PowerApps software product is a Proprietary Property of Dr.Raghunatha Ramaswamy. No company with whom Dr.Raghunatha Ramaswamy was associated in the past either as consultant or as an employee do not own the proprietary property for this software.
 
Home
PowerApps Software Modules
PowerApps Calculation Engine
Software Services
Power System Studies
Engineering Services
Power System Training
Downloads
Profile
Contact Us
Partners and Associates
Site Map
Send an Enquiry
Sample Study Cases of the Services Rendered
Real Time Security Assessment and Remedial Action Solution
The current time is ?
Optimal Power Flow Algorithm Implementation in PowerApps

PowerApps - Optimal Power Flow – Convergence Characteristics

Table of Contents

1       Introduction. 3

2       Notation. 4

3       System Data Summary and OPF convergence Characteristics. 5

3.1        6 bus Ward – Hale System.. 5

3.1.1         Loss Minimization Objective. 5

3.1.2         Loss Minimization and Economic Dispatch Objective. 5

3.2        24 Bus, Indian Test System.. 6

3.2.1         Loss Minimization Objective. 6

3.2.2         Loss Minimization and Economic Dispatch Objective. 6

3.3        89 Bus, Indian Test System.. 7

3.3.1         Loss Minimization Objective. 7

3.3.2         Loss Minimization and Economic Dispatch Objective. 7

3.4        125 Bus, Indian Test System [KPTCL] 8

3.4.1         Loss Minimization Objective. 8

3.4.2         Loss Minimization and Economic Dispatch Objective. 8

3.5        319 Bus, Indian System [KPTCL] 9

3.5.1         Loss Minimization Objective. 9

3.5.2         Loss Minimization and Economic Dispatch Objective. 9

3.6        1043 Bus, Indian Southern Grid. 10

3.6.1         Loss Minimization Objective. 10

3.6.2         Loss Minimization and Economic Dispatch Objective. 10

3.7        Gujarat Electricity Board Data [1991-94] 11

3.7.1         Loss Minimization Objective. 11

3.7.2         Loss Minimization and Economic Dispatch Objective. 11

3.8        Orissa State Electricity Board System [Around 1995] 12

3.8.1         Loss Minimization Objective. 12

3.8.2         Loss Minimization and Economic Dispatch Objective. 12

4       Conclusion. 13

 


1      Introduction

This document records the convergence characteristics the PowerApps Optimal Power Flow [OPF]. The load flow [LF] and the OPF are carried out sequentially till there is no further improvement in the performance objective or feasibility of the solution. The cycles of LF and OPF are identified as ADC in the tabular reports.

 

Two objective Functions are considered for illustration. The first one, only the transmission loss minimization is considered. In the second one, combined objective of economic dispatch and loss minimization are considered.

 

PowerApps solves the economic dispatch and transmission loss minimization as two phase optimization process as explained in the following.

 

1.    Obtain initial feasible load flow results

2.    Step 1 gives total generation requirement with transmission losses. Use this information for economic dispatch solution

3.    Use results of step 1 for reactive power optimization with transmission loss minimization [or any other suitable objective] to determine control settings for reactive power controls.

4.    Implement the solutions of steps 2 and 3 and go to step 1.

5.    Repeat steps 1 to 4 till no further controls can be implemented [optimum point is reached] or till specified number of load flow and optimization cycles covered.

 

The cost function model used by PowerApps for economic dispatch is as  

                                                                                         

 

All generators are assumed to have the same cost function model. All generators are assumed to be running. Consequently only the variable costs associated with MW generation is minimized.d with MW generation is minimized.

 

2      Notation

The tabular convergence characteristics report for various system has the following headings and corresponding meaning.

 

Column Heading

Description of the content in tabular column

ADC

Load Flow Cycle Number, 0 is the base case load flow, 1 ,2 etc are after Optimizing the Controllers at the end of previous load flows 0,1 etc

PG Total[MW]

Total MW generation at the end of load flow

PL Total[MW]

Total MW Load

P Loss [MW]

Total MW Loss [ The objective used was minimization of transmission losses, this should be seen as improving]

VMAX [pu]

Maximum bus voltage at a bus in per unit as identified by load flow solution

VMIN [pu]

Minimum bus voltage at a bus in per unit as identified by load flow solution

Sv [pu]

Absolute sum of all over and all under voltage violations in per unit. Reduction in this value implies improved voltage profile.

Nv

Number of bus voltage violations. Reduction in this value implies improved voltage profile.

Qcom[MVAR]

Total MVAR compensation

VariableCost

Variable Cost of Generation [in any specified currency units, depending on cost model]


3      System Data Summary and OPF convergence Characteristics

3.1     6 bus Ward – Hale System

     NUMBER OF GENERATOR CONTROLS                =     2

     NUMBER OF TRANSFORMER CONTROLS              =     2

     NUMBER OF CAPACITOR CONTROLS                =     2

     TOTAL NUMBER OF CONTROLS                    =     6

3.1.1      Loss Minimization Objective

ADC

PG Total

[MW]

PL Total

[MW]

P Loss

[MW]

VMAX

[pu]

VMIN

[pu]

Sv

[pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

146.612327

135

11.612327

1.1

0.855219

0.044781

1

0

3693.92537

1

144.307479

135

9.307479

1.1

0.955202

0

0

10.5

3639.027584

2

144.319266

135

9.319266

1.1

0.954126

0

0

10.5

3639.304769

 

3.1.2      Loss Minimization and Economic Dispatch Objective

ADC

PG Total

[MW]

PL

Total[MW]

P Loss

 [MW]

VMAX

[pu]

VMIN

 [pu]

Sv

[pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

146.6123

135

11.61233

1.1

0.855219

0.044781

1

0

3693.925

1

143.9538

135

8.953771

1.1

0.955852

0

0

10.5

3599.887

2

143.7244

135

8.724368

1.1

0.955202

0.000013

1

10.5

3571.063

 

Notes:

1.    Variable costs are minimized with economic dispatch

2.    With economic dispatch losses also have reduced further.

 


 

3.2     24 Bus, Indian Test System

     NUMBER OF GENERATOR CONTROLS                =     4

     NUMBER OF TRANSFORMER CONTROLS              =     7

     NUMBER OF CAPACITOR CONTROLS                =     4

     TOTAL NUMBER OF CONTROLS                    =    15

3.2.1      Loss Minimization Objective

ADC

PG Total [MW]

PL Total

[MW]

P Loss

[MW]

VMAX

 [pu]

VMIN

 [pu]

Sv

 [pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

2680.472

2620

60.47208

1

0.867126

0.656766

15

0

125740.6

1

2671.757

2620

51.75726

1.05

0.948671

0.001329

1

75

124992.5

2

2671.661

2620

51.66116

1.05

0.948813

0.001187

1

75

124984.2

3.2.2      Loss Minimization and Economic Dispatch Objective

ADC

PG Total

[MW]

PL Total

[MW]

P Loss

[MW]

VMAX

[pu]

VMIN

[pu]

Sv

[pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

2680.472

2620

60.47208

1

0.867126

0.656766

15

0

125740.6

1

2668.741

2620

48.74097

1.05

0.951578

0

0

75

118690.2

2

2668.759

2620

48.75948

1.05

0.951667

0

0

75

118691

Notes:

1.    Variable costs are minimized with economic dispatch

2.    With economic dispatch losses also have reduced further.

 

 


 

3.3     89 Bus, Indian Test System

     NUMBER OF GENERATOR CONTROLS                =    12

     NUMBER OF TRANSFORMER CONTROLS              =    23

     NUMBER OF CAPACITOR CONTROLS                =    21

     TOTAL NUMBER OF CONTROLS                    =    56

3.3.1      Loss Minimization Objective

ADC

PG Total

[MW]

PL Total

[MW]

P Loss [MW]

VMAX [pu]

VMIN [pu]

Sv

[pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

2203.259

2049.87

153.3887

1.010935

0.749948

5.525923

51

0

54213.98

1

2169.692

2049.87

119.8221

1.05

0.923664

0.065156

6

266.904

53379.55

2

2164.465

2049.87

114.5953

1.05

0.951416

0

0

375.1516

53253.67

 

3.3.2      Loss Minimization and Economic Dispatch Objective

ADC

PG Total

[MW]

PL Total

[MW]

P Loss [MW]

VMAX [pu]

VMIN [pu]

Sv

[pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

2203.259

2049.87

153.3887

1.010935

0.749948

5.525923

51

0

54213.98

1

2165.328

2049.87

115.4578

1.05

0.926642

0.049282

4

266.904

52731.02

2

2158.131

2049.87

108.2615

1.051578

0.954055

0.002966

4

364.3801

52280.68

3

2157.065

2049.87

107.1954

1.054449

0.94652

0.012911

8

364.3801

52210.73

4

2155.865

2049.87

105.9951

1.071999

0.952598

0.03088

8

320.4141

52175.45

5

2154.255

2049.87

104.3852

1.074034

0.946683

0.03885

7

302.552

52124.63

6

2153.81

2049.87

103.9396

1.074893

0.958409

0.048713

12

317.6971

52107.12

7

2153.727

2049.87

103.8568

1.056282

0.958623

0.021778

9

317.6971

52099.53

8

2153.652

2049.87

103.7817

1.057435

0.959246

0.020234

9

317.6971

52097.58

9

2153.562

2049.87

103.6917

1.074952

0.95944

0.045557

10

317.6971

52095.26

 

Notes:

1.    Variable costs are minimized with economic dispatch

2.    With economic dispatch losses also have reduced further

3.    The algorithm went on for full specified 10 number of load flow and optimization cycles with marginal improvements in the latter cycles..

 


 

3.4     125 Bus, Indian Test System [KPTCL]

     NUMBER OF GENERATOR CONTROLS                =    26

     NUMBER OF TRANSFORMER CONTROLS              =    25

     NUMBER OF CAPACITOR CONTROLS                =    18

     TOTAL NUMBER OF CONTROLS                    =    69

 

3.4.1      Loss Minimization Objective

 

ADC

PG Total

[MW]

PL Total

[MW]

P Loss

[MW]

VMAX

[pu]

VMIN

[pu]

Sv

[pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

4833.519

4643.89

189.6287

1.03

0.740645

3.027959

61

0

139108.1

1

4795.075

4643.89

151.1846

1.05

0.927916

0.127677

10

275

137096.3

2

4789.937

4643.89

146.0468

1.058903

0.94073

0.034106

7

290.5083

136831.9

3

4789.367

4643.89

145.4768

1.058903

0.941461

0.031383

10

295.5083

136802.6

4

4789.521

4643.89

145.6313

1.058903

0.941266

0.032697

9

295.5083

136810.2

 

3.4.2      Loss Minimization and Economic Dispatch Objective

 

ADC

PG Total

[MW]

PL Total

[MW]

P Loss

[MW]

VMAX

[pu]

VMIN

[pu]

Sv

 [pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

4833.519

4643.89

189.6287

1.03

0.740645

3.027959

61

0

139108.1

1

4788.748

4643.89

144.8576

1.05

0.929997

0.102979

9

275

131047.6

2

4785.032

4643.89

141.1423

1.068482

0.942649

0.063537

12

280

130853.6

3

4784.729

4643.89

140.8385

1.068482

0.945397

0.065103

13

280

130857.6

4

4784.716

4643.89

140.8263

1.068482

0.945329

0.063751

13

280

130839.3

5

4784.338

4643.89

140.4477

1.068482

0.945977

0.060669

14

280

130822.6

 

Notes:

1.    Variable costs are minimized with economic dispatch

2.    With economic dispatch losses also have reduced further

 


 

 

3.5     319 Bus, Indian System [KPTCL]

     NUMBER OF GENERATOR CONTROLS                =    22

     NUMBER OF TRANSFORMER CONTROLS              =    77

     NUMBER OF CAPACITOR CONTROLS                =    47

     TOTAL NUMBER OF CONTROLS                    =   146

 

3.5.1      Loss Minimization Objective

 

ADC

PG Total

[MW]

PL Total

[MW]

P Loss

[MW]

VMAX

[pu]

VMIN

[pu]

Sv

 [pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

4563.446

4275

288.446

1

0.637032

21.68275

245

0

172591.8

1

4496.877

4275

221.8772

1.05

0.933239

0.039275

5

296.9124

166570.9

2

4492.448

4275

217.4478

1.05

0.950973

0

0

370.7209

166176.5

3

4492.045

4275

217.0445

1.05

0.952069

0

0

394.4941

166140.7

 

3.5.2      Loss Minimization and Economic Dispatch Objective

 

ADC

PG Total

[MW]

PL Total

[MW]

P Loss

[MW]

VMAX

[pu]

VMIN

[pu]

Sv

 [pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

4563.446

4275

288.446

1

0.637032

21.68275

245

0

172591.8

1

4483.542

4275

208.542

1.05

0.93653

0.023548

3

296.9124

151933.7

2

4480.509

4275

205.5087

1.052389

0.951147

0.002389

1

355.0025

151692.3

3

4480.031

4275

205.0313

1.052895

0.952047

0.002895

1

380.7686

151657.1

4

4480.096

4275

205.0962

1.052876

0.949652

0.003224

2

380.7686

151689.3

 

Notes:

1.    Variable costs are minimized with economic dispatch

2.    With economic dispatch losses also have reduced further


 

3.6     1043 Bus, Indian Southern Grid

     NUMBER OF GENERATOR CONTROLS                =    66

     NUMBER OF TRANSFORMER CONTROLS              =   138

     NUMBER OF CAPACITOR CONTROLS                =   590

     TOTAL NUMBER OF CONTROLS                    =   794

3.6.1      Loss Minimization Objective

ADC

PG Total

[MW]

PL Total

[MW]

P Loss

[MW]

VMAX

[pu]

VMIN

[pu]

Sv

[pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

13222.2

12545.15

677.0469

1.021436

0.553079

79.19027

829

0

415815.1

1

13222.29

12545.15

677.1386

1.05

0.701053

11.32251

267

5237.901

433129.7

2

13173.37

12545.15

628.2183

1.05435

0.759467

2.142998

85

5706.414

431965.5

3

13168.13

12545.15

622.9804

1.088152

0.766347

1.755495

68

5776.631

431846.7

4

13167.27

12545.15

622.1214

1.086513

0.76956

1.715472

68

5776.631

431827.3

5

13167.53

12545.15

622.3756

1.086294

0.769564

1.695118

64

5776.631

431833.1

 

Notes:

1.    The initial load flow corresponds to infeasible [not converged] load flow and hence its variable cost is not valid. Load flow solution at the point of minimum mismatch was used for optimization solution.

2.    Losses and Variable Cost however, steadily improve from converged load flow solution of ADC 1 and above.

3.6.2      Loss Minimization and Economic Dispatch Objective

ADC

PG Total

[MW]

PL Total

[MW]

P Loss

[MW]

VMAX

[pu]

VMIN

[pu]

Sv

[pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

13222.2

12545.15

677.0469

1.021436

0.553079

79.19027

829

0

415815.1

1

13234.75

12545.15

689.5994

1.050258

0.702001

11.97724

276

5237.901

416831.6

2

13186.04

12545.15

640.8946

1.050674

0.758889

2.236873

86

5671.229

416152.7

3

13179.77

12545.15

634.6243

1.051316

0.7699

1.72662

63

5642.4

414490.6

4

13178.79

12545.15

633.6431

1.053028

0.772968

1.707763

62

5642.4

414252.3

5

13178.72

12545.15

633.5735

1.052937

0.772805

1.709201

62

5642.4

414220.1

6

13178.68

12545.15

633.5295

1.052962

0.77285

1.707772

63

5643.69

414219.2

7

13178.73

12545.15

633.584

1.052942

0.772815

1.707775

61

5642.09

414220.5

8

13178.7

12545.15

633.5527

1.052969

0.772863

1.705596

63

5643.803

414219.7

 

Notes:

 

1.    The initial load flow corresponds to infeasible [not converged] load flow and hence its variable cost is not valid. Load flow solution at the point of minimum mismatch was used for optimization solution.

2.    Losses and Variable Cost however, steadily improve from converged load flow solution of ADC 1 and above.

3.    Variable Costs Improve better with this objective compared to plain loss minimization objective.

4.    Over voltages are controlled better with this combined objective compared to plain loss minimization objective.


 

3.7     Gujarat Electricity Board Data [1991-94]

     NUMBER OF GENERATOR CONTROLS                =    20

     NUMBER OF TRANSFORMER CONTROLS              =    23

     NUMBER OF CAPACITOR CONTROLS                =    11

     TOTAL NUMBER OF CONTROLS                    =    54

3.7.1      Loss Minimization Objective

ADC

PG Total

[MW]

PL Total

[MW]

P Loss

[MW]

VMAX

[pu]

VMIN

[pu]

Sv

[pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

4047.642

3933

114.6419

1.05

0.713986

3.145116

54

0

107107

1

4023.298

3933

90.29814

1.05

0.944865

0.00914

2

260

106210.6

2

4023.792

3933

90.7917

1.05

0.971693

0

0

280

106228.5

3

4023.614

3933

90.61445

1.05

0.969762

0

0

280

106222.1

4

4023.245

3933

90.24471

1.050238

0.973029

0.000238

1

280

106208.5

 

3.7.2      Loss Minimization and Economic Dispatch Objective

ADC

PG Total

[MW]

PL Total

[MW]

P Loss

[MW]

VMAX

[pu]

VMIN

[pu]

Sv

[pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

4047.642

3933

114.6419

1.05

0.713986

3.145116

54

0

107107

1

4018.345

3933

85.3453

1.05

0.947386

0.004102

2

260

104144.6

2

4019.783

3933

86.78281

1.05

0.973307

0

0

280

104185.7

3

4019.389

3933

86.38881

1.05

0.972943

0

0

280

104165.9

4

4019.641

3933

86.64112

1.05

0.970029

0

0

280

104180.1

5

4019.269

3933

86.26866

1.05

0.97416

0

0

280

104163.7

 

Notes:

1.    Variable costs are minimized with economic dispatch

2.    With economic dispatch losses also have reduced further

 

                                                                                                                                                                                          

 


 

3.8     Orissa State Electricity Board System [Around 1995]

     NUMBER OF GENERATOR CONTROLS                =    14

     NUMBER OF TRANSFORMER CONTROLS              =    19

     NUMBER OF CAPACITOR CONTROLS                =    13

     TOTAL NUMBER OF CONTROLS                    =    46

3.8.1      Loss Minimization Objective

ADC

PG Total

[MW]

PL Total

[MW]

P Loss

[MW]

VMAX

[pu]

VMIN

[pu]

Sv

[pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

3955.887

3770

185.8874

1.04

0.654134

8.09204

82

0

119355.2

1

3922.079

3770

152.0789

1.05

0.908798

0.298497

25

185.1513

117368.7

2

3916.141

3770

146.141

1.05

0.925086

0.061712

8

185.1513

117024.5

3

3915.149

3770

145.1491

1.05

0.928355

0.038809

7

193

116967.1

 

3.8.2      Loss Minimization and Economic Dispatch Objective

ADC

PG Total

[MW]

PL Total

[MW]

P Loss

 [MW]

VMAX

[pu]

VMIN

[pu]

Sv

[pu]

Nv

Qcom

[MVAR]

Variable

Cost

0

3955.887

3770

185.8874

1.04

0.654134

8.09204

82

0

119355.2

1

3933.614

3770

163.6135

1.05

0.903117

0.415851

31

185.1513

112740.3

2

3928.594

3770

158.5938

1.05

0.921461

0.134894

14

193

112511

3

3925.758

3770

155.758

1.05

0.927761

0.026561

4

211.2418

112379.5

 

Notes:

1.    Variable costs are minimized with economic dispatch

2.    With economic dispatch losses also have NOT reduced further

 


 

4      Conclusion

The results for 8 systems starting from 6 bus test system to 1043 bus practical Indian Grid system, indicates the robustness and dependability of the PowerApps OPF algorithm

 

In most cases as observed by this author , the combined objective of economic dispatch and loss minimization was more effective, as compared to only transmission loss minimization objective.

Optimal Power Flow Algorithm


http://www.google.com
http://www.activesearchresults.com
Mail your questions, enquiries to raghunatha@powerapps.org