Secondary Control

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Abstract-- The secondary voltage control (SVC) of power

systems initiated by EDF has been developed successfully toimprove power-system voltage stability. And, with the

development of agent technique, multi-agent system (MAS) hasbeen applied in SVC to maintain the system voltage more stable.The models established in previous papers on MAS based

secondary voltage control with no sharing resources andinformation delays. So a study of the chaotic dynamics of theMAS is presented in this paper, which shows us what helps toeliminate the unstable dynamics of the MAS in resources sharing.

And a more efficient MAS model, with resources sharing, in theemergency mode is established to meet the needs of the secondary

voltage control for power system in this paper. The simulation

results of the New England 39-bus system show that the proposedMAS are efficient in managing global voltage control of power

system comparing with the normal MAS scheme..Index Terms multi-agent system (MAS), secondary voltage

control (SVC), chaos, dynamic, sharing resources.

I. INTRODUCTION

OWADAYS, secondary voltage control strategy, as a

significant segment of the hierarchical voltage control in

power systems, has been widely accepted by the scholars in

many countries and draws their great attentions. Many studies

on secondary voltage control had been done and many control

schemes appeared in recent years [1]-[4].

Distributed artificial intelligence (DAI), developed and

applied mainly for constructing large, complex and

knowledge-rich software systems, has also been studied tosolve power-system problems. As a significant part of DAI,

multi-agent system works in a decentralized control regime,

however, which requires the communication and co-operation

through coordination agents, if found necessary, not among all

the agents but only between closely related agents with

common interests [5]. From the point of view of system

control, a multi-agent based control system is different from

traditional decentralized control. As each controller is an

autonomous agent, the fundamental cooperation mechanism of

MAS lies in the task sharing and communication among

X.L. Du is with the School of Electrical Engineering Wuhan University,Wuhan, China (e-mail:[email protected]).

T.C. Lu. is with the School of Electrical Engineering Wuhan University,

Wuhan, China (e-mail: t [email protected]).L. Xu is with the Shandong Electric Power Engineering ConsultingInstitute. China .

T. Liu is with the School of Electrical Engineering Wuhan University,

Wuhan, China.

agents.

The relationships among the agents and resources are one

to one in models of previous papers. Under general

circumstance, every agent gets a fixed control target from the

manager agent. But, once an agent failed to complete the

voltage control task, there will be frequency co operations

through the manager agent [6]. So, the over-discrete resource

management based coordinated MAS has a longer response

time that with sharing resources. To build a more efficient

MAS, resources sharing should be introduced.

Without considering the information delays and imperfect

knowledge about the state of the system, the time evolution of

the agent cooperation is simple and predictable; it is relativelyeasy to program the agents to deal with variations. But, when

computational agents in these systems make choices in terms

of delayed and imperfect knowledge about the state of the

system, their dynamics can become extremely complex, giving

rise to nonlinear oscillations even chaos. The problem of

locally controlling a distributed system can be addressed in a

two ways solution in this paper. First, one could increase the

uncertainty in the agents evaluation of the merits of different

choices to stabilize the system. Another is to increase the

diversity of the system by introducing additional types of

agents that use different problem-solving methods, since

heterogeneous systems tend to be more stable than

homogeneous ones.

To improve the efficiency of normal MAS based

secondary voltage control, a new MAS with sharing resourcesis established based on the two ways upwards to maintain

power system voltage stability. Finally, the simulation results

of the New England 39-bus system [6] show that the proposed

MAS are efficient in managing global voltage control of

power system comparing with the normal MAS scheme.

II. STUDY ON CHAOTIC DYNAMICS OF MAS

To study the global dynamics of MAS, and the

consequences of control methods, a simple model is proposed

to achieve some of the key features of MAS and solving

methods. For simplicity in studying the global behavior of

large systems we take, the payoff G, for using resource r to

depend on the number of agents already using it, rather than

exactly which agents these are. Imperfect information aboutthe state of the system causes each agents payoff to differ

from the actual value. This type of uncertainty concisely

Chaos Based Multi-agent Coordination with

sharing resources for Secondary Voltage Control

in Power-system Voltage Stability

Xiaolei Du, Tiecheng Lu, Liang Xu and Tie Liu

N

1207

978-981-05-9423-7 c 2007 RPS


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captures the effect of many sources of errors such as some

program bugs, heuristics incorrectly evaluating choices etc.

Specifically, the perceived payoffs are taken to be normally

distributed, with standard deviation , around their correct

values. Although for simplicity we will consider the case in

which all agents have the same effective delay, uncertainty,

and preferences for resource use, we should mention that the

same range of behaviors is also found in more common

situations.

We consider the case of two resources here, so the systemcan be described by the fraction f of agents that are using

resource 1 at any given time. Its dynamics is then governed by

(2),

( )df

fdt

= (1)

Where a is the rate at which agents reevaluate their resource

choice and p is the probability that an agent will prefer

resource 1 over 2 when it makes a choice. Generally, p is a

function off through the density dependent payoffs. In terms

o f t h e p a y o f f s a n d u n c e r t a i n t y, w e h a v e

1 21 ( ) ( )erf( ))

2 2

G f G f = (1+

(2)

Where quantifies the uncertainty. Notice that this

definition captures the simple requirement that an agent ismore likely to prefer a resource when its payoff is relatively

large. Finally, delays in information are modeled by supposing

that the payoffs that enter into

at time t are the values they

had at a delayed time t - .For a typical system of many agents with a mixture of

cooperative and competitive payoffs, the kinds of dynamical

behaviors exhibited by the model are shown in Fig. 1. When

the delays and uncertainty are fairly small, the system

converges to an equilibrium point close to the optimal

obtainable by an omniscient, central controller. As the

information available to the agents becomes more corrupted,

the equilibrium point moves further from the optimal value.

With increasing delays, the equilibrium eventually becomes

unstable, leading to the oscillatory and chaotic behavior shownin the figure. In these cases, the- number of agents using

particular resources continues to vary so that the system

spends relatively little time near the optimal value, with the

consequent drop in its overall performance.

(a)

(b)

(c)Fig.1. Typical behaviors for the fraction f of agents using resource 1 as a

function of time for successively longer delays. (a) Relaxation toward stable

equilibrium. (h) Simple persistent oscillations. (c) Chaotic oscillations. The

payoffs are1 24 7 5.333G f f= +

for resource1 and2 4 3G f= +

for

resource 2. The time scale is in units of the delay time , = 1/4 and thedashed line shows the optimal allocation for these payoffs.

This chaotic dynamics of agent as shown in fig.1 should beavoided when applying in secondary voltage control strategy.

Two ways are proposed to achieve a stable equilibrium by

making chaos a transient phenomena: First, reward

mechanism, which has the effect of dynamically changing the

control parameters of the system dynamics in such a way that

a global fixed point of the system is achieved; Second,

sufficient diversity, which stabilize the system, in practice a

fluctuation could wipe out those agent types that would

otherwise be successful in stabilizing the system.

For the space restriction, the procedure [7] will not be

demonstrated here, fig.2 will show us the ability to control

chaos in distributed systems through a reward mechanism with

different delays.

(a)

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(b)Fig.2. Fraction of agents using resource 1 for a collection of biased agentswith (a) (chaos) no reward and (b)(chaos to stable) with reward.

III. DESIGN OF THE CHAOS BASED MAS FOR SECONDARYVOLTAGE CONTROL

In this chapter, we present the theory of the system

optimization, the normal MAS for SVC and establish a new

chaos based MAS for SVC.

A. Optimization Model of SVC

To fit the development of power system, many scholars

begin to use improved CSVC [8]. The CSVC model is

proposed as following:

2 2max

2

( ) ( )

( )

P G

G

n n

ref ref ii i

i i i

nref

i i

i

QMinZ V V f q

Q

h V V

= +

(3)

Subject to

( , ) 0ai

g x u = 1,2,...,i n=(4)

( , ) 0ri

g x u = 1,2,...,i n=(5)

min max

i i iQ Q Q

Gi

(6)

min max

i i iV V V ( )G Ci *

(7)

Where:

P

, G

and C

are sets of indices of pilot buses, voltage

regulating devices and critical buses, respectively.ref

iV

and iV

are actual voltage at bus i and set-point

voltage, respectively.

fand h are weighted factors.

iQ

and (max

iQ

,min

iQ

) are actual and limit reactive

generations at bus i, respectively.refq

is reference value of relative reactive power

generation with a region, defined by the expression

max

G

G

n

i

iref

n

i

i

Q

q

Q

=

(8)

( , )ai

g x uand

( , )ri

g x uare active and reactive injection

equations at bus i , respectively.

B. Normal MAS for Secondary Voltage control

The MAS focuses on the interaction and cooperation of

autonomous agent groups. The agent acquires up-dated

information through regular interaction with its environment

and other agents, and adjusts its actions for the benefit of its

highly self-adaptive function.

The basic configuration of the MAS for secondary voltagecontrol is shown in fig.3. The regional secondary controller

works as a coordination agent (CA) and each voltage

controllers (including generators, SVC, synchronous

condenser, static condenser, etc.) are governed by the

corresponding execution agents (EA). Distributed

coordination of the MAS can be achieved either by task

allocation based on communication among agents or

autonomous regulation based on local self-estimation. The

operation of all control agents in the MAS is for a common

objective to minimize the voltage deviation and maintain an

adequate regional voltage profile.

Fig.3. Basic configuration of the MAS for secondary voltage control

CA is the key part of the MAS. To meet the demands of the

voltage control under various system states, the corresponding

agent should take different control strategy according to the

information from the environment and pick out the different

modes (control strategies) for the agents under control. Two

modes are proposed here: the general mode and emergency

mode. After commands are received from CA, EA updates the

settings of the voltage controller to maintain the system

voltage stability, while ensuring no self interests damage.

When system runs under general circumstances, the MAS

works in general mode to achieve global optimal voltage

control and keep reasonable reactive power reserves.

According to (3), EA periodically constitutes a series of

commands and send them to CAs by dealing with the voltage-regulating information from CAs, in a coordinated way.

Generally speaking, if the CSVC is accomplished with the

linear optimization model, the control variable increment is

Coordination

agent

Execution

agent

Execution

agent

Voltage controller Voltage controller

Voltage

regulator

Voltage

regulator

Power system

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worked out and sent to primary voltage controller every 3-10s,

and the overall time constant of the secondary loop is about 1-

3 minutes. When applying (3) in a nonlinear model, it may

take much more time to find the solution. But on the other

hand, the final result and the settings of each primary

controller can be achieved in one control step. Therefore, the

nonlinear method can still satisfy the control speed of

secondary voltage control. And further more, the control

variables achieved are more accurate.

After system runs into contingencies, it is necessary forreactive power reserves near the bus where voltage violation

occurs to provide fast and effective reactive power support.

The MAS switch into the emergency mode. Firstly, in this

mode, the corresponding EA which detected the voltage

violation change the setting of primary voltage controller to

restore the voltage level rapidly. If the voltage is not restored

though the its voluntary control actions, EA should request the

CA in charge for help. Then, CA adjusts other EAs states to

recover the violated voltage rapidly.

The coordination method used in this paper is the contract

net protocol (CNP), which is widely used in MAS [6].

While applying in SVC, CA acts as manager agent and EA

as contract agent. CA takes charge of inviting public bidding

of voltage control task and awarding the control contract to the

EA which applies the bidding according to its own capability.

The system works in market mechanism for the better use of

reactive power resources. The process of coordination and

cooperation among agents is described as following:

1. Generally, all agents work at monitoring state. EA

monitor voltage of nodes adjacent; CA monitors important

nodes that EAs can not cover. State changes when voltage

violates at a certain node.

2. Once, an unrestorable voltage violation occurred on a

certain EA, the EA (called the provoked EA) should request

CA for help and. The provoked EA reports ponderance, and

then runs into requesting state.

3. CA distributes notice on the bulleting board for voltage

support assistances and invites public biding. The notice

includes fault position and ponderance. EAs evaluate theirown capability of voltage support, and bid according to

var/voltage capability, self-limitation and control priority, then

run into biding state.

4. CA receives EAs bidding and figures out the optimal

list of EAs through a genetic algorithm [9]. Then, CA sends

confirmation and awards the contract which involves the

control target and control time to the EA on the top of the list.

Then, the EA starts to execute the task, and runs into the

executing state.

5. EAs in the biding state which didnt receive the

confirmation within given time will return to the monitoring

state. The EA executes the task with autonomous control

(local secondary voltage control), and then returns to

monitoring state.

6. After CA receives confirmation that the contract has

been accomplished, CA request the provoked EA if the

voltage violation is restored. If restored, CA returns to

monitoring state, otherwise CA should award the voltage

control contract to next EA in the list for more voltage support

until the voltage recovers.

7. It means that voltage violation can not be restored

through secondary voltage control system, when CA in biding

state cant receive the bidding from EA in given time. In this

case, CA sends a message to the provoked EA indicating that

the CA fails to achieve assistance, and then returns to the

monitoring state.

8. If the provoked EA in the requesting state cant receive

the message from CA in given time or receive a confirmationmessage, it returns to the monitoring state.

C. The Chaos Based MAS for Secondary Voltage Control

The agent is one to one with the resource in the normal

MAS discussed above. Therefore, agents can not share

resources. System efficiency will decrease without taking full

advantage of resources. If one agent shares its resource with

the agent short in electrical distance, the system efficiency will

be increased, and the ability of the agent controlling voltage

will be strengthened. And with the applying of chaos control,

the procedure of resource competing will be stable.

Considering the amount of computing, processing time and the

essence of hierarchical voltage control, the number of the

sharing resources should not be too large. As a exploring job,the number is based on 2 in our paper. By this means, one

agent will share its resource with the one shortest in electrical

distance [11].

When system runs under general circumstances, CA

achieves the optimal control varieties through and send tasks

to EAs. EA waits for task, then adjust voltage controller

variables and ensures all variables within the range. The steps

are all the same as a normal MAS one. The difference only

lies in the normal states range, that the chaos based one will

switch into emergency mode much longer in time span. Under

this circumstance, the voltage will restore more quickly than

that under the normal one.

When system runs under emergency state, the procedures

are all the same as the normal ones but a new agent sequence

list. On this list, the agents with reduplicate resources are

jumped over to decrease the reduplicate tasks. Obviously,

more var resources for agents action will evidently expand

the voltage control range and put off the seconds when the

system switch into the emergency mode with a longer

response time. This makes the voltage curve smoother than

that of the normal MAS.

From the point of view discussed above, the chaos based

MAS for SVC has its priority to the normal MAS based SVC.

Here, the chaos based rule has two respects as follows:

1). reward mechanism. We reward the agent performs well

more available resources. So, actually, each agent might

dominate 2 or more resources and one at least, depends on the

mix below.

2). the right mix of diverse agents and generatingdiversities. We can define the standard of diversity as the

electrical distance. But, diversity generating is hard to be

achieved since the net structure is already given. As the result

of mix, the strong connected agents will share more resources,



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vice versa. This looks like partitioning, but actually, they are

not the same in consequence.

Here, the performance will be evaluated in terms of the

system sensitivity matrix. The more sensitive, the better one

agent performs. The principle is the same as that of a

partitioning in steps. Thats the reason why they look alike

apparently.

IV. SIMULATION RESULTS

Fig.4. New England 39-bus diagram

In this section, the chaos based MAS for secondary voltage

control is simulated on an England 39-bus system shown in

fig.4. This system, shown in Fig.6, includes 29 load buses, 9

generator buses, and one equivalent generator representing the

interconnection with an extra network. Five SVCs are

equipped in Nodes 4, 8, 11, 14, 17. All the VAR units in the

system are limited to a boundary at 100 MVA. Each controller

of the generators and static var compensators is set with a

execution agent as shown in fig.4.

A. Sharing Resources Distributing

Linearize the power flow equation, and then we get [10]:

p pV

q qV

P J JJ

Q J J V V

= = (9)

1qV q p pV qV Q J J J J V S V

= = (10)1( )qV VqV S Q S Q = =

(11)

Where:

P is the variety of active power, Q is the variety of thereactive power;

is the variety of the voltage angle, V is the variety ofthe voltage amplitude.

J: Jacobian matrix,

VqS : sensitivity matrix.According to rule no.1and 2, the agents are divided into 3

styles. The details of resources sharing in shown in following

table:

TABLE ITHE DIAGRAM OF RESOURCES DISTRIBUTING

Agent A1 A2 A3 A4 A5

resources G1,S8 G2,S11 G3,S11 G4,G5 G4,G5Agent A6 A7 A8 A9 A10

resources G6,,G7 G6,G7 G8,G10 G9,s,17 G10,G8

Agent A11 A12 A13 A14 A15

resource S4,G2 S8,S4 S11,G2,G3 S14,S11 S17,G10

B. Comparing to the normal MAS for SVC under system

contingencies

The system condition obtained from optimal power flow

calculation is regarded as the initial operating state for

simulation. In this simulation, the control behaviors of the

normal MAS and chaos based MAS under normal condition

and system contingency are investigated with the voltage

curve comparing.

When under normal state, a reactive power load injects into

node 12 by 200MVA. Fig.5 shows the voltage curve under the

chaos based MAS for SVC comparing to a normal one. When

the load is injected, the chaos based MAS is still under normal

state while the normal one has switched into the emergency

mode. So, as fig.5 shows, the voltage applied with the chaos

based method restores quickly.

Fig.5 voltage curve of bus 12 under normal stage. Broken line presents

voltage under chaos based MAS for SVC. Real line represents voltage under

normal MAS for SVC

When a 300MVA reactive load injected into node 12,

system runs into contingency. Then, CA will run steps as

discussed in chapter III.B. First, SVC11, SVC13 and G3 will

bring into service. When the voltage crosses the bounder as

shown in fig.6, system runs into emergency mode. CA call for

var supporting assistance, then a list according to EAs biding

is achieved. In this case, the list is A11, A12, A15. As shown

in fig.6, voltage restored step by step with comparing to that

under normal MAS can hardly get to the lower boundary.

The 8th International Power Engineering Conference (IPEC 2007) 1211


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Fig.6. voltage curve of bus 12 under emergency mode. Broken line presentsvoltage under chaos based MAS for SVC. Real line represents voltage under

normal MAS for SVC

After the simulation, the validity of the chaos based MAS

for SVC has been testified under both normal and emergency

mode. Its apparently that the chaos based MAS for SVC has

more advantage to eliminate the system voltage violation, and

do a lot of good to the system voltage stability when it comes

to contingency.

V. CONCLUSION

In this paper, a model of chaos based MAS for SVC is

established to maintain system voltage stability under both

normal and emergency circumstances. This type of MAS with

sharing resources and chaos based rules applied is testified tobe valid to deal with larger reactive load violation by a

simulation operated on the New England 39-bus system. It has

more priority to the normal MAS based SVC to maintain the

system voltage stability under emergency circumstances in

rapidness and efficiency.

VI. REFERENCES

[1] J. P. Paul, J. Y. Leost, and J. M. Tesseron, "Survey of the secondary

voltage control in France: present realization and investigation", IEEE

Trans. on Power System, 2 (2), 1987, pp. 505-511.

[2] A. Stankovic, M. Ilic, and D. Maratukulam. "Recent Results Secondary

Voltage Control of Power Systems". IEE Trans on Power Systems,1991, 6(1), pp. 94- 101.

[3] Y.Z. Sun, Z.F Wan, X.Y. Yao. "Study on Secondary Voltage control of

Power System". Automation of Electric Power Systems.1999, 23 (9), pp.9-14.

[4] H. Lefebvre, D. Fragnier, and J. Y. Boussion, "Secondary coordinated

voltage control system: Feedback of EDF", in Proc. IEEE/PES Summer

Meeting, Seattle, USA, July, 2000, pp. 291-295.

[5] Y. S. Fan, J. W. Cao. "Multi-agent Systems: Theory, Method and

Applications". Springer, 2002.

[6] G. H. Sheng, X.C. Jiang, and Y. Zeng. L. Mitchell, and C. J. Carter,

"Optimal Coordination For Multi-Agent Based Secondary VoltageControl In Power System, " in Proc. 2005 IEEE/PES Transmission and

Distribution Conferenc e and Exhibition: Asia and Pacific, pp.1- 6.

[7] T. Hogg, B.A. Huberman, "Controlling chaos in distributed systems",IEEE Transactions on Systems, Man and Cybernetics 21(6), 1991, pp.

1325-1332.

[8] A. Conejo, and M. J. Agullar, "Secondary Voltage Control: Nonlinear

selection of pilot buses, design of an optimal control law, and simulation

result", inProc .IEE Genar. Transm. Distrib., 145 (1), 1998, pp.77-81D.

[9] K. Iba, "Reactive Power optimization by Genetic algorithm", IEEE

Trans. on Power System, 9(2), 1994, pp.685-692.

[10] C. E. Hu, Y. M. Xue and R. G. Yang, "Optimal allocation of reactivepower sources using network partitioning", in Proc. 2004 PowerCon,

pp.222-225.

[11] D. P. Liu, G.Q. Tang and H. Chen. "Tabu Search Based Network

Partitioning For Voltage Control"

VII. BIOGRAPHIES

Xiaolei Du was born in Shandong, China; on

August 15, 1981. Received B.S. degree at the School

of electrical engineering in Shandong University in2002. Now he is pursuing his PhD degree at the

School of electrical engineering in Wuhan University.His main interests and research fields are the

optimization of voltage quality and var planning.

Tiecheng Lu was born in Jiangsu, China; on 1953.Received M.S. degree atthe School of electrical engineering in Wuhan University in .He is a professor

at the School of electrical engineering of Wuhan University. His maininterests and research fields are the internal overvoltage and the monitoring of

the overvoltage.

Liang Xu was born in Shandong, China; on 1979. Received B.S. degree at

the School of electrical engineering in Shandong University in 2002. Now heis an engineer in Shandong Electric Power Consulting Institute.


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Secondary Control