Automatic Generation Control Strategies under CPS Based on Particle Swarm Optimization Algorithm

Weihua Luo Power Dispatching and Communication Center

Liaoning Electric Power Company Limited Shenyang City, China

Whluo2000@126.com

Yibin Shi Power Dispatching and Communication Center

Liaoning Electric Power Company Limited Shenyang City, China

Abstract—the paper applied PSO (particle swarm optimization) Algorithm to AGC (automatic generation control) Strategy in interconnected power grid in the CPS (Control Performance Standard) standard. Firstly, analyze PSO, ACE (area controlling error) and CPS. Secondly, apply PSO Algorithm to AGC Strategy. The simulations on the practical power grid have shown that this control strategy is promising due to reducing the number of order effectively, improving the AGC performance, and the guarantees of the frequency quality and the safety operation in power system.

Keywords-particle swarm optimization algorithm; control performance standa;, automatic generation control

I. INTRODUCTION As the size of power system getting larger, it is getting

more and more difficult to balance load by some experience of dispatcher. Using of AGC (automatic generation control) system to control the power grid frequency and area controlling error (ACE) synthetically has good development potential. North American Electric Reliability Commission (NERC) introduced the control of performance standards CPS in 1996[1]. Nowadays the existing power grid interconnection CPS standards mostly used PID (Proportion Integration Differentiation) strategy [7]. The accuracy of the PID strategy in the automatic control method is not enough.

However, Particle Swarm Optimization algorithm instructs optimal searching by cooperation and competition of group particles between the groups [2]. It based on the population to retain the overall search strategy and used speed -displacement model. So it is simple and easy to implement. The PSO algorithm gradually shows superiority and great broad prospects in applied research of power grid since it is proposed.

The paper presents the PSO algorithm for automatic generation control strategy under the CPS in the interconnected power grid, discusses the PSO algorithm, standard deviation of ACE and CPS in power system.

The simulations on the practical power grid have shown that this control strategy is promising due to reducing the number of order effectively, improving the AGC performance, and the guarantees of the frequency quality and the safety operation in power system.

II. STUDY PANICLE SWARM OPTIMIZATION Kennedy and Eberhart first introduced particle swarm

optimization in 1995 as a new heuristic method [2]. The original objective of their research was to mathematically simulate the social behavior of bird flocks and fish schools. The first version of PSO was intended to handle only nonlinear continuous optimization problems. However, many advances in PSO development elevated its capabilities to handle a wide class of science optimization problems.

PSO initializes for a group of random particles (random solution). It finds the optimal solution through iteration. A Swarm is a collection of particles. A particle has both a position and a velocity vector [3].

1 1 ,

2 ,

( )

( )t t rand ig t t

rand g t t

V V C P X

C P X

ω+

∀

= ⊕ −

⊕ − (1)

1 1t t tX X V+ += + (2)

Kennedy and Eberhart give the PSO equations as follows [4, 5]:

Figure 1. illustration of PSO equations.

Where: 1tV + : The particle's new velocity for the next generation.ω : A measure of how much the particle "trusts" its own exploration. tV : The particle's current velocity. ⊕ : Vector

addition, 1randC : A uniformly distributed random number from

0 to 1C . A measure of how much a particle "trusts" its

tV

tVω 1tV+

2 ,( )rand g t tC P X∀ −1 ,( )rand ig t tC P X−

new position

global bestposition

,g t tP X∀ −

,ig t tP X− local bestposition

currentposition

2010 International Conference on Electrical and Control Engineering

978-0-7695-4031-3/10 $26.00 © 2010 IEEE

DOI 10.1109/iCECE.2010.830

3400

2010 International Conference on Electrical and Control Engineering

978-0-7695-4031-3/10 $26.00 © 2010 IEEE

DOI 10.1109/iCECE.2010.830

3400

neighborhood best velocity. ,ig tP : The neighborhood (from i

to g) best position. " "− : The difference of two positions is the velocity that will transform the second position into the first position. tX : The current position. 2randC : A uniformly

distributed random number from 0 to 2C Independent

from 1randC . A measure of how much a particle “trusts” the

global velocity. ,g tP∀ : The global best position. " "+ : The transformation of a position using the velocity (yields a position). 1tX + : The particle’s new “moved” position of the next generation [3].

III. STANDARD OF ACE AND CPS

A. Standard Deviation of ACE It assumes the two control area systems shown in Fig. 2:

Figure 2. Two control area systems.

There exist the following relations among the deviation of frequency ( )f HzΔ , the deviation of interchange ( )TP MWΔ , the frequency response characteristics (% / )K MW Hz , and the total system capacity ( )P MW [1, 8].

A BR RfKP

Δ + ΔΔ = − (3)

A A B B B AT

K P R K P RPKP

Δ − ΔΔ = (4)

When there is no correlation between the ACE s, the standard deviation of the ACE whole system should become less than the permitted value [9].

B. Control Performance Standard1 (CPS1) CPS1 request for a regional power grids meet equation in a

certain period of time (for example, 15 min) [6]: min

21

( )10

AVE AVE

i

ACE fCF

B n εΔ

= ∑ ii i

(5)

Where: minAVEACE is the average of ACE in one min;

AVEfΔ is the average of frequency deviation in one min; iB is

the error factor of frequency of controlling region; 1ε is controlling target value of average deviation of the RMS in interconnected power grid of 1 min annually; n are minutes during the period. Statistical indicator of CPS1 in the period of time is described in the following formula:

1 (2 ) 100%CPS CF= − × (6) The objective function of CPS: Minimal changes when

regulate power:

1 1

1 1

min ( ) ( )

( ) ( )

G

G

T t

i it i S k

T t

i i i it i S k

f c Pg k

c u k v k Rate

= ∈ =

= ∈ =

• = Δ

=

∑∑ ∑

∑∑ ∑

(7)

GS :assembly of AGC units; ( )iPg kΔ : add-subtract generating

capacity of the AGC unit at the k moment; ic :linear economic factors of the AGC unit; T : Calculation of the time; ( )iu k : values of acceleration and deceleration of AGC unit at k moment; ( )iv k : output restrictions values of the AGC at

k moment; iRate :the rate of linear conditioning of the AGC.

C. Control Performance Standard2 (CPS2)

15L And CPS2 are defined as the follows [1]:

15 151.65 ( 10 ) ( 10 )netL B Bε= − −i (8)

15

15

12CF ACEL

= (9)

int 2 1int

Number of erval that CFRTotal number of ervals

>= (10)

2 100(1 )CPS R= − (11)

15ACE is the 15-minute average of ACE. B is the error

frequency of the control area, netB is the error frequency of the regional power grid.

IV. APPLY PSO ALGORITHM TO AGC

A. Methods In PSO, the coordinates of each particle represent a possible

solution associated with two vectors, the position ( )iu k and velocity ( )iv k vectors. In N-dimensional search space,

1 2[ , , , ]i i i iNU u u u= ⋅⋅⋅ and 1 2[ , , , ]i i i iNV v v v= ⋅⋅⋅ are the two vectors associated with each particle i [2-5].

11 1 2 2

1 1

( ) ( )k k k k k ki i i i ik k ki i i

v v c b pbest u c b gbest u

u u v

ω+

+ +

⎧ = + − + −⎪⎨

= +⎪⎩(12)

Where： 1c and 2c are two accelerated constant; 1b and 2b are two randomly generated numbers with a range of [0, 1]; ω is the inertia weight;

kipbest :

1 2[ , , , ]k pbest pbest pbesti i i iNpbest u u u= ⋅⋅ ⋅ is the best position

particle achieved based on its own experience;

System capacity: AP

Frequency response

System capacity: BP

Frequency response

Generator

AGΔGenerator

BGΔ Load

ALΔLoad

BLΔ

Area A Area BfΔ

0TPΔ >

A A AR L GΔ =Δ −Δ B B BR L GΔ = Δ − Δ

34013401

kgbest : 1 2[ , , , ]k gbest gbest gbestNgbest u u u= ⋅⋅⋅ is the best particle

position based on overall swarm’s experience. The objective function which allocates generators:

15

1 200%100% 1 200%,CPS or

CPS and ACE L≥⎧

⎨ ≤ ≤ ≤⎩(13)

The constraint of AGC adjustment capacity, rate and the power grid frequency.

max

max

1

max min

1

0.030

n

j j AGCj

j j j

n

j j AGCj

S X S

AGCv AGCv AGCvf Hz

v X V

=

=

⎧ ≥⎪⎪⎪ ≥ ≥⎪⎨

Δ ≤⎪⎪

≥⎪⎪⎩

∑

∑

(14)

maxAGCS is the needed adjust capacity of AGC to the regional

power grid. “ 1jX = ” represent that a generator participate to AGC. jAGCv is the adjust AGC rate of the j generator. The

change range of fΔ comes from actual requirements.

B. Simulation In the simulation, set ω decreases linearly with the number

of iterations [6, 10, and 12]: max min

maxmax

kgg

ω ωω ω −= − (15)

maxω and minω : the largest and the smallest allowed values respectively. kg and maxg : the present and the largest number of iteration. Set: max 0.9ω = , min 0.4ω = , max 400g = ,

15 50L = . 1 21.8, 2.0c c= = .

TABLE I. PARAMETERS OF AVAILABLE AGC UNITS

Unit NO

Rate MW/min

Minimum power(MW)

Maximum power(MW)

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16

3 3 4 3 2 4 3 5 4 5 2 5 3 5 5 3

14 14 14 14 14 18 18 18 18 19 19 21 21 21 21 30

20 20 20 20 20 30 30 30 30 32 32 35 35 35 35 60

If:max

100AGCS MW= ,max

30 / minAGCV MW=

This paper used PSO algorithm and PID algorithm to AGC

The result of two algorithms as Table 2:

TABLE II. THE RESULT OF TWO ALGORITHMS

METHOD ADJUST VOLUME RATE VOLUME PSO PID

102.6MW 120.1MW

34MW/MIN 31MW/MIN

Compared the result of two algorithms, it can be found that the adjust capacity of PID is much greater than the demand, the cost is also the largest, PSO can avoid the problems and can find the optimal solution. It compare to PID and PSO by given the different interferences of load in the simulation. The result is as follow:

Figure 3. the CPS1 of PID and PSO to AGC

Figure 4. the ACE of PID and PSO to AGC.

Figure 5. the frequency of the regional power grid in PID and PSO method

The simulation examples show that the PSO algorithm can be the optimal solution by compared with the normal method. The PSO does more efficient parallel processing and faster

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convergence by used less adjustable parameters, improving the AGC performance, and the guarantees of the frequency quality.

V. CONCLUSION The paper applied PSO Algorithm to AGC Strategy in

interconnected power grid in the CPS standard. The simulations on the practical power grid have shown that this method is correct and efficacious.

REFERENCES [1] N.Jaleeli and L.S.VanSlyck, NERC’s new control performance

standards, IEEE Trans. Power Apparat Syst., Aug. 1999, vol. 14, pp. 1092–1099

[2] J. Kennedy and R.Eberhart, Particle swarm optimization, in Proc. IEEE Int. Conf. Neural Netw, 1995, vol. 4, pp. 1942–1948

[3] R.Eberhart and J. Kennedy, A new optimizer using particle swarm theory, in Proc.6th Int. Symp. Micro Machine Human Science, 1995, pp. 39–43.

[4] Y.Shi and R.Eberhart, A modified particle swarm optimizer, in Proc. IEEE World Congr. Comput. Intell., 1998, pp. 69–73.

[5] R.Eberhart and Y. Shi, Guest editorial, IEEE Trans. Evol. Compute. (Special Issue on Particle Swarm Optimization), Jun. 2004. vol. 8, no.3, pp. 201–203

[6] Liu Bin, Wang Keying, Zou Qing, Study on the application of particle swarm optimization algorithm to power regulation of CPS in interconnect power grids, 2008 IEEE Electrical Power Energy Conference, 6-7 Oct. 2008 , pp.1 - 5

[7] GAO Zong-he, TENG Xian-liang, TU Li-qun. Hierarchical AGC Mode and CPS Control Strategy for Interconnected Power Systems. Automation of Electric Power Systems, 2004, pp. 28(1):78-81

[8] D.D. Rasolomampionona, A Modified Power System Model for AGC Analysis, PowerTech, 2009 IEEE Bucharest June 28 2009-July 2 2009, pp. 1 – 6

[9] Tang Yue-zhong,Zhang Wang-jun,Zhang Jian,etc,Research on Control Performance Standard Based Control Strategy For AGC, Power System Technology, Vol.28 No.21, Nov. 2004, pp. 75-78.

[10] Wang Ya-jun, Fang Da-zhong, Research on AGC unit dispatch based on particle swam optimization algorithm, Relay, Vol.35, No.17, Sep.1, 2007, pp. 58-64

[11] Tetsuo Sasaki and Kazuhiro Enomoto, Statistical and Dynamic Analysis of Generation Control Performance Standards, IEEE Transactions on Power Systems, Vol. 17, No. 2, May 2002, pp. 476-480

[12] Li Bin, Wei Hua, Nong Wei-tao, etc, AGC Control Strategy Under Control Performance Standard for Interconnected Power Grid Based on Optimization Theory, Proceedings of the CSEE, Vol.28 No.25 Sep.5, 2008, PP. 56-60

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