*1.3. Contribution*

The available literature focus on optimal siting and sizing of DGs obtaining a better power system performance. Also, the DG integration of SPV, WTG, and BSS in the distribution system has not been discussed as of authors knowledge. The system RA is discussed individually without analyzing the impact of optimal DG integration. Thus, the two indexes have been implemented for obtaining the optimal location(s) of DG(s) in the selected EDS. Then, a Constriction Factor (CF)-based PSO technique for optimal sizing(s) of DG(s) is presented. Simultaneously, all the parameters considered in this study (as given in Table 1) are not discussed in the existing literature and thus, this work provides completeness in contribution. According to the outcomes of the study, the results are found coherent with those obtained using other techniques that are available in the literature. However, the results can be claimed to be even better since the proposed approach considers all the parameters given in Table 1, including the ELM and the reliability aspects. The comparative analysis for a reduction in electrical power loss and voltage deviation is performed by integrating the WTG, SPV, and BSS in IEEE 33 bus EDS. The results obtained are compared with the results in the literature, as described in Table 2. After obtaining the reduced power loss and improved bus voltages, the reliability assessment is accomplished. The performance analysis is done for the selected distribution system and then the system's RA is carried out with and without the integration of DGs.


**Table 1.** Published work.

**Table 2.** Work related to IEEE 33 bus with multiple DGs.


Though the research on DG siting and sizing is abundant in the literature, the RA in the EDS still prevails as an emerging area of research. Thus, the work mainly focuses on the reliability assessment of an IEEE 33 bus system is carried out in the view of loss minimization technique of WTG, SPV, and BSS integration. For the accomplishment of the mentioned tasks, the research work is performed according to the framed flowchart as shown in Figure 1. Furthermore, the following contributions are highlighted in this work.

**Figure 1.** Workflow of the research work.


The work is further continued to accomplish the mentioned contributions as follows. The problem statement, objective function, and methodologies implemented, including Index-1, Index-2, and CF-based PSO techniques are delineated in Section 2. The basics of EDS reliability assessment is formulated and explained in Section 3. In Section 4, an overview of SPV, WTG, and BSS is explained using mathematical expressions. Furthermore, the results of several cases and scenarios are elucidated with supporting graphical depictions and tables in Section 5. Finally, the conclusions with future scopes are drawn in Section 6. The Appendix A of some important data and figure is provided at the end of the work.

### *1.4. Parameters Considered for the Study*

The parameters considered for the study are described as follows.

• **DG siting and DG sizing**: The determination of bus voltages and the flow of powers is done by an Optimal Power Flow (OPF) method. The optimal siting of DGs is required for ELM during this power flow results. The performance of the power network is affected by an inappropriate location of DG. The IEEE 1547 standards for integration and operation of DG into EDSs are presented in [49].

	- **–** Expected Energy Not Supplied (EENS); MWh per year
	- **–** Average Energy Not Supplied (AENS); MWh per customer per year
	- **–** System Average Interruption Duration Index (SAIDI); hour per customer per year
	- **–** System Average Interruption Frequency Index (SAIFI); failure per customer per year
	- **–** Average System Availability Index (ASAI); pu

The calculations of these five indices are performed using Equations (A1)–(A7) of the Appendix A.2. The reliability indices considered in this work can be used in obtaining other indices, including IEAR, CAIDI and ASUI, as illustrated in Equations (42), (45) and (46c).

**Figure 2.** Models of several DG technologies.

#### **2. Problem Formulation, Objective Function (OF), and Methodology**

The bus voltage and system reliability are the most affecting factors for the EDS when losses are considered. It becomes necessary to improve these two factors by implementing distributed generation (DG) into the EDS. DG siting is one of the favored techniques used in the EDS for the improvement of the system's reliability and bus Voltage Profile (VP), including ELM. The DG location, DG size, DG power factor (pf), DG penetration, and DG type are required for the effective implementation of DGs in the EDS. Simultaneously, it is required to study the mathematical expressions, and modeling of related parameters and DGs integrated into the system. An overview of parameters considered for the ELM and mathematical modeling are elaborated in the upcoming subsections.

#### *2.1. Optimal Location*

Obtaining the optimal location of DGs is crucial part of EDS. To identify the optimal locations, two indexes are used. Index-1 is implemented only for placing the single DG and Index-2 is incorporated for placing more than one DGs in the EDS. Power loss is minimized by using Index-1 for

placing 1DG (viz. Case 1). However, Index-2 provides minimum power loss for multiple DGs (viz. Case 2 and Case 3). These two indicators are represented by Equations (17) and (18), respectively [50,51]. It can be observed from the equation of Index-1 that the large index value depicts the weakest node of the system because the complex power injected at bus *i* is large. It implies that the single DG can be placed at this particular bus. On the other hand, Index-2 shows the voltage stability, which concludes that the reduced values of this index give the weakest bus of the EDS. Table 3 shows the values of both the indexes with corresponding five buses to arrange DG optimally in a given EDS. Therefore, DGs can be placed hierarchically at these buses.


**Table 3.** Values of indexes with corresponding bus number [17,20].

In Figure 3, *Va* and *Vb* are the magnitudes of the voltages at buses *a* and *b*, respectively. *δ<sup>a</sup>* and *δ<sup>b</sup>* are the phase angles of the voltages at buses a and b, respectively. *Zl* and *Yl* are the impedance and admittance of l-line, respectively. *Rl* and *Xl* are the resistance and reactance of a l-line. *Il* is the current in the l-line. The electrical power loss in the l-line is given by (1).

$$\begin{array}{c} \begin{array}{c} V\_a \mathcal{L} \mathcal{S}\_a \\\\ Z\_l = R\_l + jX\_l \\\\ Y\_l = G\_l + jB\_l \\\\ \text{a} \end{array} \end{array} \qquad \begin{array}{c} V\_b \mathcal{L} \mathcal{S}\_b \\\\ \begin{array}{c} \\\\ Y\_{in,b} \\\\ Y\_{in,b} + jQ\_{in,b} \end{array} \end{array}$$

**Figure 3.** General 2-bus system to formulate the line loss and load factor.

$$S\_{LOSS\_l} = (V\_a - V\_b) \times I\_l^\* \tag{1}$$

$$I\_l = (V\_a - V\_b) \times Y\_l \tag{2}$$

Then the bus voltage matrix is formed by using Equation (3) where [*Zbus*] is the network impedance matrix, [*Ibus*] is the bus injection matrix, and *nbus* is the number of total buses in EDS.

$$\mathbb{E}\left[V\_{bus}\right]\_{n\_{bus}\times 1} = \mathbb{E}\left[Z\_{bus}\right]\_{n\_{bus}\times n\_{bus}}\left[I\_{bus}\right]\_{n\_{bus}\times 1} \tag{3}$$

By expanding Equation (3), the node voltages can be obtained by using Equations (4) and (5).

$$V\_a = \sum\_{i=1}^{n\_{bus}} Z\_{ai} \times I\_i \tag{4}$$

$$V\_b = \sum\_{i=1}^{n\_{bus}} Z\_{bi} \times I\_i \tag{5}$$

where *i* is 1,2,. . . ,*nbus*. *Zai*, *Zbi* and *Ii* are the element of impedance matrix that signify the *ath* row and *ith* column, *bth* row and *ith* column, and current injection at bus-i, respectively.

$$\text{Current Injection}, I\_i = \frac{(P\_{in,i} + jQ\_{in,i})^\*}{V\_i^\*} \tag{6}$$

where *Pin*,*<sup>i</sup>* and *jQin*,*<sup>i</sup>* are active power and reactive power injected at bus-i, respectively. *V*<sup>∗</sup> *<sup>i</sup>* is the voltage at bus-i. Now, put (2) and (4) to (6) in (1) then the electrical loss of the line-l is derived as (7).

$$S\_{LOSS,l} = \left[V\_a - V\_b\right] \left(\frac{\sum\_{\text{flux}}^{\text{n}\_{\text{fus}}} (Z\_{a\bar{i}} - Z\_{b\bar{i}}) Y\_I}{V\_{\bar{i}}^\*}\right)^\* \left[P\_{\text{in},i} + jQ\_{\text{in},i}\right] \tag{7}$$

For an electrical system with *nl* number of branch/lines, the line loss is given by (8).

$$\left[B\_{LOSS\_l}\right] = \sum\_{i=1}^{n\_{bus}} \frac{(V\_d - V\_b)(Z\_{ai} - Z\_{bi})^\* Y\_l^\*}{V\_i} S\_{in,i} \tag{8}$$

where *BLOSSl* is line loss, *Sin*,*<sup>i</sup>* is apparent power injected at bus-i, l is 1 to *nl*.

$$\mathbb{I}[B\_{LOSS\_I}] = \sum\_{i=1}^{n\_{bus}} \mathbb{I}[LF\_{li}] \mathbb{I}[S\_{in,i}] \tag{9}$$

$$LF\_{li} = \sum\_{i=1}^{n\_{lus}} \frac{(V\_a - V\_b)(Z\_{ai} - Z\_{bi})^\* Y\_l^\*}{V\_i} \tag{10}$$

$$LF\_{li} = \begin{cases} \text{non-zero}, & \text{if } l \text{-line is in the path of bus-i} \\ 0, & \text{Else} \end{cases} \tag{11}$$

where load factor (LF) is given by (*Va*−*Vb*)(*Zai*−*Zbi*) ∗*Y*∗ *l Vi* . *LFli* is load factor of the *lth* line due to the *ith* bus injection (it is non-zero if *lth* line is in the path of *ith* bus else zero) as described in (11). For example, a 6-bus distribution is taken for explanation as shown in Figure 4 and a general branch loss formula is derived as (12).

**Figure 4.** 6-bus EDS for Index-1 calculation.

$$
\begin{bmatrix} B\_{LOSS\_1} \\ B\_{LOSS\_2} \\ B\_{LOSS\_3} \\ B\_{LOSS\_4} \\ B\_{LOSS\_5} \end{bmatrix}\_{5 \times 1} = \begin{bmatrix} LF\_{11} & LF\_{12} & LF\_{13} & LF\_{14} & LF\_{15} & LF\_{16} \\ LF\_{21} & LF\_{22} & LF\_{23} & LF\_{24} & LF\_{25} & LF\_{26} \\ LF\_{31} & LF\_{32} & LF\_{33} & LF\_{34} & LF\_{35} & LF\_{36} \\ LF\_{41} & LF\_{42} & LF\_{43} & LF\_{44} & LF\_{45} & LF\_{46} \\ LF\_{51} & LF\_{52} & LF\_{53} & LF\_{54} & LF\_{55} & LF\_{56} \end{bmatrix}\_{5 \times 6} \times \begin{bmatrix} S\_{in1} \\ S\_{in1} \\ S\_{in2} \\ S\_{in4} \\ S\_{in5} \\ S\_{in6} \end{bmatrix}\_{6 \times 1} \tag{12}
$$

$$\|B\_{LOSS}M\|\_{5\times1} = \|LFM\|\_{5\times6} \times \|S\_{in}M\|\_{6\times1} \tag{13}$$

where [*BLOSSM*] is branch/line loss matrix, [*LFM*] is the load factor matrix, [*SinM*] is complex power injection matrix. Equation (13) is reduced according to the Figure 4 where power injection at all the buses except the source bus are available.

$$
\begin{bmatrix} B\_{LOSS\_1} \\ B\_{LOSS\_2} \\ B\_{LOSS\_3} \\ B\_{LOSS\_4} \\ B\_{LOSS\_5} \end{bmatrix}\_{5 \times 1} = \begin{bmatrix} 0 & LF\_{12} & LF\_{13} & LF\_{14} & LF\_{15} & LF\_{16} \\ 0 & 0 & LF\_{23} & LF\_{24} & LF\_{25} & LF\_{26} \\ 0 & 0 & 0 & LF\_{34} & LF\_{35} & 0 \\ 0 & 0 & 0 & 0 & LF\_{45} & 0 \\ 0 & 0 & 0 & 0 & 0 & LF\_{56} \end{bmatrix}\_{5 \times 6} \times \begin{bmatrix} S\_{in\_1} \\ S\_{in\_2} \\ S\_{in\_3} \\ S\_{in\_4} \\ S\_{in\_6} \end{bmatrix}\_{6 \times 1} \tag{14}
$$

$$\mathcal{A}\_{i} = \sum\_{l=1}^{n\_{l}} L F\_{li} \tag{15}$$

The calculation of effective power injections is done as given in (16).

$$\begin{array}{c} S\_{eff,\delta} = S\_{lin,\delta} \\ S\_{eff,\emptyset} = S\_{lin,\emptyset} \\ S\_{eff,\emptyset} = S\_{lin,\emptyset} + S\_{eff,\emptyset} \\ S\_{eff,\emptyset} = S\_{in,3} + S\_{eff,\emptyset} + S\_{eff,\emptyset} \\ S\_{eff,2} = S\_{in,2} + S\_{eff,3} \\ S\_{eff,1} = S\_{lin,1} + S\_{eff,2} \end{array} \tag{16}$$

Equation (17) shows the final equation for the calculation of Index-1. The index is implemented for attaining the optimal position of one renewable energy source as DG. In Equation (15), |*Ai*| is fully dependent on LF values of all the branches (or lines) connected between bus and the source bus (main station). The closeness of the *ith* bus from the source bus can be observed in the *LFli* as guided in Equation (10). If the *ith* bus is not near, the number of lines between *ith* bus and source bus is being plenty and the corresponding *Zai*, *Zbi*, and *Yl* parameters will account in the electrical loss component. Furthermore, if the node voltage is high, the value of *LFli* will be small and vice-versa as observed in the derived equation. The equation of Index-1 is also accounted for the effective complex power supplied by the *ith* bus. The Index-1 will be high only when both the terms are high in (17). Thus, the value of Index-1 represents its main contribution in the total electrical loss and hence, in finding the optimal siting of one RES.

$$(Index - 1)\_i = |A\_i| \times |S\_{in\_{eff\_i}}| \tag{17}$$

*Sineffi* is the effective injection of complex power, which is the sum of injected powers from other buses connected to *ith* bus as shown in Figure 4.

$$\left(\text{Index} - 2\right)\_{i+1} = |V\_i|^4 - 4(P\_{i+1}X\_j - Q\_{i+1}R\_j)^2 - 4(P\_{i+1}R\_j - Q\_{i+1}X\_j)|V\_i|^2 \tag{18}$$

where *j* is branch number, *Vi* is sending bus voltage, *Pi*+1 and *Qi*+1 are the Active Power (AP) and Reactive Power (RP) at the receiving end bus, respectively. *Rj* and *Xj* are the resistance and reactance between sending and receiving end bus, respectively.

#### *2.2. Power Balance*

The AP and RP balance expressions are shown in Equations (19) and (20).

$$P\_{\text{net}\_i} = P\_{d\_{\overline{\mathcal{S}}i}} - P\_{d \text{cm}\_i} - V\_i \sum\_{j=1}^{N\_{\text{bus}}} V\_j Y\_{i,j} \text{cos} \{\delta\_i - \delta\_j - \theta\_i + \theta\_j\} \tag{19}$$

$$Q\_{\rm net} = Q\_{d\xi i} - Q\_{d\rm em\_i} - V\_i \sum\_{j=1}^{N\_{\rm bus}} V\_j Y\_{i,j} \sin(\delta\_i - \delta\_j - \theta\_i + \theta\_j) \tag{20}$$

where *Pneti* = 0 and *Qneti* = 0 are the net AP and RP at i-bus, respectively. *Pdgi* and *Qdgi* represent DG AP and RP at i-bus, respectively. Active and reactive load demands are mentioned by *Pdemi* and *Qdemi* , respectively. *Vj* is the bus voltage at j-bus, *Yi*,*<sup>j</sup>* is the branch admittance between i, j-buses, *δ<sup>i</sup>* and *δ<sup>j</sup>* represent the phase angles of i-bus and j-bus voltages, respectively. (*θ<sup>i</sup>* − *θj*) are the impedance angle of branch connected between i and j-buses.

#### *2.3. Objective Function (OF)*

In this research the OF is considered to be APL minimization in the EDS. The reliability indices are then evaluated by fixing the optimal location and size of the DGs. The OF of the problem is given in Equation (21).

#### 2.3.1. Active Power Loss (APL)

The minimization of APL occurred in EDS is the OF considered. The primary aim of the OPF technique is to minimize the system APL as given as Equation (21).

$$\text{min}AP\_{loss} = \sum\_{i=1}^{N\_{\text{bus}}} \sum\_{j=1}^{N\_{\text{bus}}} \mathbb{C}\_{1\_{ij}} (P\_{\text{real}\_i} P\_{\text{real}\_j} + Q\_{\text{real}\_i} Q\_{\text{real}\_j}) + \mathbb{C}\_{2\_{ij}} (Q\_{\text{real}\_i} P\_{\text{real}\_j} - P\_{\text{real}\_i} Q\_{\text{real}\_j}) \tag{21}$$

where *Preali* , *Prealj* , *Qreali* , *Qrealj* are the AP and RP at *i* and *j*-buses, respectively. *Nbus* = number of buses or nodes, *C*1*ij* and *C*2*ij* are defined as follows.

$$\mathbf{C}\_{1\_{ij}} = \frac{R\_{i\dot{j}}}{V\_i V\_{\dot{j}}} \cos(\delta\_i - \delta\_{\dot{j}}) \tag{22a}$$

$$C\_{2\_{ij}} = \frac{R\_{i\dot{j}}}{V\_i V\_{\dot{j}}} \sin(\delta\_i - \delta\_{\dot{j}}) \tag{22b}$$

where *Vi*, *δ<sup>i</sup>* and *Vj*, *δ<sup>j</sup>* are the voltages and corresponding angles at *ith* and *jth* buses, respectively, *Rij* = resistance of a branch between i and j-buses.

#### 2.3.2. Reactive Power Loss (RPL)

The availability of RP ensures the AP transmission from source to load. Voltage stability margin or bus voltages are also dependent on this RP support. The RPL is obtained at different pf of DG using Equation (23).

$$RRP\_{loss} = \sum\_{i=1}^{N\_{bus}} Q\_{\mathcal{S}^{env}\_i} - \sum\_{i=1}^{N\_{bus}} Q\_{dem\_i} \tag{23}$$

where *Qgeni* and *Qdemi* are the RP generation and demand at the *ith* bus (including the slack bus), respectively. *Qdemi* = RP demand at the *ith* bus.

### 2.3.3. Reliability Indices

The indices are assessed for divergent DG reliability data by fixing the site and size of DGs. Furthermore, the reliability improvement of distribution network has been accomplished by integrating one DG and multiple DGs in the EDS. Several reliability indices exist to observe the system's reliability such as EENS, AENS, SAIDI, SAIFI, and ASAI which are also used in this study to analyze the reliability improvement. The indices of the network reliability are dependent function of failure rate (*λp*) and repair time (RT) as given in Equation (24) [20,23,52].

$$\text{Reliability Indices} = f(\lambda\_{p\prime}RT) \tag{24}$$
