Bi-level Multi-Objective planning model of Solar PV-Battery storage based DERs in Smart grid distribution system

This paper presents a novel bi-level multi-objective model for planning solar PV-battery storage (PV-BS) based DERs in Smart grid distribution system (SGDS). The planning of Solar PV and battery storage (BS) in the distribution system presents severe complexities for the system planner due to their inherent attributes. The detailed analysis considering all three planning aspects, namely technical, economics, and environmental is presented, assisting in the efficient and reliable planning operation. The four test cases are formed based upon the life cycle cost, unserved energy, penetration level, and social welfare. The level-1 proceeds with evaluating the DERs sizing along with penetration level and serves as an input to level-2, for computing the optimal placement for DERs. The proposed model is implemented on the IEEE-33 bus distribution system and solved using Butterfly-PSO (BF-PSO) algorithm. The detailed parametric and sensitivity analysis presented may aid the system planners in terms of planning preview. The simulation results validate the effectiveness of the proposed work by showing significant improvement in bus voltage profiles (upto 4%) and reduction in total power losses (upto 45%). The highest penetration level is observed for Case 2 (70%), which also corresponds to the highest LCC (k$ 147094) and thus results in the lowest emission cost (k$ 4920).


I. INTRODUCTION
Today's smart grid distribution system (SGDS) is evolving progressively due to the higher integration of renewable energy sources (RES) and socio-political goals motivating smart grid development. The growth of RES-based distributed energy resources (DERs) has preceded conventional power generation in the past few years. This paradigm shift towards RES-based DERs has contributed to the successful deployment of smart grid technologies and has led to the development of SGDS. With the advancement of new technologies, the implementation challenges go hand in hand. The inclusion of DERs pose severe threats to reliability and operation of SGDS [1]. Hence, planning of DERs integration in SGDS is of major concern for system planners. One of the significant aspects in planning of SGDS is evaluating optimal placement and optimal sizing of DERs integration. The planning problem gets even more complex with the higher penetration of RES-based DERs and battery storage (BS) incorporation. The issues which complicate the planning problem are enumerated as follows [1]: Intermittency of DERs: The uncertain behavior of irradiance and wind speed leads to variable output power from DERs such as solar PV and wind. ii.
Technical Parameters: The effect of integration of DERs on different technical parameters such as reliability, losses, voltage profile, and power exchange between grid and SGDS. iii.
High Capital Investment: The high initial investment cost associated with the RES-based DERs. iv.
Economics Parameters: For determining the degree of effectiveness, the analysis of the economic parameters such as power purchased from the grid, emission cost, and costs associated with operation & maintenance. v.
BS Integration: The optimum integration of BS with DERs requires detailed examination, else it would lead to increased system losses, voltage regulation issues, and reverse power flow. In the literature, several works reporting the optimal integration of DERs in the distribution system did not consider the intermittency of the DERs [2][3][4]. The intermittency of the RES-based DERs is imperative for DERs allocation studies, as the output from these sources is not dispatchable. Several papers reported in the literature consider the intermittent nature of RES-based DERs, addressing this with different models and approaches. The various approaches implemented in literature for modeling uncertainty of the RES-based DERs (such as generating solar irradiance and wind speed) are -Markov transition probability matrix, point estimate method (PEM) [5,6], Monte Carlo simulation (MCS) [7,8], beta probability density function (pdf) [8], Weibull pdf [7], and time-series methods. Ehsan and Yang [16] used a heuristic moment matching (HMM) based approach in which based upon the historical data, the reduced scenarios are generated for DERs and load profile, J.M. Home-Ortiz, et al. [22] used a clustering techniques k-means. In Ref. [22], the different scenarios are generated, although the correlation between the demand and metrological data are not taken into account here, along with seasonal characteristics. Still, the techniques based on scenario generation can be found to be computationally inaccurate and inefficient. However, in majority of the literature [5][6][7][8]22], the uncertainty associated with the DER hardware availability is not considered. The probabilistic model approach is effective in addressing the uncertainty of the RES-based DERs. The existing literature also neglects the impact assessment of penetration level on SGDS.
The objectives constitute the most vital consideration for the optimization problem. The literature on the multi-objective optimal integration of the DERs in SGDS can be broadly classified into three categories namely objectives based upon technical, economic, and environmental (social) parameters [9]. The objectives on technical parameters mainly constitute power loss reduction, voltage profile enhancement, unserved energy, systems reliability, and sensitivity [2][3][4][5][6][7][8][9][10][11]. Among these objectives, power loss reduction and voltage profile enhancement dominate the majority of the literature. While considering the economic criteria, the objectives mainly comprise annual energy savings, reduced power purchased from the grid, and minimized systems total cost (investment, operational, and maintenance). The environmental objectives deal withenhanced social welfare and reduced carbon emissions [5,14,22]. These three parameters are duly considered and formulated through a bi-level multi objective model discussed in subsequent sections.
Some novel works in the literature consider minimizing the -Distributed generation (DG) installation cost, power import, and DG curtailment. A tractable two-stage stochastic formulation for optimal integration of RES-based DER in the multi-phase distribution system is discussed in Ref. [10]. A differential evolution algorithm-based optimization is presented for the placement, sizing, and power factor setting [11]. A dynamic reliability-based model for DERs planning in distribution networks to maximize the profit of distribution companies is developed in Ref. [12]. Considering different time-varying load models and demand response, optimal integration of DERs in the distribution network is addressed in Ref. [13]. An effective water cycle algorithm (WCA) for multi-objective placement and sizing of DERs is discussed in Ref. [14], though the uncertainties associated with the DERs have not been given consideration here. The objective function of total harmonic distortion minimization and its impact on the power factor is evaluated in Ref. [15].
The battery energy storage (BS) constitutes an elementary component of SGDS with RES based DERs. However, it has been it is eluded from some prime literature. There are only a few literature focused on energy storage along with DERs. A scenario-based stochastic approach considering multi-type DERs and BS in the distribution network for enhancing the distribution network operators profit is shown in Ref. [16]. The optimal integration (including sizing and sitting) of BS and DERs from the perspective of the distribution system operator is discussed in Ref. [17]. Considering reliability as a planning parameter, the MILP formulation for optimal sizing and siting of energy storage is shown in Ref. [18]. Optimal allocation of PV-based DER and BS using PSO algorithm is shown in Refs. [19,21]. Considering the minimization of generation cost, the optimal placement, sizing, and control of energy storage is described in Ref. [20]. A multi-stage stochastic mixed-integer conic programming (MICP) model is shown for optimal integration of DERs and BS in a distribution system [22]. A two-stage optimal integration of DERs and BS using multi-objective multi-verse optimization (MOMVO) in a distribution network of Kabul city is presented [23]. The issue of optimal placement and sizing of DERs along with BS is widely open and yet to be addressed efficiently in literature. The Table I presents a categorical representation of various planning parameters reported in different papers along with research gaps. The identified research gaps and consequent contributions offered in this work are enlisted in Table II based on the literature survey   TABLE I

Research gaps Contributions
• While addressing the RES-based DER integration, the modeling of the metrological condition is not given due consideration along with the system availability model in the literature.

•
In this work, the multi-state modeling of the system components is carried out for Solar PV and BS along with the system hardware availability model.

•
The problem of optimal integration in the literature mainly ponders upon the optimal placement and sizing issue, whereas a prominent parameter of penetration level is often less discussed.

•
In this bi-level multi-objective model, along with the optimal placement and sizing of PV-BS, the penetration level for each case is also discussed simultaneously.

•
In the planning problem, either DERs are involved in the optimal placement and sizing problem, or only BS is considered. Both DER and BS together as a component are considered in very few literature.

•
The optimal placement and sizing are determined for both DERs and the energy storage simultaneously together in this work. Additionally, the penetration level for the DERs is also computed.

•
In the literature, majorly a single-level multi-objective problem is investigated, focusing either on the economic or technical or environmental parameters. All the economic, technical, and environmental parameters are not given due consideration simultaneously together.
• In this work, a two-level multi-objective problem is formulated. The first level corresponds to the optimal sizing of the planning components, considering the economic and environmental aspects. The second level of optimization details the optimal placement of the planning components, considering the objectives concerning technical parameters.
The highlights of this work are as follows: i.
This paper presents a bi-level multi-objective model for planning solar PV-battery storage (PV-BS) based DERs in SGDS. ii.
The adequate uncertainty modeling using beta pdf and battery state model for PV-BS respectively is presented in this work. The systems hardware availability modeling is also considered in this study, which is not addressed in significant literature. iii.
In this study, a bi-level multi-objective model is explicated underling the technical, economic, and environmental concerns associated with the DERs planning. iv.
In this bi-level approach the level-1 accounts for the optimal sizing of the planning components and obtaining their penetration level, whereas level-2 results in determining optimal placement of PV-BS simultaneously. v.
The effectiveness of the proposed bi-level model for SGDS planning is evaluated in the IEEE-33 bus distribution system by forming four test cases based upon the weighting factors associated with the objectives. vi.
The detailed parametric analysis and sensitivity analysis is exhibited for the total life cycle cost (LCC), energy not served (ENS), and power emission cost (PEC), depicting the substantial significance of all three parameters from a planning perspective. The organization of the rest of the sections is as follows -Section 2 details the multi-state modeling of system components i.e., solar PV and battery storage. Section 3 presents the description of the planning framework, which constitutes level-1 and level-2 multi-objective optimization. Section four describes the methodology implemented for evaluating the bi-level optimization problem. Section 5 presents the results and discussion of the multi-state optimization, followed by the relevant conclusion drawn from the work.

II. Multi-state Modeling (MSM) of System Components.
The DERs considered in this work comprise of solar PV units and battery storage (BS) which are to be integrated with SGDS. The output of solar PV is highly intermittent and relies on the state of irradiance and temperature. As the state of charge (SOC) of BS is dependent on power output from PV units, BS output evaluation also calls for probabilistic analysis. This section details the MSM of DERs for evaluating the output power from Solar PV and BS (PV-BS).

A. MSM OF SOLAR PV OUTPUT
The output power computation from solar PV based DERs necessitates suitable system modeling, which is discussed as follows:

1) SOLAR IRRADIANCE MODEL (SIM)
The solar PV output is strongly reliant on climatic weather conditions (solar irradiance, temperature), and hence the intermittent nature of such sources is needed to be addressed adequately. Thus, solar PV based DERs requires adequate modeling of meteorological information such as solar irradiation and temperature. There have been numerous approaches proposed in the literature for the modeling of solar irradiance. In the present work, solar irradiance has been modeled using the beta probability distribution function (pdf). The expression for solar irradiance using beta pdf for time segment ' ℎ ' is as follows [24]: Where and are the beta distribution function parameters for ' ℎ ' time segment; Γ represents gamma function; and is the solar irradiance intensity (kW/m²). The value of and parameter can be calculated as follows: Where and are represents mean and standard deviation of solar irradiance for ' ℎ ' time segment.
The evaluated beta pdfs for a particular time segment are continuous and, in order to facilitate the analysis, it is discretized into a number of states. The number of states is selected 15-20 so as to maintain an appropriate balance between accuracy and computation time. Thus, discrete pdf of solar irradiance during any time segment ' ℎ ' can be expressed as: = { , ( ): = 1: } (4) Where, : Discrete pdf of solar irradiance; : ℎ state of solar irradiance (kW/m²) for ' ℎ ' time segment; ( ): Probability of ℎ state of solar irradiance; : Number of states of solar irradiance.
The probability associated with ℎ state of solar irradiance can be calculated as:

2) HARDWARE ACCESSIBILITY MODEL (HAM)
The hardware accessibility model determines the availability status of the generating units i.e., either the unit is available or not available for generation. The HAM is evaluated based on the forced outage rate (FOR) of PV unit. The HAM adopted in this work has been discussed in detail in Ref. [24,25]. The hardware accessibility model for ℎ PV array can be defined as: , , , and , represents HAM of ℎ PV array, output power corresponding to ℎ capacity state of ℎ PV array, and the number of output states of ℎ PV array respectively.
The HAM corresponding to all PV arrays can be obtained by convolving the pdfs of all individual PV arrays and is given by: = Total number of connected PV Array.

3) SOLAR PV POWER OUTPUT MODEL
The power output from the Solar PV based DER is characteristically determined based on SIM, HAM, and power output through the PV array units. The SIM serves as an input of irradiance to the PV array units. The output power from the PV arrays can be obtained using following equations [26]: Where, is the PV cell temperature (℃); is the ambient temperature(℃); is the nominal operating temperature (℃); is the ℎ state of solar irradiance for 'n th ' time segment; is the short circuit current of PV module (A); is short circuit current temperature coefficient is the open circuit voltage of PV module (V); ( ), ( ) are the voltage and current output respectively from the Solar PV module for the case . Therefore, the maximum output power from a ' ' module PV array can be calculated as: Where, is the fill factor which is a characteristic of the material of the PV module. The power output from the Solar PV array shown in eq. 11 is subjected to the HAM, which means the output power is dependent on the unit availability and unavailability. Thus, the eq. 11 needs to be modified in accordance with the HAM. Hence, the output power from Solar PV array considering the ℎ state of HAM is expressed as: Where, is the rated output power of PV array.

B. MULTI-STATE BATTERY STORAGE MODEL (BSM)
The BS incorporation is essential with Solar PV based DER for acquiring a satisfactory level of reliability. The output of BS depends upon the state-of-charge (SOC) of its previous state, existing load conditions, and power output from generating units. A probabilistic battery storage model (BSM) is employed in this work which has been discussed in detail in Ref. [24]. The probabilistic BSM establishes a correlation between the intermittency of DERs and the BS over each time segment. In the BSM, the BS is considered as a source with different SOC levels and associated possibilities. The BSM for ℎ time segment is expressed as follows: is the battery state of charge for ℎ state and ( ) is the battery SOC probability during ℎ state for ℎ time segment. During the battery discharging mode the maximum power available for ℎ state of can be calculated as: During the battery charging mode, the maximum power that can be supplied to it can be calculated as: The probability associated with BS persisting a particular SOC is evaluated for each time segment. The output power of the BS for ( + 1) ℎ time segment is dependent on the charging/discharging that occurred in the ℎ time segment corresponding to the different states of , SIM, HAM, and load profile. Minimization of the cost of power purchased from grid.
Minimization of cost of unserved energy.
Maximization of social welfare.

Level-2 Optimization
Minimization of total power loss.

III. DESCRIPTION OF PLANNING FRAMEWORK
This paper proposes a bi-level multi-objective model for optimal integration of planning components in smart grid framework. The capacity, penetration level, and location of DERs are considered as decision variables in planning problems. The fig. 1. displays the schematic representation of the bi-level planning problem. A discussion on level-1 and level-2 has been presented in the following sub-sections.

A. LEVEL-1 OF PLANNING PROBLEM
The level-1 of planning deals with the determination of optimal component sizing i.e., the solar PV and BS capacity along with the penetration level evaluation. The problem is embedded in a multi-objective framework as a cost function wherein all three planning aspects namely economics, technical and environmental are considered. The multiobjective optimization is implemented using weighting factor technique. The expression for level-1 optimization can be expressed as: (16) Where 1 , 2 , 3 , 4 are the weighting factor and 1 is the level-1 objective function. The terms , , , and are as follows: i.
: Cost of power purchased from grid (Maximization of DER penetration). iii.
: Cost of unserved energy (Maximization of system reliability). iv.
: Cost of emissions (Maximization of social welfare).

1) : LIFE CYCLE COST (LCC)
This objective function deals with the minimization of the life cycle cost (LCC) associated with PV-BS based DERs. The LCC is the net present value of the total sum of cost incurred during the project lifespan [27]. The LCC can be expressed through following function: is the net present value of the operation & maintenance cost (k$) of the components, is the net present value of the replacement cost (k$), and is the net present salvage value (k$) of the components.

2)
: COST OF POWER PURCHASED FROM GRID (MAXIMIZATION OF DER PENETRATION) This objective function is primarily focused on maximizing the penetration level (PEN) of DERs in the grid. The penetration levels characterize the assured firm capacity supplied by the DERs. While maximizing the DERs penetration level, the power drawn from the grid is reduced simultaneously. Hence, the cost of power purchased from the grid must be minimized. The penetration level of the DERs can be given as: The objective function for the cost of power supplied from the DERs can be expressed as: Where, PEN is the penetration level of DERs, is the total number of time segments in a study period, ( ) is the energy supplied by the DER for ℎ time segment in kWh, is the energy demand for ℎ time segment in kWh and _ is the cost of energy per unit from the grid.  Social welfare can be estimated by the term called the social cost of carbon (SCC). The SCC is an estimate of the economic value of extra (or marginal) impact caused by the emission of one more ton of carbon at any point in time [28]. The SCC assessment provide an economic analysis of the benefits associated with carbon dioxide reduction. Since, RES based DERs do not contribute to harmful emissions, the SCC corresponds to conventional generators only. The net present worth of social cost of carbon emission can be given as: The power emission cost (PEC) associated with conventional generators can be calculated as: Where, is the energy output from conventional generator during ℎ planning year, is the SCC emission/unit of energy produced, $/kWh, is the number of units of ℎ component and is the expected annual energy output from ℎ unit of ℎ generation, kWh.

B. LEVEL-2 OF PLANNING PROBLEM
The level-2 of optimization deals with the planning focused on: i. : Minimization of system losses. ii. _ : Minimization of voltage deviation. Hence, the level-2 of the optimization can be expressed as: corresponds for the total system active power losses and _ for the voltage profile factor (Voltage deviation). Whereas, 5 , 6 are the weighting factors.

MINIMIZATION OF SYSTEM LOSSES
The constitutes for the total system active power losses. Hence, the expression for system losses minimization can be expressed as: Where, 5 is the weighting factor and i is the bus number, where DERs is to be installed.
Where 6 is the weighting factor. Here, voltage before DERs placement is considered as 1 p.u.

1) CONSTRAINT ON POWER FLOW BALANCE
The power flow balance must be maintained in the SGDS for all time segments.
a) The BS discharging mode: b) The BS charging mode: Where, presents the available Solar PV power output during the ℎ time segment, ℎ and is the power flow through BS during charging and discharging modes respectively, load supplied during ℎ time segment, is the unutilized power due to excess generation.

2) CONSTRAINT ON BATTERY SOC
The battery SOC is constrained by minimum and maximum permissible SOC value. The expression for ℎ SOC is taken as following ≤ ≤ (28) Where, and are minimum and maximum permissible battery SOC limits.

3) CONSTRAINT ON COMPONENT SIZING
Where, and is the minimum and maximum capacity of a Solar PV component in kW. and is the minimum and maximum capacity of the BS component in kVAr.

4) CONSTRAINT ON DERS PENETRATION LEVEL
Let be the system state corresponding to the for ℎ state of : Where, is the defined minimum penetration level and is the maximum defined penetration level.

IV. Methodology for evaluating two-level optimization problem
In order to determine the optimal sizing and penetration level in level-1, and optimal placement of DERs in level-2, an efficient hybrid metaheuristic approach called as Butterfly-Particle swarm optimization (BF-PSO) has been employed [29]. It is a modified version of the classic PSO algorithm. The BFPSO is the technique based upon the food searching process of butterfly swarms based on their intelligence. In BFPSO, every particle within the search space follows a particular velocity and inertia with the related generations and updates its positions. The sensitivity and probability range is considered between one and zero. Let us assume a vector X (i=1,2,3….N) corresponding to the N positions (population) and respective velocity v. Considering the t th iteration, let us assume vt and xt are the velocity and position (population) respectively. Also, vt-1 and xt-1 are velocity and population of the previous iteration. The velocity and position (population) of each particle for t th iteration can be given as: Where, 1 , 2 are random variable (0-1) and 1 , 2 are acceleration coefficients. The BF-PSO assist in obtaining optimal solution along with probability, sensitivity, lbest, and gbest for accurate and fast convergence. In Butterfly-PSO, lbest solutions are selected by individual's best solution. Here, separate lbest solutions are selected by each swarm then gbest acknowledged based on corresponding fitness. The food location (position) and probable amount of nectar represent the optimal problem solution and corresponding fitness. The general ranges of sensitivity and probability are considered from 0.0 to 1.0. The velocity limits can be set based on the limits of the problem variables. Hence, the function of probability and sensitivity can be stated in terms of iteration as: Where, is the butterfly sensitivity towards flower, is the probability of food for t th iteration, is the maximum number of iterations, is the t th count of iteration, , is the fitness of global best solution for t th iteration, and , is the fitness of local best solution for t th iteration. Now the final equation of BFPSO can be taken as follows: Where, is the probability of global best (generally assume =1 for global solution), is the current probability and is the time varying probability coefficient.
can be given as: = rand*P t , (rand is the random number [0, 1]) (38) The bi-level multi-objective model implementation using BF-PSO is shown through the flowchart in Fig. 2. Here, both level-1 and level-2 of optimization have been implemented through the BF-PSO. Initially, the level-1 optimization problem constituting eq. 16 is implemented through the BF-PSO, computing the component sizing with penetration level. The output parameters of the level-1 optimization serve as an input to level-2 optimization problem constituting eq. 23. Again, the BF-PSO is functioned for level-2, resulting in the optimal placement of the components Optimal Planning

Is termination criteria reached
Multi-Objective Function -

• •
_ under study. The modeling of Solar PV irradiance and BS have been discussed in detail in Section 2. The solar irradiance data and the ambient temperature data are obtained from [28]. The Fig. 3 shown the global horizontal irradiance of the India [30]. The proposed bi-level multi-objective formulation is implemented on IEEE-33 bus system [27]. The peak load for the PV-BS based SGDS is 3761 kW and 2300 kVAr. The modelling and optimization have been carried out on MATLAB/SIMULINK software version 2016b, processor intel i5 8 th Gen, and 8 GB RAM.  In this work, the period of one year is divided into four seasons (one month corresponding to one season). For each considered month, a representative day is considered. For each representative day, 14 hours of sunshine hours have been considered. Thus, a total of 56 beta pdfs are evaluated corresponding the data of four months for four seasons. However, pdfs obtained for each time segment are continuous and need to be discretized into number of states in order to facilitate analysis. The decision of selecting large number of states may prove computationally expensive whereas small number of states may override accuracy. The states between 15-20 are generally chosen to maintain a proportional balance between accuracy and time. In this study, we chose 15 states for SIM and 20 states for BSM. The Fig. 4, Fig. 5, Fig. 6, and Fig. 7, shows the beta pdfs evaluated for all four seasons (Winter, Summer, Monsoon, Autumn) respectively.     (12 pm -1 pm).

A. Results for Level-1 of a 33-bus test SGDS
As discussed in Section 3, the level-1 of planning is focused on obtaining optimum component sizing of DER and their penetration level. As discussed in Section 3, all the objective functions in level-1 are formulated as the cost functions. Thus, level-1 is focused upon the economical viabilities, DER penetration, systems reliability and emission control.
In order to facilitate a comprehensive planning formulation, four different cases have been considered by varying the weighting factors assigned for different objective functions. The weighting factors corresponding to different cases are as shown in Table III. Case 1: corresponds to the condition when 1 =1; which implies that the optimization is specifically based on minimization of project cost.
Case 2: corresponds to the condition when 2 =1; which implies the objective of minimization of power purchased from the grid or can be reflected as the maximization of DER penetration. This case is particularly of importance in view of renewable penetration due to increasing environmental concerns.
Case 3: corresponds to the condition when 3 and 4 both are given equal weightage of 0.5 each. In this scenario, the minimization of unserved energy and maximization of social welfare both are given equal importance. This case caters the fulfillment of systems reliability and reduced emissions together.
Case 4: corresponds to the condition when 1 , 2 , 3 , and The optimization has been carried out by using BF-PSO algorithm explained in Section IV. The parameters of BF-PSO are shown in Table IV. The Table V presents the results of level-1 reflecting the optimal sizing of the system components. The results have been obtained for all the four cases by evaluating different combinations of PV-BS units along with the penetration level.   As evident from Table V, for Case-1 (w1=1), it can be observed that the total capacity of PV-BS is less compared to the other cases. As here, the investment, operational & maintenance, replacement cost is considered to be minimised. Hence resulting in the lower penetration level of 30%. For Case-2, the weightage is assigned to the objective of minimization of power purchased from grid (maximization of DER penetration). Hence the optimum sizing result depicts the highest level of penetration (70%) amongst all the four cases. Correspondingly, in order to minimize the power purchased from the grid the combinations of PV-BS units have also increased significantly. In Case-3, the objectives of minimization of unserved energy (maximization of system reliability) and maximization of social welfare both are given equal weightage. Hence in this case in order to minimize the unserved energy the significant capacity of PV-BS is computed among rest of the cases. On the other hand, considering the social cost of carbon the penetration level determined is significantly high (60 %).
Considering Case-4, assigning the equal weightage to all four objectives, the optimal penetration comes out to be 40%. This scenario focuses on all the objective functions of the level-1, giving due consideration to cost, penetration level, systems reliability and reduced carbon emissions. Fig. 8, and Fig. 9 represent the plots for optimum value of LCC (k$), and PEC (k$) respectively for all four cases. It can be observed from Fig. 8 that the optimum value of the LCC is lowest (k$ 83856) for Case 1 and maximum (k$ 147094) for Case 2. It is evident from the results that the LCC cost is highest while minimizing the power purchased from grid or maximizing the DER penetration. As well as for Case 3 considering the systems reliability also contributes for a higher LCC (k$ 135075), as in this case the majority of the power demand is met largely by the conventional generation. Fig. 9 represents the emission costs for all the four cases. It is observed that the PEC is highest (k$ 10036) for Case 1 and lowest (k$ 4920) for Case 2. In Case 1 the penetration level is the minimum resulting in majority of the power demand supplied through the conventional generation. While considering the Case 2 the penetration level is the highest ensuing the lowest PEC, as in this scenario the demand is met significantly through the DERs generation also.  Fig.10, Fig.11, Fig.12, and Fig.13, shows the parametric analysis for the different combinations of PV, BS and penetration level. For the purpose of analysis, the PV capacity is varied between 7.5 MW to 29.25 MW and BS capacity is varied between 43.3 MVAr to 72.9 MVAr with penetration level ranging from 30% to 70%. The analysis is carried out for different parameters of objective function namely LCC, ENS and PEC for each case respectively. Considering all the cases from fig. 10-13, it is evident that the LCC comes out to be the minimum in case 1 and the highest frequency of LCC for this case is observed in between the range of k$80000-k$90000. Correspondingly case 2 accounts for the highest value of LCC, and the highest frequency of LCC for this case is observed in between the range of k$150000-k$180000. Hence, the parametric analysis signifies that considering Case 1 the majority of the combinations of PV, BS, and penetration level fall in range contributing least value of LCC among all four cases.

1) LEVEL-1 PARAMETRIC ANALYSIS FOR ALL FOUR CASES
Analyzing the PEC for different cases indicate that the lowest value of PEC is followed by Case 2 which leads to the objectives of maximum DER penetration. The PEC in case 1 and case 4 is highest among the four cases because in order to minimize the PV-BS total costs, the supply is met largely with the conventional generation. Hence, the emissions are highest here. Considering the ENS, it is observed that the ENS is considerably low for all the cases.

2) SENSITIVITY ANALYSIS FOR LEVEL-1
In order to provide better insight in system planning, Fig. 14-16 present the sensitivity analysis for LCC, ENS, and PEC. In this analysis the variation in the LCC, ENS, and PEC is observed for the different combination of PV and BS based upon their penetration level. From Fig. 14, it is evident that as the units of PV and BS increases it accounts for the higher penetration level and consequently the LCC increases. Whereas lower penetration level and smaller component sizing results in lower LCC. In fig. 14-16 (a), (b), (c), and (d) implies different cases from 1-4 respectively.
It can be observed from Fig. 15 that irrespective of the considered case, lower ENS level is achievable at lower penetration level. As the penetration level increases, it becomes difficult to sustain reliability standards due to intermittent behaviour of PV. The BS does contribute in smoothening of the uncertain behaviour; albeit at the increased cost.
From Fig. 16, it can be observed that lower the component sizing, lower the penetration level and higher the PEC. It is due to the fact that here the DER contribution is smaller and the majority of the load is supplied through the conventional generator. It is also observable from Fig. 16 that with the higher penetration level of PV-BS units, the energy produced from renewable sources is higher, which results in the lower PEC cost.

B. Results for Level-2 of a 33-bus test SGDS
Succeeding the optimum sizing of components, the level-2 processes for the optimum placement analysis. As mentioned in section 3, the level-2 optimization is focused on two important SGDS parameters, viz. bus voltage profile and total active power losses. Here, the weak bus (corresponding to minimum bus voltage) is evaluated with the prior assessment through the load flow analysis. In this study, the forwardbackward sweep technique is used for load flow. After determining the weak bus, only these buses are considered as candidate locations for placement in the optimization process. This serves to reduce the computational burden in the optimization. Fig. 17 presents the comprehensive results of level-1 and level-2. It can be observed that optimal bus for placement in all the four case is obtained as bus no. 14.  With reference to placement of DER in SGDS as suggested by optimal placement results, the bus voltage profile for 33bus SGDS is plotted for all four seasons in a year. This has been carried out in order to provide an assessment of seasonal variations on voltage profile. Fig 18, Fig. 19, Fig. 20, and Fig.  21, indicates the voltage profile for seasons Winter, Spring, Summer, and Autumn respectively. The description of Case 1, Case 2, Case 3, and Case 4 has already been indicated in Table  III. The Base case corresponds to the scenario without any DER penetration. It is observable that the bus voltages at each bus are within the permissible range of 1 ± 0.05 . . for all the four cases except for the base case. Also, the bus profile shows remarkable improvement as compared to the base case. The comparative analysis for voltage profile of the base case with other four cases are discussed in Table VI. Hence, this provides ancillary support to the SGDS planners to optimize their output based upon the planning aspect to be considered. All four cases follow the constraint of voltage limits, and this serves as additional assistance in planning PV-BS based DER in SGDS. The fig. 22 shows the total power losses occurred in the SGDS for four different cases. It is evident from the result that the total power losses are near 400 kW for all the cases. Hence the optimization process based upon the four different cases of level-1 is unaltered and has no effect on its operation due to level -2. Table VII shows the improvement of the total power losses for all cases with comparison with base case. It is evident from Table VII that the total losses decrease substantially with the DER integration. The total losses reduced more than 40% for all the four cases.

VI. CONCLUSION
The rapid deployment of RES-based DERs is held world-wide for motivating emission free power generation and accomplishing socio-political goals. Despite of the benefits associated with clean energy there are some concerns which the system planners must examine before integration. The inherent nature of the sources such as Solar PV, and BS calls for detailed analysis for reliable integration of DERs. The main idea behind this work is to achieve optimal planning and coordination of PV-BS based DERs in SGDS. For this, a bi-level multi-objective approach has been deployed. The paper presents the analysis on all the three aspects of planning, assisting the planners to obtained the optimized solution based upon the considered planning aspect. The intermittency of the DERs is duly considered and suitable modeling studies are performed for PV-BS. The level-1 of the planning problem comprises of the multi-objective function and results in obtaining the optimal component sizing and their penetration level. The level-2 of the planning comprises of the multi-objective function considering the system's total power losses and bus voltage profiles ensuing the optimal placement of the DERs.
The case study is carried out by considering four different test cases. The detailed study shows the significance of all four considered test cases from planning perspective. The simulation results obtained for both levels are compared to the base case (without DERs) for validating the effectiveness of the proposed model. This bi-level multi objective framework enhanced the system conditions by showing significant improvement in the bus voltage profiles and total systems power losses. From the bi-level planning model, the following points can be concluded: i. The unserved energy in the system can be very high under the case of high DER penetration, as dependency on RES based DERs may not comply with the reliability standards of the system. ii.
The emissions reduces significantly when the DERs penetration level is very high. The merits of reduced emission compromises with the higher LCC. iii.
The best bus voltage profile in SGDS among all four cases is observed under the case of highest penetration level (Case 2). iv.
The inclusion of the DERs not only improve the bus voltage profiles but also reduce the systems total power losses significantly. This study is focused on the planning of DERs which can be also extended by incorporating the control issues at the point of DERs interconnection. Work can be done on formulating the control strategies for obtaining a reliable system operation.