Twelve International Conference on Thermal Engineering: Theory and Applications February 23-26, 2019, Gandhinagar, India

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Sizing and Placement of Single Distribution Generator in Radial Distribution Network: An Analytical Study

Gargi Trivedi, Anilkumar Markana

Pandit Deendayal Petroleum University, Department of Electrical Engineering, Gandhinagar, India.

Abstract

There are several advantages of DG allocation in the power distribution systems. These advantages include decreasing in power loss and voltage profile improvement. Such benefits can be achieved and enhanced if DGs are optimally sized and located in the distribution system. In this work, an analytical way of placing and sizing of single DG in radial distribution network is proposed to make radial distribution network more reliable and efficient by improving node voltage and make system operation more economic by decreasing the power loss. The optimization index includes minimization of active power losses by keeping the voltage profiles within specified limit in the network. A 33 node radial distribution system is considered as a case study to demonstrate the effectiveness of this method. In modern load growth scenario uncertainty of load and generation model shows that reduction of power loss in distribution system is possible and all node voltages variation can be achieved within the required limit without violating the thermal limit of the system. Keywords: Radial Distribution Network, Distributed Generators, Forward/Backward Sweep Method, IEEE 33 Bus Network

1. Introduction

In power systems power losses are the key point of

consideration as it has its own worst effect on the system operations [1]. Power loss has the huge impact on network stability and power system efficiency. The power system comprises of Generation, Transmission and Distribution Networks. Among these three, majority of the total losses arise from the distribution system. To deliver the power with minimum loss, there are approaches available by power utilities as under [1-2]:

• Strengthening of feeders. • Reactive power compensation. • High voltage distribution networks. • Grading of conductor. • Allocation of distributed generators.

Smart grid is the current technology and plays the role of back bone of electrical power network. Distribution generators are indeed inherent components of smart grid system. But the sizing and optimal placement of DG’s are also plays an important role as it is supposed to supply 40% of demand load in the distribution network [2]. These DGs helps in enhancing the security, reliability and quality of electricity supply by providing active power. Smart grid is the concept which will be the change in future technology which will have the characteristic of providing transmission and distribution network with higher efficiency. Loss minimization in the power transport networks will also have advantage with the reduction in air pollutant and greenhouse gasses [12]. In the distribution network, due to the coordination of DGs there will be less requirement of load currents form the grid. This will result into fewer losses in the distribution network as less amount of current will pass through the

resistance in the power line. These losses can be more reduced by placing DGs at an appropriate place in the network.

Numerous methods such Gauss-Seidel, Newton-Raphson are generally appeared for studying the load flow of transmission networks [1]. Placement of DG with appropriate size and location are the major impactful factors for minimize the loss [13]. Forward/Backward Sweep Method (FBS) is used in this work to study its load flow and hence to calculate power losses and voltage profile [6]. Conventional load flow method should change to the new modified method as the conventional passive distribution network is changing into the active distribution network it is justified in [7]. Newton Raphson (NR) Method has its own limitations for calculating power losses in distribution where FBS is effective in that way [8]. Comparison of these methods NR and FBS are cited in [9]. Detailed calculation of power loss by FBS method is described in [10].

2. Calculation of Power Losses with and without Distributed Generators

Load flow studies can be achieved using several

methods, among them Newton Raphson (NR) is the most popular. But the difficulty with NR method is that it is inaccurate when it comes to the distribution networks. However, for the transmission networks it is still reliable and efficient. So, for the distribution network, a robust method namely Forward and Backward Sweep (FBS) method is applied. In addition, FBS method is faster and less computationally intensive compared to NR method as it doesn’t require Jacobeans to be computed. In this work the power losses in the distribution network are calculated using FBS method. It follows two steps:

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• Backward Sweep Calculation • Forward Sweep Calculation

2.1. Backward Sweep

In this step, the load current of each node in a distribution network (having N number of nodes) is determined as:

𝐼 𝐿 𝑚 =

𝑃𝐿 𝑚 ± 𝑗𝑄𝐿 𝑚

𝑉 ∗(m)

(1)

where, 𝑃𝐿(𝑚) and 𝑄𝐿(𝑚) represents the active and

reactive power demand at node 𝑚 and the over bar

notation (𝑥 ) indicates the phasor quantities, such as 𝐼 𝐿,

𝑉 . The current in each branch of the network is computed using Eq.(2)

𝐼 𝐿 𝑚𝑛 = 𝐼 𝐿 𝑛 + 𝐼 𝐿 𝑚 m∈𝛤

(2)

where, 𝑛 and 𝑚 represent the receiving and sending end

nodes. Set of 𝛤 is defining all nodes beyond the node 𝑛.

2.2. Forward Sweep

This step is used once the backward sweep step calculates the load current at each node. The forward sweep step determines the voltage at each node of a distribution network and is given by

𝑉 𝑛 = 𝑉 𝑛 − 𝐼 𝑚𝑛 *𝑍(𝑚𝑛) (3)

where, 𝑍 mn is the impedance of branch 𝑚𝑛.

2.3. BIBC and BCBV Matrix Calculations

The Forward/Backward Sweep method requires the

calculation of BIBC and BCBV matrices. Fig. 1 shows the procedures involved in FBS method. During the Backward sweep step, the Node-Injection to Branch Current Matrix (BIBC) is calculated and similarly, during Forward sweep step, the Branch-Current to Node Voltage Matrix (BCBV) is obtained.

Fig. 1. Forward/Backward Sweep Calculation Steps [9]

For the ease of readers to understand, how these matrices are calculated, we consider a 6 bus radial distribution system as shown in Fig. 2. The power injections can be converted into the equivalent current injections using Eq. (1).

Fig. 2. 6 bus radial distribution system

By applying Kirchhoff’s Current Law (KCL) to the network in Fig. 2, the branch currents B5, B3 and B1 can be expressed as,

𝐵5 = 𝐼6

𝐵3 = 𝐼4 + 𝐼5

𝐵1 = 𝐼2 + 𝐼3 + 𝐼4 + 𝐼5 + 𝐼6

(4)

Eq. (4), can further represented in compact matrix

form and hence, the Bus-Injection to Branch-Current (BIBC) can be obtained as

𝐵1

𝐵2

𝐵3

𝐵4

𝐵5

=

1 10 1

1 1 11 1 1

0 000

00

1 1 000

1 00 1

𝐼2

𝐼3

𝐼4

𝐼5

𝐼6

𝐵 = 𝐵𝐼𝐵𝐶 ∗ 𝐼

Now applying Kirchhoff’s Voltage Law (KVL) to the network shown in Fig. 2, relation between bus voltage and branch current can be expressed as

𝑉2 = 𝑉1 − 𝐵1 ∗ 𝑍12

𝑉3 = 𝑉2 − 𝐵2 ∗ 𝑍23

𝑉4 = 𝑉3 − 𝐵3 ∗ 𝑍34

(5)

By using Eq. (4) and (5) we can write the expression for voltage at bus 4

𝑉4 = 𝑉1 − 𝐵1 ∗ 𝑍12 − 𝐵2 ∗ 𝑍23 − 𝐵3 ∗ 𝑍34 (6)

Eq. (6) shows that the bus voltage can be expressed

as a function of the currents of the branches, line impedance and voltage at station node. Similar procedures can be utilized for other buses, and the Branch-Current to Bus Voltage (BCBV) matrix can be derived as

𝑉1

𝑉1

𝑉1

𝑉1

𝑉1

𝑉2

𝑉3

𝑉4

𝑉5

𝑉6

=

𝑍12 0𝑍12 𝑍23

0 0 00 0 0

𝑍12 𝑍23

𝑍12

𝑍12

𝑍23

𝑍23

1 0 000

1 00 1

𝐵1

𝐵2

𝐵3

𝐵4

𝐵5

𝑉 = 𝐵𝐶𝐵𝑉 ∗ 𝐵

The above BCBV matrix shows the relations between the bus voltages and branch currents.

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2.4. Power Loss Calculation

The single line diagram of the general distribution system is as shown in Fig. 3.

Fig. 3.Single line diagram of general distribution system [8]

In general, at 𝑘th

node, the active and reactive power

can be calculated recursively as

𝑃𝑘+1 = 𝑃𝑘 − 𝑃𝐿𝑜𝑠𝑠 ,𝑘 − 𝑃𝐿,𝑘+1 (7)

𝑄𝑘+1 = 𝑄𝑘 − 𝑄𝐿𝑜𝑠𝑠 ,𝑘 − 𝑄𝐿,𝑘+1 (8)

where, 𝑃𝑘 is real power flowing out of bus

𝑄𝑘 is reactive power flowing out of bus

𝑃𝐿,𝑘+1 is real load power at bus 𝑘 + 1

𝑄𝐿,𝑘+1 is reactive load power at bus 𝑘 + 1

Therefore, power loss in the line section connecting 𝑘

th

and 𝑘 + 1th

node, is computed as

𝑃𝐿𝑜𝑠𝑠 (𝑘 ,𝑘+1) = 𝑅𝑘𝑃𝑘

2+𝑄𝑘2

𝑉𝑘2 (9)

𝑄𝐿𝑜𝑠𝑠(𝑘 ,𝑘+1) = 𝑋𝑘

𝑃𝑘2+𝑄𝑘

2

𝑉𝑘2 (10)

where,

𝑃𝐿𝑜𝑠𝑠 (𝑘 ,𝑘+1) is real power loss in the line section

connecting buses 𝑘 and𝑘 + 1

𝑄𝐿𝑜𝑠𝑠 (𝑘 ,𝑘+1)is reactive power loss in the line section

connecting buses 𝑘 and 𝑘 + 1

3. Case study – IEEE 33 Bus Radial Distribution Network

In this work, we consider standard IEEE 33 bus

radial distribution network to test our analytical method for the placement of DG in order to reduce the power losses. Fig. 4 shows the single line diagram of 33 bus distribution system. The test system is having the total load of 3.72 MW and 2.3 MVAr. The standard line and bus data for this test system is taken from [8]. Note that bus no. 1 is considered as slack bus.

The test system, IEEE 33 bus radial distribution system is simulated using MATLAB R2015a environment with the help of FBS method, discussed previously. Voltage profile at each node is obtained as shown in Fig. 5. Also, the total power loss in the network is reported as 221KW.

Fig. 4. Single line diagram of 33 bus distribution test

system [6]

3.1. Placement of DG

As discussed previously, the power loss in the

distribution network can be drastically reduced with the inception of distributed generator in the network. We propose an analytical way of placing the DG in the network along with its sizing. We assume that all buses are available for the placements of DGs except the bus no. 1, which is a slack bus.

Note that total load on the considered test system is

3.71 MW. Therefore, maximum DG size cannot be greater than the total load of the system. We simulated the system, with the placement of single DG at individual bus locations. Starting from bus no. 2, we place minimum DG size of 0.1 MW with the increment of 0.1 MW till 3.7 MW size. We calculated the power loss for this system when DG is placed bus no. 2. It is found that single DG size of 3.7 MW at bus no. 2 gives minimum power loss of 201 KW. We continued this simulation for remaining buses as well, till bus no. 33. Fig. 6 shows the simulation results of optimal DG size where the losses are minimum for each bus from bus no. 2 to bus no. 33. Correspondingly, Fig. 7 shows the minimum power loss for a particular DG placement at each bus. As can be seen from Fig. 6 and Fig. 7 that DG size of 2.49 MW at bus no. 6, results into minimum power loss of 111.1709 KW. The entire simulation was done considering the system operating at unity power factor.

Similarly, Fig. 8 and Fig. 9 show the simulation

results, considering the system operating with 0.8225 power factor. The power loss is still reduced to 74.9 KW, when DG of size 2.5 MW is placed at bus no. 6. Fig. 5 shows the voltage profile at each node when DG is placed at bus no. 6. It is observed from Fig. 5 that voltage stability is maintained throughout the network.

Fig. 5. Voltage profile without DG placement

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Fig. 6. Sizing of DG at each bus with unity pf

Fig. 7. Power loss at each bus when single DG is placed respectively, operating with unity pf

Fig. 8. Sizing of DG at each bus with 0.8225 pf

Fig. 9. Power loss at each bus when single DG is placed respectively, operating with pf of 0.8225

7. Conclusion and Future Work

The reduction in the power loss in radial distribution network is observed when distributed generators are placed at appropriate location in the system. Analytical study shows that in IEEE 33 bus radial distribution network placing DGs, size of 2.49 MW and 2.5 MW at bus no. 6 results into the minimum power loss in the network when system operates with unity and 0.8225 power factor, respectively. In future, authors also wish to place multiple DGs in the distribution network. These DGs can be optimally placed and their sizing can be optimally obtained through optimization techniques along with maintaining the voltage profile at each node.

References

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