UNIVERSIDAD DE LOS ANDES

Coordination of overcurrent relays for a

industrial distribution network using

OpenDSS

Juan David Perez Osorio

Supervisor: Gustavo Andres Ramos Lopez

Examiner 1: Paulo de Oliviera de Jesus

Examiner 2: Esperanza Susana Torres Gutierre

Submitted in fulfilment of the requirements for the Degree of

Master in Electrical Engineering

Engineering Faculty

Department of Electrical and Electronic Engineering

January - 2019

Author’s Declaration

1. I am aware that any fraud in this thesis is considered a serious offense in college. By

signing, deliver and present this proposal Thesis or Graduation Project, I express testi-

mony that this proposal was developed in accordance with standards established by the

University. Similarly, assure you that I did not participate in any kind of fraud and at

work concepts or ideas that are taken from other sources are properly expressed.

2. I am aware that the work that I perform include ideas and concepts of the author and

the Advisor and may include course materials or previous work in the University and

therefore, give proper credit and I will use this material in accordance with human rights

standards copyright. Likewise, I will not publications, reports, articles and presentations

at conferences, seminars or conferences without review or authorization of the Counsel

who represent in this case the University.

Signature:

Nombre: Juan David Perez Osorio

Codigo: 201017066

C.C.: 1022380780

Date: Jan - 2019

i

UNIVERSIDAD DE LOS ANDES

Abstract

Engineering Faculty

Department of Electrical and Electronic Engineering

Keywords: Industrial distribution network, radial system, overcurrent relay, coordination of

protections, optimization, gradient descent, heuristic methods, genetic algorithm.

The aim of this proposal is to develop a strategy to coordinate overcurrent relays in a industrial

distribution system, by implementing a general software for future studies and optimizing the

response time of the system when a fault occurred. For this objective 3 different approaches (1

linear and 2 nonlinear) were implemented as a computational tool using OpenDSS, Labview

and Matlab.

UNIVERSIDAD DE LOS ANDES

Abstract

Engineering Faculty

Department of Electrical and Electronic Engineering

Palabras Clave: red de distribucion industrial, sistema radial , rele de sobrecorriente, coor-

dinacion de protecciones, optimizacion,gradiente descendiente, metodos heuristicos, algoritmo

genetico.

El prinicipal proposito de este desarrollo es el de crear una estrategia de coordinacion de

reles de sobrecorriente en un sistema de distribucion industrial, implementado un sotware

apra futuros estudios y tratando de optimizar el tiempo de respuesta del sistema ante la pres-

encia de una falla. Para esto 3 diferentes enfoques fueron realizados (1 lineal y 2 o lineales)

utilizando como herramientas computacionales OpenDSS, Labview y Matlab.

Acknowledgements

First I want to thank Gustavo Ramos for his support and guide in the development of this

work and all his suport with the struggles during the project. Second to all my master part-

ners who encourage me to follow with the next steps.

I want also to thank my parents David Perez, Elizabeth Osorio and Bibiana Paez, who always

believe in me and help me with their emotional and economical support through these years

of studies. Finally my beloved girlfriend Bibiana Paez for being in every hard moment and

happy moment to support me with her knowledge and company during these two years of my

master studies.

iv

Contents

Author’s Declaration i

Abstract ii

Acknowledgements iv

List of Figures vii

List of Tables viii

1 Introduction 1

2 Objectives 3

2.1 General objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Specific objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3 Scope and final product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Work methodology 4

3.1 Overcurrent relay model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.1.1 State machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.1.2 TC curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 Formulation of optimization problem . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2.1 Linear problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2.2 Nonlinear problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4 Justification 9

5 Work done 11

5.1 Software implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5.1.1 Proposed Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5.1.2 Relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5.1.3 Fault and nominal current . . . . . . . . . . . . . . . . . . . . . . . . . . 14

v

Contents vi

6 Work validation 15

6.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

6.1.1 System IEEE 242 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

6.1.2 Comparison between standard and linear algorithm . . . . . . . . . . . 16

6.1.3 Comparison between genetic algorithm and gradient descent algorithm 19

7 Conclusions 21

List of Figures

1.1 Example of a diagram for overcurrent coordination [1] . . . . . . . . . . . . . . 2

3.1 State Machine for overcurrent relays . . . . . . . . . . . . . . . . . . . . . . . . 5

4.1 System to justified the use of a optimization tool to solve the coordinationproblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

5.1 Architecture of the solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5.2 Main program of the solution implemented in Labview . . . . . . . . . . . . . . 12

5.3 Scheme of software functionality . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5.4 Scheme of software functionality . . . . . . . . . . . . . . . . . . . . . . . . . . 14

6.1 Architecture of the solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

6.2 Relay protecting motor with 4160V nominal rated . . . . . . . . . . . . . . . . 18

6.3 Relay protecting motor with 480V nominal rated . . . . . . . . . . . . . . . . . 18

vii

List of Tables

3.1 Constants for Time Current Curves according to for ANSI equations . . . . . . 6

4.1 Currents for the system in figure 4.1 with presence of a fault . . . . . . . . . . 9

4.2 Results of the problem using a genetic algorithm and gradient descent algorithm 10

6.1 Types of curves for the standard . . . . . . . . . . . . . . . . . . . . . . . . . . 16

6.2 Comparison between standard and linear algorithm . . . . . . . . . . . . . . . . 17

6.3 Results of Time dial settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

6.4 Comparison between standard and linear algorithm adding fuse times . . . . . 17

6.5 settings for Gradient Descent Algorithm . . . . . . . . . . . . . . . . . . . . . . 19

6.6 settings for Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

6.7 Comparison between genetic algorithm and gradient descent algorithm . . . . . 20

viii

Chapter 1

Introduction

Currently the study of protections in electrical networks is a common and old subject. The

IEEE standard electrical power system device function numbers C37.2-1987 created in 1987

[2] presently contains most of the currently protection functions used at the moment. Some

of them are the 50 and 51 protection functions for instantaneous overcurrent and time over-

current.

Those functions are commonly use to protect industrial networks; normally the studies are

made graphically like the one show in figure 1.1, where usually there is a gap between the

protection curves in order to protect the system. Although when the systems are complex is

not so easy to coordinate the gap, to give the switch enough time to act and clear a fault as

soon as possible.

Professor Urdaneta was one of the first to propose the use of optimization to adjust the over-

current relay protection in transmission systems [3]. In his paper he propose a linear algorithm

to configure the minimal amount of relays, when a generator changes its dispatch of energy.

New studies have used this idea such as [4]where a Mixed linear Program was propose to solve

the coordination problem in distribution systems.

In order to coordinate the protections for industrial power system using an optimization

methodology, some issues arise such as unbalance systems because in a industrial system not

all the loads present are connected to three phases, some of them use only one or two phases.

Moreover some methodology do not consider the whole equation to calculate a trigger time,

to simplified the optimization problem.

With the last in mind this study proposes a new scope which consist in the use of a virtual

relay as the ones in [5] that would be implemented in order to manage easily the protections

1

List of Tables 2

Figure 1.1: Example of a diagram for overcurrent coordination [1]

of a industrial network. Then a new methodology will be present to deal with unbalanced net-

works and achieving better response times with a backup protection using a complete model

for trigger times. Finally using an appropriate network simulator as OpenDss that can solve

unbalanced power flows; a software is developed to repeat easily the porpoise methodology

making it as simple as possible to use it for future works.

The order of this paper will be the following: first, the use of a virtual relay model will be

explained; second, the approaches to solve the coordination problems through optimization

tools will be propose. Third, the tool to create coordinate overcurrent relays will be explained;

fourth results using the IEEE 242 system [6] are shown and fifth a conclusion will be given

with further works proposals.

Chapter 2

Objectives

2.1 General objectives

The principal objective of this thesis is to design and implement a methodology to use opti-

mization tools to protect industrial systems with overcurrent relays.

2.2 Specific objectives

The specific objectives of this work are presented in 3 different tasks:

• Design of a methodology using optimization tools. Taking into account the unbalance

present in those types of networks.

• Implement the final methodology in a environment to be used for students and re-

searchers

• Prove the methodology in a knowing industrial system in the literature.

2.3 Scope and final product

The commitment of this thesis was to give a functional software that configure automatically

the relays present of any network using 3 different approaches, and making it adaptable for

further works. Also with an friendly interface for any user.

3

Chapter 3

Work methodology

3.1 Overcurrent relay model

The relay models were the instantaneous and time overcurrent protection, corresponding to

the ANSI device numbers 50 and 51 respectively. In this section will be explained the model

for both protection device and how to find the lap time in a time overcurrent relay.

3.1.1 State machine

To model the protection function, a state machine was designed due its facility to capture the

protection functions in a single state machine. The design of the last is show in figure 3.1.

The first state of the machine is called normal. In this state the relay does not trip the asso-

ciated switch, and its unique transition is when the current seen by the Current Transformer

(CT) is bigger than the pickup current set in the relay, call it in the machine abnormal con-

dition.

the second stated is name Stand by, where the relay detects a bigger current than the pickup

current. Consecutively the relay must wait the programmed time to send a trip signal to the

switch. In a instantaneous overcurrent relay the time is always fixed according to the settings.

But the instantaneous overcurrent relay varies its time following a Time Current Curve.

The last state named Lock Out is state to forbid the switch to operate until the relay is reset

manually.

4

List of Tables 5

Figure 3.1: State Machine for overcurrent relays

3.1.2 TC curves

The standard curves used in protections follows a function shown in equation 3.1. The result

of this functional is the time where the relay should send the trip signal to the switch.

f(Im, Ip|A,B,L,C, TD) = TD

A(ImIp

)B− 1

+ L

+ C [s] (3.1)

A, B, L are fixed constant depending on the standard curve used. C is a pure delay applied

to the TC curve, TD is the Time multiplier setting for IEC curves or Time Dial for IEEE

curves. Im correspond to the measured current and Ip is the pick up current. The constants

used to model the ANSI function 51 are shown in Table 3.1 for every type of curve.

List of Tables 6

Table 3.1: Constants for Time Current Curves according to for ANSI equations

Characteristic Curves A L B

Definite time 0.2 0.18 1Moderately inverse time 0.55 0.18 1

Short Time 0.2 0.015 1Modified inverse time 1.35 0.055 1

Modified very inverse time 1.35 0.015 1Inverse time 5.4 0.18 2

Very inverse time 5.4 0.11 2Extremely inverse time 5.4 0.03 2

3.2 Formulation of optimization problem

To coordinate the protections there are three methodologies implemented. One formulating a

linear optimization problem, knowing this has a solution using the gradient descent algorithm,

and the other two establishing one nonlinear problem using the gradient descent algorithm

and a heuristic method (genetic algorithm) due to nonconvexity of the problem.

The objective function will be to minimize the trigger time of all the relays in a system with

the restriction that the protection will act effectively when a fault occurs.

3.2.1 Linear problem

First we take equation 3.1 and split the terms in a sum and define the following variable:

ti(Im, Ip|A,B,L, TD) = TD

A(ImIp

)B− 1

+ L

(3.2)

ti will represent the trigger time of the ith relay. Observe that if the variables A, B, L, Ip,Im

are fixed ti is a linear term for TD.

If a standard curve is fixed and Ip is define for each relay, it is possible to calculate for a

specific fault, the term multiplying TD.

Therefore it can be formulate the following linear problem to solve the coordination of pro-

tections.

min

N∑i=1

(tpi +

∑tbj

)(3.3)

List of Tables 7

Subject to:

TDmin ≤ TDi ≤ TDmax (3.4)

tbj − tpi ≤ TI∀i ∈ {1, ..., N}∀j ∈ Bi (3.5)

Where N is the number of relays in the system. tpi is the trip time on a fault in the node

downstream from the switch, where the CT is measuring. tbi corresponds to the trip time

from the relays of backup.

According to Shrafa [7] the time dial is always set between 0.1 and 3. TI is the interval time

between a principal relay and backup one. This condition ensures that there won’t be an

intersection of the curves in the current fault.

Bi is a set including the backup relays of the ith relay.The decision variable for this formulation

is only the time dial setting of each relay. So it should be note that for this method to function,

it would be necessary to define the type of curve to be used in every relay and the pickup

current.

3.2.2 Nonlinear problem

The nonlinear problem is very similar to the linear one. But, to have a better result. The

number of variables of decision and the number of restrictions is increased.

Then the optimization problem is stated as:

minN∑i=1

(tpi +

∑tbj

)(3.6)

Subject to:

TDmin ≤ TDi ≤ TDmax (3.7)

Amin ≤ Ai ≤ Amax (3.8)

Bmin ≤ Bi ≤ Bmax (3.9)

Ipmin ≤ Ip ≤ Ipmax (3.10)

tbj − tpi ≤ TI∀i ∈ {1, ..., N}∀j ∈ Bi (3.11)

Looking at table 3.1 the value of L is always near 0. So in order to reduce computational

process L is fixed to be 0. Hence the decision variable for this case would be A,B,TD,Ip.

According to manufactures A is between 0.135 and 5.4 and B between 0.02 and 13.5. Finally

List of Tables 8

to define the limits of Ip there must be taken into account the nominal current and fault

current measure by the CT.

Chapter 4

Justification

In this chapter a justification for the optimization will be given. Additional a further expla-

nation of the main problem will be given the following chapter.

To justified the optimization problem porpoise that can not be solve using the Lagrange mul-

tiplier method a simple system was implemented in ETAP and the problem was solve in the

non linear case with the two methodology.

A system with an network equivalent, two switches, 1 transformer and 1 load (AC Motor) is

presented in figure 4.1

The system has an equivalent network with X/R of 10 and a short-circuit of 100 MVA for

three-phase. The X/R relation of the transformer is 13 with a percentage of impedance of

8.35 with nominal rated of 10 MVA. Finally the motor has nominal power of 900 HP at 4.8

kV.

The currents obtain in ETAP where use it to calculate settings for both relays in the system

giving the ones in table 4.1. Finally to verified that the system can not be solved was imple-

Table 4.1: Currents for the system in figure 4.1 with presence of a fault

Node to Fault Current CB1[kA] Current CB2[kA]

None 0.0369 0.106Bus3 3.9 11.21Bus 4 4.18 0.754

mented the no linear problem proposed. And the results are shown in table 4.2. Where it

can be seen that both answer were different and in the optimization tool in Matlab the stop

criteria was not decreasing in the feasible direction.

9

List of Tables 10

Figure 4.1: System to justified the use of a optimization tool to solve the coordinationproblem

Table 4.2: Results of the problem using a genetic algorithm and gradient descent algorithm

Node to Fault Gradient descent CB1 Gradient descent CB2 Genetic Algorithm CB1 Genetic Algorithm CB2

Pickup Current 0.0369 1.6345 0.04 1.12A 0.5365 0.6919 0.141 0.14B 8.065 8.166 12 13.2

TD 1.685 1.371 0.12 0.11

Chapter 5

Work done

5.1 Software implementation

The main architecture of this proposal can be appreciated in figure 5.1. Any network can

be simulated in OpenDSS, then the information of the system is analyze in Labview and

the relays model were programmed in Labview to control the switches present in the system.

Matlab was used to solve the optimization problems and communicate the optimal settings

for each device due to its complete libraries to implemented various optimization algorithms,

the optimization library of Labview is not robust enough to solve all the problems, especially

with the heuristic methodology.

Figure 5.1: Architecture of the solution

11

List of Tables 12

Figure 5.2: Main program of the solution implemented in Labview

5.1.1 Proposed Solution

The functionalities of the software are shown in figure 5.4. The main advantages are that any

system developed in OpenDss a robust power flow software with free license can be used in a

simpler way to add relays to all desire switches in a network. Moreover a appropriated relay

coordination can be developed automatically and then change if the solution is no a desired

one. The module to simulate and find the operation of the relays when the presence of a fault

is seen in figure 5.3.

A module to save and read Relay configurations was implemented to save time for a study

of relays coordination. Also a module to see graphically the TC curves was implemented,

to assure visually that the coordination was made correctly. The main interface is shown in

figure 5.2.

5.1.2 Relays

One problem for a general solution is how to find the backup relays in the existences ones.

For this in Labview is calculate the Adjacency Matrix of the network define as:

aij =

1 if exist a link between i and j

0 Otherwise(5.1)

List of Tables 13

Figure 5.3: Scheme of software functionality

List of Tables 14

Figure 5.4: Scheme of software functionality

Where i and j are nodes of the network. Having this matrix, each relay must save the nodes

that the switch is connected.When the algorithm to solve the optimization problem is running,

the program review all the relays in the system and search in the adjacency matrix which

relays are connected in the neighborhood of the switch to associated the backup relays.

5.1.3 Fault and nominal current

As mention in the previous section, to solve the nonlinear problem it is needed the information

of the fault currents and nominal currents. To get this information a snapshot of a power flow

is solve for the nominal current. Then a fault is put it into the node downstream from the

switch. The types of fault analyzed in this study where the most common in the industry a

single phase fault and a three phase fault.

Once all fault currents are founded, the minimum current is selected to be the restriction of

maximum pick up current in order that if the algorithm detects that the current of pick up

have to be almost the maximum, when a fault occurs the relay can detect it. But to have

margin of error the lower bound is increase a percentage of the nominal current, in the same

way to the upper bound is reduce a percentage of the minimal fault current.

Chapter 6

Work validation

6.1 Results

Figure 6.1: Architecture of the solution

15

List of Tables 16

There were two principals comparisons made to check the effectiveness of the proposal algo-

rithm using the IEEE standard 242 corresponding to the buff book.The first one was using

the same curves and pickup currents from the standard, to compare the times obtain in the

norm and the ones using the algorithm. The second one was comparing the genetic algorithm

with the gradient descent algorithm.

6.1.1 System IEEE 242

The system in figure 6.1 has 8 switches and 3 fuses to protect the system. In this results the

8 relays were associated to the 8 switches available. In the standard the curves are shown in

table 6.1, Most of the curves use to protect this system are extremely inverse.

Table 6.1: Types of curves for the standard

Switch Type of curve

CB1 Moderately Inverse

CB2 Very Inverse

CB3 Extremely inverse

CB4 Extremely inverse

CB5 Very Inverse

CB6 Extremely inverse

CB7 Extremely inverse

CB8 Extremely inverse

6.1.2 Comparison between standard and linear algorithm

In table 6.2 it shown the results of trip times for the 8 switches in the standard and in the

methodology with the same type of curves and the pickup currents founded in the next section.

The settings of Time Dial are shown in table 6.3, it can be seen that all the settings are near

to the minimum of the Time Dial Setting. For this reason the times are smaller than the ones

in the standard. Finally in this case using the linear algorithm all the relays work properly

to a single ground to phase fault with impedance of 0.1 ohms.

The times present in the standard were very different from the ones in the algorithm develop,

because the standard have first a relay to protect both Loads with fuse, therefore the times

will increase in the relays, but the time will be have a better performance that the one used

in the IEEE 242.

In figure 6.3 and figure 6.2, it is show the two fuse protecting the motors as final consumers

List of Tables 17

Table 6.2: Comparison between standard and linear algorithm

Switch Trip time Standard[ms] Trip time Linear[ms]

CB1 40 35

CB2 800 20

CB3 400 10

CB4 380 21

CB5 200 94

CB6 350 94

CB7 500 20

CB8 300 61

Total [ms] 2970 355

Table 6.3: Results of Time dial settings

Switch Linear TD Ip[kA]

CB1 0.1 7.3

CB2 0.1 45

CB3 0.11 3.8

CB4 0.101 39.7

CB5 0.1 190.2

CB6 0.1 193.7

CB7 0.1 40.3

CB8 0.1 198

of the system this time must be added to the ones find by the algorithm to make a better

comparison. Adding every single time that the fuse introduce to each fault give the result

show in table 6.4. Where it can be seen that the times are near the ones in the standard 242

with a better time responds.

Table 6.4: Comparison between standard and linear algorithm adding fuse times

Switch Trip time Standard[ms] Trip time Linear[ms]

CB1 40 215

CB2 800 210

CB3 400 210

CB4 380 171

CB5 200 134

CB6 350 194

CB7 500 230

CB8 300 211

List of Tables 18

Figure 6.2: Relay protecting motor with 4160V nominal rated

Figure 6.3: Relay protecting motor with 480V nominal rated

List of Tables 19

6.1.3 Comparison between genetic algorithm and gradient descent algo-

rithm

For the results in this section single ground to phase faults where put it in the system to

prove the methodology. Tables 6.5 and 6.6 have the results settings of running the genetic

algorithm and the gradient descent algorithm. The results of response time are shown in

Table 6.5: settings for Gradient Descent Algorithm

Switch A B Ip TD

CB1 0.53 2.5 7.35 1.84

CB2 1 0.029 44.6 3

CB3 1 0.02 4 3

CB4 1 0.02 40.6 3

CB5 0.18 4.11 197.73 1.62

CB6 1 0.02 194.88 3

CB7 1 0.02 40.61 3

CB8 1 0.02 196.38 3

Table 6.6: settings for Genetic Algorithm

Switch A B Ip[kA] TD

CB1 0.53 2.5 7.3 2

CB2 1 0.029 45 2.8

CB3 1 0.02 3.8 2.8

CB4 1 0.02 39.7 2.8

CB5 0.18 4.11 190.2 1.5

CB6 1 0.02 193.7 2.8

CB7 1 0.02 40.3 2.8

CB8 1 0.02 198 3

table 6.7, where it can be seen that the genetic algorithm achieve smaller times, but the

results are very near to the ones founded by the other algorithm. The time response for both

methodology sometimes is near 0, this will be not desire, because this coordination does not

consider transients currents such as a start motor current therefore a single delay for all relays

must be considered to prevent false triggers in the protection system.

List of Tables 20

Table 6.7: Comparison between genetic algorithm and gradient descent algorithm

Switch Trip time gradient[ms] Trip time genetic[ms]

CB1 0.1 0.2

CB2 21.16 20.8

CB3 20 17.5

CB4 21.16 20.06

CB5 0.01 0.02

CB6 0.06 0.05

CB7 21.2 19.4

CB8 47.3 43.3

Total 130.99 121.33

Chapter 7

Conclusions

A new methodology was implemented for industrial systems protections using optimization

tools and having a more precise model in the linear case and the simplified one in the nonlinear

one. All of the 3 methodologies implemented in this proposal achieve a correct coordination

for faults downstream of the relay. But the methodology with better results to find the min-

imal response time for the whole system was the genetic algorithm, due the possibility of the

solution finding by the gradient descent algorithm was stoke in a minimum local but no the

global one as expected. And that the linear problem use fewer variables to solve the problem.

Likewise the methodology implemented, was useful to replicate and make studies of coordi-

nation of protections for a industrial distribution system and find times for any fault. Due to

the development of the software using OpenDSS, any network model in this software can be

use to coordinate easily the protections present in the system. Moreover new functions can be

added to the relay model to have a better coordination program using not only overcurrent

protection, but any protection function use in industrial systems.

For further works can be added new modules to model the damage curves of any device in the

system and also a module to coordinate also protections with fuse. Also other programming

language can be used to solve the optimization problem like Python to make it open source

with the objective of making this software a tool available for anyone.

21

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