Optimal Voltage Regulator Placement Using Fuzzy Logic

Published Date: 02 Nov 2017

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.