Optimal Voltage Regulator Placement

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02 Nov 2017

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6.1 INTRODUCTION

The power distribution network is constantly being faced with an ever growing load demand; this increasing load has resulted in increased burden on the system and reduction in voltages. The radial distribution network also has a typical feature that the voltages at buses reduce from substation to tail end. This decrease in voltage is mainly due to insufficient amount of reactive power. Even in certain industrial areas under critical loading, it may lead to voltage collapse. Thus to improve the voltage profile and to avoid voltage collapse, reactive compensation is to be provided.

It is well known that losses in a distribution system are significantly high compared to that in a transmission system. The need of improving the overall efficiency of power delivery has forced the power utilities to reduce the losses at distribution level. Many arrangements can be worked out to reduce these losses like network reconfiguration, shunt capacitor placements etc. Installation of voltage regulators on distribution network will help in reducing energy losses, peak demand losses, improvement in the system voltage profile, system stability and power factor of the system. However, to achieve these objectives, keeping in mind the overall economy, the size and location of voltage regulators should be decided. Thus, optimal placement of voltage regulator has been considered for loss reduction and voltage improvement in radial distribution systems.

Voltage regulator or Automatic Voltage Booster (AVB) is essentially an auto transformer consisting of a primary or existing winding connected in parallel with the circuit and a second winding with taps connected in series with the circuit. Taps of series winding are connected to an automatic tap changing mechanism.

When a booster is installed at a bus, it causes a sudden voltage rise at its point of location and improves the voltage at the buses beyond the location of AVB. The percentage of voltage improvement is equal to the percentage setting of boost of AVB. The increase in voltage in turn causes the reduction in losses in the lines beyond the location of AVB. Multiple units can also be installed in series to the feeder to maintain the voltage within the limits and to reduce the line losses.

In recent years, considerable attention has been focused in the selection of voltage regulators in a radial distribution system to reduce the losses and improve the voltage which in turn reduces the capital investment involved and provides a better quality supply to the consumers. Reactive power control and voltage control of RDS using shunt capacitors and voltage regulators are reported in [12-14]. They have proposed an analytical method for the application of voltage regulators with the integrated control of voltage and reactive power (volt/var).

Safigianni and Salis [59] have proposed a method to find the optimal number and placement of voltage regulators in radial distribution system using sequential algorithm but they have not considered the effect of load variation on selection of voltage regulators. This method works on the principle of "Pull-Back-regulators", which is basically a recursive method and is not a direct solution to find optimal number and location of VRs. Souza et al. [84, 85] have presented a method to find the size and location of voltage regulators in radial distribution system using genetic algorithm by considering the search space as a discrete and finite group.

Many authors [101,113,125] have reported different methods using plant growth simulation, evolutionary programming and particle swarm optimization to find the optimal location and size of voltage regulators in radial distribution system. Ganesh et al. [126] also have presented a method of voltage regulator placement in unbalanced radial distribution systems using genetic algorithm. Rama Rao and Sivanagaraju [129] have proposed a method to place the voltage regulator and to find its tap position using Plant growth simulation algorithm.

Recently, many researchers have reported on placement of voltage regulators for radial distribution systems either using analytical method or evolution techniques such as genetic algorithm, particle swarm optimization etc. In this chapter, a method is proposed to determine optimal location of voltage regulators using fuzzy expert system and the tap setting of voltage regulator using an analytical method.

The objective function and the constraint for the optimization problem are presented in Section 6.2. The problem formulation for placement of VR and calculation of its tap position is explained in Section 6.3. Identification of sensitive bus for VR placement using Back Tracking algorithm is described in Section 6.4. In Section 6.5, identification of sensitive bus using FES and steps of the algorithm of the proposed method is explained. The effectiveness of proposed methods are tested with different examples of distribution system and the results obtained are compared with the results of existing methods are presented in Section 6.6.

6.2 MATHEMATICAL FORMULATION

The problem of determination of optimal number and location of Voltage Regulator (VR) can be formulated as an optimization problem. The objective function is to maximize the net savings function (F) is expressed as

… (6.1)

where

Plr = Reduction in power losses due to installation of VR

= (Power loss before installation of VR - Power loss after installation of VR)

Ke = Cost of energy in `./kWh

Lsf = Loss factor = 0.8 × (LF)2+ 0.2×LF

LF = Load Factor

= Number of voltage regulators

KVR = Capital cost of each voltage regulator

λ = the rate of annual depreciation and interest charges for VR

= Installation cost of VR. (Generally it is taken as percentage of cost of VR)

6.2.1 Constraint

The objective function is subjected to the following constraint

The voltage at each bus should lie within the voltage limits.

Vmin.≤Vi≤Vmax. i=1,2, …..no. of buses

6.3 PROBLEM FORMULATION OF VOLTAGE REGULATOR PLACEMENT

In order to maintain the voltage profile and to reduce the power losses voltage regulators are installed in the distribution systems.

VR provides 10% change of voltage.

It boosts voltage in four steps of 2.5% each or16 steps of 0.625% each.

It has line drop compensation to maintain constant voltage at its location.

KVA rating = (rated voltage × %boost of VR× rated current)/100

It causes sudden voltage rise in discrete steps at its location leading to better voltage profile and reduction in losses.

The VR problem consists of two sub problems, that of optimal placement and optimal choice of tap setting. The first sub problem determines the location and number of VRs to be placed and the second sub problem decides the tap positions of VR. Two methods have been proposed to obtain the optimal location of voltage regulators in radial distribution systems.

Back Tracking algorithm

Using Fuzzy Expert System

The tap positions of VR are calculated using an analytical method. The procedural steps of the above two methods are explained in Sections 6.4 and 6.5 respectively.

6.3.1 SELECTION OF TAP POSITION OF VR'S

By finding the optimal number and location of VRs then tap positions of VR is to be determined as follows.

In general, VR position at bus ‘i’ can be calculated as

… (6.2)

where

tap = tap position of VR

Vi1 = the voltage at bus ‘i’ after installation of VR

Vi = the voltage at bus ‘i’ before installation of VR

Vrated = Rated voltage

‘+’/‘-’for boosting/bucking of voltage.

Tap position (tap) can be calculated by comparing voltages obtained prior to installation of VR with the lower and upper limits of voltage.

The bus voltages are computed by load flow analysis for every change in tap setting of VR’s, till all bus voltages are within the specified limits. Then obtain the net savings, with above tap settings for VR’s.

6.4 BACK TRACKING ALGORITHM

In this section, the analytical method named as Back Tracking Algorithm is explained to find the optimal number and location of voltage regulators in radial distribution system using Figs. 6.1 (a) and (b).

Let the voltage regulators are initially located at buses 8, 11, 13 and 18 as shown in Fig. 6.1(a). It is proposed to reduce the number of VRs in a radial distribution system by shifting the VR’s to the junction of laterals (such as from buses 11 and 13 to bus 10) and observe the voltage profile. If it satisfies the voltage constraint, then this will be taken as optimal location for the single VR at bus 10 instead of two VRs at buses 11 and 13 (shown in Fig. 6.1(b)). This procedure is repeated starting from the tail end buses towards the source bus and find the optimal number and location of VRs.

8 9

1 6 7

5 11

2 3 10 12

4

13 14 15

16 18

17

19

Fig. 6.1(a) 19 bus RDS before shifting of Voltage regulators

8 9

1 6 7

5 11

2 3 10 12

4

13 14 15

16 18

17

19

Fig. 6.1(b) 19 bus RDS after shifting of Voltage regulators

After finding the optimal number and location of voltage regulators, the tap setting of voltage regulators can be calculated using Eqn. (6.2).

The steps of the algorithm for finding optimal number and location of voltage regulators are as follows:

6.4.1 Steps for optimal voltage regulator placement in RDS using back tracking algorithm:

Step 1: Read line and load data.

Step 2: Conduct load flow analysis for the system and compute the voltages at

each bus, real and reactive power losses of the system.

Step 3: Identify the buses, which have violation of voltage limits.

Step 4: Obtain optimal number of VRs and location of VRs by using back

tracking algorithm.

Step 5: Obtain the optimal tap position of VR using Eqn. (6.2), so that the voltage

is within the specified limits.

Step 6: Again run the load flows with VR, then compute voltages at all buses,

real and reactive power losses.

Step 7: Determine the reduction in power loss and net saving using objective

function (Eqn. (6.1)).

Step 8: Print the results.

Read System line and load data, base kV and kVA, iteration count (IC) =1and tolerance (ε) = 0.0001

Start

Perform load flows and calculate voltage at each bus, real and reactive power losses. Identify the buses, which have violation of voltage limits.

Obtain optimal number of VRs and location of VRs by using back tracking algorithm

Obtain optimal tap position of VR using Eqn. (6.2), so that the voltages is within the specified limits

Yes

No

Perform load flow with voltage regulator

Check for convergence

IC=IC+1

Compute bus voltages, real and reactive power losses

Stop

Compute bus voltages, real and reactive power losses. Also calculate objective function using Eqn. (6.1)

6.4.2 Flow chart for optimal voltage regulator placement using back tracking algorithm:

Fig. 6.2 Flow chart of optimal voltage regulator placement using back tracking

algorithm

6.5 OPTIMAL VOLTAGE REGULATOR PLACEMENT USING FUZZY LOGIC

The fuzzy logic is used to identify the optimal location to place the Voltage Regulator in a radial distribution system under normal or varying load conditions so as to minimize the losses while keeping the voltage at buses within the specified limits.

For the voltage regulator placement problem, rules are defined for Fuzzy Expert System (FES) which determine the suitability of a bus for placement of voltage regulator and are explained in Section 5.3.For determining the suitability of a bus for placement of voltage regulator, a set of multiple antecedent fuzzy rules have been established which are as given in Table 5.1, as discussed in Chapter 5.

The range of power loss indices varies from 0 to 1, the voltage range varies from 0.9 to 1.1p.u. and the output [Voltage Regulator Suitability Index (VRSI)] range varies from 0 to 1. These variables are described by five membership functions of high, high-medium/normal, medium/normal, low-medium/normal and low. The membership functions of power loss indices, voltage and output are already explained in Section 5.3.2 with the help of Figs. 5.1 to 5.3.

6.5.1 Algorithm for optimal voltage regulator placement in RDS using FES:

Step 1: Read line and load data of RDS.

Step 2: Run load flows for the system and compute the voltages at each bus, real and reactive power losses of the system.

Step 3: Install the voltage regulator at every bus and compute the total real power loss of the system in each case and calculate the power loss indices using Eqn. (5.2).

Step 4: The power-loss indices and the bus voltages are the inputs to the fuzzy expert system and the output from FES is Voltage Regulator Suitability Index (VRSI).

Step 5: Identify the buses at which the Voltage Regulator Suitability Index (VRSI) is having the highest value, which gives the optimal location for placement of voltage regulators.

Step 6: Obtain the optimal tap position of VR using Eqn. (6.2), so that the voltage is

within the specified limits.

Step 7: Run the load flow with VR, then compute voltages at all buses, real and

reactive power losses.

Step 8: Determine the reduction in power loss and net saving by using objective

function (Eqn. (6.1)).

Step 9: Print the results.

Step 10: Stop.

Yes

No

Read Distribution System line and load data, base kV and kVA, iteration count (IC) =1and tolerance (ε) = 0.0001

Start

Perform load flows and calculate voltage at each bus, real and reactive power losses

Calculate the loss reduction by running load flow by placing voltage regulator at each bus, considering one bus at a time

Calculate power loss reduction indices, PLI using Eqn. (5.2)

Calculate optimal tap position of VR using Eqns. (6.2), so that voltage is within limits

Select the optimal location for the voltage regulator placement is selected by considering the maximum value of VRSI

Obtain voltage regulator suitability index, VRSI from the FES by providing PLI and bus voltages as inputs to the FES

Stop

Compute voltages, power flows, real and reactive power losses, objective function and Print the results

Perform load flow with voltage regulator

Check for convergence

IC=IC+1

Compute bus voltages, real and reactive power losses

6.5.2 Flow chart for optimal voltage regulator placement using FES:

Fig. 6.3 Flow chart of optimal voltage regulator placement using FES

6.6 ILLUSTRATIVE EXAMPLES

The above proposed methods are tested with three different radial distribution systems having 15, 33 and 69 buses.

6.6.1 Example - 1

Consider a 15 bus system whose single line diagram is shown in fig. 2.3 and data as given in Appendix A (Table A.1). The total real power loss and minimum bus voltage are 61.7933 kW and 0.9445 p.u. before employing VRs. Using Back tracking algorithm the optimal number, location and tap setting of VR obtained is given in Table 6.1. The Voltage Regulator Suitability Index, optimal location and tap setting of voltage regulator obtained using FES are given in Table 6.2. The voltage profile of the system before and after placing of voltage regulator is given in Table 6.3. The minimum voltage is improved from 0.9445 p.u. to 0.9561 p.u. with back tracking algorithm. The improvement in voltage regulation is 1.16%. Using FES, the minimum voltage is improved from 0.9445 p.u. to 0.9977p.u. The improvement in voltage regulation is 5.32%. Comparison of results of both proposed methods are given Table 6.4 for 15 bus RDS.

Table 6.1 Optimal bus number and tap setting of VR using Back Tracking

algorithm for 15 bus system

Bus No. to place VR

Tap setting of Voltage regulator in p.u.

Type of Tap position

3

0.0875 (14 steps)

Boost

Table 6.2 VRSI and tap setting of voltage regulator using FES for 15 bus system

Bus No. to place VR

Voltage Regulator Suitability Index in FES

Tap setting of Voltage regulator in p.u. using FES

Type of Tap position

2

0.50

0.075 (12 steps)

Boost

Table 6.3 Voltage Profile without and with Voltage Regulators

Bus No.

Bus Voltages before VR placement

Bus Voltages with Voltage regulator at bus 3 (Back Tracking Algorithm)

Bus Voltages with Voltage regulator at bus 2 (Fuzzy Expert System)

1

1.0000

1.0000

1.0000

2

0.9713

0.9713

1.0485

3

0.9567

1.0442

1.0364

4

0.9509

1.0389

1.0311

5

0.9499

1.0380

1.0302

6

0.9582

0.9583

1.0363

7

0.9560

0.9561

1.0342

8

0.9570

0.9570

1.0351

9

0.9680

0.9680

1.0453

10

0.9669

0.9670

1.0443

11

0.9500

1.0380

1.0302

12

0.9458

1.0343

1.0264

13

0.9445

1.0331

1.0290

14

0.9486

1.0368

1.0288

15

0.9484

1.0366

0.9977

Table 6.4 Comparison of results of 15 bus RDS

Parameter

Before VR placement

With VRs

VR at bus 3 using Back Tracking Algorithm

VR at bus 2 using FES

Ploss(kW)

61.7933

58.8129

46.5467

Qloss (kVAr)

57.2973

54.5563

42.8456

Min. Voltage (p.u.)

0.9445

0.9561

0.9977

Net saving (`.)

-----

1,31,421/-

6,68,214/-

Voltage regulation (%)

5.5500

4.3927

0.23

percentage loss reduction

-----

4.8232

24.6736

It is observed that from Table 6.4, without voltage regulators in the system the power loss is 61.7933 kW and percentage voltage regulation is 5.55. With voltage regulators at optimal locations (obtained with back tracking algorithm) at bus 3 the power loss is reduced to 58.8129 kW and percentage voltage regulation is reduced to 4.3927. The net saving is `. 1,31,421/-.With voltage regulator at optimal locations (obtained with FES) at bus 2 the power loss is reduced to 46.5467 kW and percentage voltage regulation is reduced to 0.23. The net saving is `. 6, 68,214/-. From the above results it is observed that placement of voltage regulator using FES gives a better voltage profile and higher reduction in losses compared to back tracking algorithm. The voltage profile and variation of real power loss at each branch with and without voltage regulator are shown in Figs. 6.4 and 6.5 respectively.

Fig. 6.4 Real power loss of 15 bus RDS with and without Voltage regulator

Fig. 6.5 Voltage profile of 15 bus RDS with and without Voltage regulator

6.6.2 Example -2

Consider the 33 bus system whose single line diagram is shown in Fig. 2.5, and data as given in Appendix A (Table A.2). The total real power loss and minimum bus voltage are 202.5022 kW and 0.9131p.u. before employing VR. The tap setting and optimal number and location of voltage regulator obtained using Back tracking algorithm is given in Table 6.5. The Voltage Regulator Suitability Index, optimal location and tap setting of voltage regulator obtained using FES are given in Table 6.6.

Table 6.5 Optimal bus number and tap setting of VR using Back Tracking

algorithm for 33 bus system

Bus No. to place VR

Tap setting of Voltage regulator in p.u.

Type of Tap position

6

0.10 (16 steps)

Boost

Table 6.6 VRSI and tap setting of voltage regulator using FES for 33 bus system

Bus No. to place VR

Voltage Regulator Suitability Index in FES

Tap setting of Voltage regulator in p.u. using FES

Type of Tap position

5

0.40

0.06875(11 steps)

Boost

6

0.40

0.01875 (3 steps)

Boost

Comparison of results of both proposed methods are given Table 6.7 for 33 bus RDS.

Table 6.7 Comparison of results of 33bus RDS

Parameter

Before VR placement

With VRs

VRs at buses 6 to 18 and 26 to 33

VR at bus 6 using Back Tracking Algorithm

VR at bus 5, 6 using FES

Ploss in kW

202.50

187.92

184.35

153.09

Qloss in kVAr

135.23

123.28

120.30

102.40

Min. Voltage in p.u.

0.9131

0.9682

0.9683

0.9715

Net saving (`.)

-----

(-) 5,95,250/-

9,70,784/-

23,91,882/-

Voltage regulation (%)

8.6918

3.180

3.1726

2.850

percentage loss reduction

-----

7.20

8.9640

24.40

It is observed from Table 6.7, that without voltage regulators in the system the power loss is 202.5022 kW and percentage voltage regulation is 8.6918. With voltage regulators at buses 6 to 18 and 26 to 33, the power loss is 187.92 kW and percentage voltage regulation is 3.180% but the net saving is (-) `.5, 95,250/- (cost of voltage regulators itself is more than cost of total energy losses).With voltage regulators at optimal locations (obtained using back tracking algorithm) at bus 6 the power loss is reduced to 184.35 kW and percentage voltage regulation is reduced to 3.1726. The net saving is `.9, 70, 784/-.With voltage regulators at optimal locations (obtained using FES) at buses 5 and 6 the power loss is reduced to 153.09 kW and percentage voltage regulation is 2.850. The net saving is `.23, 91, 882/-.

The results of proposed FES method and results of DPSO method [113] are given in Table 6.8. By implementing DPSO method it is observed that 5 buses are selected as optimal locations and VRs are placed at 2 locations only (as tap positions at other buses are equal to zero), whereas in proposed FES method only 2 buses are selected as optimal locations for placement of VRs. The net savings in proposed FES method is `. 23,91,882/- which is higher than the existing DPSO method for which value is `. 20,71,586.93/-.

Table 6.8 Comparison of results with the existing method

Name of the Quantity

Without VR

With VR using DPSO [113]

With VR using proposed method

Optimal location and size (volts)

Bus No.

Tap Position

Bus No.

Tap Position

2

0

5

11

3

0

6

3

4

0

--

--

5

12

--

--

6

1

--

--

Real power loss (kW)

202.50

154.299

153.09

Reactive power loss (kVAr)

135.23

103.37

102.40

Net Savings (`.)

-----

20,71,586.93

23,91,882.00

Min. Voltage (p.u.)

0.9131

0.9714

0.9715

Voltage Regulation (%)

8.6918

2.86

2.850

Percentage Loss Reduction

-----

23.88

24.40

Execution time (Sec)

19.129183

7.590868

The voltage profile and real power loss with and without VRs are shown in Figs. 6.6 and 6.7 respectively.

Fig. 6.6 Real power loss of 33 bus RDS with and without Voltage regulator

Fig. 6.7 Voltage profile of 33 bus RDS with and without Voltage regulator

6.6.3 Example - 3

Consider 69 bus system whose single line diagram is shown in Fig. 2.6 and the data which is given in Appendix A (Table A.3). The total real power loss and minimum bus voltage are 224.95 kW and 0.9092 p.u. prior to using VRs. The tap setting and optimal number and location of voltage regulator obtained using Back tracking algorithm is given in Table 6.9. The Voltage Regulator Suitability Index, optimal location and tap setting of voltage regulator obtained using FES are given in Table 6.10. The minimum voltage is improved from 0.9092 p.u. to 0.9565p.u. with back tracking algorithm. The improvement in voltage regulation is 4.3502%. Using FES, the minimum voltage is improved from 0.9092 p.u. to 0.9705 p.u. The improvement in voltage regulation is 2.9496%.

Table 6.9 Optimal bus number and tap setting of VR using Back Tracking

algorithm for 69 bus system

Bus No. to place VR

Tap setting of Voltage regulator in p.u.

Type of Tap position

57

0.10 (16 steps)

Boost

Table 6.10 VRSI and tap setting of voltage regulator using FES for 69 bus system

Bus No. to place VR

Voltage Regulator Suitability Index in FES

Tap setting of Voltage regulator in p.u. using FES

Type of Tap position

6

0.50

0.05625 (9 steps)

Boost

Comparison of results of both the methods are given Table 6.11 for 69 bus RDS.

Table 6.11 Comparison of results of 69 bus RDS

Parameter

Before VR placement

With VRs

VRs at buses 57 to 65

VR at bus 57 using Back Tracking Algorithm

VR at bus 6 using FES

Ploss (kW)

224.95

214.32

202.38

155.83

Qloss (kVAr)

102.14

123.55

93.848

76.18

Min. Voltage (p.u.)

0.9092

0.95649

0.9565

0.9705

Net saving (`.)

-----

(-) 1,15,30,892/-

12,12,585/-

34,14,868/-

Voltage regulation (%)

9.0811

4.3503

4.3502

2.9496

percentage loss reduction

-----

21.2088

10.0333

30.7268

It is observed from Table 6.11, without voltage regulators in the system the power loss is 224.95 kW and percentage voltage regulation is 9.0811. With voltage regulators at buses only from 57 to 65, the percentage power loss is 214.32 kW and percentage voltage regulation is 4.3503 but the net saving is (-) `.1, 15, 30,892/- (cost of voltage regulators itself is more than cost of total energy losses). With voltage regulators at optimal location (obtained with Back tracking method) of bus 57 the percentage power loss is reduced to 202.38 kW and percentage voltage regulation is reduced to 4.3502. The net saving is `.12, 12,585/-. The voltage regulator at optimal locations (obtained with FES) at bus6, the power loss is reduced to 155.83 kW and percentage voltage regulation is 2.9496. The net saving is `.34, 94,868/-.

The results of proposed FES method and DPSO method [113] are given in Table 6.12. By DPSO method it is observed that 5 buses are selected as optimal locations and VRs are placed at 3 buses only (as tap positions at other buses are equal to zero), whereas in proposed FES method only one bus is selected as optimal location for placement of VR. The net savings in proposed FES method is `. 34, 14, 868/- which is higher than the existing DPSO method for which value is `. 32, 75, 802.49/-. The minimum voltage in DPSO method is 0.950295 p.u. where as in the proposed FES method is 0.9705p.u.

Table 6.12 Comparison of results with the existing method

Name of the Quantity

Without VR

With VR using DPSO [113]

With VR using proposed method

Optimal location and size (volts)

Bus No.

Tap Position

Bus No.

Tap Position

56

0

6

9

57

0

---

---

58

16

---

---

59

-12

---

---

60

16

---

---

Real power loss (kW)

224.95

156.40

155.83

Reactive power loss (kVAr)

102.14

76.38

76.18

Net Savings (`.)

-----

32,75,802.49

34,14,868/-

Min. Voltage (p.u.)

0.9092

0.950295

0.9705

Voltage Regulation (%)

9.0811

4.97

2.9496

Percentage Loss Reduction

-----

30.62

30.7268

Execution time (Sec)

26.913390

27.830290

The voltage profile and variation of real power loss at each branch with and without VRs are shown in Figs. 6.8 and 6.9 respectively.

Fig. 6.8 Real power loss of 69 bus RDS with and without voltage regulator

Fig. 6.9 Voltage profile of 69 bus RDS with and without voltage regulator

6.7 CONCLUSIONS

In radial distribution systems it is necessary to maintain voltage levels at various buses by using capacitors or conductor grading or placing VR at suitable locations. In this chapter, a method using voltage regulators is discussed to maintain the voltage profile and to maximize the net savings. The proposed Back tracking algorithm determines the optimal number, location and tap positions of voltage regulators to maintain voltage profile within the desired limits and reduces the losses in the system which in turn maximizes the net savings. In addition to the back tracking algorithm, a method using Fuzzy Logic is proposed and results of both the methods are compared. The proposed FES method provides better voltage profile and also reduces the power loss which has further increased the net savings compared to the back tracking algorithm. Further the results obtained by proposed FES method are compared with an existing DPSO method.

CHAPTER - 7

OPTIMAL DISTRIBUTED GENERATOR PLACEMENT USING FUZZY LOGIC

7.1 INTRODUCTION

A power system is an interconnected system composed of generating stations, which convert fuel energy into electrical energy, sub-stations that distribute electrical energy to loads through transmission lines that tie the generating stations and distribution substations. According to the voltage levels, an electrical power system can be sub divided as a generating system, a transmission system and a distribution system.

The concept of a distributed generation is installation of smaller modular resources in a distributed manner closer to the point of load. Dispersed generations could be photovoltaic cells, wind generation, battery storage, fuel cells etc. Such locally distributed generation has several merits from the point of environmental restriction and location limitations, as well as transient and voltage stability of the power system.

The objective of this chapter is to optimally locate the distributed generators for minimized power losses under the constraint of the total injection of installed distributed generation and bus voltages. Distributed Generation (DG) includes the application of small generators, scattered throughout a power system, to provide the electrical power needed by consumers. It often offers a valuable alternative to traditional sources which utility planners should explore in their search for the best solution to provide quality supply to industrial, commercial and residential consumers.

Several methods of loss reduction by placing distributed generators in distribution systems have been reported over the years. Kim et al. [47] have proposed Hereford ranch algorithm to optimally locate the DG to reduce the system overall real power loss under the constraint of the total injection of installed dispersed generation. Naresh Acharya et al. [97] have suggested a heuristic method to select appropriate location and to calculate the size of DG for minimum real power loss. Though the method is effective in selecting location, it requires more computational effort as it is heuristic process which requires exhaustive search for all possible locations and this method uses approximate loss formula which may lead to inappropriate solution.

Le et al. [99] have proposed method to optimize the size and location of DG based on the level of power loss reduction. In this method the proposed objective function considers only the percentage loss reduction. The optimization methodology, which is based on the sequential Quadratic programming (SQP) algorithm, assesses the compatibility of different generation schemes depending on the level of power loss reduction and cost of DG and obtain the final solution, which validate the constraints of voltage and size of DG. Shukla et al. [112] have proposed a methodology to calculate the optimal size of DG using GA and the appropriate locations by an analytical method based on loss sensitivity analysis.

In this chapter, a method is presented to determine the optimal location of distributed generators using fuzzy expert system by considering power losses and voltage at each bus simultaneously and the size of distributed generators is determined by an analytical method. This method has the versatility of being applied to the large distribution systems and having any uncertain data.

The mathematical formulation of the proposed method is explained in Section 7.2 and the determination of size of DG using analytical method is explained in Section 7.3. The identification of sensitive buses for DG placement using fuzzy logic is described in Section 7.4 and the steps of the algorithm to obtain optimal location and size of DG are presented in Section 7.5. The effectiveness of the proposed method is tested with different examples of radial distribution system and the results obtained are compared with the existing methods is presented in Section 7.6.

7.2 MATHEMATICAL FORMULATION

The objective function to maximize the net savings function (F) by placing the proper size of distributed generators at suitable locations is formulated as

… (7.1)

where

Plr = Reduction in power loss due to installation of DG

= (Power loss before installation of DG - Power loss after installation of

DG)

Ke = Cost of energy in `. /kWh

= Total capacity of distributed generators in kW

λ = annual rate of depreciation and interest charges of DG

KDG = Capital cost of distributed generator per kW

7.2.1 Constraints

The objective function is subjected to the following constraints

The voltage at each bus should lie within the voltage limits.

Vmin.≤Vi≤Vmax. i=1, 2, ….. no. of buses

The injected power should not exceed the sum of total load and the total real loss of the system

… (7.2)

where nbus = total number of buses

7.3 PROCEDURE TO CALCULATE DISTRIBUTED GENERATOR SIZE

The total I2R loss (TPL) in a radial distribution system having 'k' number of branches is given by

… (7.3)

where

Ik is the magnitude of branch current can be calculated from load flow solution

Rk is the resistance of the kth branch

k is the number of branches

Assume that a DG is placed at bus 'i', it produces a current of IDG, and for a radial distribution network it changes only the current of branches which are connected to the bus, ‘i’. The currents of other branches which are not connected to bus ‘i’ are not affected. Thus, new current of the kth branch is given by

… (7.4)

where

Ak =1 if kth branch is connected to bus, i

= 0 otherwise

The loss TPL' associated with the is given by

… (7.5)

Effective branch current is reduced due to injection of local generating current, Ak IDG; therefore, the reduction in power loss due to the introduction of DG at bus ‘i’ is given by

… (7.6)

… (7.7)

The value of IDG can be calculated by maximizing the loss reduction, Pi, and can be obtained by equating ∂(Pi)/∂IDG = 0. After simplification,

… (7.8)

Then the DG size can be calculated as

… (7.9)

where Vi = voltage at ith bus

7.4 IDENTIFICATION OF DG LOCATION USING FUZZY LOGIC

The Fuzzy logic is used to identify the suitable optimal location of DG in a radial distribution system so as to minimize the losses while keeping the voltage at buses within the limits and also by taking the cost of the DGs into account. For the Distributed Generator placement problem, similar rules are defined for Fuzzy Expert System (FES) to determine the suitability of a bus for Distributed Generator placement which is explained in Chapter 5.

For determining the suitability for DG placement at a particular bus, a set of multiple antecedent fuzzy rules have been established. The rules are summarized in the fuzzy decision matrix which is given in Table 5.1 and the same procedure using Eqns. (5.3) and (5.4) can be adopted for DG placement. Based on the FES, the algorithm and flow chart developed for locating optimal DG placement is presented in the next section.

7.5 ALGORITHM FOR OPTIMAL DISTRIBUTED GENERATOR PLACEMENT IN RDS USING FES

Step 1: Read line and load data of RDS.

Step 2: Run load flows for the system and compute the voltages at each bus, real and reactive power losses of the system.

Step 3: Install the Distributed Generator at every bus and compute the total real power loss of the system for each case and calculate the power loss indices using Eqn. (5.2).

Step 4: The power loss indices and the bus voltages are the inputs to the fuzzy expert system.

Step 5: The outputs of FES are defuzzified using centroid defuzzification method. Then find the optimum value of Distributed Generator Suitability Index (DGSI), which gives the best suitable buses for a Distributed Generator placement.

Step 6: Obtain the size of DG using Eqn. (7.9).

Step 7: Run the load flows with DG, then compute voltages at all buses, real and reactive power losses.

Step 8: Determine the reduction in power loss and net saving by using objective function (Eqn. (7.1)).

Step 9 : Print the results.

Step 10: Stop

Read Distribution System line and load data, base kV and kVA, iteration count (IC) =1and tolerance (ε) = 0.0001

Start

Perform load flows and calculate voltage at each bus, real and reactive power losses

Calculate the loss reduction by running load flow by placing distributed generator at each bus, considering one bus at a time

Calculate power loss reduction indices, PLI using Eqn. (5.2)

Obtain the size of DG using Eqns. (7.9)

Select the optimal location for the DG placement by considering the maximum value of DGSI

Obtain distributed generator suitability index, DGSI from the FES by providing PLI and bus voltages as inputs to the FES

Stop

Compute voltages, angles, power flows, real and reactive power losses, objective function and Print the results

Perform load flow by placing the DG at best locations

Check for convergence

Yes

No

IC=IC+1

Compute bus voltages, real and reactive power losses

7.6 FLOW CHART FOR OPTIMAL DISTRIBUTED GENERATOR PLACEMENT USING FES

Fig. 7.1 Flow chart of optimal distributed generator placement using FES

7.7 ILLUSTRATIVE EXAMPLES

The proposed method is tested with three different radial distribution systems having 15, 33 and 69 buses.

7.7.1 Example – 1

Consider a 15 bus system whose single line diagram is shown in Fig. 2.3 and data of this system is given in Appendix A (Table A.1). The total real power loss and minimum bus voltage before DG placement are 61.7993 kW and 0.9445p.u. The Distributed Generator Suitability Index at various buses is given in Table 7.1 It is observed that, the value of DGSI is highest for bus number 15 which gives the optimal location for DG placement.

Table 7.1 Distributed Generator Suitability Index and size of Distributed

Generator of 15 bus RDS

Bus No.

DGSI

Bus No.

DGSI

1

0.5000

9

0.2500

2

0.2413

10

0.2466

3

0.2500

11

0.5012

4

0.5000

12

0.4703

5

0.2521

13

0.3880

6

0.5000

14

0.3399

7

0.5000

15

0.5383

8

0.2500

The optimal location and the actual size of the distributed generator obtained by the proposed method are given in Table 7.2. In addition, voltage improvement at this bus, loss reduction and net savings due to placement of distributed generator are also given. The effect of using the nearest standard size distributed generator instead of actual size of the distributed generator is presented in Table 7.3 and it is observed that the changes in loss reduction and net saving are marginal. The real power loss reduction due to DG placement is from 61.7933 kW to 27.0161 kW i.e., a reduction of 56.28% of the original real power loss.

Table 7.2 Summary of results of 15 bus RDS with and without actual size of DG

Bus No.

Without DG

With DG

Voltage (p.u.)

Voltage (p.u.)

Size of DG (kW)

15

0.9484

0.9796

568

Without DG

With DG

Improvement

Ploss

(kW)

Qloss

(kVAr)

Ploss

(kW)

Qloss

(kVAr)

Ploss

(kW)

Qloss

(kVAr)

61.7933

57.2967

33.1254

27.5647

28.6679

29.7320

Net Saving (`.)

Without DG

With DG

-----

5, 79, 435/-

Min. Voltage (p.u.)

0.9445

0.9586

Voltage Regulation (%)

5.55

4.14

Table 7.3 Summary of results of 15 bus RDS with and without standard size of DG

Bus No.

Without DG

With DG

Voltage (p.u.)

Voltage (p.u.)

Size of DG (kW)

15

0.9484

0.9861

600

Without DG

With DG

Improvement

Ploss

(kW)

Qloss

(kVAr)

Ploss

(kW)

Qloss

(kVAr)

Ploss

(kW)

Qloss

(kVAr)

61.7933

57.2967

27.0161

22.6945

34.7772

34.6022

Net Saving (`.)

Without DG

With DG

-----

6,55,120/-

Min. Voltage (p.u.)

0.9445

0.9666

Voltage Regulation (%)

5.55

3.34

The voltage profile of the system before and after DG placement is given in Table 7.4. The minimum voltage is improved from 0.9445p.u. to 0.9666 p.u.; hence the improvement in voltage regulation is 2.21%.

Table 7.4 Voltage profile before and after DG placement of 15 bus RDS

Bus No.

Before DG placement

After DG placement

Voltage magnitude (p.u.)

Voltage magnitude (p.u.)

1

1.0000

1.0000

2

0.9713

0.9831

3

0.9567

0.9785

4

0.9509

0.9799

5

0.9499

0.9789

6

0.9582

0.9702

7

0.9560

0.9680

8

0.9570

0.9689

9

0.9680

0.9798

10

0.9669

0.9787

11

0.9500

0.9720

12

0.9458

0.9679

13

0.9445

0.9666

14

0.9486

0.9777

15

0.9484

0.9861

The voltage profile and the variation of real power loss in each branch with and without DG are shown in Figs. 7.2 and 7.3 respectively.

Fig. 7.2 Voltage profile of 15 bus RDS with and without DG

Fig. 7.3 Real power loss of 15 bus RDS with and without DG

7.7.2 Example - 2

Consider a 33 bus system whose single line diagram is shown in Fig. 2.5 and data of this system is given in Appendix A (Table A.2). The total real power loss and minimum bus voltage before DG placement are 202.5022 kW and 0.9131p.u. The Distributed Generator Suitability Index and size of distributed generator (nearest standard size of distributed generator to the actual value) at the optimal bus are given in Table 7.5. The summary of results with and without distributed generator is given in Table 7.6. The minimum voltage is improved from 0.9131p.u. to 0.9505 p.u.; hence the improvement in voltage regulation is 3.74%.

Table 7.5 DGSI and size of Distributed Generator of 33 bus RDS

Bus No.

Distributed Generator Suitability Index

Distributed Generator size (kW)

30

0.9190

1900

Table 7.6 Summary of results of 33 bus system with and without DG

Description

Proposed method

Before DG placement

After DG placement

Real power loss (kW)

202.7060

64.5463

Reactive power loss (kVAr)

135.2388

47.3560

Min. Voltage in (p.u.)

0.9131

0.9505

Net saving (`.)

----

24,27,198/-

Total size of DG (kW)

1900

---

Voltage Regulation (%)

8.69

4.95

Percentage loss reduction

-----

68.16

From the results, it is observed that real power loss has reduced from 202.7060 kW to 64.5463 kW i.e., 68.16% of loss reduction and minimum voltage improved from 0.9131 p.u. to 0.9505p.u.due to DG placement. Thus voltage regulation is improved from 8.69% to 4.95%. The comparison of results with existing methods [97,130] is given in Table 7.7.

Table 7.7 Comparison of test results of 33 bus system with existing methods

Description

Existing method [130]

Existing method [97]

Proposed method

Before DG placement

After DG placement

Before DG placement

After DG placement

Before DG placement

After DG placement

Real power loss (kW)

203.9088

105.0231

211.2000

111.2400

202.7060

64.5463

Min. Voltage (p.u.)

0.9118

0.9498

0.8931

0.9452

0.9131

0.9505

Net saving (`.)

----

17,78,972/-

---

18,15,624/-

----

24,27,198/-

Total size of DG (kW)

2577.5

---

2490

----

1900

---

The voltage profile and the variation of real power loss in each branch with and without DG are shown in Figs.7.4 and 7.5 respectively.

Fig. 7.4 Voltage profile of 33 bus RDS with and without DG

Fig. 7.5 Real power loss of 33 bus RDS with and without DG

7.7.3 Example - 3

Consider a 69 bus system whose single line diagram is shown in Fig. 2.6 and data of this system is mentioned in Appendix A (Table A.3). The total real power loss and minimum bus voltage before DG placement are 224.95 kW and 0.90919p.u. The Distributed Generator Suitability Index and Distributed Generator size (nearest standard size of distributed generator to the actual value) at the optimal bus is given in Table 7.8. The summary of results with and without DG placement is given in Table 7.9. The minimum voltage is improved from 0.90919p.u. to 0.9681p.u., hence the improvement in voltage regulation is 5.891%.

Table 7.8 DGSI and size of Distributed Generator of 69 bus RDS

Bus No.

Distributed Generator Suitability Index

Distributed Generator size (kW)

61

0.9200

1550

Table 7.9 Summary of results of 69 bus system with and without DG

Description

Proposed method

Before DG placement

After DG placement

Real power loss (kW)

224.9804

38.2331

Reactive power loss (kVAr)

102.1574

21.8079

Min. Voltage in (p.u.)

0.90919

0.9681

Net saving (`.)

----

35,51,265.50/-

Total size of DG (kW)

1550

---

Voltage Regulation (%)

9.081

3.19

Percentage loss reduction

-----

83.00

From the results, it is observed that real power loss has reduced from 224.9804kW to 38.2331kW i.e., 83% of loss reduction and minimum voltage improved from 0.90919 p.u. to 0.9681p.u.due to installation of DG. Thus, voltage regulation is improved from 9.081% to 3.19%. The comparison of results obtained by the proposed method and the existing methods [97,112] is given in Table 7.10.

Table 7.10 Comparison of test results of 69 bus system with existing methods

Description

Existing method [112]

Existing method [97]

Proposed method

Before DG placement

After DG placement

Before DG placement

After DG placement

Before DG placement

After DG placement

Real power loss (kW)

225.00

84.43

219.28

81.44

224.9804

38.2331

Net saving (`.)

----

27,78,500/-

---

27,05,050/-

----

35,51,265.50/-

Total size of DG (kW)

1872

---

1810

----

1550

---

The voltage profile and variation of real power loss at each branch with and without DG are shown in Figs. 7.6 and 7.7 respectively.

Fig. 7.6 Voltage profile of 69 bus RDS with and without DG

Fig. 7.7 Real power loss of 69 bus RDS with and without DG

7.8 CONCLUSIONS

In this chapter, the installation of DGs of proper size at optimal locations are used for the minimization of losses and hence to improve the voltage profile of the system. A method is proposed to identify the optimal location of DG in a radial distribution system using Fuzzy logic and an analytical method is used to find the size of DG. The effectiveness of the proposed method is illustrated and the results are presented. The results obtained are better than the existing methods in terms of loss reduction and net savings.

CHAPTER - 8

CONCLUSIONS

8.1 SUMMARY

In this work, investigations are carried out on the control aspects of distribution systems, using fuzzy logic to optimize the net savings employing different voltage regulating devices or conductor grading for reducing the power losses and improvement of voltage profile. The results obtained during the course of this work are presented and a few suggestions for future research in this area are presented in this chapter.

In Chapter 2, a simple load flow technique for solving radial distribution systems has been presented. The advantage of the proposed method is that, it requires solution of simple algebraic equation to determine the receiving end voltage. The algorithm presented completely exploits the radial features of the distribution system.

A Bus Incidence Matrix is formed for the system and is processed to describe the structure of radial distribution system having number of branches using a data structure.

The effectiveness of the proposed method is tested with different examples of 15, 33 and 69 bus radial distribution systems.

In Chapter 3, the above proposed load flow method is extended to 3 phase unbalanced radial distribution systems. For analyzing 3 phase unbalanced system, method of symmetrical components is employed and the components of 3 phase network are represented by their equivalent circuit models.

The advantage of proposed bus identification method is independent of the type of configuration of the unbalanced system and can handle random bus numbering scheme of distribution system.

The proposed method has been demonstrated with 25 bus and IEEE 37 bus three phase unbalanced radial distribution systems and the results are presented.

In Chapter 4, a method has been proposed for selecting the optimal branch conductor of radial distribution feeders using fuzzy logic. The proposed method selects the optimal branch conductor by minimizing an objective function, which represents annual cost of energy losses and annual depreciation cost of conductors.

The main advantages of the proposed method are: (i) it can keep the minimum voltage within prescribed limits and (ii) the current flowing through each branch is less than the maximum current carrying capacity of the branch conductor.

It is also possible to determine the period for which the same set of selected optimal conductors will be suitable even taking the annual load growth into consideration without violating the limits on voltage and current carrying capacity of the conductors.

The proposed method is very simple and its effectiveness has been demonstrated through practical examples of 26 and 32 bus radial distribution systems.

In Chapter 5, a method has been proposed to determine optimal location for capacitor placement in radial distribution systems using fuzzy logic, taking into consideration both the power loss index and bus voltages. The size of the capacitor is determined using index based method.

The FES considers loss reduction and improvement of voltage profile simultaneously in deciding the optimal locations of the capacitors.

The proposed method has been tested with different radial distribution systems having 15, 33, 34 and 69 buses and the results obtained show the effectiveness of proposed method.

In Chapter 6, two methods have been proposed to determine suitable buses to place voltage regulators in radial distribution systems. The first method is an analytical method, named as ‘Back Tracking Algorithm’ and the second method is based on fuzzy logic approach and are used to find optimal locations of voltage regulators in radial distribution systems. The optimal tap position of voltage regulator is determined to maintain the voltages within acceptable limits using analytical method which maximizes the objective function.

The proposed FES method provides a better voltage profile and loss reduction compared to analytical method (Back Tracking Algorithm).

The effectiveness of the proposed method has been demonstrated through 15, 33 and 69 bus radial distribution systems.

In Chapter 7, the fuzzy logic is employed to identify the optimal location of distributed generator to be placed in radial distribution system which maximizes the net savings. An analytical method is used to obtain the size of distributed generator. The proposed method has been tested with different examples having 15, 33 and 69 bus radial distribution systems and results are presented.

Comparison of performance of various devices (Capacitors, Voltage regulators, Distributed generators) is given in Tables 8.1 to 8.3.

Table 8.1 Comparison of performance of various devices for 15 bus RDS

Description

Without compensating device

With compensating device

Capacitor

Voltage regulator

Distributed Generator

Min. Voltage (p.u.)

0.9445

0.9667

0.9977

0.9666

% voltage regulation

5.55

3.33

0.23

3.34

Real power loss (kW)

61.7933

32.1427

46.5467

27.0161

% real power loss reduction

----

47.98

24.6736

56.28

Total capacity of the device

----

1400 kVAr

0.075 (12 steps of Boost)

600 kW

Net Saving, `.

----

6,74,695/-

6,68,214/-

6,55,120/-

Table 8.2 Comparison of performance of various devices for 33 bus RDS

Description

Without compensating device

With compensating device

Capacitor

Voltage regulator

Distributed Generator

Min. Voltage (p.u.)

0.9131

0.9503

0.9715

0.9505

% voltage regulation

8.69

4.97

2.850

4.95

Real power loss (kW)

202.5022

145.0658

153.09

64.5463

% real power loss reduction

----

28.36

24.40

68.16

Total capacity of the device

----

1050kVAr

0.06875 (11 steps)

0.01875(3 steps) of Boost

1900kW

Net Saving, `.

----

14,57,428/-

23,91,882/-

24,27,198/-

Table 8.3 Comparison of performance of various devices for 69 bus RDS

Description

Without compensating device

With compensating device

Capacitor

Voltage regulator

Distributed Generator

Min. Voltage (p.u.)

0.9092

0.9441

0.9705

0.9681

% voltage regulation

9.0811

5.59

2.9496

3.19

Real power loss (kW)

224.9457

152.0469

155.83

38.2331

% real power loss reduction

----

32.40

30.7268

83.00

Total capacity of the device

----

1350 kVAr

0.05625 (9 steps of Boost)

1550 kW

Net Saving, `.

----

20,65,298/-

34,14,868/-

35,51,265.50/-

In general, it is observed from the results given in Tables 8.1 to 8.3 for different radial distribution systems the improvement in voltage profile is better with voltage regulators compared to capacitors and distributed generators.

In addition, it is observed that the reduction in real and reactive power losses is more effective with distributed generators compared to capacitors and voltage regulators. It is also observed that, the net savings obtained with distributed generators and voltage regulators is higher compared to that of capacitors.

The relative effectiveness of these components for overall system improvement is system dependent and loading conditions of the system.

8.2 SCOPE FOR FUTURE WORK

As a result of investigations carried out in this work in the area of distribution systems, the following suggestions for future research seem to be worth pursuing.

The application of the proposed method using fuzzy logic requires further investigation in respect of 3 phase unbalanced systems. It also requires further investigations for applying this methodology for Network reconfiguration in radial distribution systems and voltage stability studies for different load models

In this thesis, in order to optimize the various objectives considered for distribution system, fuzzy logic has been employed. With recent advances in optimization techniques such as Tabu Search, Artificial Bee Colony algorithm can be used for further investigation.



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