Combined Firm and Renewable Distributed Generation and Reactive Power Planning

The benefits of integrating Distributed Generation (DG) into the distribution networks depend on the characteristics of different types of DG units, loads and Reactive Power Sources (RPS). These benefits can be optimized if the firm DG units such as biomass energy and renewable DG units such as photovoltaic (PV) and wind system are optimally sized, located and coordinated with reactive power sources. In this paper, by assuming that the Distribution System Operator (DSO) has got the ownership and operation of DG units and RPS, a new planning strategy is proposed for determining the optimal placement and rating of DG units and RPS. This strategy overcomes the challenge of intermittency of renewable production in order that this planning will assist the system operators in defining the better integration strategies of firm and intermittent energy systems and reactive power sources in distribution networks. The proposed planning is based on single objective optimization so that it optimizes one of the following objective functions every time: the system energy losses, voltage stability margin, self-adequacy of microgrids defined on the distribution system and exchange of active and reactive powers between the distribution system and upstream network. The proposed technique accounts for the uncertainties associated with solar irradiance, wind speed and demand through a probabilistic optimization. The formulation of each planning problem is presented and applied to the 69-bus distribution system. The results of different planning strategies are compared and analyzed. Furthermore, the impact of the planning with each objective function on other indices is evaluated.

With increasing the penetration of distributed generation, especially renewable resources as one of the main requirements of smart grid development, the planning of the renewable resources along with the firm ones has been getting great importance. The aim of DG planning is to determine the location and capacity of the dispersed resources on a distribution system. DG planning is based on defining an optimization problem taking into account different techno-economic objectives and constraints. Utilizing the benefits of DGs in distribution networks and minimizing their adverse effects depends on the proper planning of these resources in the network. Since the consumption and production patterns at an active distribution system, including non-dispatchable generation, do not commonly match, attaining the planning goals while maintaining network constraints is more difficult. In addition to DG planning, the concept of integration of DG planning with the planning of reactive power sources has been presented to determine the optimal location and capacity of both resources simultaneously. The joint planning of DGs and RPSs can considerably enhance their benefits for distribution networks, especially when there are variable DGs. Each distribution network operator emphasizes one or some of the objective functions for planning the active or/and reactive resources according to their network problems and priorities. Multi-objective optimization for considering conflicting objectives is a difficult task in view of selecting a suitable solution algorithm and decision for selecting the final solution among Pareto solutions, especially when there are many objective functions. In addition, some objectives are not conflicting, and optimizing one of them improves other objectives. Therefore, considering only an objective function and using a single objective optimization formulation is an advantage and a more practical method so that many researchers have been focused on only an objective function [1], [2]. This paper intends to emphasize the importance and practicality of single objective DG and reactive power planning, especially when the problem is a probabilistic one with many states of load and generation through investigating different selected objective functions on results of defined probabilistic planning for simultaneous renewable and firm DG and reactive power.
Probabilistic load-generation model [5], [6] and Monte-Carlo simulation (MCS) [17] have been used for considering the stochastic nature of renewable energy resources and other uncertainties such as load growth, fuel price and output power of a Plug-in Electric Vehicle (PEV) in DG planning. Chance Constrained Programming (CCP) is one of the stochastic programming methods for dealing with uncertainties [17], [19].
Reactive power planning is an important economic and technical issue in the distribution system. Optimal reactive power planning in distribution systems has been done by researchers with several objective functions varying from energy losses and costs reduction to enhancing the reliability of distribution systems. Since simultaneous DG and reactive power planning/operation leads to many benefits, some studies such as [11]- [13], [15], [20], [22] consider DG and reactive power sources at the same time.

C. CONTRIBUTION AND ORGANIZATION OF THE PAPER
Two important challenges of renewable DG planning are: 1) The production pattern of the renewable generation is usually different from the load pattern depending on weather conditions and economic and social conditions of consumers of distribution system and type of the connected loads. In addition, the difference between generation and consumption patterns varies with the variation of seasons and years. Therefore, renewable DG planning may give no feasible solution or nonacceptable solutions. Using the firm DG units along with the renewable ones and simultaneous planning of these units is a basic way to encounter this challenge. Another technique to get the maximum benefits from renewable DG planning is simultaneous planning of DG and distributed reactive power sources. The proposed planning formulation in this paper considers simultaneous planning of firm and variable DG and reactive power sources to reach the planning objectives.
2) Each distribution network operator emphasizes one or some of the objective functions for planning the active or/and reactive power sources according to their network problems and priorities. Multi-objective optimization for considering conflicting objectives is a difficult task in view of selecting a suitable solution algorithm and decision for selecting the final solution among Pareto solutions. In addition, some objectives do not conflict, and optimizing one of them improves other objectives. Therefore, considering only an objective function and using a single objective optimization formulation for DG and reactive power planning is an advantage for the distribution network operator. For this purpose, the paper proposes a DG and reactive power planning with only an objective function. In addition, the proposed planning problem is solved for four individual objective functions defined from different perspectives by Distribution Network Operators (DNOs), and the impact of optimization of each objective function on indices associated with other objectives is investigated.
The main contributions in this paper are: • Investigating importance and practicality of single objective DG and reactive power planning, especially when the problem is a probabilistic one with many states of load and generation by defining a joint planning problem for renewable distributed generation (firm and variable) and reactive power sources on the multi-year planning horizon • Investigating two important and known objective functions, system energy losses and voltage stability margin, along with two new objective functions defined in this paper based on the new paradigm of constructing microgrid in the distribution system, self-adequacy of microgrids, and the active and reactive power exchanged between the distribution network and the upstream network VOLUME 9, 2021 • Introducing a methodology for reduction of concerned objective functions by each distribution utility to convert the complex planning problem to a single objective problem or a multi-objective problem with minimum objective functions through solving the optimization problem with only one objective function and investigating the optimal solution for each objective function on other objective functions to specify correlated or conflicting objective functions The rest of the paper is organized as follows. The problem formulation is explained in Section II. The test system and case studies are introduced in Section III. Section IV presents the results and discussion. Finally, section V concludes the paper.

II. PROBLEM FORMULATION
This section presents the probabilistic formulation for the objective functions and constraints of the proposed DG and reactive power planning. The used methodology is based on generating a probabilistic generation-load model [6] to solve the planning problem, including firm and volatile distributed generation resources and reactive power sources. The model is obtained by listing all possible combinations of renewable DG output power with their probabilities and the load for the whole year. In this method, Beta and Weibull probability density functions (pdf) are respectively generated for solar irradiance and wind speed of each hour of a typical day for each season of one year (four seasons) in order to represent the random behavior of the different renewable resources during each period.
The mathematical model described in the paper, including considered objective functions and constraints, has been formulated as non-linear programming (NLP) on a GAMS environment and solved by solvers KNITRO and CONOPT.

A. OBJECTIVE FUNCTIONS 1) MINIMIZING ENERGY LOSSES
The network energy losses changes with the introduction of DG to the distribution network through variation of active and reactive power flows. One of the common objectives in the DG planning is to maximize the utility profit by reducing the system energy losses during the planning period. Reducing energy losses can have such positive environmental and economic impacts as relieving the feeders and transformers as well as improving the voltage profile. On the other hand, an improperly allocated DG can give rise to excessive losses. Therefore, the objective function of the planning problem can be defined as minimizing the energy losses in the distribution system on the planning horizon considering load and renewable generation scenarios and annual load growth.
where h, s and y are hour, scenario and year indices, respectively. The network energy loss, energy losses associated with each scenario s, hour h and year y and probability of scenario s at hour h are indicated by P l , P loss s.h.y and pr s,h respectively. According to the load and generation modeling, there are 90 similar hours per season. The network losses for each s, h and y is calculated by where N bus and G ij denote the number of network buses and real component of admittance of line ij respectively. The magnitude and angle phase of voltage of bus i at scenario s, hour h and year y are denoted by V i,s,h,y and δ i,s,h,y respectively.

2) MAXIMIZING VOLTAGE STABILITY MARGIN
The long feeders with heavy loading in the distribution network suffer small voltage stability margins. Thus, DG and reactive power sources planning can be defined to enhance the voltage stability margin of the distribution network. Maximizing the objective function V index defined in (3) where And If the value of V index is more than unity, using DG units and reactive power sources has a positive impact on the voltage index. Thus, maximizing V index leads to the best location for installing the DG units and reactive power sources to improve voltage stability.

3) MAXIMIZING SUPPLY ADEQUACY OF MICROGRIDS
One of the new paradigms in smart distribution networks is to take advantage of integrating the DG units and reactive power sources to form microgrids in the distribution network. Hence, it can continue to supply important loads autonomously and separately from the network in the case of an emergency. A microgrid is a small electrical distribution network including loads, distributed energy sources and some control systems to control loads and energy sources. Microgrid must have active and reactive supply adequacy to continue its service in the islanding mode with the least load interruption when it disconnects from the upstream system. In other words, a more self-sufficient and more self-healing microgrid is a result of the less generation-load imbalance within it. In addition, active and reactive supply adequacy help make appropriate infrastructure for fast and efficient restoration of the smart electrical grid after a blackout in the power system. Thus, DG and reactive power sources planning can be performed in a way to attain the best condition in view of the active and reactive supply adequacy of constructed microgrids in the distribution system.
A probabilistic index for both active and reactive supply adequacy is defined based on the load-generation scenarios by (6) to evaluate the supply adequacy of the constructed microgrids within the distribution system. The index is calculated by summation of the weighted square of the mismatch between generation and consumption plus losses for both active and reactive powers and all load-generation scenarios and all microgrids during the planning horizon. Supply adequacy of microgrids, active power adequacy of microgrids and reactive power adequacy of microgrids are denoted by SA, F P and F Q respectively.

4) MINIMIZING EXCHANGED POWER WITH THE UPSTREAM NETWORK
When the distribution network includes one microgrid only, the well-matched distribution system and self-sufficiency of the microgrid can be attained by minimizing the exchange of active and reactive powers between the distribution network and the upstream network. Thus, dependency of the distribution system to the main system and the adverse effects of the distribution network on the upstream network and vice versa are reduced. Consequently, when the distribution system is disconnected from the upstream system due to some problems in the power system or distribution system, the load supply can be continued with minimum difficulty by providing some control facility and disconnecting some non-sensitive or insignificant loads. In addition, reducing the exchanges of active and reactive powers between the distribution network and the upstream network can lead to a reduction of energy losses and occupied capacity of the feeder connecting the distribution system to the main power system.
A probabilistic index based on the load-generation scenarios is defined as (9) to attain this objective. The index calculates the summation of the weighted square of the exchanged active and reactive powers between the distribution and upstream systems for all load-generation scenarios during the planning horizon.
where EP, SL, P SL,s,h,y and Q SL,s,h,y denote exchanged power index, slack bus (the connection point of distribution system to the main system), and the exchanged active and reactive powers between the distribution and upstream system in scenario s, hour h and year y respectively.

1) POWER FLOW EQUATIONS
Constraints presented in (10) and (11) satisfy the active and reactive power balance at each bus of the network, respectively. The annual load growth (g) in the planning problem is taken into account by (12).

PS
where PS W s.h , PS S s.h , PS B s.h are the ratios of generation of wind, solar and biomass DGs at scenario s and hour h to their installed capacities, respectively, and LS h,y is the load level at hour h and year y. The capacity of wind, solar and biomass DGs and reactive power sources installed at bus i are denoted by P W DGi , P S DGi , P B DGi and Q DERi respectively. P Di and Q Di are peak active and reactive load at bus i. Y ij and θ ij show the magnitude and phase angle of element ij of the nodal admittance matrix.

2) VOLTAGE LIMITS
The slack bus voltage and the allowable range of magnitude and phase of the bus voltage are as follows.

3) MAXIMUM PENETRATION OF DG UNITS
Constraints of the maximum installable capacity of DG (P DGmaxi ) at each bus and allowable penetration of DG in the system (x P Di ) are expressed by (17) and (18), respectively. CF W , CF S and CF B are capacity factors of wind, solar and biomass DGs, respectively.

III. TEST SYSTEM
This section presents the general data and other required data related to the formulated problem for the test system. The well-known PG&E 69-bus distribution system is selected as the test system for studying the defined planning problems.
The system data can be found in [23]. For this study, the candidate buses for connecting the DG units are {20, 46, 49,50, 53} according to [15]. The candidate buses for connecting the reactive power sources have been also selected as {10, 31, 49, 50, 51, 52, 53, 54, 55, 57, 59} by using the sensitivity analysis. It is assumed that the DG units operate at a unity power factor and all buses in the system have the same wind profile and solar irradiance. The hourly solar irradiance and wind speed data have been utilized from historical data, and biomass energy is considered a firm generation. The hourly load data given in [6] and the annual peak load for the system under study [23] are used to obtain the hourly load model for the typical day of each year season. A maximum limit for DG capacity equal to 1200 kW and a maximum limit for reactive power sources capacity equal to 1200 kVAr are assumed for each candidate bus. The maximum penetration of DG units is assumed equal to 50% of the peak load. When the objective is maximizing the supply adequacy of microgrids, the defined microgrids on the test system are shown in Fig. 1. The microgrids have been chosen according to the results obtained in [12].
To study the proposed DG and reactive power planning defined in this paper, 2 scenarios and 16 cases for each scenario are proposed as follows.
Scenario 1: n y = 1 Fig. 2 shows the values of index P l for all cases in scenario 1 when the objective function of the planning problem is annual energy losses. It is observed that annual energy losses reduce in all 15 cases (2-16) with respect to the base case. When active and reactive distributed generation sources are utilized in the distribution network, the loads are supplied close to where the energy is consumed instead of thoroughly demanding the loads from the upstream network. Hence, feeder capacities are less occupied, and the system energy losses reduce. The most reduction occurs in case 16 (BWSQ) that biomass, wind, PV and reactive power sources are present at the same time. Case 13 (BSQ) also leads to annual energy losses near to that of case 16. It is obvious that reactive power sources have a profound impact on reducing energy losses. Generally, the impact of biomass energy on the reduction of losses is more than wind and solar-based DGs due to their intermittent production. The wind-based DG has the least impact on the loss reduction with respect to other sources; however, its impact is magnified when wind system is used along with solar or/and reactive power sources. Fig. 3 shows the values of V index for 16 cases in scenario 1 when the objective function of the planning problem is the voltage stability function. Utilizing DG and RPS, especially in high load demand buses, causes a reduction in buses voltage drop and, as a result, an increase in voltage stability margin. For instance, the voltage magnitude of bus 55 at the peak hour is 0.909 PU in the base case, while it reaches 0.994 PU at the same hour in case 6. As observed, the impact of reactive power sources is more than that of active power sources. Reactive power sources and biomass units lead to the most improvement in the voltage stability index so that the most increase in V index is obtained in case 13 (BSQ).   by adding active and reactive power generation close to the consumers in the constructed microgrids; therefore, the SA index improves. As it is observed, biomass and reactive power sources have the most impact on the supply adequacy index. When all kinds of DG units are added to reactive power sources, the index reaches the least value. Fig. 5 shows the values of EP for 16 cases in scenario 1 when the objective function of the planning problem is the exchanged power with the upstream network. Utilizing DGs and RPS in the distribution network reduces power received from the upstream network. The most reduction in EP occurs in case 16 (BSWQ) that there are biomass, wind, PV and reactive power sources. Case 13 (BSQ) also leads to a low value for EP. The impact of biomass energy on the reduction of EP is more than wind and photovoltaic DGs. The wind-based DG has the least impact on the index EP with respect to other sources; however, its impact is magnified when wind system is used along with solar, biomass and reactive power sources. Wind-based DG has less impact on all objective functions than other sources because the profile of wind production is different from the profile of load in the performed studies. Simultaneous use of renewable sources, including PV and wind systems, considerably improves the indices with respect to exploiting only wind or solar energy. The best result of DG planning is related to the simultaneous use of biomass and VOLUME 9, 2021 solar energy, while the best result is obtained for all indices by simultaneous planning of biomass, solar and reactive power sources. Fig. 6 compares the variation of annual energy losses for cases 2, 3, 6, 11, 13 and 16 to the base case when the planning problem is solved by considering different objective functions. It is observed that the annual energy losses seriously increase in cases 2, 6, 13 and 16 when the objective function of the planning is voltage stability index. Due to the overuse of reactive power sources to improve voltage profile, the reactive current of feeders increases considerably. Therefore, considering V index as an objective function in planning reactive power sources will dramatically increase energy losses, SA index and EP index. The common feature of cases 2, 6, 13 and 16 is accompanying reactive power planning with DG planning. Applying V index as an objective function does not cause a significant variation in the energy losses in case 11; however, it has a suitable impact on reducing energy losses in the case 3 (biomass DG planning). As expected, the most reduction of annual energy losses is related to objective function P l . Using objective function SA can also lead to a considerable reduction of energy losses near to results obtained by objective function P l while using objective function EP presents a moderate impact on the reduction of energy losses. Similarly, Figs 7 to 9 compare the variation of voltage stability index, supply adequacy index and exchanged power with the upstream network with respect to those in the base case for cases 2, 3, 6, 11, 13 and 16 when the planning problem is solved by considering different objective functions.     Tables 2 to 5 give optimal location and size of DG units and reactive power sources for the best case in view of different objective functions in scenario 1. It is observed that the most amount of reactive power is required for improvement of V index which is mostly assigned to buses 10, 31, 49, 50, 51, 57 and 59. On the other hand, the most capacity of reactive    power sources have been respectively assigned to buses 51, 54 and 59 when the objective function is P l , SA or EP. It is also observed that the distribution of biomass, wind and PV production among the candidate buses considerably vary when different objective functions are used. For instance, the most capacity of biomass has been assigned to bus 53 in the case of using P l as an objective function, while bus 20 should host the most biomass energy in the case of using objective function V index . The most use of wind and solar energy is related to objective function EP, which mostly has been assigned to bus 20.

B. SCENARIO 2
Figs 10 to 13 respectively show percentage improvement of energy losses, voltage stability index, supply adequacy of microgrids and optimal exchanged power with the upstream network for all cases with respect to the base case in scenarios 1 and 2. The results of the proposed planning for scenario 2 and comparison of them with ones of scenario 1 demonstrates that the percent of the variation of each objective function in the 15 cases due to solving the single objective   optimization problems with respect to those in the base case are almost the same for both scenarios. Indeed, scenario 1 and scenario 2 correspond two different problems because although the used objective function is identical in both scenarios, scenario 1 considers load levels in one year, but scenario 2 studies more load levels regarding annual load growth during 5 years; in addition, renewable energy patterns are assumed the same for all years. Thus, it is natural that the assigned capacities of different types of sources are different in scenarios 1 and 2. In other words, we expect different   patterns of capacities for different types of sources in two scenarios while attaining the optimal solution of the intended objective function, and the alteration of patterns is different for different objective functions.
Specifically, when the network energy losses is considered as the objective function of the planning problem, the pattern of the assigned capacities of different types of DG and reactive power sources in case 16 (the best case) is the same for both scenarios as shown in Table 6. However, the capacities of all resources in scenario 2 have been increased by about %8 with respect to those in scenario 1 due to the increase of system load during years 2, 3, 4 and 5 of the planning horizon. Similar results with the objective function of energy losses are obtained for objective function SA, as the total capacity allocated to each resource type has increased by 8% compared to scenario 1 (Table 8). For objective function V index , the capacities of the resources are the same for both scenarios 1 and 2 except that the total capacity of biomass energy decreases from 1842 kW in scenario 1 to 1500 kW in scenario 2 due to assigning the zero capacity to bus 46 in scenario 2 as shown in Table 7. In the case of using EP as an objective function in the planning problem, the pattern of assigned resources to the candidate buses is approximately the same for both scenarios as shown in Table 9. Although the capacities of reactive power TABLE 8. Optimal location and size of DG Units and reactive power sources for the best case in view of index SA in scenario 2 (case16).

TABLE 9.
Optimal location and size of DG Units and reactive power sources for the best case in view of index EP in scenario 2 (case16). and solar energy have increased about %8 in scenario 2 with respect to scenario 1, the capacity of wind-based DGs has increased about 39 percent, and the capacity of biomass units has decreased about 5 percent.

V. CONCLUSION
This paper proposes a probabilistic joint firm and renewable DG and reactive power planning to overcome the challenge of non-compatibility of renewable generation and load patterns and maximize benefits of renewable DG units, including photovoltaic and wind systems. The proposed technique accounts for the uncertainties associated with solar irradiance, wind speed, and load growth during the planning horizon to plan a safe and optimal system. The paper intends to emphasize the importance and practicality of single objective DG and reactive power planning, especially when the problem is a probabilistic one with many states of load and generation. Two important ones are system energy losses and voltage stability margin, which have been studied on the well-known 69-bus test system along with two new objective functions defined in this paper based on the new paradigm of constructing microgrid in the distribution system, self-adequacy of microgrids defined on the distribution system and exchange of active and reactive powers between the distribution system and upstream network. This is done by solving the optimization problem with only one of four objective functions and investigating the optimal solution for each objective function on the other three objective functions to specify correlated or conflicting objective functions. Generally, the best results objective functions P l , SA and EP are obtained when renewable DG units are used along with firm DGs and reactive power sources (case 16). Case 13 (BSQ) gives the best results for the objective function V index . Based on the results of all scenarios and cases, it is concluded that objective functions P l and SA and approximately EP are oriented ones while voltage stability index can be considered as an objective function that conflicts with other ones.
It is recommended that each distribution company uses the proposed method as a general one regarding the especial problems of every network or/and national and local policies. The results of this method can lead to the reduction of concerned objective functions by the distribution utility and the complex planning problem to a single objective problem or a multi-objective problem with minimum objective functions.