1 Introduction

The exhausting fuel sources for conventional energy sources (CES), non-expanding transmission and distribution networks and ever increasing demand for electricity have made the power system operation and control very complex. On the other side, the dependency on CES is considerably high for energy balance and causing for greenhouse gases (GHG) emission and consequently contributing for environment pollution significantly. Under these circumstances, integration of renewable energy sources (RES) and adoption of electric vehicle (EV) technology have become mandatory in various power grids and transportation sectors across the world respectively [1]. As per International Renewable Energy Agency (IRENA) statistics released in March 2019, the total RE integration in 2018 has been reached to 2364.4 GW including off-grid across the world [2]. In 2018, the global electric car fleet exceeded 5.1 million and the growth is almost double as compared with 2017 statistics [3]. From these statistics, it can be said that these two exponential trends are getting high attention across the world due to their potential for reducing GHG emission and contributing towards sustainable practices. However, the intermittent nature of RES and unpredictable nature of EV load pattern needs to be addressed potentially for avoiding the possible operational and controlling issues in power systems. By integrating RES and EV charging stations (CSs)/parking lots (PLs)/ fleets at improper locations, the expected technical benefits to the power system can become negative. In this era, performance analysis of RDNs w.r.t. different type of loads such as residential, industrial, commercial, agriculture and electric vehicle etc., is inevitable and preventive measures for ensuring high reliable supply are needed to focus much.

As known, the major weak segment in power systems is the distribution system and optimization of its performance is always an important criterion in power system operation and control. Optimal network reconfiguration (ONR), installation of capacitor banks (CBs), and integration of distribution generation (DGs) are some of the remedial ways for some extent to improve the performance of radial distribution networks (RDN). The major objective of optimal allocation of DGs problem is to improve the performance of the distribution system and maximization of economic benefits to the utilities. In literature, optimal allocation of DGs has been addressed highly by various traditional (non-heuristic) and non-traditional (heuristic) approaches, whereas optimal allocation of EV infrastructure or charging stations (CSs) is also getting high attention among the researchers in recent times. Over the past few decades, numerous methodologies have been proposed by different researchers for allocating the DGs in distribution system optimally [4, 5]. Although the optimal allocation of DGs problem in RDNs is widely addressed in literature, sufficient research is not focused considering emerging electric vehicle load penetration. In order to provide charging infrastructure, optimal allocation of EV fleets is an important factor since there is a possibility for degrading the performance of RDNs due to their integration at inappropriate locations. The methodologies can be classified like non-heuristic approaches (NHA) and heuristic approaches (HA). In comparison, HAs are simpler, derivative-free and easy to implement for solving the complex, non-linear optimization problems than NHAs and hence some of the recent HAs applied for solving the DGs allocation problem have been discussed here.

In [6], chaotic stochastic fractal search (CSFS) algorithm is applied to solve DG allocation for real power loss minimization. In [7], spring search algorithm (SSA1) and in [8], gbest-guided artificial bee colony (GABC) algorithm are proposed for solving the simultaneous allocation of DGs and CBs by aiming techno-economic-environment benefits in network operation. In [9], considering real power loss minimizations the DGs are integrated optimally using teaching–learning based optimization (TLBO) algorithm. In [10], bacterial foraging optimization algorithm (BFOA) is proposed for simultaneous allocation of DGs and CBs towards loss minimization and voltage profile improvement. Hybrid grey wolf optimizer (HGWO) is proposed for loss minimization via optimal allocation of multi-type DGs in 33-, 69- and Indian 85-bus systems [11]. In [12], multi-type DGs and CBs are optimized using optimal power flow (OPF) embedded with generic analytical expressions for determining the sizes. In [13], an enhanced genetic algorithm (EGA) is proposed for minimizing the real power losses via allocating simultaneous DGs and CBs in the network. In [14], war optimization algorithm (WOA), particle swarm optimization (PSO), cuckoo search algorithm (CSA), firefly algorithm (FA) and bat algorithm (BA) are applied for sizing the multiple solar PV systems towards loss minimization. In [15], weight improved particle swarm optimization algorithm (WIPSO) and self adaptive differential evolution algorithm (SADE) have been proposed for solving the simultaneous allocation of renewable type DGs and CBs by minimizing the multi-objective function formed using real and reactive power losses and voltage profile. In [16], ant lion optimization (ALO) algorithm is proposed for minimizing the multi-objective function using real power loss, voltage profile and voltage stability via optimally locating and sizing the renewable DGs. In [17], grasshopper optimization algorithm (GOA) is adopted for allocating multiple DGs, fixed and switched CBs for minimizing real power losses. In [18], PSO is adopted for sizing the multiple DGs and CBs for minimizing the economic aspects at network operation and planning stages. In [19], a shuffled frog leaping algorithm (SFLA) is applied for minimizing real power loss and consequently economic efficiency of distribution system operation is evaluated via allocating the multiple DGs. In [20], a multi-objective whale optimization algorithm (MOWOA) is applied for identifying the locations and sizes of solar PV and wind turbine systems considering different types of load models. The objective function is formulated for optimizing the real power loss index, voltage index and cost benefit indices simultaneously. Salp swarm algorithm (SSA2) [21] and water cycle algorithm (WCA) [22] are proposed for attaining techno-economic-environmental benefits via simultaneous allocation of DGs and CBs. In [23], hybrid approach using grasshopper optimization algorithm (GOA) and cuckoo search algorithm (CSA) is proposed for allocating the multi-type multiple DGs towards technical benefits. In [24], hybrid approach using fuzzy logic controller (FLC), ALO and PSO is proposed for solving the renewable type DG integration problem towards technical benefits. In [25], elephant herding optimization (EHO) algorithm is applied for determining single multi-type DG location and size considering techno-economic aspects. In [26], ALO is proposed for optimal sizing of DGs considering techno-economic benefits. In [27], a multi-objective PSO (MOPSO) is applied for solving optimal allocation of renewable DGs and CBs.

Recently, the optimal allocation of DGs problem is addressed using quasi-oppositional chaotic symbiotic organisms search (QOCSOS) algorithm by aiming for reduction in real power loss, improvement in voltage profile and enhancement in voltage stability [28, 29]. The study revealed that the DGs with non-unity power factor can improve RDNs performance significantly than the DGs with unity power factor. Coyote optimization algorithm (COA) [30] is proposed for optimal integration of DGs in RDNs considering multi-objective function, formed using real power loss, operating cost and voltage stability. In [31], an improved variant of COA as enhanced coyote optimization algorithm (ECOA) is proposed for solving simultaneous optimal network reconfiguration and DG allocation problem. In [32], harmony search algorithm (HSA) is pursued for solving simultaneous optimal network reconfiguration and DG allocation problem in unbalanced RDNs. In [33], chaotic sine cosine algorithm (CCSCA) and in [34], an improved raven roosting optimization (IRRO) algorithm are introduced for solving multi-objective optimal allocation of multiple DGs problem. In similar to [35], a new pathfinder algorithm (PFA) is proposed for obtaining simultaneous optimal network reconfiguration and DG allocation. Similarly, hybrid genetic particle swarm optimization (HGPSO) [36], stochastic fractal search optimization algorithm (SFSOA) [37] and biogeography-based optimization (BBO) [38] are some of such recent meta-heuristic approaches for solving optimal allocation of DGs problem considering technical aspects. Further, the reader can also find recent reviews on distribution system performance improvement via optimal allocation of DGs, CBs and network reconfiguration and their combination [39,40,41,42]. At this stage, it can be concluded that the performance of RDNs can be improved significantly via optimal allocation of DGs and/or ONR problem.

On the other side, optimal allocation of EV charging infrastructure has been motivated and attracted by various researchers in recent times. According to the survey presented in [43], optimal allocation of EV charging infrastructure problem has been solved in three categories, (1) transportation-network, (2) distribution-network and (3) transportation-distribution-networks. Considering the possibility of degradation in the performance of RDNs due to EV fleet load, integration of EV charging stations at optimal location is essential. In line to the DGs allocation methods referred above, distribution-network based optimal allocation of EV fleets along with DGs allocation is proposed in this paper and claimed as one of the major contributions in this paper. Notably, the optimal allocation of DGs problem is a non-linear multi-objective optimization problem which needs to be solved for discrete and continuous variables simultaneously. In addition, the problem can become more complex for simultaneous allocation of DGs and EV fleets in large-scale RDNs and needs large computational time. According to the no-free-launch theorem [44], there is no single specific heuristic algorithm which can solve all type of optimization problems. Hence, the researchers are still inspiring to introduce new heuristic algorithms and applying them to different optimization problems.

In the above reviewed literature, there are many such heuristic and meta-heuristic algorithms that have been used for solving optimal allocation problem. To the best of authors’ knowledge, future search algorithm (FSA) [45] has not been applied for solving the either optimal allocation of DGs problem and/or optimal allocation of EV fleet problem in RDN. In addition, most of the works have been analyzed considering multi-objective function for techno-economic aspects, but limited numbers of works have been only focused on techno-environmental aspects in the DG allocation problem [7, 21, 22]. Also, the charging infrastructure required for serving the emerging EV load demand is not focused much. In competition to the existing literature works, FSA is first applied for solving only DGs allocation problem alone and later simultaneous allocation of DGs and EV fleets is proposed as a countermeasure to the degrading performance of RDN w.r.t. EV fleet allocation.

Rest of the paper is organized as follows: Sect. 2 addressed the modeling of DGs and EV fleet load. In Sect. 3, a multi-objective optimization problem constrained by various technical, operational and planning issues is presented. In Sect. 4, the mathematical relations of FSA and the steps used in solving the formulated multi-objective problem is explained. In Sect. 5, various case studies on practical agriculture and rural residential feeders are presented. The major contributions, research findings and the superiority of proposed FSA approach over existing algorithms is concluded in Sect. 6.

2 Modeling of relevant concepts

In this section, static modeling of DGs and EV fleet load are explained considering RDN load flow study.

2.1 Distribution generation

The electric power generation sources in different forms placed near to the load centres and integrated directly to the distribution networks are known as DGs. As per the active and/or reactive power compensation, these DGs can be modeled as negative loads and their classification along with modeling as follows:

2.1.1 Type-1 DG (active power compensation sources)

Photovoltaic, micro turbines and fuel cells which are incorporated into the main grid with the help of converters/inverters are good examples of real power compensation sources. In this model, the real power load at bus-i will be reduced by an amount equal to DG’s real power output with unity power factor (upf) and is given by:

$$ P_{di,new} = P_{di,base} - P_{DG,i} $$
(1)

2.1.2 Type-2 DG (reactive power compensation sources)

Shunt CBs (in either fixed or/and switched form) are the best examples for reactive power compensation sources particularly at the distribution network. In this model, the reactive power load at bus-i will be reduced by an amount equal to DG reactive power output and is given by:

$$ Q_{di,new} = Q_{di,base} - Q_{DG,i} $$
(2)

2.1.3 Type-3 DG (complex power compensation sources)

Wind farms and synchronous generators are example of complex power compensation sources. The power factor lies between 0.7 and 1. In this model, the active power will be reduced by an amount equal to DG active power and reactive power will be either increment/decrement by an amount equal to DG reactive power load at bus-i and is given by:

$$ P_{di,new} + jQ_{di,new} = \left( {P_{di,base} - P_{DG,i} } \right) + j\left( {Q_{di,base} \pm P_{DG,i} \tan \left( {\phi_{DG,i} } \right)} \right) $$
(3)

where \(P_{di,base}\) and \(Q_{di,base}\) are the active and reactive power loads at bus-i, respectively; \(P_{di,new}\) and \(Q_{di,new}\) are the modified active and reactive power loads with DG integration at bus-i, respectively; \(P_{DG,i}\) and \(Q_{DG,i}\) are the active and reactive power generations/injections by DG integrated at bus-i, respectively; \(\phi_{DG,i}\) is the power factor angle of DG at bus-i.

As per the above models, the DGs compensate either active power or reactive power or both and cause a decreased net loading effect on the feeder. The decreased load balances usually at slack bus in load flow studies. By the redistribution of power flows with reduced loading, the net voltage profile, transmission loss and stability margins can improve significantly.

2.2 Electric vehicle fleet

Here, it is assumed here that all types of EVs in an EV fleet are integrated to the utility via AC/DC converter with an operating power factor of nearly unity. It is also assumed that the total number EVs in an EV fleet are arranged in p rows and q columns and each EV may have different power ratings [46]. Since EV is basically powered by batteries, its corresponding loading effect during charging mode is modeled by considering voltage dependent load modeling [47]. By summing all EV power ratings, the total real power demand of an EV fleet is determined. The following Eqs. (4) and (5) represents the real and reactive power demand at bus-n after EV fleet integration respectively.

$$ P_{d\left( n \right)}^{t} = P_{L\left( n \right)}^{0} \times \left( {\frac{{V_{\left( n \right)}^{t} }}{{V_{\left( n \right)}^{0} }}} \right)^{\alpha } + \sum\limits_{i = 1}^{p} {\sum\limits_{j = 1}^{q} {\left[ {P_{ev,ij} \times \left( {\frac{{V_{\left( n \right)}^{t} }}{{V_{\left( n \right)}^{0} }}} \right)^{{\alpha_{ev} }} } \right]} } $$
(4)
$$ Q_{d\left( n \right)}^{t} = Q_{L\left( n \right)}^{0} \times \left( {\frac{{V_{\left( n \right)}^{t} }}{{V_{\left( n \right)}^{0} }}} \right)^{\beta } + \sum\limits_{i = 1}^{p} {\sum\limits_{j = 1}^{q} {\left[ {Q_{ev,ij} \times \left( {\frac{{V_{\left( n \right)}^{t} }}{{V_{\left( n \right)}^{0} }}} \right)^{{\beta_{ev} }} } \right]} } $$
(5)
$$ Q_{ev,ij} = P_{ev,ij} \times \tan \left( {\phi_{ev,ij} } \right) $$
(6)

where \(P_{L\left( n \right)}^{0}\) and \(Q_{L\left( n \right)}^{0}\) are nominal real and reactive power loads at bus-n respectively; \(P_{L\left( n \right)}^{t}\) and \(Q_{L\left( n \right)}^{t}\) are modified real and reactive powers at time t respectively; \(P_{d\left( n \right)}^{t}\) and \(Q_{d\left( n \right)}^{t}\) are the real and reactive power loads at location n after integration of EV load respectively; \(P_{ev,ij}\) and \(Q_{ev,ij}\) are the real and reactive loads due to an EV at ith row and jth column in the fleet; \(V_{\left( n \right)}^{o}\) and \(V_{\left( n \right)}^{t}\) are the voltage magnitude of bus-n at nominal and time specified respectively; \(\alpha\) and \(\beta\) are the exponents for real and reactive powers respectively; \(\alpha_{ev}\) and \(\beta_{ev}\) are the exponents of EV’s real and reactive power loads respectively.

3 Problem formulation

In the operation and control of RDN, minimization of real power loss is one of the major goals. This can be achieved mainly by improving the voltage profile across the network, and consequently loss can reduce by having reduced current flow through each branch/element. In addition, an improved voltage profile can result in enhanced voltage stability.

Primarily, the voltage magnitude at any bus-j (Vj) in the distribution system is dependent on its active power load (Pj), reactance of the branch (xij), power factor (pf) or in other words, reactive power load (Qj), and preceding end bus voltage (Vj) as in:

$$ V_{j} = \left( {V_{i} - \frac{{Q_{j} x_{ij} }}{{V_{i} }}} \right) - j\frac{{P_{j} x_{ij} }}{{V_{i} }} $$
(7)

Hence, by controlling active power and reactive power demands with different types DGs, the voltage deviation w.r.t. reference voltage (Vr) has to be minimized for having adequate voltage profile and stability margins and consequently reduced real power losses in the network can be achieved significantly.

3.1 Objective function

In order to achieve efficient operation, minimization of active power loss is one of important aspects and is determined using (8):

$$ \min f_{1} = \min \left\{ {P_{loss} = \sum\limits_{k = 1}^{nbr} {\frac{{r_{k} \left( {P_{j}^{2} + Q_{j}^{2} } \right)}}{{V_{i}^{2} }}} } \right\} $$
(8)

where nbr is the number of branches in the network, rk is the resistance of branch-k, Ploss the total active power loss in the network.

By various power system blackout incidents across the world, voltage stability has become one of the primary concerns of the system operator [48]. Hence by optimizing the penetration level of different types of DGs and EV fleet, the network voltage stability is aimed to maximize. Perhaps, voltage stability assessment of RDN and its enhancement are the typical tasks to the system operator. In this paper, the impact of DGs and EV fleet on voltage stability of distribution network is analyzed using the methodology proposed in [49] and given by (9).

$$ VSI_{i} = \left| {V_{i} } \right|^{4} - 4\left( {P_{di} x_{ij} + Q_{di} r_{ij} } \right) \ge 0 $$
(9)

where \(VSI_{i}\) = voltage stability index of node-i (i = 2, 3, …, \(nbus\)); \(r_{ij}\) and \(x_{ij}\) are the resistance and reactance of the branch connected between bus-i and bus-j respectively; \(P_{di}\) and \(Q_{di}\) are the real and reactive power loads at bus-i respectively; \(\left| {V_{i} } \right|\) is the voltage magnitude of bus-i. The condition for stable operation of the radial distribution network is \(VSI_{i} \ge 0\). The bus with lowest \(VSI\) can be treated as a critical bus for voltage collapse and its corresponding index value can be considered as a stability index for the entire network.

After assessing system stability, the major focus of this paper is to enhance it by means of allocating DGs and EV fleets optimally. Hence maximization of the lowest \(VSI_{i}\) of the entire network can ensure increased stability margin.

$$ \min f_{2} = \min \left\{ {{1 \mathord{\left/ {\vphantom {1 {\min \left( {VSI_{i\forall nbus} } \right)}}} \right. \kern-\nulldelimiterspace} {\min \left( {VSI_{i\forall nbus} } \right)}}} \right\} $$
(10)

Finally, the overall multi-objective function is formulated using real power loss and voltage stability index, as given in Eq. (11).

$$ OF = \min \left( {f_{1} + f_{2} } \right) $$
(11)

In Greenhouse Gas (GHG) emission, CO2, SO2 and NOx are the most effective pollutants with power generating stations. By reducing the real power loss and dependency on grid power via optimal allocation of DGs and EV fleets, the power generation from grid reduces and consequently environmental benefits can be achieved. The emission factors with grid power are NOx = 5.06 lb/MWh, SO2 = 11.6 lb/MWh and CO2 = 2031 lb/MWh [50]. Mathematically, the emission can be calculated as follows:

$$ E_{Grid} = \left( {CO_{2} + NO_{x} + SO_{2} } \right) \times \left( {P_{D} + P_{loss} } \right) $$
(12)

By knowing the total power generation includes network real power demand (\(P_{D}\)) and total real power losses (\(P_{loss}\)) in distribution, the emission (\(E_{Grid}\)) from CES can be determined.

3.2 Operational constraints

The aforementioned objective functions are optimized by having the following VSI, node voltage (\(V_{i}\)) and branch flow (\(\left| {S_{l} } \right|\)) operational constraints, real power (\(P_{DG,g}\)) and reactive power generation (\(P_{DG,g}\)) generation limits by DGs compensation in the network.

$$ VSI_{i} > 0\quad i = 1,2,...,nbus $$
(13)
$$ V_{\min } \le V_{i} \le V_{\max } \quad i = 1,2,...nbus $$
(14)
$$ \left| {S_{l} } \right| \le \left| {S_{l,\max } } \right|\quad l = 1,2,...nbr $$
(15)
$$ P_{DG,g} \le \sum\limits_{i = 1}^{nbus} {P_{di} + \sum\limits_{i = 1}^{nfl} {P_{dfi} } } $$
(16)
$$ Q_{DG,g} \le \sum\limits_{i = 1}^{nb} {Q_{di} } + \sum\limits_{i = 1}^{nfl} {P_{dfi} } \tan \left( {\phi_{fi} } \right) $$
(17)

where \(nfl\) is the number of EV fleets, \(P_{df}\) and \(\phi_{f}\) are the power rating of one EV fleet and power factor of AC/DC converter respectively; \(V_{\min }\) and \(V_{\max }\) are the lower and upper limits for the bus voltage magnitude, respectively; \(S_{l,\max }\) is the maximum power flow limit of branch-l; \(P_{DG,g}\) is the total real power generation by all DGs in the network, \(P_{dfi}\) is the total active power demand of the EV fleets in the network.

4 Future search algorithm

All individuals on the planet search for the best life. In the event that any individual discovered that his life isn't acceptable, he attempts to imitate the life of the best individual around the globe. The future search algorithm (FSA) utilizes this conduct to locate the best arrangements [45]. The FSA is defined by numerical conditions. It can refresh the irregular beginning and it uses the nearby inquiry between individuals, what's more, the worldwide pursuit between the narrative’s ideal people. The others HSA start its means by a random population and it formulates its iterations dependent on the best optima of the random beginning. This best population might be a long way from the initial population, this makes the HSA take many iterations to come to the global optima. The FSA can defeat this issue and it refreshes the irregular population each every iteration. In every HSA, there is a local best population between the multi-variables and global optima between the iterations. Some of HSA update its new population dependent on the nearby best population as it were. In any case, the others update its new population dependent on the global best optima as it were. These strategies may take a long number of iterations. The FSA uses the local best solution and the global optima for finding the best population. Some of HSA have more and complex mathematical models which can take additional time and a long number of iterations to come to the global optima.

4.1 Modeling of future search algorithm

The proposed FSA is worked by simple mathematical conditions. In this section, the fundamental mathematical equations involved in the FSA are presented.

Generate random initialization using Eq. (18), in which S is the solution, k is the current solution, d is the dimension of search space or number of countries, Lb and Ub are the lower and upper boundaries of the variables in the optimization problem.

$$ S\left( {k, :} \right) = L_{b} + \left( {U_{b} - L_{b} } \right).*rand\left( {1, d} \right) $$
(18)

The objective function of each initial population is defined as a local solution (LS) and the best among all is defined as a global solution (GS). The FSA uses both LS and GS to find the optimal solution in its process.

The exploitation feature of the FSA is modeled using Eq. (19) by using the best influenced person or LS of each country.

$$ S\left( {k, :} \right)_{L} = \left( {LS\left( {k, :} \right) - S\left( {k, :} \right)} \right)*rand() $$
(19)

The next step is to characterize the exploration feature of the FSA which uses the global influenced person or GS and is given in Eq. (20).

$$ S\left( {k, :} \right)_{G} = \left( {GS - S\left( {k, :} \right)} \right)*rand() $$
(20)

By observing the local and global influenced persons across the world, each person may change his way of leading the life or current variables and it is modeled as given in Eq. (21) using the local and global influenced solutions.

$$ S\left( {k, :} \right) = S\left( {k, :} \right) + S\left( {k, :} \right)_{L} + S\left( {k, :} \right)_{G} $$
(21)

At this stage, the FSA updates the GS and LS and uses to modify the initial population using Eq. (22) and this is the major characteristic of FSA to define its exploration ability than other HSA.

$$ S\left( {k, :} \right) = GS + \left( {GS - LS\left( {k, :} \right)} \right)*rand() $$
(22)

This process repeats until the convergence criteria reaches by computing LS and GS using Eq. (19) and Eq. (20) respectively, finding the new solution using Eq. (12) and update LS, GS, and initial population of Eq. (18) using Eq. (22). The population size indicates the number of nations searching by a person for his comfortable life. The more nations mean the more local influenced persons (LSs). These individual local best persons can again be influenced by the global best person (GS). Hence defining new GS and LS at each iteration and again using them for updating the optimal solution within the same iteration is the key feature of FSA for outperformance than the other HSA. Generally, the maximum number of iterations (kmax) are taken to stop the iteration process of all HASs and it remains the same in FSA also. This stage can be treated as that the person reaches a satisfactory level in life or his goal, by which he may stop searching further. Also, from the mathematical equations point of view, FSA is also said to be the simplest without necessity to tune any controlling variables and proven its superiority than various other HSAs by its fast convergence rate characteristics and capability to escape premature convergence [45].

4.2 Application of FSA for solving simultaneous optimal allocation of DGs and EV fleets

The solution methodology of FSA for solving optimal allocation of DGs and EV fleet problem is followed the following steps.

  • Step 1 Read the test system bus data and branch data, dimension of search space \(d\) (includes number of DGs, number of EV Fleets and size of DGs) and number of countries \(n\) and maximum number iterations \(k_{\max }\).

  • Step 2 Generate initial population using Eq. (18) and evaluate the objective function value using Eq. (11). Since the locations of DGs and EV Fleets are discrete variables, round(x) function is used and whereas DG sizes remain the same as generated using random number theory within the search space. From the solutions, define each solution as a local solution (LS) and best among all as a global solution (GS).

  • Step 3 Perform exploitation stage related to each country for each LS using Eq. (19) and exploration stage related to overall world using Eq. (20) respectively.

  • Step 4 Using LS and GS in Step (2) and Step (3), update the solution of each person using Eq. (21) and update LS and GS solutions.

  • Step 5 Update the initial random population generated at Step (2) using Eq. (18) for new population using Eq. (22) and check for updating LS and GS before increment in iteration count k.

  • Step 6 Check for \(k = k_{\max }\).

  • Step 7 If not, repeats Step (3) to Step (6), else, stop and print the results.

5 Results and discussion

In this section, the effectiveness of the proposed FSA for solving optimal allocation of CBs/DGs problem is demonstrated. For the purpose, the simulation studies on two real-time test systems namely 106-bus agricultural feeder and 36-bus system represents a small portion of residential feeder in Srikalahasti, Chittoor, AP, are presented and discussed here. The bus data and line data of these test systems are provided in Appendix A1 and A2 respectively. The simulations are performed in a PC with specification of 4 GB, 64-bit OS and Intel® Core™ i5-2410 M CPU @ 2.3 GHz processor using MATLAB program [51].

5.1 Practical 106-bus agriculture feeder

The practical system has 106 buses interconnected by 105 branches and operating at 11 kV. In this system, the following case studies are performed for two scenarios: (1) peak loading condition and (2) average loading conditions.

  • Case 1: Optimal allocation of CBs.

  • Case 2: Optimal allocation of DGs operating at unity power factor.

  • Case 3: Simultaneous allocation of CBs and DGs operating at unity power factor.

5.1.1 Scenario-1: peak loading condition

The peak constant power load of the system is (1218.68 kW + j 775.947 kVAr). According to voltage-dependent load modeling [52], the exponents for real and reactive powers are considered as 0.08 and 1.6 respectively for representing the agriculture loads such as pumps, fans and motors. From the load flow results, it is observed that total system load of (1216.372 kW + j 747.002 kVAr) and the test system is suffering from a total loss of (27.78 kW + j 20.21 kVAr). Also, the lowest voltage magnitude and stability index are observed as 0.9709 p.u. and 0.8887 at 105th bus respectively.

Case 1: In this case, FSA is applied to minimize real power losses via optimally allocation three CBs in the system. Also, the smallest size of CB is chosen as 50 kVAr. Under ideal VAr compensation (i.e., total reactive load on network made zero), the system has a total loss of (19.8591 kW + j 14.4472 kVAr). It means, by optimal allocation of CBs, the objective function value should not be less than 19.8591 kW. The best locations (buses 61, 104 and 106) and sizes in kVAr (i.e., 200, 200, 100) obtained by FSA are given in Table 1. In comparison to the base case, the improved performance of the system is as follows: the losses are decreased to 21.1203 kW from 27.78 kW and the minimum voltage magnitude and VSI at 100th bus are observed as 0.9787 p.u. and 0.9176 respectively.

Table 1 FSA results of real-time 106-bus feeder under peak loading conditions
Full size table

Case 2: In this case, FSA is applied to maximize voltage stability index via optimally allocation three DGs in the system. Under ideal active power compensation (i.e., total active load on a network made zero), the VSI of the system is 0.964. By integrating DGs with upf, the VSI may not be more than this value. Using FSA, the optimal locations (buses 32, 16 and 10) and DG sizes in kW (i.e., 399, 281 and 466), the VSI is reached to 0.9546. Correspondingly, the system real power loss and minimum voltage magnitude at 105th bus are 8.6547 kW and 0.9885 p.u. respectively.

Case 3: In this case, FSA is applied to optimize multi-objective function of loss plus voltage stability index via optimally simultaneous allocation of three DGs and three CBs in the system. The best objective function value 2.9723 is obtained by FSA via DGs at buses 57, 95, and 68 with sizes in kW, 446, 463 and 153, and CBs at buses 47, 23, and 79 with sizes in kVAr, 200, 150 and 200. The real power losses are The minimum voltage magnitude of 0.996 p.u. is observed at 44th bus and correspondingly VSI is reached to 0.984.

The results of three cases are given in Table 1. The voltage profiles of test system under different conditions are given in Fig. 1. In comparison to the base case, the real power losses of 1.988 kW, which have decreased by 92.8427%.

Fig. 1
figure 1

The voltage profiles of 106-bus under peak loading conditions

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5.1.2 Scenario-2: average loading condition

On the other side, the system has an average constant power load of (1106.251 kW + j 743.99 kVAr). Considering voltage-dependent load modeling, the load flow is performed and observed as total load (1104.323 kW + j 718.5 kVAr), total loss of (23.517 kW + j 17.108 kVAr), and the lowest voltage magnitude and stability index are observed as 0.9732 p.u. and 0.8972 at 105th bus respectively.

Case-1: The case study is repeated by considering average loading conditions. By having CBs at buses 8, 98 and 77 with a capacity of 150 kVAr, 200 kVAr and 200 kVAr respectively, the losses are decreased to 16.925 kW from 23.517 kW and minimum voltage at 105th bus is increased to 0.9805 p.u. from 0.9732 p.u. and stability index improved to 0.9242 from 0.8972.

Case-2: Similarly, the VSI is optimized considering average loading conditions on the system. The results of FSA are as follows: the optimal locations (buses 97, 7 and 8) and DG sizes in kW (i.e., 373, 220 and 453), the VSI is reached to 0.9653. Correspondingly, the system real power loss and minimum voltage magnitude at 105th bus are 7.6946 kW and 0.9912 p.u. respectively.

Case-3: Similarly, the procedure is repeated for minimizing simultaneously loss and VSI in this case. The best objective function value 3.2352 is obtained by FSA via DGs at buses 56, 69, and 97 with sizes in kW, 342, 374 and 316, and CBs at buses 24, 48, and 77 with equal sizes of 150 kVAr. The minimum voltage magnitude 0.9956 p.u. is observed at 94th bus and correspondingly VSI is reached to 0.9826. In comparison to the base case, the real power losses (2.2526 kW) are decreased by 90.42%.

The comprehensive results of FSA for three cases under peak and average loading conditions are given in Table 2. The voltage profiles of the test system under different conditions are given in Fig. 2. For the results, it can be said that the P compensation via DGs has resulted in better results than only Q compensation via CBs and combined P and Q compensation has better results than either P or Q individual compensation.

Table 2 FSA results of real-time 106-bus feeder under average loading conditions
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Fig. 2
figure 2

The voltage profiles of 106-bus under average loading conditions

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The impact of CBs/DGs integration is resulted in minimizing the real power loss and grid dependency, consequently, GHG emission. As given in Eq. (12), the GHG emission before and after CBs/DGs integration is calculated for both peak and average loading conditions and presented in Fig. 3. The percentage of reduction in GHG emission is calculated w.r.t. base case and given in Fig. 4. By observing Figs. 3 and 4, it can be said that the integration of CBs may result in improving system performance effectively but not in emission, since the grid dependency for total demand (load + loss) is not decreased much. On the other side, by having either DGs or combination of both DGs and CBs are results for reduced grid dependency and consequently the emission is decreased significantly and reduction rate is increased significantly. Notably, the emission reduction is more in Case-2 (i.e., only DGs) when compared with Case-3 (i.e., CBs and DGs), since the penetration of DGs is more in Case-2. Hence, at this point, it can be said that the integration of simultaneous allocation of CBs and DGs can contribute technically and environmentally in network operation.

Fig. 3
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GHG emission under different cases (106-bus system)

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Fig. 4
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Percentage of reduction in GHG emission under different cases (106-bus system)

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5.2 Practical 36-bus residential feeder

The test system has 36 buses interconnecting by 35 branches, and serving a total constant power load of (2798.1 kW + j 1946.4 kVAr) at 11 kV. By considering 0.92 and 4.04 as exponents for real and reactive power in voltage-dependent load modeling for residential loads [26], the load flow is performed. From the results, it is observed that total system load of (2791.1 kW + j 1922.9 kVAr) the test system is suffering from a total loss of (7.8571 kW + j 5.7163 kVAr). Also, the lowest voltage magnitude and stability index are observed as 0.9956 p.u. and 0.9825 at 11th bus respectively. Since it is a residential feeder, the performance improvement is simulated for only with DGs operating at upf (i.e., solar PV systems) for the following cases.

Case 1: Feeder performance improvement via optimal allocation of DGs with upf for base load considering loss minimization. The best DG sizes in kW are 789, 423 and 1193 at buses 6, 19 and 18 respectively. The real power compensation resulted as follows: In comparison, the real power loss decreased to 3.5736 kW and is equal to 54.52% reduction with base case. Correspondingly, the minimum voltage at the 11th bus is observed as 0.9974 p.u. and VSI is 0.9896.

Case 2: Analysis of feeder performance with EV loads penetration. At each bus, 10% load increment is assumed towards EVs adoption. In general EVs charge batteries via AC/DC charger and it is assumed that the operating power factor of the charger is 0.98, hence, the reactive power consumption by EV load is equal to 10% real power load × tan(cos−1(0.98)). As per voltage-dependent load modeling, the exponents of increased real and reactive power are considered as 2.59 and 4.06 respectively. The system load under this case is (3068.3 kW + j 1977.4 kVAr). Under these conditions, the system performance is as follows, the total losses are (9.0233 kW + j 6.5647 kVAr), lowest voltage at 11th bus is 0.9953 p.u. and correspondingly VSI is 0.9814. Here it can be observed that the losses are increased, voltage profile and VSI are decreased with additional EV load on the system.

Case 3: Feeder performance improvement via optimal allocation of DGs with upf considering loss minimization and VSI improvement: By using proposed FSA for solving DGs allocation problem at this case, the best solution obtained is as follows: the locations of DGs are 36, 9 and 35 and their sizes in kW are 550, 541 and 1073 respectively. By having this real power compensation, the losses are decreased to (3.7216 kW + j 2.7075 kVAr), minimum voltage profile at 11th bus is increased to 0.9975 and VSI is raised to 0.99 respectively.

Case 4: Feeder performance improvement via optimal allocation of EV fleet considering loss minimization: In this case, the increased 10% of loading condition (279.11 kW + j 192.29 kVAr) across the network is taken as a load of single EV fleet and optimized its location. The proposed FSA is finalized the 2nd bus as optimal location for EV fleet integration, correspondingly the system loading is (3069.74 kW + j 2114.45), the losses (8.1275 kW + j 5.9130), the lowest voltage at 11th bus is 0.9955 p.u and system stability index is 0.9823.

Case 5: Feeder performance improvement via simultaneous optimal allocation of DGs and EV fleet considering loss minimization and voltage stability maximization: In this case, the increased loading condition across the network is taken as total power rating of a single EV fleet and optimized its location along with DG locations and sizes. FSA resulted lowest objective function by EV fleet location at 2 and DGs sizes in kW and locations are: 1179(7), 1317(17), 427(30), correspondingly the losses (3.6418 kW + j 2.6495 kVAr), lowest voltage at 11th bus is 0.9981 and VSI is 0.9923.

The comprehensive results of all the cases are given in Table 3 and correspondingly the voltage profiles are given in Fig. 5. From Fig. 3, the base case voltage profile across the network is improved by having DGs (case-1) declined. Similarly by having EV load distribution across the network, the voltage profile is declined significantly (case-2). At this stage also, it is also possible to improve network profile by having DGs at best locations (case-3). On the other side, by having a charging facility to support spatially distributed EV load (as seen in case-2) at some best locations as EV fleet, the voltage profile can be improved significantly (as seen in case -4). This situation can be further improved by having EV fleets and DGs at optimal locations (as seen in case-5). From these case studies, it can be said that the improved voltage profile is almost flat across the network in case-5, hence, the distribution losses are decreased and consequently VSI is improved significantly.

Table 3 FSA results of real-time 36-bus feeder
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Fig. 5
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Voltage profile 36-bus system for different cases

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As determined in the 106-bus system, the GHG emission is calculated for different cases in this test system also and the percentage of reduction/increment in emission w.r.t. the base case is given in Fig. 6. In case-1, the grid dependency for base case loading is decreased via DGs allocation, whereas in case-2 and case-4, it is increased due to EV load. But as compared to case-2 (EV load is distributed spatially), in case-4, it is less due to concentrated EV load as fleet at optimal location. Hence, in case-2 and case-4, the emission is increased. The negative effect in case-2 and case-4 is managed effectively by having DGs in case-3 and case-5 respectively. Hence, in case-3 and case-5 resulted in reduction in emission. But as compared to case-3, case-5 is given more reduction in emission due to optimal location of both EV fleet and DGs in the network.

Fig. 6
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Changes in emission reduction/increment w.r.t. EV load, fleet and DGs (36-bus system)

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5.3 Comparison of FSA performance with other HSAs

The results of FSA for Case-5 are compared with other HAs, namely, Grasshopper Optimization Algorithm (GOA) [53], Teaching Learning-based Optimization (TLBO) [54], Cuckoo Search Algorithm (CSA) [55], Flower Pollination Algorithm (FPA) [56] and Particle Swarm Optimization (PSO) [57]. Since FSA is not required to control any parameters, we have not changed any parameters of other algorithms also. In PSO, the range for inertia weighting factor is decreased linearly about 0.9 to 0.4 during a run and the social and cognitive coefficients are taken equally as 2. In CSA, the switching parameter is set to 0.8. In TLBO, the teaching factor may become randomly either 1 or 2 with equal probability during a run. For GOA, the intensity of attraction and the scale of attractive length are considered as 0.5 and 1.5 respectively. For all algorithms, the following parameters are considered commonly: population = 50, iterations = 50, search variables = 7 (i.e., 3 for DG locations, 3 for DG sizes and 1 for EV fleet location). The lower limit and upper limits for locations = [2, nbus] and DG sizes = [0, 1500].

In order to determine the robustness of FSA in solving optimization problems, each algorithm is simulated for 25 independent run simulations for case-5 in the 36-bus system and compared their performance characteristics in terms of best, mean and worst objective functions. The boxplots given in Fig. 7 for Case 5 in the 36-bus system are allowed to clear and analyze these features. At this point, it can be said that the FSA is a more robust and efficient algorithm than other used algorithms. The best solution obtained by each algorithm over 25 independent run simulations are given along with average computational time in Table 4. Also, the best cost/solution improvement obtained by FSA is quantified and defined as [58]:

$$ BSI\left( \% \right) = \frac{best\, solution\, of\, compared\, method - best\, solution\, of\, proposed\, FSA}{{best\, solution\, of\, compared\, method}} \times 100\% $$
(23)
Fig. 7
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Boxplot for comparison HSAs for case-5 in 36-bus system

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Table 4 Comparison of best solution obtained by different HSAs for case-5 (36-bus system)
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The more BSI value of an algorithm indicates more distance from the best solution obtained by proposed FSA. All these performance matrices are less with FSA over other compared algorithms, hence it can be said that the FSA is effective in resulting global solutions frequently. The convergence characteristics of different algorithms for case-5 in the 36-bus system for best solution provided in Table 4 are given as new Fig. 8.

Fig. 8
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Convergence characteristics of various algorithms

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6 Conclusion

This research presented the application of a new nature –inspired meta-heuristic algorithm called future search algorithm for solving the simultaneous allocation of distributed generation and electric vehicle fleets in radial distribution systems. The proposed methodology mimics human behavior in search for better living life by inspiring a local popular/ successful leader in a zone. In FSA, the population size indicates the number of nations searching by a person for his comfortable life. The more nations mean the more local influenced persons. These individual local best persons can again be influenced by a global best person. Hence defining new GS and LS at each iteration and again using them for updating the optimal solution within the same iteration is the key feature of FSA for outperformance over other HAs.

The simultaneous allocation of DGs and EVs has been formulated as a multi-objective function using real power loss, average voltage deviation index (AVDI), voltage stability index (VSI) and greenhouse gas (GHG) emission. In comparison with PSO, FPA, TLBO, CSA and GOA, the proposed FSA has resulted in the lowest objective function. The statistical analysis based on 25-individual run time results, FSA has shown its superiority in terms of robustness and consistency. In conclusion, FSA has outperformed other simulated HAs in solving the multi-objective, non-linear and complex optimization problem.

The simulation results on a practical 106-bus agriculture feeder for simultaneous allocation of multiple DGs, and a 36-bus rural feeder for simultaneous allocation of DGs and EV fleet are presented. From the case studies, the EV load penetration has resulted in degrading the feeder performance significantly in terms of increased real power losses, decreased voltage profile and consequently resulted in lowering the voltage stability margin. In counter to this scenario, the optimal placement and sizing of DGs and EVs resulted for improvement in feeder performance significantly. Also, the environmental benefits in terms of reduced GHG emission have shown the necessity of the RE and EV technologies adoption globally.

However, the randomness in EV fleet load, intermittency of renewable energy and timely varying network loading conditions can create potential operating issues in the modern distribution networks. Under these circumstances, validation of proposed methodology for enhancing the performance of distribution network by using simultaneous smart charging scenario in EV fleets and timely optimal network reconfiguration w.r.t. network loading conditions need to be further analyzed. Also, the computational efficiency of the proposed meta-heuristic FSA algorithm in solving such complex multi-objective optimization problems needs to be further investigated and treated as future scope of this research.