of biomass
The content of moisture is estimated on the basis of dry and wet. 35 where, m tot represents the total mass, including moisture, m dry represents the mass of the dry substance, and m tot − m dry represents the moisture mass.

Heat balance in a complete combustion
Generally, the heat generated from combustion is equal to the heat required for vaporizing the available water plus heat related to vaporize water mass and heat lost in the atmosphere. Higher heating value (HHV) and lower heating value (LHV) are the parameters used to calculate the amount of hear from the biomass. HHV represents the heat required for the combustion per unit mass, while LHV is the subtraction of heat related to the vaporization of the existing water and water product from the heat required for combustion. The LHV for dry biomass is represented by, where, H represents hydrogen content in dry biomass, which is 5%-7% and q is water condensation heat, equals to 2.4 MJ/kg. The variation between HHV and LHV is normally equal to 1-1.5 MJ/kg. Actual amount of LHV calculated from LHV dry is as follows: where, h is moisture content on the wet basis.
In each ton of grain generally the ratio of dry matter at anthesis and final grin is among 1.29-1.50 t/ha. By taking an average of 1.4 ton/ha, the total amount of biomass available is 1,302,130.2 tons. In this work, the capacity factor is selected as 80%. For normal operating conditions, the total biomass required by the power plant to generate 2.7 MW with co-firing capacity of 5%, heat rate 80% and HHV 80% is as follows:

Shunt capacitor modeling
To supply reactive power support, shunt capacitor (QGs) are used. The advantages of shunt capacitors are lower cost, improved voltage profile, and reduced losses. The maximum amount of capacitance value required can be calculated as follows 13,37 : where, U is an integer. In this work, U is taken as 9. Therefore, the required value of QG is 1.35 MVAr.

METHODOLOGY AND PROBLEM FORMULATION
This section discusses the problem formulation for the optimal placement and sizing of the DGs and QGs resources used in this work by using MWOA.

Optimal placement and sizing of DGs and QGs
The backward/forward load flow is used for performing the load flow analysis of the selected distribution network. In the process of optimization, active and reactive powers are injected from DG and QG, respectively based on the feeder current carrying capacity. It is less than the peak load, that is, sum of the power loss and power demand. In this work, to make the integration and compensation safe from the reverse current flow, it is taken as 80% of the total capacity limit as a network optimization constraint, while performing the system optimization for the radial distribution network using load flow. The ultimate goal of this work is to minimize the aggregate active power loss with minimized VD in the distribution network. This can be given as: where, S i = P + jQ, n and m represent the number of branches and buses, respectively. To optimize the above objective function under constraint conditions, the power flow equation should satisfy all the equality constraints presented below: P sub + P DG = P loss + P load (41) where P sub and Q sub are the aggregate active and reactive power, injected by the sub-station into the network, P DG and Q shunt are the gross real and reactive power, injected by the DG and QG, respectively. P loss and Q loss are the aggregate active and reactive power losses in the network. P load and Q load are the gross active and reactive demands of the system.
The inequality constraints are as follows: Voltage constraints are given by: where, V min is set to 0.95 and V max is fixed to 1.05. Feeder integrating capacity 17,18 is limited by its maximum thermal loading limit, that is, Location of DG (under the assumption that first bus is taken as slack bus) 2 ≤ DG position ≤ n buses (45)

Whale optimization algorithm (WOA)
WOA is the recent meta-heuristic algorithm developed by Mirjalili and Lewis 29 in the year 2016. The whales are highly intelligent animals. The special hunting behavior of the humpback whales inspired WOA, which prefer to hunt krill or small fishes, closer to the sea surface. Humpback whales special hunting called a bubble net-feeding method. For hunting, they swim around the prey and create distinct bubbles along a circle or nine-shaped path. 29 From the basic characteristic of hunting, the following points are observed from the WOA.

Encircling prey
One character of Whales predicts the current position is exact and in circles the prey. This character of social behavior is transformed in the mathematical equation, as the current best candidate solution set in the objective function. All other social groups will try updating their position status toward the best hunter. The behavior modeled is as: where, − → X * , − → X represent the current position of best solution and position vector. Current iteration is denoted by t.

Bubble net-hunting method
In this hunting, character of whales, used two methods, 1. This time the whale encircles the prey and then shrinks from the far to the center: 2. Spiral position updating: The whale shows a mimic helix-shaped movement to the prey, this property of whale can be represented in spiral equation: Prey may use more than two paths simultaneously, when whales hunt. In this work, 50% probability (Prob) is taken for the above two methods. 3. To get the global possible optimum, updating has done with randomly

Implementation of MWOA
Here the MWOA is implemented using program algorithm with and without bound called by the same iteration and fitness limit. This implementation is presented in Figure 2 and performed as follows:

RESULTS AND COMPARATIVE ANALYSIS
This work performed on the Ghion and Bata feeder of the Bahir Dar distribution network. Bahir Dar substation-II has the 230/132/15 kV and 230/66/15 kV buses, which are power sources to four feeders (i.e., Air force, Bata, Ghion and Papyrus) and the other substation-I supply three feeders (i.e., Sematate, Boiler and Industry). For this study, two feeders, namely, Ghion and Bata are selected because the real power losses and voltage violations at these feeders are beyond the permissible limits. Figures 3 and 4 presented the single line diagrams of Ghion and Bata feeders, respectively. Further, Appendix Tables A1-A5 presented the various data, related to the modeling of the selected feeders.

F I G U R E 3 35-Bus Ghion feeder of Bahir Dar distribution system
Real power loss minimization by using integrating the active and reactive power source is applied to the two critical feeders of Bahir Dar radial distribution network. These feeders are connected from the Bahir Dar substation-II 400/230/66/15 kV bus. Feeder 5 is named as Ghion, which has 35 buses, while the other feeder named as Bata feeder has 40 buses.
Using the line and load data of the selected radial distribution network, backward/forward sweep load flow is performed to get the total feeder loss and initial voltage profile of the selected buses. In reasonable conditions, without any optimization, the total active load at the Bata feeder is 1.8262 MW with 1.5353 MVAr reactive loads. Ghion feeder has 3.43257 MW active and 2.5776 MVAr reactive loads. Additionally, the initial loss at the Bata feeder is 0.1262149 MW, and Ghion feeder is 0.3395703 MW.
In this work, for the system loss minimization, DG and QG sources are optimally sized and placed at the selected feeders by the MWOA optimization method. MWOA results are compared with the MPSO. The method is implemented using a MATLAB R2016 programming language with computer properties of 2.2 GHz processor and 7.58 GB RAM with core i7. The MATLAB program code is executed using the WOA algorithm. The proposed method minimized real power loss by optimizing the objective function under constraint conditions. For comparison, the parameters of the controlling values of MPSO are set as: the number of iterations is equal to 100, w is equal to 0.95, C l is equal to 2, C 2 is equal 2. In the case of MWOA, the iteration is the same as MPSO and the dimensions (dm) representing the total active power is set to one. The first bus is selected as the slack bus. The results are discussed in the following sub-sections.

Real power loss minimization
The result of the load flow provides the total real line losses as 339.5703 kW. When DG and QG are used as the source of optimization in the Ghion feeder, as seen from Table 9, the total active power loss after MWOA optimization is reduced to 22 kW. For comparative analysis, by implementing the MPSO optimization, the loss reduced to 27 kW. From the above result, the total power saved after the implementation of MWOA is 317.6 kW while with MPSO is 312.6 kW for Ghion feeder. Therefore, results concluded that MWOA provided better results compared to MPSO. After the placement of DG and QG, the voltage profile is also upgraded. The load flow indicates that the average voltage profile of the feeder before the optimization is about 0.961 pu. The profile after the optimal sizing and placement of DG and QG by using MWOA is improved to 1.0258 pu while with MPSO is improved to 0.988 pu. The per branch profile of voltage after and before the optimization is shown in Figure 5. The minimum value of voltages, before the placement of DG and QG are 0.9436 pu (at bus 35) and 0.9437 pu (at bus 34). With the MWOA optimization of the system, which is used for the placement and size of DG and QG, the value of voltages at the mentioned buses is improved to 1.0189 pu (at bus 35) and 1.0194 pu (at bus 34), while with the MPSO optimization, the values of voltages are improved to 0.9955 pu (at bus 35) and 0.9960 pu (at bus 34). Figure 5 presented the comparative analysis of voltage profiles of Ghion feeder before and after the optimization performed using MWOA and MPSO. 30

4.2
Optimization of Bata feeder

Real power loss minimization
The result of the load flow provides the total real line losses as 126.2149 kW. In the optimization process of the 40-bus Bata feeder by optimally integrating DG and QG, as seen from

Voltage profile improvement of Bata feeder
After the optimal placement of DG and QG, the voltage profile of various buses the Bata feeder is improved. The average voltage profile of the feeder before the optimization is 0.9727 pu. The voltage profile after optimally placing the DG and QG with the help of MWOA is improved to 0.9991 pu while with MPSO, it is improved to 0.9890 pu. Figure 6 presented the comparative analysis of voltage profiles of Bata feeder before and after the optimization, performed by MWOA and MPSO.

F I G U R E 6
Voltage profile improvement of the 40-bus Bata feeder before and after the optimization

Performance comparison study of existing system with MWOA and MPSO
This work optimizes the real power loss minimization problem by satisfying all the constraints. The active power loss is reduced, and the voltage profiles are improved. It is often robust to consider feeder voltage regulation related to the profiles of feeder voltage. Voltage profile indicates the magnitude of the voltage with respect to its location on the feeder. One way to determine the quality of power is maintaining the receiving end voltage magnitude closer the same to the sender end. For bring this achievement practically, the capacitor and DG are applied in this work for Bahir Dar distribution system. The size and placement of DG and shunt capacitor are performed by MWOA which illustrated using the 35-bus Ghion feeder and 40-bus Bata feeder, the practical feeders of the Bhir Dar distribution system. The real power losses, DG and QG sizes with location and average voltage profile of these feeders before and after the optimization is presented in Tables 9 and 10. Optimal location and size of DG and QG are found with the help of MWOA and compared with MPSO. After optimization, the power loss had reduced from 339.5703 to 22 kW in Ghion feeder and from 126.2149 to 22.4 kW in Bata feeder using MWOA. It had reduced from 339.5703 to 27 kW in Ghion feeder and from 126.2149 to 51.3 kW in Bata feeder using MPSO.
The algorithm developed for the power loss reduction by applying shunt compensation of capacitor and DG integration had improved the overall system voltage profile. As a result, the voltage profile before the optimization is 0.96, after optimization with MPSO, it is improved to 0.988 pu, and after optimization with MWOA, it is improved to 0.997 pu for Ghion feeder. The voltage profile of Bata feeder before and after optimization is 0.9726. After optimization with the MPSO is improved to 0.989 and with MWOA improved to 0.9991 pu in Bata feeder. From the results, MWOA provided better performance as compare to the MPSO optimization approach. Biomass resource is utilized as the backup source in this work. To minimize the investment cost of the biomass, it should be installed at 16th bus of Ghion feeder and 35th bus of Bata feeder. The total DG value calculated from MWOA optimization is about 2.7 MW. Since biomass is utilized as back up, its value should equal to the total power demanded from DG, that is, 2.7 MW. For normal operating conditions, the total biomass required by the power plant to generate 2.7 MW with co-firing capacity of 5%, heat rate 80% and HHV 80% are 1,182,600 tons/year.
The QG value of the two feeders after WOA optimization is 1.35 MVAr. The value of QG can be found in multiple of 150 kVAr.

Investment cost of overall system
For the development of wind, solar and biomass power plant based DG system, the investment cost and shunt capacitor cost is summarized in Table 11 31,34 : The investment cost of the system, optimized using WOA for the selected two feeders is presented in Table 12. Since wind capacity factor is higher, it is reasonable to choose two wind turbines and the rest should be solar energy. The biomass is used as backup source to avoid intermittence nature of wind and solar energy. Hence, it would cover all the power supplied by solar and wind during their off condition. Further, shunt capacitor is used to supply reactive power, required by the system.

CONCLUSION
Localizing the active generation and reactive power demands had reduced the power loss. In this research, multiobjective-based WOA optimization is applied to minimize the practical system losses. In this work, two practical feeders of the Bahir Dar distribution network was considered to perform the loss minimization as well as voltage profile improvement. MWOA was compared with the MPSO, which shows the superiority of the initial one in terms of loss minimization and voltage profile improvement. A detailed economic analysis is also presented, which shows the total investment cost required for the DG and capacitor bank installation. As the future enhancement of this work, maximum loading condition of the selected feeders can be incorporated to show the performance of the optimization techniques at peak loading. Further, in whole Bahir Dar distribution network can be considered under different constraints conditions of the power system for the better understanding of the system performance. Further, other machine learning based optimization techniques can be utilized in real time manner for dynamic operation optimization of the system. The proposed work can also be applied to other types of the multi-energy networks. 38

DATA AVAILABILITY STATEMENT
Research data are not shared.

CONFLICT OF INTEREST
The authors declare no potential conflict of interest.