Electric Power System Operation: A Petri Net Approach for Modeling

and Control

Milton Souza

1

, Evangivaldo Lima

2

and J´es Cerqueira

3

1

Faculdade de Tecnologia Senai-Cimatec, Avenida Orlando Gomes, Piat˜a, Salvador, Bahia, Brazil

2

Universidade do Estado da Bahia, Rua Silveira Martins, Salvador, Bahia, Brazil

3

Universidade Federal da Bahia, Aristides Novis, Salvador, Bahia, Brazil

Keywords:

Petri Nets, Electric Power System, Model, Supervisor, Constraint.

Abstract:

In this paper the operation of electric power system is treated as a discrete event system and a Petri Net is

used as formal tool to achieve it. Each component of power system is modelled as a single Petri Net and the

complete model is reached by composition of these single Petri Nets. Properties such as: parallelism, conﬂict,

concurrency and others are used to study the operation of the modelled system. In this study are detected

undesired behaviors on the dynamics of system. The theory of supervisory control is used to avoid these

undesired behaviors forcing the system to have a controlled behavior. To obtain a controlled system a set of

constraint are modelled by linear inequalities and the systems is forced to obey it. A case study application is

presented to illustrate the proposed model here.

1 INTRODUCTION

The power system is modeled using math tools such

as, differential equations and the main goal is to ob-

tain the optimal operation state. In the basic level, the

power system generates, transforms and distributes

the electric power to the loads.

Next, there is the layer of control equipment. This

equipment helps maintain the power system at its nor-

mal voltage and frequency, generates sufﬁcient power

to meet the load and maintains optimum economy and

security in the interconnected network. The control

equipment is organized in a hierarchy of its own, con-

sisting of local and central control functions.

The equipments control of electric power systems

is governed by a set of procedures that are required

to ensure that any intervention on the system and will

be performed under safe condition, considering the

inherent dangers coming from the presence of live

conductors, parts and components. In the last years

the formalization of the general rules and methods

adopted in the preparation, control and actuation of

electrical procedures has been proposed. The Electric

Power System modeling using Petri nets is one of this

formal methods used by researchers.

In this sense, the system evolution and its state

changes is obtained in graphical and analytical form

allowing the better understand of logic in the proce-

dures and to allow its immediate consistency. In ad-

dition, the check of the correctness of the procedures’

operating sequences could be followed. In the work

of (A. Ashouri and Noroozian, 2010), the Petri nets is

used, in addition of SCADA system, to diagnose fault

protection elements. In (Vescio et al., 2015) has been

used Marked Petri nets to represent EPS and through

its dynamics and mathematical structure to ﬁnd unde-

sirable conditions. In this work is presented the equip-

ment control of electric power systems using supervi-

sory control theory and Place Invariants of Petri nets

(Lima and D´orea, 2002).

In this sense, this paper is organized as follow:

In the section 2 is presented the theoretical basis of

supervisory control using place invariants of Petri

Nets(PN). Electric Power Systems(EPS) is described

in the section 3. The case study is treated in the sec-

tion 4. Conclusions and future expectations end this

work.

2 SUPERVISORY CONTROL

Many researchers used Petri nets as a tool for model-

ing, analyzing and synthesize control laws for DES.

There are many works applied in the literature (Mu-

rata, 1989),(Boissel and Kantor, 1995),(Zhou and

Souza, M., Lima, E. and Cerqueira, J.

Electric Power System Operation: A Petri Net Approach for Modeling and Control.

DOI: 10.5220/0005977904770483

In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2016) - Volume 1, pages 477-483

ISBN: 978-989-758-198-4

Copyright

c

2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

477

Dicesare, 1992),(Boucher, 1996), (Moody, 1998).

Assuming the model of a given modeled plant

in Rdp is (N, M

0

) where N = (P, T, D, W) and D =

Post − Pre is a set of all reachable markings starting

in the initial mark M

0

in the corresponding PN. As-

suming also that the control objective is to restrict the

state plant evolution from state S to subset S

′

, S

′

∈ S.

This constraint imposed by the control is described by

a set of linear inequalities:

L∗ M(k) ≤ b (1)

Where L ∈ Z

qxn

, b ∈ Z

q

, M ∈ Z

m

.

The compured controller will act not only to allow

the ﬁring for a transition leading to the occurrence of

an unwanted state. It sets an extreme condition of the

controller action. To determine the unknown param-

eters of the controller: M

c

(0) e D

c

is calculated as

follows:

From the control speciﬁcations given in equation 1 is

noted that

L∗ M(k) + M

c

(k) = b, (2)

where k = 0, 1, . . . m and M

c

(k) is a positive vector of

integers inserted as a break to make the inequality in

equality. For k = 0 is determined that the driver mark

is given by:

M

c

(0) = b− L∗ M(0) (3)

2 - Multiplying both sides of equation 5 by the ma-

trix [L I] and applying invariance property from the

equation 2, it is determined that the controller inci-

dence matrix is given by:

D

c

= −L∗ D (4)

The equations 3 and 4 are used for solve control

problems. The equation 3 is used to compute initial

marking to the controller while equation 4 show how

Places-controller are linked with transitions in the

plant(EPS model) (Lima and D´orea, 2002), (Moody,

1998).

The controllers are places linked by arcs in the

model pc

1

, . . . , pc

q

and their marking M

c

(k) ∈ N

q

re-

spectively. The initial marking and the way the con-

troller is connected to transitions can be obtained by

taking an extended Petri net with (M, M

c

)

T

. If a tran-

sition t

j

ﬁre,the PN state change according the equa-

tion 5.

M(k+ 1)

M

c

(k+ 1)

=

M(k)

M

c

(k)

+

D

D

c

∗ σ

j

(5)

3 ELECTRIC POWER SYSTEM

The Electric Power Systems can be deﬁned as a set

of physical equipment and connected electrical circuit

elements, which act in a coordinated manner in order

to generate, transmit and distribute electrical energy

to consumers. The generation makes up the func-

tion of converting some form of energy into electri-

cal, transmission carries electricity from production

centers to consumption centers or to other electrical

systems, connecting them. Distribution distributes the

power received from the transmission system to large,

medium and small consumers (Vescio et al., 2015).

3.1 Modeling of Electric Power Systems

(EPS)

The electrical system should be carefully represented

by appropriate modeling tool. The tool has relation-

ship to type of study to be performed. For protec-

tion studies, for example, values of short-circuit cur-

rents should be calculated. Therefore, each system

component must be modeled and represented from

the perspective of its behavior to short-circuit cur-

rents. This modeling is relatively easy due to the

simpliﬁcations made in the equivalent circuits of the

components. The suitability of the model for stud-

ies of short-circuit is made with the use of symmetri-

cal components, which leads to the obtaining of three

system models: positive sequence, negative sequence

and zero sequence (Grainger and Stevenson, 1994).

3.2 Single Line Diagram of EPS

Because the system operates normally balanced, it

replaces its three-phase representation by a sym-

bolic representation, known as single-line diagram.

The importance of the single-line diagram is clearly

present the topology and concisely the signiﬁcant

power system data. The single-line diagram can con-

tain different information depending on the type of

study, such as for power ﬂow, short circuit, stabil-

ity and protection (Anderson, 1998). An example of

single-line diagram is shown in Figure 1.

3.3 Elements of Electric Power System

The electric power systems can be composed of some

basic components that together have the function gen-

erate, transmit, distribute or connect other electrical

power systems (Grainger and Stevenson, 1994). some

of these elements are:

1. Generator - Element active power generator

2. Power Transformer - They increase or decrease

the currents and voltages of the EPS

3. Transformer as Mesure Instrument - parame-

ters in order to monitor, control and protection.

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

478

4. Bus - elements used as points of interconnection

between the EPS components.

5. Breakers - Switching used to turn on or off a EPS

normal or abnormal condition.

6. Switch - Device designed to isolate (sectioning)

parts (subsystems, equipment etc.) of electrical

circuits. They are installed aiming at breaking the

network to minimize the effects of planned out-

ages or not, establish visible sectioning in equip-

ment such as automatic circuit reclosers, switches

oil, establish bypass in equipment such as voltage

regulators, etc.(Grainger and Stevenson, 1994).

4 MODELING OF EPS

OPERATION USING

PLACE-TRANSITION PETRI

NETS

This chapter is a case study of modeling a EPS us-

ing Place-Transition Petri net. Therefore, it has to be

a single line diagram EPS consisting of 2 buses (B

1

and B

2

) 6 circuit breakers (D

1

, D

2

,· · · ,D

6

), 5 switches

(S

1

,· · · , S

5

) 1 transformer and 3 energy consumers.

Figure 1 shows the single line diagram for this study.

Figure 1: Bus Feeder System and Power Supply.

From:(ABB, 2010).

4.1 Modeling of the EPS Free Behavior

The development of the free behavior model in PN as-

sociated to elements of the EPS Figure 1, taking into

account:

• breakers and switches have two possible states on

or off

• The transformer T and buses B

1

and B

2

will be

modeled by three states, which are power off state,

energized via feeder PS

1

and energized via feeder

PS

2

• In this model will not be provided abnormal oper-

ation of the elements.

The Figures 2 and 3 show these representations in

Petri net. The presence of token in a place will in-

dicate the current state of the element.

Figure 2: Petri Net Model for Switch and Breaker.

Figure 3: Petri Net Model For Transformer and Bus.

From the individual model, determines the com-

plete model of the system. The composition of PS

1

feeder is shown in Figure 4. The places of P

1

to P

6

represent the sets of circuit breaker and switches that

will energize the input bus B

1

, P

7

represents that Bus

B

1

is energized via PS

1

and P

8

the opposite state. the

complete model is made by 6 places representing PS

2

P

9

to P

13

. The same way bus B

1

, the transformer and

the output bus B

2

have in their models information

about power supply origin see Figure 3. They have

three places those represent energized via PS

1

or PS

2

and another to represent the off-state. The transformer

Electric Power System Operation: A Petri Net Approach for Modeling and Control

479

Figure 4: Model of Free Behavior of the EPS.

is represented by the states P

19

, P

20

and P

21

and the

output bus B

2

by the states P

24

, P

25

and P

26

respec-

tively. Power up these elements are linked to S

5

and

D

3

when P

18

and P

23

are marked. All consumers are

powered up by individual circuit breakers represented

by places P

27

to P

32

that enable energy consumption

by two distinct paths PS

1

and PS

2

. To represent con-

sumers, the model has places of inﬁnite capacity with

dual transition. The enabled transitions provide infor-

mation about the origin of the supplied energy. The

even transitions are enabled and ﬁred when the power

supply is PS

1

and odd transitions PS

2

.

4.2 Supervisory Control Theory

Applied to EPS

The free behavior of the proposed example presents

several EPS operating problems. There are charac-

teristics of power components that make up a EPS to

be taken into account when turn on or off the power.

As shown in (Zhao and Mi, 2006) breakers are the

EPS equipment designed to make power on and off.

Switches should isolate or integrate a region of a EPS

when in power off state.

To avoid the modeled example may have improper

representation (eg open switch when circuit breaker is

on state) should expand this PN model putting super-

visors places distributed in all sectors of the prior PN.

These places are dedicated to develop constraints in

breakers and switches models as shown in (Zhao and

Mi, 2006). The following constraints are identiﬁed in

the studied model:

1. The procedures for energization via B

1

must start

with the connection of the keys S

1

and S

2

. For

this, you should impose the following constraint,

M

P

2

+ M

P

6

≤ 2;

2. After the P

36

controller close the switches S

1

and

S

2

, the circuit breaker controller of D

1

receives

the privilege for its opening or closing, 2∗ M

P

4

+

M

P

36

≤ 2;

3. Similarly, energization via B

2

must start with the

connection of the keys S

3

and S

4

. For this, you

should impose the following constraint, M

P

9

+

M

P

13

≤ 2;

4. After the controller P

38

close the switches S

3

and

S

4

, the circuit breaker controller of D

2

should gain

the status to take any action on it. this restriction

is described as follows: 2∗ M

P

11

+ M

P

38

≤ 2;

5. The switch S

5

may change status (on / off) when

the input bus is power off. This is possible to cre-

ate a Constraint from the state that is power the

bus off P

16

and the state is S

5

connected P

18

then

we have: M

P

16

+ M

P

18

≤ 1;

6. The controller for handling breaker D

3

of the out-

put bus energization will have autonomy to op-

erate it only when the status of switch S

5

is on.

This condition generates inequality linked with

the marking of the states that represent them, P

17

and P

22

. It is then: M

P

17

+ M

P

22

≤ 1;

7. The last supervisor shall be responsible for rout-

ing the way which will be energized when the bus

power down. The supervisor function is monitor

the B

1

power down through the place (P

16

. It is

write the following restriction:. M

P

16

+ M

P

7

≤ 1

To illustrate the implementation of the controllers

consider the inequalities generated from the feeder

free behavior modelPS

1

. As shown in the literature,

see (Grainger and Stevenson, 1994), the maneuvers of

switches and circuit breakers must comply their con-

structive features as real representative system. Thus,

the model dynamic should express such conditions.

So supervisor control theory will restrict the model

dynamics. The new PN transform the free behavior

in the actual operating conditions of EPS elements.

From item 1 and 2 above, follow the equations:

a) Constraint M

P

2

+ M

P

6

≤ 2

0 1 0 0 0 1

∗

M

P

1

M

P

2

M

P

3

M

P

4

M

P

5

M

P

6

≤ [2]

b) Constraint 2∗ M

P

4

+ M

P

36

≤ 2

0 0 0 2 0 0 1

∗

M

P

1

M

P

2

M

P

3

M

P

4

M

P

5

M

P

6

M

P

36

≤ [2]

Extracting the PNs for both cases the incidence matri-

ces and the initial marking (D

1

and M

10

) and (D

2

and

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

480

M

20

) we have:

D

1

=

−1 1 0 0 0 0

1 −1 0 0 0 0

0 0 −1 1 0 0

0 0 1 −1 0 0

0 0 0 0 1 −1

0 0 0 0 −1 1

e M

01

=

1 0 1 0 1 0

T

D

2

=

−1 1 0 0 0 0

1 −1 0 0 0 0

0 0 −1 1 0 0

0 0 1 −1 0 0

0 0 0 0 1 −1

0 0 0 0 −1 1

−1 1 0 0 −1 1

e M

02

=

1 0 1 0 1 0 2

T

by these information and using equations3 and 4 are

found the controller 1 and 2 characteristics. Such in-

formation are represented in the expanded Petri net by

places P

36

and P

37

;

a) controller1 Features

D

c1

=

−1 1 0 0 −1 1

M

c10

= [2]

b) Controller2 Features

D

c2

=

1 −1 2 −2 1 −1

M

c20

= [0]

Figure 5 shows the expanded model of Petri net feeder

(PS

1

) bus of the EPS case study. The Figure 5 shows

that the PN is started with switches and Breaker in off

state (P

1

, P

3

and P

5

with marking). In this condition,

only Controller1 is enabled (P

36

2 marks) allowing the

switches models S

1

and S

2

go to the on state. t

1

and

Figure 5: Petri Model of PS

1

Feeder.

t

5

ﬁring takes P

2

and P

6

to receive tokens represent-

ing the switches were turned on. This sequence of

ﬁring takes disabling Controller1 and enabling Con-

troller2 that received 2 marks. This condition enables

the transition t

3

ﬁring takes the model of D

1

to on

state, meaning that B

1

was energized. The same con-

dition can be obtained by the equation 5

M

1

M

2

M

3

M

4

M

5

M

6

M

c

1

M

c

2

=

1

0

1

0

1

0

2

0

+

D

D

c

1

D

c

2

∗ σ (6)

Where

D

D

c

1

D

c

2

=

−1 1 0 0 0 0

1 −1 0 0 0 0

0 0 −1 1 0 0

0 0 1 −1 0 0

0 0 0 0 −1 1

0 0 0 0 1 −1

−1 1 0 0 −1 1

1 −1 −2 2 1 −1

and σ is the transition sequence that will ﬁre, t

1

t

3

t

5

σ =

1 0 1 0 1 0

T

computing get the following result:

0 1 0 1 0 1 0 0

T

The result shows the PN conditions obtained in pre-

vious analysis. Places P

2

, P

4

and P

6

receive marks

representing the circuit breaker and switches in on

states. This condition makes the transition t

13

en-

abled, if ﬁre, place P

16

loss marking (Bus Off) to

place P

14

(Bus On) indicating bus B

1

power on via

PS

1

. Note that transition t

13

is connected to places

by self-loops. this connection maintain narking after

t

13

ﬁring. This is critical to guarantee the states of

switches and breakers with bus power on. The Figure

6 is a simpliﬁed way to represent EPS PN model stud-

ied with controllers those restrict the free behavior of

their switches and circuit breakers. The ﬁgure shows

two-way arrows to show the ﬂow of PN-controller in-

formation. Thus, if transition t

j

ﬁres, the controller

receives or losses marking given by the weight of its

arcs. The set of controllers C

1

, C

2

, C

3

, C

4

, C

5

and C

6

receive information through their enabled input tran-

sitions or disable other output transition. these actions

impose free behavior model(without control) com-

ply the constraints those are imposed. Such dynamic

avoid ﬁring transitions those take the PN to forbidden

Electric Power System Operation: A Petri Net Approach for Modeling and Control

481

Figure 6: Simpliﬁed diagram of the PN Expanded with con-

trollers.

state. opening of the switch S

1

with the breaker D

1

closed is a forbidden state.

Note the Figure 6 that set of controllers C

1

and

C

2

, C

3

and C

4

are controllers of the PN feeders PS

1

and PS

2

. The controller C

5

selects the path that the

expanded PN will represent B

1

state energized or via

PS

1

or via PS

2

. These dynamics two ways for take B

1

in on state:

• P

14

which indicates that model is energizing via

PS

1

;

• while the state P

15

represent energizing via PS

2

.

To energize the transformer, the EPS example, uses

the switch S

5

. S

5

operation should be done when

the bus is power off and the secondary of the trans-

former devoid of energy consumers. Thus, the repre-

sentative model of the EPS should include such re-

strictions. The constraints have been implemented

through two controllers C

6

and C

7

. C

6

function is re-

stricting against closing S

5

for energized bus andC

7

is

restricting against opening with circuit breaker D

3

in

on state. C

6

and C

7

are represented in simpliﬁed PN

block diagram Figure 6.

5 CONCLUSION

The electric power system operation is completely

modeled by a Petri nets. The model can be achieved

through the creation of single PN for each part of sys-

tem. The free behavior of each elements that make up

the system then are interconnected to form the repre-

sentation of power system. This representation is free

of any constraint of the elements make up the EPS.

This article was called free model or free behavior of

the electric power system.

The existing memory effect on the opening and

closing of a circuit breaker in the PN model was

solved using a feature of Petri nets called self-loop.

This is done by interconnecting one place and transi-

tion by two arcs in opposite directions to each other.

Thus, the turn on circuit breaker do not lost a token

by energizing a bus transition is enabled by the place

up switch can shoot without any loss of the marking

place in dynamic network.

The model of free behavior of the electric power

system does not describe the actual behavior of EPS

elements. Decoupling between individualized mod-

els of its elements provide the appearance of undesir-

able states or states that would cause risk to integrity

of the EPS. To eliminate such states, the model was

expanded using local supervisors. The Local super-

visors are places inserted in the free model that have

the ability to restrict undesirable states through inhi-

bition of controllable transitions ﬁring. The imple-

mentation of these controllers are made from inequal-

ities that describe such constraint. These inequations

determining the initial marking, the weights of input

and output arcs for each supervisor. The evolution of

the dynamics of the new network is presented as a se-

quence of markings of places that fully comply with

the procedures and or care that you have to turn on or

off an electric power system without weakening the

actual functionality of the EPS.

The existing mememory effect on the opening and

closing of a switcher and breaker in the PN model

was solved using a feature of Petri nets called self-

loop. This is done by interconnecting one place and

transition by two arcs in opposite directions to each

other. Thus, the turn on switcher do not lost a token

by energizing a bus transition is enabled by the place

up switch can shoot without any loss of the marking

place in dynamic network.

The model of free behavior of the electric power

system does not describe the actual behavior of EPS

elements. Decoupling between individualized mod-

els of its elements provide the appearance of undesir-

able states or states that would cause risk to integrity

of the EPS. To eliminate such states, the model was

expanded using local supervisors. The Local super-

visors are places inserted in the free model that have

the ability to restrict undesirable states through inhi-

bition of controllable transitions ﬁring. The imple-

mentation of these controllers are made from inequal-

ities that describe such constraint. These inequations

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

482

determining the initial marking, the weights of input

and output arcs for each supervisor. The evolution of

the dynamics of the new network is presented as a se-

quence of markings of places that fully comply with

the procedures and or care that you have to turn on or

off an electric power system without weakening the

actual functionality of the EPS.

Going beyond that as future work should improve

the model by entering the protection elements and ap-

ply this model in the study of diagnosability.

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