Decentralized ADRC for LFC in Deregulated Environments

Decentralized ADRC for LFC in Deregulated Environments Hong Zhou1*, Yuchun Hao2 and Wen Tan3 School of Control & Computer Engineering, North China Electric Power University, Zhuxinzhuang, Dewai, Beijing, China Beijing Huadian Tianren Electric Power Control Technology Co. LTD, Haidian, Beijing, China School of Control & Computer Engineering, North China Electric Power University, Zhuxinzhuang, Dewai, Beijing, China *1zhou.hong@ncepu.edu.cn; 2sxhaoyuchun@sina.com; 3wtan@ncepu.edu.cn Abstract Active disturbance rejection control (ADRC) method is investigated in this paper to design decentralized load frequency controllers (LFC) for deregulated multi‐area power systems. ADRC can treat the connections among control areas and the effects of possible contracts as new disturbance signals, and uses an extended state observer (ESO) to estimate and compensate them quickly. Thus, it can achieve good disturbance rejection performance and is a good candidate for LFC design. Simulation results for a three‐area power system show that the proposed method is simple to apply in practice and good performance can be achieved. Keywords Active Disturbance Rejection Control (ADRC); Load Frequency Control (LFC); Deregulated Power Systems; Generation Rate Constraints

Introduction During the past decades, the power industry has changed from vertically integrated industry to numbers of entities. With the size and complexity of the deregulated power systems increasing, more disturbances in power system control and operation are introduced, which requires novel control strategies to be developed to achieve load frequency control (LFC) goals and maintain the reliability of the power gridat an adequate level (Kundur, 1994). A lot of studies have been done on LFC in deregulated environments. Several control strategies for LFC are proposed in the literature (Christe and Bose,1996; Kumar, et al., 1997; Donde, et al., 2001; Rerkpreedapong, et al., 2003; Bevani, et al., 2004; Bhatt, et al., 2010). These studies try to modify the conventional LFC by taking the change of

environments in the power systems into consideration. In this case, there are different uncertainties and various disturbances in each control area. As a result, conventional controllers based on classical theory are not very suitable for the LFC problem in deregulated environments. This paper applies a decentralized active disturbance rejection control (ADRC) to design LFC controllers in deregulated environments. ADRC was developed by J. Han (1998; 2009). The idea is to estimate the internal uncertain dynamics and the external disturbances in real time and then compensate it quickly. In Dong et al. (2012) and Tan et al. (2013), active disturbance rejection control method is applied to design LFC systems. It is shown that three‐order ADRC is a good candidate for load frequency control and excellent damping performance can be achieved. In this paper, LFC in deregulated environments is investigated. The connections among control areas and the effects of possible contracts can be treated as disturbances for ADRC, and they can be estimated by using the extended state observer and thus can be compensated quickly. Active Disturbance Rejection Control (ADRC) ADRC does not have to know the complete models of the controlled plant and the disturbance. The plant is assumed to have the following form y ( r ) (t )  bu(t )  f ( y(t ), u(t ), d(t )) (1)

where f(y,u,d) is a combination of the unknown dynamics and the external disturbance of the plant. It is denoted as the generalized disturbance and assumed to be unknown in ADRC design.

48 Hong Zhou, Yuchun Hao and Wen Tan

In ADRC framework, the central idea is to estimate the unknown generalized disturbance. To achieve it, an extended state observer (ESO) is used. Let z1  y , z2  y , L , zr  y ( r ‐1) , zr 1  f ( y , u, d) (2)

Assuming that f ሺሶy,u,d) is differentiable and let f  h , then (1) can be written as  z  Ao z  Bo u  Eo h (3)   y  Co z T

where z   z1 z2  zr zr 1  , and 0  0 Ao     0 0 

1 0  0 0    0 1  0 0 , ,Bo            0 0  1 b 0 0 0  0 ( r 1)( r 1)  ( r 1)1

0   0 Eo     , Co  1 0 0  0 1( r 1) (4)   0  1  ( r 1)1

A full‐order Luenberger state‐observer can be designed as  zˆ  Ao zˆ  Bo u  Lo ( y  yˆ ) (5)   yˆ  Co zˆ

where

Lo

is

the

observer

gain

vector

T

Lo   1  2   r  r 1  . When Ao  LoCo is asymptotically stable, zˆ1 (t ), zˆ r (t ) will approximate

y(t) and its derivatives (up to order r), and zˆ r 1 (t ) will approximate the generalized disturbance f. So the estimated generalized disturbance can be used in control to reject it more quickly. If we choose the control law as u(t ) 

 zˆ r 1 (t )  uo (t ) , b

then the original plant (1) becomes y ( r ) (t )  f ( y , u, d)  zˆ r 1 (t )  uo (t ) (6)

If the ESO is properly designed, i.e., zˆ r 1 (t )  f ( y , u, d) , then the original plant is reduced to an rth‐order integral system y ( r ) (t )  uo (t ) . The final system can be effectively controlled with the following feedback law uo (t )   k1 y(t )  k2 y (t )    kr y ( r 1) (t ) . Since zˆ1 (t ), zˆ r (t ) approximate y(t ), , y ( r 1) (t ) , the final control law can

be approximated as

k1 zˆ1 (t )    kr zˆ r (t )  zˆ r 1 (t ) :  Ko zˆ (7) b 1 where Ko   k1 k2  kr 1 . b u(t )  

It is obvious that an ADRC has two sets of gains to tune: Lo , the observer gain for ESO, and Ko , the controller gain for rth‐order integral plant. For practical reason, the tuning of these two gains are reduced to two tuning parameters as suggested in Gao(2006): ωc, the controller bandwidth, and ωo, the observer bandwidth, so an ADRC is a ‘general’ control structure that is independent of the original plant model. Except the relative order r of the model and the gain ‘b’, it does not need to know the detailed structure and the parameters of the model, so it is quite similar to PID control which has a fixed control structure that is independent of plant models. Decentralized LFC in Deregulated Environments

In a conventional power system, the generation, transmission and distribution are owned by a single vertically integrated utility (VIU). In the deregulated power systems, the VIU does not exist any more, instead, it is replaced with generation companies (GENCOs), distribution companies (DISCOs), transmission companies (TRANSCOs) and independent system operator (ISO). Each area of an N‐ area deregulated power system has the structure shown in Figure 1. Signals which are different from the ones in the conventional environments are shown in the dash dotted lines. GENCOs have the liberty to participate in the LFC task and DISCOs may contract with any available GENCOs in their own or other areas. Thus, there might be various combinations of possible contracted scenarios between DISCOs and GENCOs . This case is called ‘bilateral transactions’, and Augmented Generation Participation Matrix (AGPM) can be used to express the possible contracts (Bevrani et al., 2004). It shows that the participation factor of a GENCO with a DISCO. The AGPM for a N‐area power system is given by  AGPM 11  AGPM 1N    AGPM       (8)  AGPM N 1  AGPM NN 

Decentralized ADRC for LFC in Deregulated Environments 49

PLOC,i



Pdi

1 R ni

1 R 1i

GENCO 1i

PCi



apf1i



apf ni ,i



1 1 sTH1i



X G ,ni 1 1  sTHni i

X G ,1



1 Pm,1i 1  sTT 1i   1 1  sTTnii Pm,n i

GENCO ni i Ki

f i

K Pi 1  sTPi



N

1 s

Tij   j 1 j i

i

Ptie,i

Bi

 N

 Tij f j 1i   n ,i i

i

j 1 j i

FIGURE 1. BLOCK DIAGRAM OF AREA #i.

where

contracted tie‐line power flow ξi.

 gpf( si 1)( z j 1)  gpf( si 1)( z j  mj )       AGPM ij    (9) gpf   gpf ( si  nj )( z j  m j )   ( si  nj )( z j 1) 

Here ni and mi denote the numbers of GENCOs and DISCOs in Area #i and i 1

i 1

k 1

si   ni , z j   mj , s1  z1  0, for i , j  1, , N (10)

Each element of AGPM, gpfij (generation participation factor) shows the participation factor of GENCO i in DISCO j based on the contract. The diagonal sub‐ matrices of AGPM, AGPM ii , reflect the local load demands of Area#i and off‐diagonal sub‐matrices,

AGPM ij , reflect the demands of DISCOs in Area #j on GENCOs in Area #i. There are two objectives in the load frequency control problem for multi‐area power systems: regulate the frequency deviation of each area to its nominal value; and maintain the tie‐line power flows to their scheduled values. To achieve the goals, area control error (ACE) is used as the feedback variable. For Area #i, the ACE is defined as ACEi  Ptie ,i  error  Bi fi (11)

where Ptie ,i  error is the error between Ptie ,i (the scheduled tie‐line power flows from other areas to Area #i) and ξi (the total contracted tie‐line power flows from other areas to Area #i). This is different from the conventional case where there is no

The local load frequency control in Area #i takes the form Pci   Ki ( s)ACEi . It is obvious that a contract in an N‐area power system has impacts on the feedback control through ACEi , which means that a contract will certainly affect an N‐area LFC system that is designed in the conventional environment without considering the contract. In conventional environments, decentralized LFC controllers are designed assuming that Ptie ,i  0 , (i  1, , N ) (Tan, 2011). The same idea applies to the

deregulated environments. In this case it is assumed that Ptie ,i  error  0 , i.e., the deviation of the scheduled tie‐line power flow is equal to the deviation of the contracted power flow. Then the load frequency control for Area #i will be Pci   Ki ( s)Bi fi . The essential difference between LFC in conventional environments and in deregulated environments is that load disturbances affect other areas through tie‐line in the conventional situation, while in deregulated environments they affect not only through tie‐line but also through various possible contracts. The variable contracts make the load disturbance rejection problem in the deregulated environments more difficult as the loads distribute in various forms and the requirements on load disturbance rejection are stricter than that in the conventional situation, which motivates us to apply active disturbance rejection control in deregulated environments. Simulation Example

Considering a three‐area power system discussed in

50 Hong Zhou, Yuchun Hao and Wen Tan

Tan et al.,(2012) and Shayeghi and Shayanfar(2006), There are two GENCOs and two DISCOs in each control area. For this three‐area power system, decentralized plant model can be obtained.  119.5 s2  2103s  5534  P1  5 s  35.67 s4  408.9s3  1900s2  6293s  10740  95.37 s2  1771s  4721  (12)  P2  5 4 3 2      37.45 449.9 2064 5999 9270 s s s s s   96.42s2  1723s  4351  P3  5 4 s  35.38 s  399.5 s3  1799 s2  5827 s  9658 

kc  0.1 for all turbines, the responses of the proposed

controllers are shown in Figure 2(B). It is shown that the decentralized ADRC without anti‐GRC scheme has large overshoot due to the generation rate constraint, and it is oscillatory in Area #2. With the anti‐GRC scheme, the constraints are compensated efficiently and good disturbance performance is achieved.

The relative orders of the local models are all 3, so we choose third‐order ADRC for each control area. The parameters of each ADRC are listed in TABLE 1. TABLE 1 THE PARAMETER VALUES OF ADRC

Parameter B ω c ω o

Area #1 119.5

Area #2 95.37

Area #3 96.42

3

30

The performance of proposed control strategy is tested and compared with the decentralized PID controllers proposed in Tan et al. (2012). The following AGPM is considered, which is an example of combined Poolco and bilateral based contracts between DISCOs and available GENCOs.

(A)WITHOUT GRC

0 0.25 0 0.5 0   0.25   0 0.25 0 0   0.5 0.25  0 0.5 0.25 0 0 0 AGPM    (13) 0 0.5 0.75 0 0   0.25  0 0.25 0 0 0.5 0    0 0 0 0 1  0

Suppose there are large step load demands 0.1 puMW by all DISCOs at t=1. The deviations of the frequency and the scheduled tie‐line power flow of the control system are shown in Figure 2(A). The frequency deviations of the three areas are quickly driven back to zero and have very little settling time. The responses of the optimized PID controller designed in Tan et al. (2012) are also shown for comparison. It is observed that the proposed decentralized ADRC controller achieves better freqeuncy damping in all three areas, and the tie‐line power flow deviations return to zero. In practice, there are generation rate constraint (GRC) in the turbines. Supposing that the generation rate is 0.1 puMW/sec for each turbine in the system. Without the anti‐GRC scheme for ADRC, the proposed decentralized ADRC degrades. However, with the anti‐GRC scheme proposed in Tan et al. (2013) with

(B)WITH GRC FIGURE 2. SIMULATION OF THE THREE‐AREA POWER SYSTEM(SOLID: ADRC; DASHED: PID (Tan et al. 2012) ).

Conclusions

Decentralized LFC for multi‐area power systems in deregulated environments was studied in this paper. Considering the various disturbances and uncertainties of a complex restructured power system, ADRC was applied to design the decentralized LFC controller. Simulation results show that the decentralized ADRC performs better than decentralized PID controller. ACKNOWLEDGMENT

This work was supported by the National Natural Science Foundation of China under Grant 61174096,

Decentralized ADRC for LFC in Deregulated Environments 51

the Natural Science Foundation of Beijing under Grant 4122075. REFERENCES

L. Dong, Y. Zhang, and Z. Gao. A robust decentralized load frequency controller for interconnected power systems. ISA Trans., 51(3):410–419, 2012. P. Bhatt, R. Roy, and S. P. Ghoshal. Optimized multi‐area

D. Rerkpreedapong, A. Hasanovic, and A. Feliachi. Robust load frequency control using genetic algorithms and linear matrix inequalities. IEEE Transactions on Power Systems, 18(2):55‐61, 2003. H. Bevrani, Y. Mitani, and K. Tsuji. Robust decentralized AGC in a restructured power system. Energy Conversion & Management, 45(15):2297‐312, 2004. H. Shayeghi and H. A. Shayanfar. Decentralized robust AGC based on structured singular values. Journal of Electrical Engineering, 57(6):305‐317, 2006. H. Shayeghi, H. A. Shayanfar, and O. P. Malik. Robust decentralized neural networks based LFC in a deregulated power system. Electric Power Systems Research, 77(3):241‐251, 2007. J. Han. Active disturbance rejection controller and its applications (in chinese). Control and Decision, 13(1):19–23, 1998. J. Han. From PID to active disturbance rejection control. IEEE Trans. Ind. Electron., 56(3):900–906, 2009. J. Kumar, K. H. Ng, and G. Sheble. AGC simulator for price‐ based operation I. A model. IEEE Transactions on Power Systems, 12(2):527‐532, 1997. J. Kumar, K. H. Ng, and G. Sheble. AGC simulator for price‐ based operation II. Case study results. IEEE Transactions on Power Systems, 12(2):533‐538, 1997.

AGC simulation in restructured power systems. International Journal of Electrical Power & Energy Systems. 32(4):311‐322, 2010. P. Kundur. Power System Stability and Control. New York: McGraw‐Hill; 1994. R. D. Christie and A. Bose. Load frequency control issues in power system operations after deregulation. IEEE Transactions on Power Systems, 11(3):1191‐200, 1996. V. Donde, M. A. Pai, and I. A. Hiskens. Simulation and optimization in an AGC system after deregulation. IEEE Transactions on Power Systems, 16(3):481‐489, 2001. W. Tan. Decentralized load frequency controller analysis and tuning for multi‐area power systems. Energy Conversion & Management, 52(5):2015‐2023, 2011. W. Tan, H. Zhou, and C. F. Fu. Linear active disturbance rejection control for load frequency control of power systems (in Chinese). Control Theory & Applications, 30(12):1607–1615, 2013. W. Tan, H. Zhang, and M. Yu. Decentralized load frequency control in deregulated environments. International Journal of Electrical Power & Energy Systems, 41(1):16‐26, 2012. Z. Gao. Active disturbance rejection control: A paradigm shift in feedback control system design. Proceedings of American Control Conference, Minneapolis, MN, June 2006, 2399–2405.

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