Comprehensive analysis of distributed energy resource penetration and placement using probabilistic framework

Integration of distributed energy resources (DERs) affect system performance in mul-titude of ways such as reliability, losses and voltage proﬁle. Thus, increasing distributed energy resource penetration necessitates impact assessment particularly when DERs comprise of stochastic RES based distributed generators (DGs) and storage system. This paper presents a formulation for the analysis of DER penetration and placement on system losses and voltage proﬁle in probabilistic framework. Penetration level has been deﬁned, giving due consideration to stochastic behaviour of RES based distributed generators. The work presented incorporates analysis and consideration of two important factors in placement problem, that is, intermittent nature of RES based distributed generators and dual nature of storage units. In order to account for uncertainties inherently present in RES, probabilistic load ﬂow has been used in this work. Placement problem is solved for three different penetration levels, that is, 20%, 40% and 60% using utterﬂy particle swarm optimisation. The impact of seasonal effect on system losses and voltage proﬁle in correlation with penetration levels has also been investigated. Results provide useful insights for identiﬁcation of optimum penetration level.


INTRODUCTION
Distributed energy resources (DER) are defined as small-scale generation units (DGs) and energy storage technologies connected at distribution network [1,2]. Integration of DERs offer an array of benefits and provide a promising alternative to centralised generation [3]. One of the major benefits offered by DER integration is the reduction in line losses and improvement in voltage profile. Due to their proximity to load centres, DERs can positively contribute towards reduction in line losses; particularly if the feeder is heavily loaded. Integration of DERs can have significant impact on voltage profile of the distribution grid. The presence of DERs may raise system voltage slightly [4]. This will not create any problem, if the consumers connected to network had been experiencing low voltages wherein the DER integration will provide required voltage support and will contribute towards a flat voltage profile. However, if consumers had a normal voltage profile earlier, the DER integration may cause voltage to even cross-defined upper limit. Thus This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2021 The Authors. IET Renewable Power Generation published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology based on existing network and loading conditions, voltage profile has been used as an objective or a constraint in distributed generator (DG) planning problem. Liu et al. [5] have formulated a multi-objective problem considering different cost functions and voltage profile. Masaoud et al. [6] and Yarahmadi et al. [7] have solved sizing and siting problem of wind generators considering voltage stability as the objective. A bi-level optimisation for PV and storage allocation has been framed by Sharma et al. [8]. Singh et al. [9] have used sensitivity for improvement in losses and voltage. Elnashar et al. [10] have used losses, voltage profile and short circuit level as objectives for DG sizing and siting problem. Danilo et al. [11] have proposed a mixed integer linear programming based approach for improving voltage and energy efficiency. Voltage has also been used as a constraint in various planning studies. Ugranlı and Karatepe [12] have reported placement of multiple-DG unit for power loss reduction constrained by voltage limits. Voltage profile has also been used as a constraint in placement problem by Kryonidis et al. [13] and Liu et al. [14]. However inappropriate size and location can lead to increase in losses and deterioration of voltage profile [12]. Thus planning from the perspective of line loss reduction is a sizing, as well as, locational issue.

Literature survey
There has been significant contribution by researchers in determining optimum size and location of DERs for line loss reduction. The literature survey conducted on DER sizing and placement can be broadly classified under following groups: (i) Studies involving only dispatchable DERs (such as, diesel generators, biomass): Amongst the literature involving dispatchable DERs, Ugranlı et al. [12] have investigated behaviour of multiple-DGs in terms of capacity and load uncertainty using ANN. Andrés et al. [15] have determined the optimal size and location using a modified teaching-learning based algorithm. Esmaili [16] have used fuzzification to address multi-objective problem of losses and voltage stability margin. Impact of reverse power flow in context of increasing DG penetration has been studied by Sgouras et al. [17]. An effective methodology for determining optimum DG location has been proposed by Singh and Parida [18] based on system planner's decision and analytical hierarchy. Multi criteria decision model [19] has also been used for determining the allocation of high impedance fault detectors on distribution feeder. Reddy et al. [20] have considered critical load pick up as the objective for solving optimal DG placement problem using fuzzy multi-criteria decision-making (MCDM). Voltage has been used as a constraint in this study. However, loss analysis has not been considered.
(ii) Studies involving RES based DERs which have stochastic behaviour (such as, solar and wind): With renewable energy penetration on increasing trend, it is essential to analyse the impact of integration of RES based DERs on losses. Amongst the literature involving RES based DERs, Caampued et al. [21] have presented evaluation of wind power penetration on system losses. However, penetration level as defined in ref. [21] does not address the stochastic behaviour of wind energy. Garzon et al. [22] have studied voltage variation in presence of PV systems without storage. Ali et al. [23] have investigated the impact of penetration of wind and solar penetration on voltage profile. Impact on system losses has not been considered. Solar photovoltaic, biomass and wind system have been considered for integration in ref. [24] but effect of DG penetration has not been studied. Naghdi et al. [25] and Saric et al. [26] have used probabilistic models of renewable DGs for loss minimisation. A static voltage stability optimisation formulation has been developed by Liu et al. [27] with solar and wind based DERs. Analysis considering time series data of RES based sources has been carried out in ref. [5]. Optimal allocation of wind based DERs using probabilistic model has been done considering various types of time and voltage dependent-load models [7]. The influence of stochastic uncertainties has been handled by using affine arithmetic model by Zhao et al. [28]. Zio et al. [29] have used probability density functions to model load uncertainty but variability of DGs has not been considered. An effective analysis has been put forward by Quezada et al. [30] wherein effect of different DG technologies, penetration levels, DG dispersion and location on system losses has been examined. However, the penetration level as defined in the work does not ensure that for every considered time interval, penetration of DG units will be equal to the defined one. This is significant in context with RES based DGs due to their stochastic nature. Atwa et al. [31] proposed a methodology for optimally allocating different types of RES based DGs for loss reduction. The methodology is based on generating a probabilistic generation model that combines all possible operating conditions of RES based DGs along with their probabilities of occurrence. A multi-objective formulation using game theory has been proposed by Soleymani et al. [32] considering solar and wind based DERs. The impact of intermittency on penetration level has not been examined. Multi-criteria assessment of RES has been carried out by Janjic et al. [33] and Tanwar and Khatod [34] using analytical hierarchy process. An integrated decision making planning approach has been proposed by Kazmi et al. [35] which embeds MCDM with unanimous decision making for sizing and siting of PV and D-STATCOM.
(iii) Studies involving stochastic DERs and storage: Amongst the literature involving stochastic DERs and storage, Qiu et al. [36], have addressed optimal allocation of energy storage to help integration of wind energy. El-Zonkoly [37] discussed optimal scheduling and placement of PV and storage based system. A bi-level optimisation framework has been developed considering RES based DGs and battery storage [8]. However, loss minimisation and voltage profile improvement has not been targeted in these papers. In ref. [38] a bi-level optimisation model has been proposed to determine the optimal location and sizing of battery energy storage system. However, the analysis is focused only on battery storage and does not consider the sizing/placement of RES based sources. Seyed et al. [39] have determined the optimal allocation of PV/wind/storage/fuel cell based micro-grid. Kalkhambkar et al. [40] and Chedid et al. [41] have determined allocation of solar/wind based DGs and storage. However, impact of penetration level has not been analysed. In order to have a swift perception of research gaps, a summary of literature survey is presented in Table 1.

Research gaps
Based on literature survey following conclusions can be drawn: (i) Though impact of integration of conventional DG units on line losses and voltage profile has been widely studied, majority of studies fail to acknowledge the impact of tion of storage has been found essential in order to provide firm support to renewables. With the increasing inclination towards RES, storage integration is expected to gain increasing importance in near future. However, none of the analyses consider the impact of adding storage units along with RES based DERs on system losses and voltage profile. (iii) With regards to studies analysing the impact of variation of penetration level on system losses and voltage profile, it has been observed that penetration level as defined in literature does not take into account the stochastic nature of RES.
Optimal placement becomes more challenging when DERs comprise of solar/wind based DERs and storage due to following reasons: • The solar energy is not available for nearly half of the time.
The wind energy has a highly intermittent nature. Thus correlation between intermittency and placement has to be adequately analysed. • The storage is an energy limited source. The availability of energy in storage is dependent on excess energy available from RES based DERs. The major problem encountered in placement of storage is due to the fact that storage behaves as a source when it is in discharging mode and behaves as a load when in charging mode exhibiting dual nature. This can become particularly significant in systems with high DER penetration wherein power drawn and supplied by storage is quite high.

Contributions and organisation
In order to address research gaps discussed in Section 1.2, this paper proposes a generalised formulation embedded in probabilistic framework for impact assessment of DER penetration and placement on system losses and voltage profile. Though RES based DERs comprise of a variety of generating sources, wind and solar have been considered in this paper as they are emerging as most preferred technologies. In order to adequately address the stochastic behaviour of RES based DERs, the penetration level corresponding to a time segment is defined as a function of meteorological conditions of that particular time segment. The assessment of repercussion of penetration level on system losses and voltage profile has been investigated on hour by hour basis. The optimum placement problem is formulated with the objective of loss minimisation. In order to incorporate the uncertainties associated with RES, load flow has been carried out using backward-forward sweep algorithm embedded in probabilistic framework. The proposed methodology has been applied to a 33-bus radial distribution feeder. Remainder of the paper is organised as follows: Section 2 explains mathematical formulation used in the paper. A brief discussion on mathematical models of DERs has been provided. Formulation of dispatch strategy and active/reactive power injection matrix has also been discussed. Section 3 explains problem formulation. In Section 4 solution methodology in probabilistic framework has been presented. Section 5 presents a case study wherein the proposed formulation is implemented. A detailed discussion on analysis of result has been carried out. Section 6 presents the relevant conclusions and future scope of work.

MATHEMATICAL FORMULATION
In order to address intermittent behaviour of RES based DERs and their corresponding correlation with storage units; a probabilistic model has been developed by author in previous work [42][43][44]. The detailed description of mathematical model can be obtained from [42]. The probabilistic model comprises of renewable energy source model (RESM) and battery storage model (BSM). RESM includes all possible combinations of solar irradiance and wind speed along with their associated probabilities. Solar irradiance is modelled using standard beta probability density function and wind speed using Weibull probability density functions. BSM comprises of multiple states of battery SOC and associated probabilities. The probabilistic BSM is integrated with RESM in order to correlate effect intermittency of RES with battery SOC. Thus, in accordance with above models, the system state corresponding to b th state of BSM t and k th state of RESM t for t th time segment is represented as S t k,b .

Distributed energy resource penetration
With RES based DERs, penetration level is a function of meteorological parameters. Thus, it becomes essential to investigate penetration level on hour by hour basis. In this paper, penetration of DERs is meant to ensure a firm capacity addition which means that at all points of time and for all system states, DERs should be able to fetch a percentage of load defined by minimum penetration level [44]. In order to in order to ascertain high standards of planning, analysis is carried out for minimum penetration level and maximum allowable penetration level which are explained as follows: A. Minimum penetration level: This refers to minimum percentage of load that must be supplied by DERs for each time segment irrespective of system states. Thus, for any time segment 't' in study period, The power purchased from grid is bounded by def min irrespective of states of RESM, and BSM. Hence maximum power which can be drawn from grid for t th time segment can be expressed as: where, P t G max = maximum permissible power from grid for t th time segment, kW. A. Maximum allowable penetration level def min : This refers to maximum percentage of load which DERs are allowed to supply for each time segment. Thus, for any time segment t in study period, Due to highly stochastic nature of RES, a system designed to ensure def min has to take into account worst periods of wind and sun. However, system can definitely deliver much higher amount of generation during favourable meteorological conditions. Thus economically it makes all sense to allow higher amount of penetration from DERs than def min whenever it is feasible to do so. However, allowing higher amount of power from DERs can adversely affect system losses and voltage profile. The def max puts an upper limit to amount of power which DERs are allowed to supply so that system losses and voltage profile are constrained within specified limits. A thorough analysis of impact of def min and def max is essential in order to come up with a well-planned system.

Dispatch strategy
For t th time segment load which must be supplied by DERs is constrained by minimum penetration level and is expressed as: For t th time segment, maximum load which DERs are allowed to supply is constrained by maximum allowable penetration level (explained in Section 2, Part B) and is expressed as: The assumptions made in this study are as follows: (i) PV arrays are assumed to supply only active power.
(ii) WTGs are synchronous machines and are assumed to be operating at a lagging power factor of 0.8 or above [30]. (iii) The storage units are discharged at a lagging power factor of 0.8 or above and are charged at unity power factor. (iv) All storage capacity is considered as a single unit and is not distributed along the feeder.
The DERs are dispatched in following order: • PV arrays are first to be dispatched since they have lowest operating costs. • WTG units come in next to PV arrays.
• Storage units are given least priority in dispatch order. The primary objective of storage integration in this work is to counteract intermittent nature of RES by providing a firm backup. Hence, they are dispatched only when power from RES is not available either due to unfavourable meteorological condition or a unit outage.
The dispatch strategy proposed in this work is enumerated as follows:

Active power injection matrix
The active power injected by PV arrays and WTG units is calculated based on dispatch strategy discussed in Section 2.2. For each system state S t k,b , the PV arrays are dispatched first. The active power injected by m th PV array is P m . If the output power from PV arrays is more than that required by load, the excess power is used to charge battery. The active power injection from PV arrays can be expressed as [P 1 ]. Once, the output power from PV arrays is exhausted, WTG units are dispatched. The active power injected by n th WTG unit is P n WTG t,k,b . If the output power from WTG units is more than that required by load, the excess power is used to charge battery. The active power injection from WTG units can be expressed as [P 1 ]. The battery can inject or draw active power based on power flows. If output power available from generators is more than L t DER min , storage goes into charging mode. In case of power deficit, storage bank exhibit discharging mode and injects active power. The formulation of active power injection matrix based on proposed strategy is depicted in Figure 1. The active power injection matrix can be expressed as:

Reactive power injection matrix
The PV arrays are assumed to be operating at unity power factor. Hence reactive power supplied by them is zero. The WTGs and storage units are assumed to supply reactive power at a power factor between 0.8 lag to unity based on reactive power requirement of load. Thus, Thus reactive power injection matrix can be expressed as:

PROBLEM FORMULATION
The system losses and voltage profile respond differently to different DER penetration levels. One of the major contributions of this work is analysis and consideration of two important factors in placement problem which have not been accounted in previous studies. The factors which drive placement problem in this work are as follows: (i) Intermittent nature of RES based DGs: The generation from RES based DGs is highly unpredictable, thus, location which might be appropriate for injection of low power levels might be turned down at other instants when power availability increase during high periods of wind and sun. (ii) Dual nature of storage units: The storage exhibits dual nature; behaving as load or source based on availability of power from RES and system loading conditions. Thus location which might be appropriate with storage as source might not be appropriate with storage as load.
Due to above factors, it is possible that DER penetration reduces losses at one instant of time and at some other instant losses may even rise above the losses without DER penetration. Similar perception holds true regarding voltage profile as well. Hence, an in depth analysis considering above factors FIGURE 1 Evaluation of active power injection based on proposed dispatch strategy is required in order to achieve maximum benefits from DER penetration.

Objective function
The objective function for DER placement can be stated as: where, P loss = Annual expected energy loss, kWh.

Constraints
The problem of finding optimal placement of DERs is subjected to following constraints: A. Constraint on load supplied by DERs: The load which is to be supplied by DERs for any time segment is constrained by defined minimum penetration level and maximum allowable penetration level.
B. Constraint on voltage limits on each bus: The magnitude of voltage at all buses in network must comply with defined voltage limit. Thus, voltage magnitude at i th bus V i is subjected to strict voltage constraints.
C. Constraint on battery parameters: In order to ensure optimum life, battery is subjected to constraints on battery state of charge as follows: Figure 2 presents the block diagram of proposed methodology in probabilistic framework. A brief discussion of butterfly particle swarm optimisation (BFPSO), probabilistic load flow (PLF) and evaluation of objective function in probabilistic framework is presented in following subsections.

Optimisation technique
The problem of finding optimal placement of DERs is a constrained non-linear, discrete combinatorial optimisation problem. The optimal placement problem for each penetration level is solved by using BFPSO. BFPSO is a modified version of PSO [45,46]. The BF-PSO mimics the natural intelligence and information sharing mecha- Step 1 Step 2

Evaluation of Fitness Function
Load Modelling Determination of optimal placement using BFPSO (Bus no. 2-33)

FIGURE 2
Proposed methodology in probabilistic framework nism which the butterflies exhibit during nectar search process. The butterflies use sense of smell to determine possible direction of food, communicate with each other and accordingly move in a cooperative manner towards food position. In addition to parameters of standard PSO (inertia weight and acceleration coefficients), BF-PSO incorporates following parameters: (i) Sensitivity of butterfly towards flower(S) (ii) Probability of food (nectar) (P) (iii) Time varying probability coefficient (α) These parameters considerably improve the ability of algorithm to find better quality solutions in minimum possible time. The ranges of sensitivity and probability are considered varying between 0.0 and 1.0 and are expressed as a function of iteration as follows: where, ITER max = maximum number of iterations and ITER k = k th iteration count.
where, FIT pbest i ,k = fitness of personal best solution of i th particle in k th iteration, FIT gbest,k = fitness of global best solutions in k th iteration, P k is the probability of k th iteration. The velocity and position of the particles for k th iteration is continuously updated based on personal best (pbest) and global best (gbest) as follows [45]: . (17) x id (k + 1) = x id (k) + k v id (k + 1). (18) where, v id , x id , Pbest id and gbest d represent velocity, position, personal best and global best respectively of d th dimension of i th particle, w k is inertia weight for k th iteration, C 1 and C 2 are acceleration coefficients and r 1 and r 2 are random number in the interval [0, 1], P kg is the probability of global best (generally assume P kg = 1 for global solution) and k is time varying probability coefficient. k is calculated as follows: where, rand is the random number [0, 1].

Probabilistic load flow using backward-forward sweep
The deterministic load flow (DLF) has been traditionally used by system planners for determination of losses. DLF calculates power flows in network for specified generation. This is acceptable in system incorporating conventional generating units. However, for systems with RES based DGs, DLF fails to incorporate uncertainties associated with these sources.
In order to overcome difficulties associated with DLF, PLF has been used in this paper [47,48]. In contrast with DLF which uses deterministic values, the input to PLF is specified by pdfs so that system uncertainties are given due consideration. In this work PLF is solved using backward/forward sweep algorithm [49].

Objective function evaluation in probabilistic framework
In order to incorporate uncertainties associated with DERs, calculation of objective function has been carried out in a probabilistic framework. The PLF employing backward-forward sweep algorithm estimates power flows and losses in network. The power flow and loss for system state corresponding to S t k,b is a function of active power injection matrix P t k,b and reactive power injection matrix Q t k,b . The probability of system state corresponding to S t k,b can be expressed as: where, operator 'P ' represent the probability. The expected value of power loss for k th state of RESM t and b th state of BSM t can be expressed as: where, P_Loss t k,b = variable representing expected power loss for S t k,b , kW, f = function of P t k,b ,Q t k,b and L t to compute power losses in the system. For t th time segment, the amount of active and reactive power injections, given by Equations (6) and (10) respectively, are dependent on RESM RESM t , BSM BSM t and load L t . Hence, f has been considered as function of RESM t , BSM t and L t . Since RESM t , BSM t and L t are variable during t th time segment, their function f is also a variable during same time segment kW.
The expected value of power loss for t th time segment can thus be calculated as: The expected value of energy loss over entire study period can thus be calculated as: where, l (t ) = length of t th time segment, hours.

CASE STUDY: RESULTS AND DISCUSSIONS
The proposed formulation has been applied to a 12.66 kV, 33bus distribution system derived from [50]. The schematic diagram of radial distribution feeder is shown in Figure 3. The distribution feeder is connected to grid at bus number 1 through substation and has a peak load of 3.755 MW. The distribution system has been assumed to be located at Jaisalmer, Rajasthan,   14 14 India. The data for solar irradiance and ambient temperature for the site has been taken from ref. [51] and wind speed data has been obtained from ref. [52]. As explained in Section 2, for probabilistic RESM and BSM, 15 states of solar irradiance, 15 states of wind speed and 20 states of battery SOC have been considered [42]. SOC min and SOC max have been assumed as 30% and 100%, respectively [42]. The chronological load shape has been obtained from ref. [53]. The load is assumed to be constant for a particular time segment. In order to analyse impact of penetration level of DERs, three different minimum penetration levels, for example, 20%, 40% and 60% have been considered in this study. The optimal sizing for different DER penetration levels has been carried out using the formulation presented by authors in refs. [43,44]. The optimal placement problem has been solved using methodology explained in Section 4. The placement problem is solved for each minimum penetration level using BFPSO. Maximum voltage limit on each bus is taken as 1.05 p.u. Minimum voltage limit on each bus is constrained by base case minimum voltage on each bus. Table 2 presents losses and real and reactive power drawn from grid without DER penetration The optimal sizing and placement results for different penetration levels are presented in Table 3.
As is evident from Table 3, for 20% minimum penetration configuration, though storage is integrated, its capacity is not substantial. Thus, placement of PV arrays and WTG units is not affected by dual nature of storage units for 20% minimum penetration configuration. However, for 40% and 60% minimum penetration configurations, the capacity of storage integrated into system is substantial. It is evident from optimal placement results for 40% and 60% minimum penetration configurations presented in Table 3, that half of the WTG capacity is placed along with storage units. The placement of WTG and storage units on the same bus for 40% and 60% minimum penetration configurations as suggested by optimal placement results are analysed as follows: Since order of dispatching units is solar, wind and then storage, the availability of spare solar power after supplying load is quite low. Thus charging power to storage units is not usually supplied by PV arrays. However, WTG units have surplus availability during good periods of wind and also during sunshine hours. Thus WTG units are mostly responsible for charging storage units. During charging period, storage units pose as a load which is significant enough to cause an increase in power loss. This also results in voltage drop on the line thereby raising voltage issues. However, placement of storage unit on same bus as WTG unit solves this problem. Thus WTG units and storage are located on the same bus.
Hence, although optimal placement of storage with storage acting as source might have been different, considering it as a load requires placement of WTG unit on the same bus. Therefore, placement of DERs comprising of storage units is a challenging issue and requires detailed analysis in order to come up with an optimal solution.
Having determined optimal placement of DERs corresponding to each minimum penetration configuration, impact of varying maximum allowable penetration level is investigated. As discussed in Section 2.2, the system designed for a defined minimum penetration level is capable of delivering higher amounts of power during favourable meteorological conditions. Allowing higher def max amplifies economic viability of DER integration. In this section impact of allowing higher values of def max is studied on system losses and voltage profile with respect to all three minimum penetration configurations. The analysis is focused on determining following information: (i) The effect of varying def max on annual active and reactive energy losses. (ii) Analysis of losses and voltage profile on hour by hour basis. This is essential in order to understand effect of intermittency. It can be observed from Figure 4 that for def min = 20%, after an initial decline in losses, an increasing trend is observed beyond def max = 40%. However, as shown in Figures 5 and 6, for def min = 40% and 60%, losses increase steadily.  Table 4 presents the optimum value of def max following objectives:

Effect of variation of maximum allowable penetration level on active and reactive energy losses
(i) Determination of def max which fetches minimum system losses. (ii) Determination of def max which fetches maximum DER penetration constrained by base case losses.
It can be observed from Table 4, that increasing def min beyond 20% does not render any benefit from the perspective of loss minimisation. However, from the perspective of maximising DER penetration, def min = 20% is the most suitable penetration level. The utilisation of resources is maximum in this case. At higher penetration levels, the system has enough redundancy in order to maintain reliability standards during worst periods of wind and sun. Hence, power which system can supply also increases. It is apparent from Table 4, that def max is minimum with def min = 60%.

FIGURE 6
Variation of active and reactive energy losses with def max for def min = 60%

FIGURE 7
Hourly variation of active energy losses for def min = 20%

FIGURE 8
Hourly variation of active energy losses for def min = 40%  show the hourly variation of active energy losses for def min = 20%, 40% and 60%, respectively, w.r.t. def max presented in Table 4. From Figures 7-9, following important observations can be made:

Analysis of hourly variation of active energy losses
(i) In comparison with losses without DER penetration, losses with DER penetration are lower all year around for all the three considered def min when def max = def min . (ii) When the value of def max is increased and chosen from perspective of maximising DER penetration, losses do not stay below the base level throughout the year. The losses are higher during summer and monsoon months as compared to base case losses. This is due to increase in availability of sunshine hours during summer months and better wind speed during monsoon months. Nevertheless, increase in losses beyond base case during summer and monsoon months is compensated by decrease in losses for rest of the time segments. Thus, total losses still stay below the base case level.  show the shows voltage profile on each bus for def min = 20%, 40% and 60% respectively w.r.t. def max presented in Table 4.

Analysis of voltage profile
From Figures 10-12, following important observations can be made: (i) With DER penetration voltage profile shows improvement on all buses compared with when no DERs are placed. (ii) On comparing voltage profile for def min = 40% and def min = 60% with voltage profile for def min = 20%, it can be observed that minimum voltage achieved with def min = 40% and 60% is higher in comparison with that achieved through def min = 20%. This is attributed to increase in availability of power from DERs for higher def min .
This can further be explained with reference to optimal placement results presented in Table 3. It can be seen that now storage and half of the WTG capacity are placed on the same bus. As discussed earlier, the charging power to storage units is mostly supplied by WTGs. Now, even when battery is in charging mode and storage is acting as a load, there is no drop in the line since storage and WTG units are placed on the same bus.
Thus, it can be concluded that placement of storage units in conjunction with RES based DGs require special considerations and has to be dealt carefully.

CONCLUSION AND FUTURE SCOPE
In view of increasing DER penetration, it is imperative to analyse the effect of different penetration levels on various system parameters. This paper presents a formulation for impact assessment of DER penetration level and placement on system losses and voltage profile. The main contributions of this paper can be summarised as follows: (i) A generalised formulation embedded in probabilistic framework has been developed for impact assessment of DER penetration and placement on system losses and voltage profile. (ii) The planning formulation presented in this paper is bestowed with following specific features: a. Acknowledgement of intermittent nature of RES based DGs in placement problem. b. Analysis of effect of dual nature of storage units in placement problem. (iii) Penetration level has been defined and analysed so as to adequately address the stochastic behaviour of RES based DERs. (iv) Assessment of effect of penetration level on system losses and voltage profile on hour by hour basis. A thorough analysis of def max for a particular def min has been carried out.
In order to establish the importance of investigating DER penetration, three different minimum penetration levels have been studied. Impact of variation of maximum allowable penetration level has been studied for each of the minimum penetration configurations. Following inferences have been drawn based on study carried out in this work: • The generation from RES is highly unpredictable, thus location which might be appropriate for injection of low power levels might be turned down at other instants when power availability increases during high periods of wind and sun.
• The storage exhibits dual nature; behaving as load or as a source based on availability of power from RES and system loading conditions. Thus location which might be appropriate with storage as source might not be appropriate with storage as load. • Due to intermittent nature of RES based DGs it is possible that DER penetration reduces losses at one instant of time and at some other instant losses may even rise above losses without DER penetration. • Increasing DER penetration beyond a certain level can result in degradation of line losses and voltage profile.
The analyses presented in this work will assist system planners to choose optimum DER penetration level. Nevertheless, grid integration of DERs calls for increased analysis. Thus, present study can be further extended in following research areas: • This paper deals with the planning issues concerning DER penetration. However, the work can be further extended to incorporate operational issues as well. • Formulation of control strategies considering the effect of DER penetration level can be done. • The formulation presented in this paper is a generalised one and can be applied for analysis of large power systems. The analysis can be further extended to meshed distribution network as well. Feeder reconfiguration in conjunction with different DER penetration levels can also be studied for loss minimisation.

Parameters
PV Photovoltaic RES Renewable energy sources SOC min , SOC max Lower and upper limit respectively for battery SOC t Index representing t th time segment Variables V min , V max Minimum and maximum permissible voltage magnitude respectively, p.u. WTG Wind turbine generator