Benefits Maximization of Distribution Company with Optimal Placement of Distributed Generation and Shunt Capacitor

doi:10.21203/rs.3.rs-1531025/v1

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Benefits Maximization of Distribution Company with Optimal Placement of Distributed Generation and Shunt Capacitor

https://doi.org/10.21203/rs.3.rs-1531025/v1

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In the present scenario of rising environmental concern and enormous load growth, the distribution system owners must undertake the decision of distribution system planning to keep the secure operation of the system and to survive in the competitive energy market. The enormous load growth can be tackled by installing new conventional generation units and increasing the feeders’ capacity. But this will cause environmental pollution and problem for the system owner from a financial standpoint. Under such circumstances, this study proposed a planning approach for optimal allocation of distribution generation (DIG) and shunt capacitor (SC) intending to maximize the technical and economic benefits of the system. Renewable energy sources based on DIG, such as solar and wind energy systems are taken into account. The time-varying characteristics of active and reactive power demand are also considered. A multi-stage planning model is considered where the planning horizon of 10 years is divided into two stages. A soft computing technique, namely Particle Swarm Optimization (PSO) technique, is applied to solve the problem. Moreover, the 33-bus distribution network is taken as the test system and different planning scenarios are considered for an in-depth planning and analysis purpose.

Electrical Engineering

Multi-stage planning

PSO

Voltage profile Enhancement index

Cost Index

Active and Reactive loss reduction index

The electrical distribution system is the further most part of the power system, where different types of consumers such as industrial, residential, commercial, and agricultural are connected and at a given time, the distribution system owners must fulfill the demand of these consumers [1]-[3]. However, with the economic growth in recent times, the load demand of these consumers is increasing day by day [2]. On the other hand, due to the introduction of the different electricity distribution companies, there has been unscheduled power exchange between these companies [4]-[5]. These factors cause the operation of most of the power systems utilizes near to their stability limit, which takes the system towards voltage collapse point and makes the operation of the distribution system a challenging issue [4]. These problems can be solved by increasing the capacity of the substation from where the power is taken or by installing new conventional power plants [5]. Moreover, the feeders’ capacities need to be increased to handle the increase in the power flow due to enormous load growth in recent times [5]. These solutions can be effective, but the implementation cost will be much high. Therefore, it is difficult for the distribution system owner to invest a huge amount of money in a single time. Apart from the financial issues, the installation of new generating stations is also not possible due to the environmental concerns [4]-[6]. As a result, there are some issues arises, such as low voltage profile, higher line losses, etc [1]-[3].

Under such conditions, the distribution system owners must opt for the installation of DIG technology in their system. DIG can be based upon renewable energy sources or non-renewable energy sources [7]. Non-renewable energy sources can be useful, but utilization of these sources causes environmental pollution [7]. In this regard, it is useful to use renewable-based energy systems such as solar energy systems, wind energy systems, etc [8]-[9]. Solar energy system generates electrical power under the influence of solar irradiation, whereas wind speed is the key factor for power generation in wind energy system [9]. These devices can be useful to reduce line losses and to improve voltage profile [7]-[8]. Both these devices generate active power to the system and meet the active power growth of the system [7]-[9]. But they are unable to meet the reactive power growth. In such context, there is a need for a reactive power source and for this case, a shunt capacitor (SC) can be used [10]-[12].

Literature review reveals that in most articles, the planning was conducted in a single stage, which will cause difficulty for the distribution system owner [5]-[12]. Hence, a multi-stage model can be utilized for planning purposes. In this process, the planning period can be divided into stages and it will provide a cost-effective solution to the system owner. On the other hand, researchers mostly ignored the fact that there are different types of customers in the distribution system and their power demand is not constant. In such a context, the active and reactive power variation of loads must be considered for system planning. Furthermore, a detailed economic analysis of the system planning was mostly ignored by the researchers. However, economic analysis is important from the viewpoint that the planning investment must be economical for a planning period.

The integration of these devices can handle the load growth and offer various potential benefits for the system. To reflect that the active and reactive power demand is never constant, time-varying characteristics of both types of power demand are taken into account. The planning is conducted for 10 years of the planning horizon and for the convenience of the system owner, the planning period is divided into two stages. In the 1st stage, planning is done from 0 to 5 years, and planning is done considering 6 to 10 years in the 2nd planning stage. The proposed technique is applied to the 33-bus distribution system.

After a detailed introduction in Section 1 of the manuscript, Section 2 presents the modeling of load, DIG, and SC. The considered objective functions are discussed in Section 3. Section 4 represents the solution algorithm and step-wise procedure of optimization. The result and analysis part is given in Section 5 and the conclusion of this study is represented in Section 6.

A. Modeling of Load

In this study, a distribution system is taken into account and these types of the system include different customers’ types such as industrial, residential, agricultural, and commercial [8], [13]. The power demand of these consumers is not constant parameters. Actually, with the time horizon of an hour, day or year, these are kept changing. Therefore, it will not be good if a constant value of the load is considered for the analysis purpose. Considering this factor, the variation of the active and reactive power demand of the system is illustrated in Fig. 1. This figure indicates time-varying characteristics of loads for 24-hour time duration and it is assumed in this study that the variation is the same for all the days of a year.

B. Modeling of DIG

Proper modeling of DIG is important from the standpoint that it needs to be integrated with the load flow model. Here, the DIG is selected to give only active power to the system. Therefore, it is modeled as a PQ model to integrate it with the distribution system load flow analysis [8]-[9]. DIG is modeled as a negative load in the analysis, as discussed with the help of Fig. 2.

A sample distribution system is shown in Fig. 2 that consists of 3 buses and a DIG is incorporated at bus 2 of the system. The active and reactive load demand of the consumers at the bus is P_L and Q_L, respectively. The active power supplied by DIG is P_D, whereas DIG supplies no reactive power. Since DIG is modeled as negative load, the equivalent active and reactive power demand at Bus 2 can be calculated accordingly (1) and (2), respectively.

$${\text{P}}_{\text{L}}^{\text{e}\text{q}\text{v}}={\text{P}}_{\text{L}}-{\text{P}}_{\text{D}}$$

$${\text{Q}}_{\text{L}}^{\text{e}\text{q}\text{v}}={\text{Q}}_{\text{L}}-0$$

where,

${\text{P}}_{\text{L}}^{\text{e}\text{q}\text{v}}$ : Equivalent Active power at Bus 2.

${\text{Q}}_{\text{L}}^{\text{e}\text{q}\text{v}}$ : Equivalent Reactive power at Bus 2.

${\text{P}}_{\text{L}}$ : Active power load at Bus 2.

${\text{Q}}_{\text{L}}$ : Reactive power load at Bus 2.

${\text{P}}_{\text{D}}$ : Active power supplied by DIG.

Figure 2. Single line diagram of 3-bus distribution system integrated with DG.

C. Modeling of SC

Proper modeling of SC is important from the standpoint that it needs to be integrated with the load flow model. Here, the main function of SC is to compensate for the reactive power demand. Therefore, it is modeled as a PQ model to integrate it with the distribution system load flow analysis [10]-[12].

A sample distribution system is shown in Fig. 3 that consists of 3 buses and an SC is incorporated at bus 2 of the system. The SC is denoted as ‘SC’. The reactive power supplied by SC is Q_S whereas SC supplies no active power. The equivalent active and reactive power demand at Bus 2 can be calculated accordingly (3) and (4), respectively.

$${\text{P}}_{\text{L}}^{\text{e}\text{q}\text{v}}={\text{P}}_{\text{L}\text{o}\text{a}\text{d}}-0$$

$${\text{Q}}_{\text{L}}^{\text{e}\text{q}\text{v}}={\text{Q}}_{\text{L}}-{\text{Q}}_{\text{S}}$$

Figure 3. Single line diagram of 3-bus distribution system integrated with SC.

The optimal allocation of DIG and SC is important from the standpoint that if they are incorporated at the right bus location of the system, the distribution company will get benefitted. To calculate the obtained benefits, concentration must be given on the technical and economic benefit evaluation of the system. In such a context, the technical and economic indexes are developed in this study.

A. Voltage Profile enhancement Index (VPEI)

Since DIG and SC devices supply active and reactive power to the system, there will be a significant voltage profile improvement in the area where these devices are incorporated [13]-[14]. Apart from this, the other buses also face a considerable voltage profile enhancement. Therefore, VPEI is a vital criterion that must be considered as a decisive factor while carrying out the optimal placement of these devices. In this method, the voltage profile (VP_n) of the n^th node of the system is defined in (5)

$${\text{V}\text{P}}_{\text{n}}=\frac{\left({\text{v}\text{o}\text{l}}_{\text{n}}-{\text{v}\text{o}\text{l}}^{\text{m}\text{i}\text{n}}\right)\times \left({\text{v}\text{o}\text{l}}^{\text{m}\text{a}\text{x}}-{\text{v}\text{o}\text{l}}_{\text{n}}\right)}{\left({\text{v}\text{o}\text{l}}^{\text{n}\text{o}\text{m}}-{\text{v}\text{o}\text{l}}^{\text{m}\text{i}\text{n}}\right)\times \left({\text{v}\text{o}\text{l}}^{\text{m}\text{a}\text{x}}-{\text{v}\text{o}\text{l}}^{\text{n}\text{o}\text{m}}\right)}$$

where

vol_n: Voltage magnitude of the n^th bus

${\text{v}\text{o}\text{l}}^{\text{n}\text{o}\text{m}}$ : Nominal value of bus voltage that is taken as 1 p.u.

${\text{v}\text{o}\text{l}}^{\text{m}\text{i}\text{n}}$ : Minimum permissible limit of system voltage which is considered to be 0.9 p.u.

${\text{v}\text{o}\text{l}}^{\text{m}\text{a}\text{x}}$ : Maximum permissible limit of system voltage which is considered to be 1.1 p.u.

The overall network Voltage Profile Index (VPI) of the system is given in (6):

$$\text{V}\text{P}\text{I}=\frac{1}{\text{L}}\sum _{\text{n}=1}^{\text{L}}{\text{V}\text{P}}_{\text{n}}$$

where L is the number of load buses in the network.

Therefore, the VPEI of the system can be calculated by (7)

$$\text{V}\text{P}\text{E}\text{I}=\frac{{\left(\text{V}\text{P}\text{I}\right)}_{\text{w}\text{i}\text{t}\text{h} \text{d}\text{e}\text{v}\text{i}\text{c}\text{e}}}{{\left(\text{V}\text{P}\text{I}\right)}_{\text{w}\text{i}\text{t}\text{h}\text{o}\text{u}\text{t} \text{d}\text{e}\text{v}\text{i}\text{c}\text{e}}}$$

B. Cost Index (CI)

$\text{C}\text{I}=$ $\frac{\text{O}\text{b}\text{t}\text{a}\text{i}\text{n}\text{e}\text{d} \text{B}\text{e}\text{n}\text{e}\text{f}\text{i}\text{t} \left(\text{O}\text{B}\right)}{\text{I}\text{n}\text{v}\text{e}\text{s}\text{t}\text{m}\text{e}\text{n}\text{t} \text{C}\text{o}\text{s}\text{t} \left(\text{I}\text{C}\right)}$ (8)

$$\text{I}\text{C}={\text{C}\text{o}\text{s}\text{t}}_{\text{D}\text{I}\text{G}}^{\text{i}\text{n}\text{s}}+{\text{C}\text{o}\text{s}\text{t}}_{\text{D}\text{I}\text{G}}^{\text{m}\text{a}\text{i}\text{n}}+{\text{C}\text{o}\text{s}\text{t}}_{\text{S}\text{C}}^{\text{i}\text{n}\text{s}}+{\text{C}\text{o}\text{s}\text{t}}_{\text{S}\text{C}}^{\text{m}\text{a}\text{i}\text{n}}$$

$${\text{C}\text{o}\text{s}\text{t}}_{\text{D}\text{I}\text{G}}^{\text{i}\text{n}\text{s}}={\text{P}}_{\text{D}\text{I}\text{G}}\times {\text{C}}_{\text{D}\text{I}\text{G}}$$

$${\text{C}\text{o}\text{s}\text{t}}_{\text{D}\text{I}\text{G}}^{\text{m}\text{a}\text{i}\text{n}}={\text{P}}_{\text{D}\text{I}\text{G}}\times {\text{M}}_{\text{D}\text{I}\text{G}}\times {\text{N}}_{\text{P}\text{l}\text{a}\text{n}}$$

$${\text{C}\text{o}\text{s}\text{t}}_{\text{S}\text{C}}^{\text{i}\text{n}\text{s}}={\text{Q}}_{\text{S}\text{C}}\times {\text{C}}_{\text{S}\text{C}}$$

$${\text{C}\text{o}\text{s}\text{t}}_{\text{S}\text{C}}^{\text{m}\text{a}\text{i}\text{n}}={\text{Q}}_{\text{S}\text{C}}\times {\text{M}}_{\text{S}\text{C}}\times {\text{N}}_{\text{P}\text{l}\text{a}\text{n}}$$

where,

${\text{C}\text{o}\text{s}\text{t}}_{\text{D}\text{I}\text{G}}^{\text{i}\text{n}\text{s}}$ : Installation cost of DIG ($).

${\text{C}\text{o}\text{s}\text{t}}_{\text{D}\text{I}\text{G}}^{\text{m}\text{a}\text{i}\text{n}}$ : Maintenance cost of DIG ($).

${\text{C}\text{o}\text{s}\text{t}}_{\text{S}\text{C}}^{\text{i}\text{n}\text{s}}$ : Installation cost of shunt capacitor ($).

${\text{C}\text{o}\text{s}\text{t}}_{\text{S}\text{C}}^{\text{m}\text{a}\text{i}\text{n}}$ : Maintenance cost of shunt capacitor ($).

P_DIG: Power output of DIG in KW

Q_SC: Power output of shunt capacitor in KVAr.

C_DIG: Cost of DIG per KW.

C_SC: Cost of shunt capacitor per KVAr.

M_DIG: Maintenance cost of DIG.

M_SC: Maintenance cost of a shunt capacitor.

N_plan: The planning horizon that is taken as 10 years.

$$\text{O}\text{B}={\varDelta \text{P}}_{\text{a}\text{c}\text{t}\text{i}\text{v}\text{e}}+{\varDelta \text{Q}}_{\text{r}\text{e}\text{c}\text{t}\text{i}\text{v}\text{e}}$$

$${\varDelta \text{P}}_{\text{a}\text{c}\text{t}\text{i}\text{v}\text{e}}=\left({\text{P}}_{\text{w}\text{o}\text{d}}-{\text{P}}_{\text{w}\text{d}}\right)\times {\text{C}}_{\text{a}\text{p}}\times {\text{N}}_{\text{P}\text{l}\text{a}\text{n}}$$

$${\varDelta \text{Q}}_{\text{r}\text{e}\text{c}\text{t}\text{i}\text{v}\text{e}}=\left({\text{Q}}_{\text{w}\text{o}\text{d}}-{\text{Q}}_{\text{w}\text{d}}\right)\times {\text{C}}_{\text{r}\text{p}}\times {\text{N}}_{\text{P}\text{l}\text{a}\text{n}}$$

where,

P_wod: Active power from the grid without a device.

P_wd: Active power from the grid with a device.

Q_wod: Reactive power from the grid without a device.

Q_wd: Reactive power from the grid with a device.

C_ap: Unit price of active power from the grid

C_rp: Unit price of reactive power from the grid.

C. ALRI & RLRI

$\text{A}\text{L}\text{R}\text{I}=$ $\frac{{\left({\text{P}}_{\text{L}}\right)}_{\text{w}\text{i}\text{t}\text{h} \text{D}\text{I}\text{G}}}{{\left({\text{P}}_{\text{L}}\right)}_{\text{w}\text{i}\text{t}\text{h}\text{o}\text{u}\text{t} \text{D}\text{I}\text{G}}}$ (17)

$\text{R}\text{L}\text{R}\text{I}=$ $\frac{{\left({\text{Q}}_{\text{L}}\right)}_{\text{w}\text{i}\text{t}\text{h} \text{D}\text{I}\text{G}}}{{\left({\text{Q}}_{\text{L}}\right)}_{\text{w}\text{i}\text{t}\text{h}\text{o}\text{u}\text{t} \text{D}\text{I}\text{G}}}$ (18)

where,

P_L: Active power loss of the system.

Q_L: Reactive power loss of the system.

D. Conversion of the multi-objective problem into a single-objective problem

After bringing all the considered objectives in the same range, the multi-objective optimization problem is converted into a single objective optimization problem using proper weighting coefficients as shown in Eq. (19).

Minimize

$\text{F}={{\text{w}}_{1}\times \left(\frac{1}{\text{V}\text{P}\text{E}\text{I}}\right)+\text{w}}_{2}\times \left(\frac{1}{\text{C}\text{I}}\right)+{\text{w}}_{3}\times \text{A}\text{L}\text{R}\text{I}$ $+{\text{w}}_{4}\times \text{R}\text{L}\text{R}\text{I}$

(19)

E. Constraints

In this study, different power system constraints are taken into account for the integration of DIG and SC into the distribution network. The constraints can be classified as active power balance, reactive power balance, bus voltage magnitude, power flow constraints, and DIG and SC capacity constraints.

Active and Reactive power balance: The summation of the active power taken from the grid and DIG generated power must be equal to the summation of total active power load demand and the active power loss. Similarly, the summation of the reactive power taken from the grid and SC-generated power must be equal to the summation of total reactive power load demand and the reactive power loss.
Bus voltage magnitude: The bus voltage magnitude of all the buses must be under 0.9PU and 1.1 PU i.e. the permissible limit.
Power Flow Constraint: The amount of power flow through all the feeders must be under the thermal capacity limit of that feeder.
DIG and SC capacity constraints: The total capacity of DIG must be less than the total active power load of the system, whereas the total installed capacity of SC must be less than the total reactive power capacity of the system.

The working principle of PSO is inspired by the social behavior of bird flocking or fish schooling and it is based on swarm intelligence. This technique is an optimization procedure that is stochastic in nature. Dr. Eberhart and Dr. Kennedy had developed this algorithm in 1995 [19].

In this algorithm, a group of populations is randomly developed inside a predefined search space. The population that has the best fitness value guides the other particle so that optimal position can be reached. A randomized velocity is associated with each particle, which moves along the search space. The position and velocity upgrading formula for all the population is based on the equations (20) and (21), respectively.

${{\text{v}}_{\text{d}}^{\text{i}\text{t}+1}=\text{w}\times {\text{v}}_{\text{d}}^{\text{i}\text{t}}+\text{c}}_{1}\times \text{r}\text{a}\text{n}\text{d}\left({\text{p}\text{b}\text{e}\text{s}\text{t}}_{\text{d}}^{\text{i}\text{t}}-{\text{s}}_{\text{d}}^{\text{i}\text{t}}\right)+{\text{c}}_{2}\times$ $\text{r}\text{a}\text{n}\text{d}\left({\text{g}\text{b}\text{e}\text{s}\text{t}}_{\text{d}}^{\text{i}\text{t}}-{\text{s}}_{\text{d}}^{\text{i}\text{t}}\right)$ (20)

$${ \text{s}}_{\text{d}}^{\text{i}\text{t}+1}={ \text{s}}_{\text{d}}^{\text{i}\text{t}}+{\text{v}}_{\text{d}}^{\text{i}\text{t}+1}$$

where,

${\text{s}}_{\text{d}}^{\text{i}\text{t}}$ : Current position of the d^th particle in the d-dimensional space.

${\text{v}}_{\text{i}\text{d} }^{\text{i}\text{t}}$ : Current velocity of the d^th particle in the d-dimensional space.

${\text{p}\text{b}\text{e}\text{s}\text{t}}_{ \text{d}}^{\text{i}\text{t}}$ : pbest of d^th particle for the it^th generation. ${\text{g}\text{b}\text{e}\text{s}\text{t}}_{ \text{d}}^{\text{i}\text{t}}$: The global best particle of the entire swarm. ${\text{v}}_{\text{d}}^{\text{i}\text{t}+1}$: The updated velocity.

${\text{s}}_{\text{d}}^{\text{i}\text{t}+1}$ : The updated position.

w: The inertia weight.

rand: any random number in [0, 1].

In the standard PSO algorithm, the value of inertia weight i.e. ‘w’ is taken as constant throughout the iterative process. This may result in local optima since when the optimization process reaches the global optimal point, then the solution may overshoot the global optimum solution due to the larger value of ‘w’ [19]-[20]. With an aim to increase the global convergence probability of the PSO algorithm, the value of ‘w’ is taken to be adaptive i.e. with the change of iteration, ‘w’ value will also change. According to this philosophy, the value of ‘W’ is calculated using the following formula:

$${\text{w}}_{\text{I}\text{t}}={\text{w}}_{\text{m}\text{a}\text{x}}-\left({\text{w}}_{\text{m}\text{i}\text{n}}\times \frac{\text{I}\text{t}}{{\text{I}\text{t}}_{\text{m}\text{a}\text{x}}}\right)$$

Where

${\text{w}}_{\text{I}\text{t}}$ : Value of weighting factor at It^th iteration.

${\text{w}}_{\text{m}\text{a}\text{x}}$ : Maximum value of weighting factor.

${\text{w}}_{\text{m}\text{i}\text{n}}$ : Minimum value of weighting factor.

It: Current Iteration

${\text{I}\text{t}}_{\text{m}\text{a}\text{x}}$ : Maximum Iteration.

In this study, DIG and SC are incorporated in the system with an aim to maximize the potential benefits. The optimal location and capacity of both the devices must be appropriately chosen and accordingly, they are taken as the decision variables. The population structure (P) of PSO algorithm is shown below:

$$P=\left[\begin{array}{ccc}{S}_{1}^{DIG}& {S}_{2}^{DIG}& \begin{array}{ccc}{S}_{1}^{SC}& {S}_{2}^{SC}& \begin{array}{cc}{L}_{1}^{DIG}& \begin{array}{ccc}{L}_{2}^{DIG}& {L}_{1}^{SC}& {L}_{2}^{SC}\end{array}\end{array}\end{array}\end{array}\right]$$

where the size and location of DIG is represented as {${S}_{1}^{DIG}, {S}_{2}^{DIG}$}and {${L}_{1}^{DIG}, {L}_{2}^{DIG}$}, respectively, whereas the size and location of SC is represented as {${S}_{1}^{SC}, {S}_{2}^{SC}$}and {${L}_{1}^{SC}, {L}_{2}^{SC}$}, respectively,

The flow-chart of the proposed PSO-based optimal allocation process is illustrated in Fig. 2.

Since the distribution system exhibits a large X/R ratio, there may be a high possibility of convergence issue for the Newton Raphson load flow analysis. In this regard, the power flow analysis is conducted using the backward forward sweep load flow method. The base power is taken as 100 MVA, whereas the base voltage is considered to be 12.66 kV.

In this study, the DIG and SC are incorporated, and to reflect the practical aspect of system planning, the load growth is considered at 3% annually. The planning horizon is taken to be 10 years. However, unlike most literature, the planning is not conducted in a single stage. Here, the planning horizon is divided into two planning stages as described below:

Planning Stage 1: System planning for 0-5 years.

Planning Stage 2: System planning for 6-10 years.

In each planning stage, DIG and SC are integrated in the system according to the load quantity, and to do a detailed analysis, different planning scenarios are considered as given below, which will assist the distribution system operator in finding the best planning option for their system.

Table 1: Different scenarios that are taken into account in this study.

Devices	Scenarios
Devices	1	2	3	4
DIG	NC	C	NC	C
SC	NC	NC	C	C

C: Considered; NC: Not Considered

In this study, an improved version of the PSO algorithm is used as an optimization technique for allocating DIG and SC. In the standard PSO, the weighting factor ‘w’ is taken as a constant. But, in the improved version, w is varied linearly from its maximum value to the minimum value. The maximum and minimum value of ‘w’ is taken as 0.9 and 0.4, respectively. The value of other tuning parameters of PSO i.e. C1 and C2 are taken as 1.7. The maximum number of iteration is taken as 100 and the population number is chosen to be 200. The maximum number of iteration is set as the convergence criteria.

A. Optimum Deployment Results

The optimal location, optimal size, and the values of the objective functions namely VPEI, ALRI, PLRI, and CI for the 1st planning stage are given in Table 2. In scenario 2, the optimal locations of DIG are obtained as bus 12 and 30 with a capacity of 975.3 KW and 1045.8 KW whereas in scenario 3, the optimal locations of SC are found to be bus 11 and 30 with a capacity of 509.9 KVAr and 943.3 KVAr, respectively. On the other hand, in scenario 3, both the device are integrated simultaneously and the obtained locations of DIG and SC are buses {12, 30} and buses {26, 33}, respectively. The optimal sizes of these devices are attained as {942.7, 1010.3} KW, {927.9, 494.1} KVAr. The objective values of different scenarios also indicate that the values of VPEI are increased, whereas the values of ALRI and RLRI decrease in all the scenarios. This represents that these devices improve voltages and reduce losses and it is evident from the table that scenario 4 i.e. both the device simultaneously incorporated provide the highest benefits. However, the values of CI indicate that the maximum value is obtained in the case of scenario 3. Moreover, the value of CI is less than 1 in the case of scenario 2, which indicates that this scenario is not beneficial for planning as evident from an economic standpoint. Comparing scenarios 2 and 3, it can be concluded that scenario 2 provides better results for VPEI, ALRI, and RLRI, establishing the superiority of DIG over SC.

The optimal location, optimal size, and the values of the objective functions namely VPEI, ALRI, PLRI, and CI for the 2nd planning stage are given in Table 2. It is clear from the table that the obtained values of optimal locations in planning stage 2 are mostly different from what was obtained in planning stage 1. The objective values of different scenarios also indicate that the values of VPEI are increased, whereas the values of ALRI and RLRI decrease in all the scenarios. This represents that these devices improve voltages and reduce losses and it is

Table 2: Optimal allocation results for Planning Stage 1.

Scenarios	Optimal location	Optimal Size	VPEI	ALRI	RLRI	CI
Scenario 1 (BASE CASE)	-	-	1.0000	1.0000	1.0000	1.0000
	-	-
Scenario 2 (WITH DIG)	12	975.3	1.3776	0.3986	0.4077	0.9516
	30	1045.8
Scenario 3 (WITH SC)	11	509.9	1.2259	0.7116	0.7143	10.4551
	30	943.3
Scenario 4 (WITH DIG & SC)	12	942.7	1.4142	0.1682	0.1892	1.1951
	30	1010.3
	26	927.9
	33	494.1

Table 3: Optimal allocation results for Planning Stage 2.

Scenarios	Optimal location	Optimal Size	VPEI	ALRI	RLRI	CI
Scenario 1 (BASE CASE)	-	-	1.0000	1.0000	1.0000	1.0000
	-	-
Scenario 2 (WITH DIG)	6	1956.5	1.5906	0.345	0.3711	1.588
	24	1065.1
Scenario 3 (WITH SC)	24	557.4	1.3969	0.6913	0.6918	14.7713
	26	333.2
Scenario 4 (WITH DIG & SC)	7	1581.7	1.6837	0.3004	0.3451	1.8849
	24	1158.3
	10	1407.6
	33	236

Table 4: Detailed Economic Analysis for different Planning Stages.

	Planning Stages	Investment (A)	Benefit (B)	Net Savings (B-A)	CI (B/A)
Scenario 1 (BASE CASE)	Stage 1	0	0	0	-
	Stage 2	0	0	0	-
	Net (1+2)	0	0	0	-
Scenario 2 (WITH DIG)	Stage 1	1897701	1805921	-91780	0.9516
	Stage 2	2837045	4505369	1668324	1.5880
	Net (1+2)	4734746	6311290	1576544	1.3330
Scenario 3 (WITH SC)	Stage 1	43596	455811	412215	10.4553
	Stage 2	25893	382472	356579	14.7713
	Net (1+2)	69489	838283	768794	12.0635
Scenario 4 (WITH DIG & SC)	Stage 1	1839654	2404125	564471	1.3068
	Stage 2	2580904	4864525	2283621	1.8848
	Net (1+2)	4420558	7268650	2848092	1.6443

evident from the table that scenario 4 i.e. both the device simultaneously incorporated, provides the highest benefits. However, the values of CI indicate that the maximum value is obtained in the case of scenario 3. Unlike planning stage 1, the value of CI in a scenario in the 2^nd planning stage is obtained more than 1, which indicates a financial benefit of the distribution company in utilizing this scenario for system planning. Similar to the 1^st planning stage, scenario 2 provides better results for VPEI, ALRI and RLRI as compared to scenario 1, establishing the superiority of DIG over SC.

B. Detailed Economic Analysis

The obtained values of CI as given in Tables 2-3 indicate that CI is attained to be the highest in the case of SC. As described in subsection 3.B, CI is a ratio of total benefit and total investment. To find out the economic feasibility of the devices, it is important to calculate net saving after the planning horizon is over. Accordingly, a detailed analysis of the economic performance is performed stage-wise for different scenarios, as shown in Table 4, in terms of investment, benefit, net savings, and CI. The investment is the highest in scenario 1 due to a higher penetration level of DIG, whereas the investment is the lowest for scenario 2, which is because of the lower installation cost of SC. Table 4 clearly shows that in 1^st planning stage, the investment is more as compared to the savings in the case of DIG incorporation only. Therefore, the net saving is negative in this case. However, in the 2^nd planning stage, there is a positive value of net saving for the case of DIG. Analyzing the table, it can be concluded that the highest value of net saving considering both the planning stages is obtained for scenario 4, indicting the economic superiority of incorporating these devices in the system simultaneously.

C. Analysis of different scenarios based on Voltage profile, line loss, and power flow

1^st and 2^nd planning stage is illustrated in Figures 4 and 5, respectively. These figures indicate that in the base case when there are no devices in the system, the voltage profile is very worse for both the planning stages. However, with the incorporation of DIG and SC, voltage profile is improved for almost all the buses and the voltage magnitudes tend to reach the nominal value of 1 P.U. As compared to the case of Sc, DIG presents a better enhancement of voltage profile. However, for both the planning stages, the voltage profile improvement is the highest when both the devices are incorporated simultaneously in the distribution system. Moreover, it is important to note that due to more increment of load in planning stage 2, the voltage magnitudes became less in stage 2.

A comparative analysis between different considered scenarios based on active and reactive power losses is also conducted and the graphical representation of active and reactive power losses is shown in Figures 6 and 7, respectively, for planning stages 1 and 2. The reduction of both the losses is more in scenario 2 as compared to scenario 3, which indicates more loss reduction capability of DIG over SC. It can also be noted that the values of active and reactive power losses are more in planning stage 2 as compared to planning stage 1 due to the increment of the load value.

In this study, the planning horizon is considered to be 10 years and a yearly load growth of 3% is taken into account. Hence, the power flow is a matter of concern for the distribution company and in this regard, a power flow analysis is carried out in the presence of these devices. The active and reactive power flow for different scenarios in the 1^st planning stage is indicated in Figures 8 and 9, respectively, whereas the power flow in planning stage 2 is indicated in Figures 10 and 11.

Figures 8 and 10 indicate that with the incorporation of DIG, there is a significant reduction of active power flow through most of the feeders since DIG can act as a local power source and provide active power to the local loads. On the other hand, when only SC is incorporated in the system, there is not a significant reduction of active power. The small amount of reduction in active power is due to the active loss reduction by SC. The highest reduction of active power flow is possible with the simultaneous incorporation of DIG and SC.

Figures 9 and 11 indicate that with the incorporation of SC, there is a significant reduction of reactive power flow through most of the feeders since SC can act as a local power source and provide reactive power to the local loads. On the other hand, when only DIG is incorporated in the system, there is not a significant reduction of reactive power since there is no reactive power output from DIG. The small amount of reduction in reactive power is due to the reactive loss reduction by DIG. Moreover, the highest reduction of reactive power flow is possible with the simultaneous incorporation of DIG and SC.

D. Convergence Characteristics

The convergence characteristics of the proposed improved PSO for different scenarios is shown in Figures 12 and 13, respectively for planning stage 1 and 2. In both the figures, the PSO algorithm converges to the minimum value when DIG and SC are incorporated simultaneously. Therefore, this scenario provides maximum potential benefits to the system owner. However, these figures clearly show that the number of iteration the optimization technique takes to converge is the highest for the case of simultaneous incorporation of DIG and SC. This is because the size of the problem becomes more when both the devices are incorporated simultaneously and accordingly, it takes more iteration to converge. On the other hand, the converge value of F indicates overall more benefit of DIG as compared to SC. Further, these figures also indicate that the number of iteration to converge is more in the case of DIG as compared to SC for both the planning stages.

In the present time, the enormous growth of load creates various difficulties in the operation of the distribution system, and accordingly, DIG and SC are incorporated in the distribution system to handle the load growth and to obtain various potential benefits for the system. A PSO-based optimization technique is presented to optimally deploy these devices with an objective to minimize real and reactive power losses of the system, increase voltage profiles and maximize the economic benefits. A variable profile for both active and reactive power demand is also taken into account and different logical indexes are developed. The planning is conducted for 10 years that is divided into two stages.

The proposed technique is applied to the 33-bus distribution system and the obtained results reveal that a significant amount of potential benefit can be obtained. From an economic standpoint, DIG is not suitable to be utilized in 1st planning stage since the net saving is negative. However, considering 10 years of planning time, DIG provides more benefit in comparison with SC. Moreover, in the case of the simultaneous incorporation of DIG and SC, the net saving is the highest. Further, this scenario is the best in terms of loss reduction and voltage magnitude improvement. Regarding the power flow analysis, there is a significant reduction of active power flow through the feeders for the case of DIG and reactive power flow reduction for the case of SC. This is because DIG provides only active power to the system, whereas SC provides only reactive power to the system.

Conflict of Interest

The authors declare that there is no conflict of interest.

Funding

This research received no external funding.

Hemmati, R, Hooshmand, R & Taheri, N 2015, ‘Distribution network expansion planning and DG placement in the presence of uncertainties,’ International Journal of Electrical Power and Energy Systems, vol. 73, pp. 665–673.
Lia, Y, Fenga, B, Lia, G, Qib, J, et al., 2018, ‘Optimal distributed generation planning in active distribution networks considering integration of energy storage,’ Applied Energy, vol. 210, pp. 1073–1081.
Hien, N.C, Mithulananthan, N & Bansal, R.C 2013, ‘Location and sizing of distributed generation units for loadabilty enhancement in primary feeder,’ IEEE Systems Journal, vol. 7, no. 4, pp. 797–806.
Heydeman, J, Tripathy, S.C, Paap, G.C & Van-Der-Sluis L 2000, ‘Digital and experimental study of voltage collapse and instability in power systems,’ International Journal of Electrical Power and Energy Systems, vol. 22, no. 4, pp. 303–311.
Zou, K., Agalgaonkar, A.P, Muttaqui, K.M & Perera, S 2012, ‘Distribution system planning with incorporating DG reactive capability and system uncertanity,’ IEEE Transactions on Sustainable Energy, vol. 3, no. 1, pp. 764–773.
Zhang, X, Karady, G.G & Ariaratnam, S.T 2014, ‘Optimal allocation of CHP based Distributed Generation on Urban Energy distribution networks,’ IEEE Transactions on Sustainable Energy, vol. 5, no. 1, pp. 246–251.
Ali E.S, Abd Elazim S.M & Abdelaziz A.Y 2018, ‘Optimal allocation and sizing of renewable distributed generation using ant lion optimization algorithm,’ Electrical Engineering, vol. 100, pp. 99–109.
Yammani, C, Maheswarapu, S & Matam, S.K 2016, ‘Optimal placement and sizing of distributed generations using shuffled bat algorithm with future load enhancement,’ International Transactions on Electrical Energy Systems, vol. 26, no. 2, pp. 274–292.
Aien, M, Khajeh, M.G, Rashidinejad, M & Fotuhi-Firuzabad, M 2014, ‘Probabilistic power flow of correlated hybrid wind-photovoltaic power systems,’ IET Renewable Power Generation, vol. 8, no. 6, pp. 649–658.
Mohssen, S, Mahmoud, S, Haghifan, R & Salehi, J 2013, ‘Simultaneous placement of distributed generator and capacitor in distribution network considering voltage stability index,’ International Journal of Electrical Power and Energy System, vol. 46, pp. 366–375.
Zou, K, Agalgaonakar, A.P, Muttaqui, K.M & Perera, S 2009, ‘Voltage support by Distributed Generator units and shunt capacitor in distribution system,’ In IEEE Power & Energy Society General Meeting, pp. 1–8.
Kayal, P & Chanda, C.K 2016, ‘Strategic approach for reinforcement of intermittent renewable energy sources and capacitor bank for sustainable electric power distribution system,’ International Journal of Electrical Power and Energy Systems, vol. 83, pp. 335–351.
Poornazaryan, B, Karimyan, P, Gharehpetian, G.B & Abedi, M 2016, ‘Optimal allocation and sizing of DG units considering voltage stability, losses and load variations,’ International Journal of Electrical Power and Energy Systems, vol. 79, pp. 42–52.
Aien, M, Khajeh, M.G, Rashidinejad, M & Fotuhi-Firuzabad, M 2014, ‘Probabilistic power flow of correlated hybrid wind-photovoltaic power systems,’ IET Renewable Power Generation, vol. 8, no. 6, pp. 649–658.
Gampa, S.R, & Das, D 2015, ‘Optimum placement and sizing of DGs considering average hourly variations of load,’ International Journal of Electrical Power & Energy Systems, vol. 66, pp. 25–40.
Mistry, K.D & Roy, R 2014, ‘Enhancement of loading capacity of distribution system through distributed generator placement considering techno-economic benefit with load growth,’ International Journal Electric Power Energy System, vol. 54, pp. 505–515.
Taher, S.A & Afsari, S.A 2014, ‘Optimal location and sizing of DSTATCOM in distribution systems by immune algorithm,’ International Journal of Electrical Power & Energy Systems, vol. 60, pp. 34–44.
Tolabi, H.B, Ali, M.H, & Rizwan, M 2015, ‘Simultaneous reconfiguration, optimal placement of DSTATCOM, and photovoltaic array in a distribution system based on fuzzy-ACO approach,’ IEEE Transactions on Sustainable Energy, vol. 6, no. 1, pp. 210–218.
Kumar, E.V, Raja, G.S & Jerome, J 2016, ‘Adaptive PSO for optimal LQR tracking control of 2 DOF laboratory helicopter,’ International Journal of applied soft computing, vol. 41, pp. 77–90.
Kumar, T & Thakur, T 2014, ‘Comparative analysis of Particle Swarm Optimization variants on Distributed Generation allocation for network loss minimization,’ in proc. 1st int. conf. Networks & Soft Computing (ICNSC), India, August 19–20, pp. 167–171.

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Benefits Maximization of Distribution Company with Optimal Placement of Distributed Generation and Shunt Capacitor

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1. Introduction

2. Modeling Of Load, Dig And Sc

3. Objective Functions

4. Solution Algorithm

5. Results And Discussions

6. Conclusion

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