Reliability analysis and matpower simulation of IEEE14 node based on mixed entropy measure

Reliability analysis and matpower simulation of IEEE14 node based on mixed entropy measure

Zhenhua ShaoZhixiong Zhong Wenzhong Lin 

China Digital Fujian IoT Laboratory of Intelligent Production Minjiang University, Fujian 350108, China

Fujian Province Key Laboratory of Information Processing and Intelligent Control Minjiang University, Fujian 350108, China

College of Computer and Control Engineering, Minjiang University, Fujian 350108, China

Corresponding Author Email: 
172097792@qq.com
Page: 
573-588
|
DOI: 
https://doi.org/10.3166/EJEE.20.573-588
Received: 
|
Accepted: 
|
Published: 
31 December 2018
| Citation

OPEN ACCESS

Abstract: 

 With the increasingly large-scale interconnection of power system, the object of this paper was to analyze the fragility of the fault of IEEE14 nodes based on the mixed entropy measure.The mixed entropy approach was adopted to quantify the fragile links in the system, which is made up by the flow entropy and the risk entropy. The simulation experiments involved in the study were implemented in the MATPOWER toolbox of the MATLAB platform. The results obtained in this study include that   the flow entropy is the key factor on unbalanced distribution of power grid, furthermore the safety of the whole power grid can be achieved a quantitative assessment by the risk entropy. The simulation experiments of IEEE-14 node   involved in the study were implemented in the MATPOWER toolbox of the MATLAB platform. The results were presented in the form of data and histograms. The impacts of the obtained results are that the transfer entropy is modified by distribution entropy of power flow. the findings of this study may do good to the power network vulnerability analysis with large nodes.

Keywords: 

 mixed entropy, chain failures, vulnerability, reliability analysis

1. Introduction

Power systems are the large-scale interconnected systems consisting of subsystems with unknown parameters. Chained failures may cause large scale blackout and lead to serious consequences. Moreover, it is rather difficult to search the modes of chained failures and analyze the consequences. In order to deal with chained failures of power grid and reasonable and effective evaluation on power system reliability, many researchers pay much more attention on reliability analysis on power system or power network (Thomasian and Blaum, 2006; Creen et al., 2003; Christopher et al., 2014; Iacoboaiea et al., 2016; Blažej and Juraj, 2014 Carvalho et al., 2018). Furthermore, security-constrained power flow optima and redistribution of power flow plays an important role in the propagation of chain failures (Kazemdehdashti et al., 2018; Wang et al., 2018; Fang et al., 2017; Barocio et al., 2017).

There are a large number of studies on analysis on solving security-constrained optimal power flow (SCOPF) with the help of Monte Carlo simulation (Monticelli et al., 1987; Stott et al., 1987; Wood et al., 2014; Momoh, 2009; Zhu, 2009). While the major shortcoming of random-gradient-based methods is that the power flow quantitative evaluation and the reliability analysis cannot be reached on small sample. Moreover, the list popular evolutionary algorithm methods (e.g. genetic algorithms, evolution strategies, differential evolution, artificial immunological systems, etc.) is not a global optimization method. The system stability and vulnerability analysis on power grid is influenced by the initial iteration value and the random-gradient direction (Shahidehpour et al., 2002; Capitanescu, 2011; Capitanescu and Wehenkel, 2012). Conversely, the mixed entropy method will be introduced to cope with the power network vulnerability analysis with large nodes (Phan and Kalagnanam, 2012; Marano-Marcolini et al., 2012; Wang et al., 2013).

The basic idea for using mixed entropy method in network vulnerability analysis is the nonlinear combination of power flow entropy and risk entropy (Ardakani and Bouffard, 2013; Platbrood et al., 2014; Wang et al., 2018). On one hand, network risk entropy plays an important role in assessment on system symmetry and topological structure of the whole network. On the other hand, the power flow entropy is the combination of power flow transfer factor and power flow distribution factor. The former is connected with the branch outage, while the latter is connected with the chain failures. The difference between network risk entropy and power flow entropy is shown in Table 1. Finally, the proposed method of mixed entropy measure of IEEE-14 node involved in the study were implemented in the MATPOWER toolbox of the MATLAB platform. The results were presented in the form of data and histograms.

Table 1. Comparison between different entropy

Type of entropy

Power flow transfer factor

Power flow distribution factor

 Risk entropy

Emphasis point

Potential fault with branch outage

Outage resistance

Uncertain of system outage

Advantage

Transfer connected with power flow

Chain failure connected with branch

Reliability analysis connected with unbalance grid

Disadvantage

Reliability analysis is ignored

Network unbalance is ignored

Power flow transfer is ignored

The reminder of this paper is organized as follows. Section 2 presents the methodology introduction for the mixed entropy measure. Section 3 describes the power flow fluctuation of load side and generation side. Simulation and analysis are studied in Section 4. The conclusions are drawn in Section 5.

2. Methodology

There are three subsections are made up in this Section. In the first one, the basic entropy theory is described. In the second subsection, the basic concept of IEEE 14 node framework is introduced. Finally, in the third subsection, load fluctuations under three different conditions are discussed.

2.1. Basic theory of entropy on power flow

The definition of entropy is:

$H=-\sum\limits_{i=1}^{N}{I{}_{i}\ln }I{}_{i}$  (1)

2.1.1. Power flow entropy QE

QE is made up by power flow transfer factor QTiand power flow distribution factor QDi. QE=QTiQDi

$\Delta {{P}_{ji}}={{P}_{ji}}-{{P}_{j0}},j\ne i$ (2)

where ∆Pji is transfer number of branch j to branch i, δji is transfer impact rate, ET is the power flow entropy factor.

$\Delta {{P}_{ia}}={{P}_{ia}}-{{P}_{i0}}$  (3)

$\Delta {{P}_{a}}=\sum\limits_{i=1}^{N}{({{P}_{ia}}-{{P}_{i0}})}$  (4)

${{\delta }_{ia}}=\frac{\Delta {{P}_{ia}}}{\Delta {{P}_{a}}}$ (5)

${{E}_{Dia}}=-{{\delta }_{ia}}\ln {{\delta }_{ia}}$ (6)

${{E}_{Di}}={{E}_{DiaG}}-{{E}_{DiaL}}={{\delta }_{iaL}}\ln {{\delta }_{iaL}}-{{\delta }_{iaG}}\ln {{\delta }_{iaG}}$ (7)

${{Q}_{Di}}=\frac{1}{2}\frac{1}{{{N}_{G}}{{N}_{L}}}\sum\limits_{{{a}_{G}}\in G}{\sum\limits_{{{a}_{L}}\in L}{\left\{ {{E}_{Di}}+\max {{E}_{Di}} \right\}}}$ (8)

Where ∆Pia is the increment of power flow, ∆Pa is the sum of the increment of power flow for node a, δia is the distribution impact rate from node a to branch I,  EDia is the power flow entropy between node a and brunch I, EDi is the sum distribution impact rate of brunch I.

2.1.2. Power flow risk entropy HR

The risk entropy HR and VR between branch j and branch i is defined as:

${{V}_{R}}=\frac{{{H}_{Rj}}-{{H}_{\min }}}{{{H}_{\max }}-{{H}_{\min }}}$  (9)

$\Delta {{P}_{ij}}=\left| {{P}_{ij}}-{{P}_{i0}} \right|$  (10)

$\Delta {{P}_{j}}=\sum\limits_{i=1}^{L}{\left| {{P}_{ij}}-{{P}_{i0}} \right|}$ (11)

${{\eta }_{ij}}=\frac{\Delta {{P}_{ij}}}{\Delta {{P}_{j}}}$  (12)

${{H}_{Rj}}=-\sum\limits_{i=1}^{L}{{{\eta }_{ij}}\ln }{{\eta }_{ij}}$  (13)

where ∆Pijis the real power variation between node j and brunch I, ∆Pj is the total real power variation of node j, hij is the relative change rate between node j and node i, HR is the risk entropy of node i, and VR is the index for reliability analysis.

2.2. power flow calculation of IEEE 14

As is shown in Figure 1, the whole frame of IEEE14 system is made up by 5 generator bus (1,2,3,6,8) and 11 load nodes (2,3,4,5,6,9,10,11,12,13,14), and the active power and real power parameters are shown in table 2 and table 3.

Figure 1. The whole frame of IEEE14 system

Table 2. Power flow calculation parameters of IEEE 14

Node Number

P(MW)

Q(MVar)

S(MVA)

Node 2

21.70

12.70

25.14

Node 3

94.20

19.00

96.10

Node 4

47.80

-3.90

47.96

Node 5

7.60

1.60

7.77

Node 6

11.20

7.50

13.48

Node 9

29.50

16.60

33.85

Node 10

9.00

5.80

10.71

Node11

3.50

1.80

3.94

Node12

6.10

1.60

6.31

Node13

13.50

5.80

14.69

Node14

14.90

5.00

15.72

Table 3. Upper limit active power value and real power value of generators

Generator number

Pmax

Pmin

Qmax

Qmin

Generator 1

332.4

0

10

0

Generator 2

140

0

50

-40

Generator 3

100

0

40

0

Generator 6

100

0

24

-6

Generator 8

100

0

24

-6

2.3. load fluctuation under three different conditions

In order to simplify the calculation process results, there are only three load fluctuation conditions considered in this paper. And the generators reactive power constraints are shown in Table 4. And the load fluctuations under different conditions are shown from Table 5 to Table 7. Condition A: the reactive power is increased and the real power is constant. Condition B: the real power is increased and the reactive power is constant. Condition C: the reactive power and the real power are increased in the same proportion.

Table 4. Reactive power constraints of generators

 

generator1

generator2

generator3

generator6

generator8

NODE 2

-11.68*

47.55

25.04

12.72

17.61

NODE3

5.57

26.44

68.48*

12.61

17.40

NODE4

-2.85*

49.60

33.71

18.61

21.26

NODE5

-14.46*

43.88

25.59

13.45

17.86

NODE6

-15.16*

40.18

24.32

16.00

17.57

NODE9

-11.74*

36.09

23.63

18.32

20.22

NODE10

-15.22*

40.99

24.51

14.41

18.07

NODE11

-16.8*

42.52

24.85

13.75

17.72

NODE12

-15.78*

41.73

24.68

15.71

17.68

NODE13

-14.78*

39.54

24.19

17.88

17.73

NODE14

-14.32*

39.55

24.30

17.52

18.72

NODE WITH

RECATIVE POWER

53.72*

33.09

75.69

49.15

27.30

Where * stands for reactive power constraints

Table 5. Load fluctuations under condition A

NODE NUMUBER

RESULTS

generator

load fluctuations factor

NODE2

bus2 P: 2.169630e+01

Q: 1.270000e+01

The generator of number 1 has violated Q constraints

1

(0~1]

NODE3

bus3 P: 9.420303e+01

Q: 19

The generator of number 1 has violated Q constraints

1

(0~1]

NODE4

bus4 P: 4.780117e+01

Q: -3.900000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE5

bus5 P: 7.603479e+00

Q: 600000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE6

bus6 P: 1.120091e+01

Q: 7.500000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE9

bus9 P: 2.950021e+01

Q: 1.660000e+01

The generator of number 1 has violated Q constraints

1

(0~1]

NODE10

bus10 P: 9.003560e+00

Q: 5.800000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE11

bus11 P: 33504797e+00

Q: 1.800000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE12

bus12 P:6.103778e+00

Q: 600000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE13

bus13 P: 1.349652e+01

Q: 5.800000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE14

bus14 P: 1.1490364e+01

Q: 5+00

The generator of number 1 has violated Q constraints

1

(0~1]

Table 6. Load fluctuations under condition B

NODE NUMUBER

RESULTS

generator

load fluctuations factor

NODE2

bus2 P: 2.17000e+01

Q: 270000e+01

The generator of number 1 has violated Q constraints

1

(0~1]

NODE3

bus3 P: 9.420000e+01

Q: 19

The generator of number 1 has violated Q constraints

1

(0~1]

NODE4

bus4 P: 4.780000e+01

Q: -3.900000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE5

bus5 P: 7.600000e+00

Q: 1.600000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE6

bus6 P: 1.120000e+01

Q: 7.500000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE9

bus9 P: 2.950000e+01

Q:1.660000e+01

The generator of number 1 has violated Q constraints

1

(0~1]

NODE10

bus10 P: 9

Q: 5.800000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE11

bus11 P: 3.500000e+00

Q: 1.800000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE12

bus12 P: 6.100000e+00

Q: 1.600000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE13

bus13 P: 1.350000e+01

Q: 5.800000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE14

bus14 P: 1.490000e+01

Q: 5

The generator of number 1 has violated Q constraints

1

(0~1]

Table 7. Load fluctuations under condition C

NODE NUMUBER

RESULTS

generator

load fluctuations factor

NODE2

bus2 P: 2.170000e+01

Q: 1.270000e+01

The generator of number 1 has violated Q constraints

1

(0~1]

NODE3

bus3 P: 9.420000e+01

Q: 19

The generator of number 1 has violated Q constraints

1

(0~1]

NODE4

bus4 P: 4.780000e+01

Q: -3.900000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE5

bus5 P: 7.600000e+01

Q: 1.600000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE6

bus6 P: 1.120000e+01

Q: 7.500000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE9

bus9 P: 2.950000e+01

Q: 1.660000e+01

The generator of number 1 has violated Q constraints

1

(0~1]

NODE10

bus10 P: 9

Q: 5.800000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE11

bus11 P: 3.500000e+00

Q: 1.800000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE12

bus12 P: 6.100000e+01

Q: 1.600000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE13

bus13 P: 1.350000e+01

Q: 5.800000e+00

The generator of number 1 has violated Q constraints

1

(0~1]

NODE14

bus14 P: 1.490000e+01

Q: 5

The generator of number 1 has violated Q constraints

1

(0~1]

Compared table 3 with table 4 and table 5, we can draw a conclusion that the maximum load fluctuations factor is 1 under three different conditions. Otherwise, reactive power constraints of generators will be happened.

3. Mixed entropy of IEEE 14 network

In order to verify the efficiency of mixed entropy measure on IEEE14 network, the different set of experiments are carried out in the MATPOWER toolbox of the MATLAB platform. Moreover the flow charts of power flow transfer entropy and power flow distribution entropy are shown in Figure 2 and Figure 4. Moreover, the experiment results of two entropy methods under MATPOWER toolbox are shown in Figure 3 and Figure 5.

Figure 2. Flow chart of power flow transfer entropy

Compared with the Figure 3 and Figure 5, we can draw the conclusion that the permutation of transfer entropy and distribution entropy are shown in table 8-10. and the sequence of distribution entropy is shown in fig.6.which means that the node 2 is the vulnerabilities in the whole network. The first set is based on IEEE 14 BUS test system. For a comparison between the mixed entropy method and power flow entropy method (or risk entropy method), the different scheduling order are shown in Fig.6 and Fig.7.As can be seen from the Fig.6(mixed entropy method), the node 3,4,5 have the same risk entropy. However, we can only draw the conclusion that the node 2 is the vulnerabilities in the whole network.

Figure 3. Experiment results of transfer entropy under MATPWOER

Figure 4. Flow chart of power flow of distribution entropy

Figure 5. Experiment results of distribution entropy under MATPWOER

Table 8. Transfer entropy

number

test1

test2

test3

test4

test5

average

node2

1.298603

1.298620

1.298616

1.298626

1.298620

1.30

node3

1.929835

1.929849

1.929832

1.929824

1.929825

1.93

node4

2.112372

2.112372

2.112372

2.112372

2.112372

2.11

node5

1.828546

1.828548

1.828549

1.828547

1.828549

1.83

node6

2.633288

2.633288

2.633282

2.633289

2.633287

2.63

node9

2.739682

2.739690

2.739687

2.739690

2.739692

2.74

node10

2.683222

2.683221

2.683219

2.683225

2.683216

2.68

node11

2.532113

2.532119

2.532114

2.532116

2.532116

2.53

node12

2.742392

2.742389

2.742391

2.742390

2.742389

2.74

node13

2.716629

2.716629

2.716629

2.716629

2.716629

2.72

node14

2.698687

2.698684

2.698684

2.698688

2.698687

2.70

Table 9. Distribution entropy

Number

test1

test2

test3

test4

test5

average

node2

-0.09355856

-0.08894123

-0.07713753

-0.1428928

-0.1347842

-0.11

node3

-0.6137061

-0.6127401

-0.6151092

-0.6107501

-0.6131079

-0.61

node4

-0.7826699

-0.7856685

-0.7851088

-0.7717788

-0.7743651

-0.78

node5

-0.7570722

-0.7396852

-0.7577844

-0.7399870

-0.7579246

-0.75

node6

-1.335513

-1.339591

-1.340334

-1.331429

-1.333509

-1.34

node9

-1.432500

-1.433163

-1.430637

-1.427934

-1.431422

-1.43

node10

-1.365670

-1.350894

-1.350821

-1.362479

-1.354593

-1.36

node11

-1.285974

-1.295250

-1.287376

-1.291148

-1.291902

-1.29

node12

-1.444787

-1.446974

-1.448250

-1.449639

-1.451017

-1.45

node13

-1.426913

-1.423656

-1.421644

-1.422398

-1.426396

-1.42

node14

-1.384793

-1.392451

-1.390621

-1.388106

-1.388971

-1.39

Table 10. Measure of distribution entropy

Number

2

3

4

5

6

9

10

11

12

13

14

Measure

-0.14*

-1.18

-1.65

-1.37

-3.52

-3.92

-3.64

-3.26

-3.97

-3.86

-3.75

Where * is the maximum value

Figure 6. Sequence of distribution entropy

Figure 7. Sequence of risk entropy

4. Conclusion

In this paper, the mixed entropy measure method is proposed to analyze the fragility of the fault of IEEE14 nodes. Compared with the power flow entropy method or the risk entropy method, the proposed method has the advantage that the sequence of distribution entropy can be quantized with the number of distribution entropy. On the other hand, the proposed method can achieve better solutions for the same computational effort. Further research work includes that a high performance method for the power network vulnerability analysis with large nodes.

Acknowledgments

This paper is supported by Natural Science Foundation of Fujian Province under grant (grant number 2016H6019, 2016J01267), in part by Scientific and Technological Projects of Fuzhou City (grant number 2016-G-53), in part by scientific research project of Xiamen City (grant number 3502Z20189033), in part by the Scientific Research Items of MJU [grant number MJY18003]

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