1. Introduction

World has been revolutionized by the modern power system and facing huge power demand since last decade. To cater the increasing demand of electricity, DG plays an important role. DGs are small scale dispersed sources of electric power, placed close to the loads being served.

The voltage instability and power loss phenomenon is one of the most important topic of research related to the power generation system. The high R/X ratio in radial distribution systems contribute more to power losses which has noticeable economic and environmental effects. Installation of optimal sized of DGs at optimal location contributes to utility, improves voltage profile as well as power loss minimization. Optimal placement and sizing of DG are complex, nonlinear problems subjected to different constraints. In this regard, a lot of work has been done using different algorithms and techniques. Capacitors and DG installation are widely used to mitigate these problems. Improvement of voltage profile and power loss reduction are achieved by optimal placement and sizing of capacitors by swarm approach ⁽¹⁾ and Ant Colony Optimization (ACO) algorithm ⁽²⁾. In ⁽³⁾, a comprehensive formula by improved analytical (IA) method is proposed for optimal size and location of DG, but voltage profile improvement and power loss minimization are not considered. Considering load growth mixed Particle Swarm Optimization (PSO) algorithm is used for optimal dispatchable DG allocation ^(4,5) proposed a methodo- logy to solve network reconfiguration problems with placement of DGs simultaneously considering an objective function for minimizing power losses and improvement of voltage profile. A multi objective optimization problem solved using chaos embedded symbiotic organism search algorithm is proposed in ⁽⁶⁾ for determination of DGs. For finding the optimal size and location of DG, optimization methods are used, including Bat-inspired algorithm ⁽⁷⁾ and Binary PSO ⁽⁸⁾. Hybrid algorithm of PSO and ACO is used for optimal reconfiguration in distri- bution system for loss reduction and voltage profile improvement ⁽⁹⁾. Convex probabilistic integration of the wind generation in smart distribution is presented in ⁽¹⁰⁾. Integrated database approach is used for multi objective network reconfiguration of distribution system using discrete optimization techniques ⁽¹¹⁾. In ⁽¹²⁾, distribution feeder reconfiguration is used for power loss minimization of smart grid with electric vehicle. A chaos distributed antenna search algorithm is used considering variation of load and DG ⁽¹³⁾. Dataset approach and water cycle algorithms are also used for distribution network planning enhancement by network reconfiguration and integration of DG ⁽¹⁴⁾.

In this paper, multiple DGs including PVs, fuel cells, micro turbines, gas turbines and wind turbines are classified in three types. This classification is based on their ability of active and reactive power generation. Since conventional load flow methods are not suitable for solving unbalanced radial distribution system problems. Therefore the impact on power and voltage profile is analysed by distribution version of load-flow method. Iterative method is used for optimal placement and sizing of DGs and the effectiveness of multi type DG penetration is shown by percentage power loss reduction.

The rest of this paper is organized as follows. In Section 2, detail explanation of the base system and different DG types are highlighted. Section 3 discusses the particularities related to load flow analysis and power loss calculations; in Section 4, the results and discussions are presented. Finally, in Section 5, conclusions are drawn.

2. Mathematical Problem Formulation

The system design, load-flow analysis, voltage profile, and power calculations based on objective function considering the constraints are explained in this section.

2.1 Load-Flow Analysis

Load-flow analysis is one of the most important factor for planning and operation studies of power system. The conventional load-flow methods, such as Newton-Raphson and fast decoupled load-flow for transmission systems were not preferred for distribution systems because of their low convergence rates ⁽⁹⁾. As the distribution networks are radial with high R/X ratio and unbalanced loads, therefore, it is essential to use the distribution version of the load-flow method.

The objective of load-flow analysis was to calculate the voltages at bus, line currents, and active and reactive power losses in each branch. A simple two bus radial distribution network is considered, as shown in Fig. 1. The number of buses nb and number of branches m are related by nb=m+1, taking R and X as resistance and reactance of the branch, respectively. $P_{LA}$ and $Q_{LA}$ are the active and reactive powers of load connected to bus A. $I_{L}$ is the line current of distribution system. The subscript ‘L’ in $P_{LB}$ and $Q_{LB}$ refers to load connected at bus B.

A flat voltage of 1 p.u is assumed for all the nodes. Load currents were computed using (1)

Fig 1 General two bus distribution network

(1)

$I_{LA(k)}=\dfrac{P_{LA}(k)-j Q_{LA}(k)}{V_{A}^{\ast}(k)}$

where,

$\quad$k = 2, 3, 4, ……, m

$\quad$$P_{LA}$(k)= Active power of load connected to bus A

$\quad$$Q_{LA}$(k)= Reactive power of load connected to bus A

$\quad$The charging current was computed using (2) as stated;

(2)

$I_{CA}(k)=y_{0}(k)\times V_{A}(k)$

As we know that, the summation of load currents and charging currents of all nodes beyond branch n, is equal to branch current I(n) stated as

(3)

$I(n)=\sum_{k=n+1}^{m}I_{LA}(k)+\sum_{k=n+1}^{m}I_{CA}(k)$

A simplified equation of sending end and receiving end voltages, branch current and impedances is given by

(4)

$V(a_{2})=V(a_{1})-I(n)\times Z(n)$

where,

$\quad$n = Branch number

$\quad$$a_{1}$= Sending end of branch n

$\quad$$a_{2}$= Receiving end of branch n

$\quad$Branch impedance : $Z=R+j X$

From the above equations, the total real and reactive power losses of a branch can be shown as

(5)

$P_{loss}=|I(n)|^{2}\times R(n)$

(6)

$Q_{loss}=|I(n)|^{2}\times X(n)$

2.3 Objective Function and Constraints

The objective function of the problem is formulated to minimize the active and reactive power losses in distribution system as

(11)

$\min imize f =\min .(P_{t otal-loss}+j Q_{t otal-loss})$

The constraints followed are as shown in Eqs. (12)-(15).

The active power generated by each DG unit ($P_{DG}$) is limited to be less than or equal to the total active load of the network.

(12)

$P_{DG}\le\sum_{k=1}^{m}P_{L}(k)$

The reactive power generated by each DG unit ($Q_{DG}$) must be less than or equal to the total reactive load of the network.

(13)

$Q_{DG}\le\sum_{k=2}^{m}Q_{L}(k)$

The magnitude of bus voltages are limited by specified minimum and maximum voltage limits.

(14)

$V_{\min}\le |V_{k}|\le V_{\max}$

The thermal capacity (S) of each branch is limited by its maximum thermal capacity.

(15)

$S_{n}\le S_{\max}$

Fig 2 Flow chart of iterative method

3. Mathematical Problem Formulation

4. Results and Discussions

To investigate the impact of multi type DGs penetration of optimal size in optimal location obtained by proposed methodo- logy, standard IEEE-33 bus radial distribution system is con- sidered as a base system using MATLAB programming.

4.1 Test System

The IEEE-33 bus system is shown in Fig. 3. The supplied voltage from bus 1 considered as substation was set as 12.66kV, the total active and reactive power provided by the load buses were 3715 kW and 2300 kVAR, respectively. Other information of the test system are summarized in Table 1.

Fig 3 Single line diagram of IEEE-33 bus system

Table 1 IEEE-33 bus test system

Specifications	IEEE-33 bus system
Buses	33
Lines	32
Feeder	1
Loads	32
Slack bus	Bus 1
PQ buses	Bus 2 ~ Bus 33

4.2 Simulation Results

In this section, the simulation results for optimal placement and sizing of multi type DGs are obtained by using iterative method and further compared against PSO and IA techniques ⁽⁴⁾ as shown in Table 2.

Table 2 Optimal location and sizing of multi type DGs using different techniques

	Type 1	Type 2	Type 3
Iterative Method
Location	6	30	6
Size (KVA)	2592	1314	2556.1+j1710.7
PSO
Location	6	30	6
Size (KVA)	2590.3	1258.3	2550+j1761
IA
Location	6	30	6
Size (KVA)	2490	1240	2470+j1728

4.2.1 Voltage Profile Improvement

Power flow analysis was carried out on IEEE-33 bus distri- bution system as discussed in previous section for without DG and all types of DG units in MATLAB, and their voltage profiles are shown in Fig. 4.

Voltage profiles were improved for all types of DG integration. Type 3 DG penetration shows a remarkable improvement due to its ability of generating both active and reactive powers which reduces the current and thus improves the voltage.

Fig 4 Voltage profile by each type of DG injected in IEEE-33 bus system

4.2.2 Power Loss Minimization

The impact of multiple type DG integration on active power loss and reactive power loss were calculated on each branch. A considerable decrease in power loss values were noticed when type 3 DG was placed in the distribution system, which are shown in Fig. 5 and Fig. 6.

Fig 5 Active power loss (KW) at each branch

Fig 6 Reactive power loss (KVAR) at each branch

The total active power and reactive power losses along with percentage reduction for without DG and each type of DG placed in distribution system are as listed in Table 3 and shown in Fig. 7.

Fig 7 Total power losses and their percentage reduction

The active and reactive power losses for type 3 DG integration are 62.72 kW and 49.48 kW, respectively, which are less than power losses for type 1 and type 2 DG integration. Therefore, the percentage active and reactive power loss reduction is greater for type 3 DG integration due to simultaneous intro- duction of both active and reactive powers.

Table 3 Power losses after and before DG integration

IEEE-33 bus	Ploss (KW)	Qloss (KVAR)	Ploss (%) reduction	Qloss (%) reduction
Without DG	206.72	138.00	-	-
Type 1	105.10	75.87	49.15	45.02
Type 2	145.08	97.68	29.81	29.21
Type 3	62.72	49.48	69.66	64.14

5. Conclusion

The main focus of this study was to investigate the impact of increasing DG penetration on the system. A standard IEEE-33 bus distribution system with three different types of DG units was considered which led us to summarize our conclusion as follow;

(1) The simulation results with DG penetration showed remarkable improvement in system voltage profile.

(2) The obtained outcomes clearly indicated that the ‘Type 3’ DG integration was found to be more effective in mini- mizing the active and reactive power losses to 69.66% and 64.14%, respectively.

In future work, it would be more interesting to enhance the maximum allowable DG penetration known as ‘Hosting Capacity’ of the distribution system via smart inverter and other techniques.