Application of an NLPID controller on a UPFC to improve transient stability of a power system

Y.L.Kang, G.B.Shrestha and T.T.Lie

Abstract: To put flexible AC transmission systems (FACTS) devices into realistic use, it is necessary to consider the whole picture of the application of FACTS devices. Hence, components-based simulation should be studied, including the whole system design and the power electronics parts, such as switching schemes and converter controls. These issues are essential to the practical usage of FACTS devices. With all these components included, especially the presence of GTO and power electronics devices, the nonlinearity characteristics in the system are dominant. Thus, the acquisition of system state-space equations becomes time consuming and unrealistic. This leads to complexity in the modelling and designing the control mechanism. For example, the conventional A, B, C mechanism-based control theory becomes impractical and less effective. It becomes necessary to seek a new control method, which will be independent of system model. In the paper, a components-based unified-power-flow-controller (UPFC) model is developed. A novel tracker of differential (TD) and a nonlinear PID (NLPID) control system are proposed to be the main control of the UPFC. Digital simulation studies have been conducted and the results show that the proposed NLPID is very effective and efficient in enhancing the transient stability of a power system. In addition, the results also show that the proposed controller is adaptive and robust.

1 Introduction

Flexible AC transmission systems (FACTS) devices are increasingly being applied to improve system control, there- fore helping to utilise transmission systems to their maxi- mum capabilities. There are several different types of FACTS devices [I]. A unified power flow controller (UPFC) is a promising option for improving power-system stability. The practical realisation of the UPFC requires a solid-state ACIAC converter, which can be implemented by two similar voltage-source inverters operated from a com- mon DC link capacitor as shown in Fig. I .

Theoretical analysis and its model development on FACTS devices have attracted much attention. Wang has developed FACTS control, mainly based on a linearised Phillips-Heffron model [2, 31. In [4], two applications of the sampled regulator design method (SRDM) to FACTS control have been presented. This method is used to over- come the nonlinearity of a power system, especially as it is used for the design of a DC voltage regulator and SVC AC voltage control, respectively. On the other hand, compo- nents-based simulation on FACTS devices has started to make an impact in the application of FACTS devices in a practical and realistic sense. For example, simulation based on the feasible GTO switches and converter topologies; incorporation of the appropriate booster and exciter trans- former into system, semiconductor switch control and a

0 IEE, 2001 ZEE Proceedings onlie BO. 20010526 DOL 10.1049/ip-gtd20010526 Paper first received 25th April 2000 and in revised form 5th March 2001 The authors are with thc School of Electiical and Electronic Engineeiig, Nm- yang Technological University, Singapore 639798, Republic of Singapore

UPFC cascade control become the main focuses in the applications of FACTS devices.

In [5], the UPFC has been modelled at the component level using the PSCADEMTDC software package, which can provide eficient and precise time-step solutions to any complex electrical networks, including the state and time controlled switches. The series voltage phase angle and magnitude injection have been controlled, respectively, in a conventional way to enhance the dynamic performance of a power system.

As the power system size increases, the complexity of parametric system modelling makes the design of the controller more difficult. Obtaining the state-space equation can be a difficult, sometimes impossible task due to the nonlinearity and uncertainty of parameters in the system. Hence, while taking both stability and control performance into consideration, other concerns in designing the control- ler are not only to handle the uncertainty and nonlinearity of the system plant P, but also to overcome the difficulty of establishing an A, B, C mechanism based model of the power system.

With the intention of designing a controller independent of the system model, Han [6] proposed a new concept of robust and adaptive control. In addition, Han has further developed the nonlinear PID controller (NLPID). Ni et al. [7] utilised the new developed NLPID controller to control the STATCOM.

In this paper, a comprehensive procedure for designing an effective and robust controller for a FACTS device by using the NLPID is presented. An NLPID controller is validated by means of relatively practical digital simulation software PSCAD/EMTDC.

This approach to UPFC realisation has the following two distinct features: (i) The whole system model is devel- oped at the components level and a detailed three-phase

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send

exciting transformer boosting transformer

setting value --+ syncronism system -

measured DC voltage - - control parameters

c- system data UPFC control +-- measured parameters

i g end L).....

Fig. 1 System schematic diugxun with UPFC instulled cit .sendbig end oj~~an~sinission line

model of the UPFC is also developed using PSCAD/ EMTDC software package; (ii) An NLPID controller is applied and a new tracker of differential (TD) is designed in the main control of the UPFC. The control scheme is implemented and verified using PSCAD/EMTDC software package.

2 Power system configuration

Consider a generator supplying power through a double circuit transmission line equipped with a UPFC as shown in Fig. 1. Exciter and booster transformers are installed, respectively, at the shunt and series branches. Without much loss of the generality, a basic UPFC with two volt- age-source three-phase inverters operated from a common DC link capacitor is used in this study for reviewing the basic operating principles and its control modes. Three- phase short-circuit faults will be applied at the middle of the transmission line as shown in Fig. 1. Detailed configu- ration of the system components level implementation is given in Appendix 7.1.

The main function of the UPFC is to inject an AC volt- age with controllable magnitude and phase angle, at the power frequency, in series with the voltage and the trans- mission line via the booster transformer. By inserting a controllable AC voltage, the UPFC regulates the magni- tude and phase angle of the transmission-line voltage at its series terminal, to achieve a prescribed real and reactive power in the line, and thus enabling the improvement of system dynamic performance.

The series voltage injection responds to the power varia- tions of the transmission line, while the shunt compensa- tion is controlled to maintain the system busbar voltage and to stabilise the DC link of the UPFC. Hysteresis current forcing (HCF) and sinusoidal pulse-width modula-

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tion (SPWM) have been used as the switching schemes for the converter and the inverter, respectively. These switching schemes are implemented in the EMTDCPSCAD software package. The proposed NLPID controller is used to control the phase angle of the series branch.

Hysteresis current forcing is used as the switching scheme for the exciter branch. In HCF switching, the AC side current is forced to track a referenced current by high- frequency switching of the switch pairs of the converter bridge. The reference current was the fundamental current measured at the sending end of transmission lines. The phase-locked loop (PLC) has been used to co-ordinate system three-phase signal and controller output signal so that synchronisation can be achieved.

3 rejection rontroller

3. I Description of the control methodology Most control methods are based a the so called A, B, C mechanism. It means that the control algorithm depends on the system equation. In practice, however, most systems are nonlinear in nature and include many uncertain factors, and therefore the system equations are uncertain. A control method based on the system equation is less effective and therefore unrealistic to a certain extent.

In this paper, a NLPID control method with a tracker of differential (TD) [6, 71 is proposed to obtain a low-noise derivative of a specific nonlinear input signal. In addition, an extended state observer (ESO) is utilised in the feedback channel to reject the noise incurred by the measurement signal from time to time. All these combinations are also known as an auto-disturbance-rejection controller.

The constitution of a conventional PID controller is demonstrated by Fig. 2. There are several drawbacks with the usage of the conventional PID:

Nonlinear PID control - auto disturbance

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(i) Signal y is the output of lag-network, which would be varied in a continuous way, but the control input v will vary in a discrete way, or step change. It is unreasonable for the discrete signal to be tracked by a continuous signal. (ii) It is difficult to obtain the error derivative dddt without an appropriate derivative tracker. (iii) The control algorithm has been limited to the linear composition of the sum of SE, E and dddt, which represent the past, present and future of the error signal, respectively.

I____

7 flTl-. ' nonlinear

5 TD(IJ *y, algorithm- dc/dt

VP YP

Fig. 2 Conventioncrl PID controller

With respect to the defects mentioned here, the possible solutions could be as follows: Solution 1: According to the input signal and features of control object, the transient process could be governed in a continuous way instead of a discrete way, so that the per- formance specifications would be well met. Solution 2: Tracker of differential (TO) could be designed so that dddt would be obtained in a precise way. Solution 3: Appropriate nonlinear algorithm could be applied. From those possible solutions, the following theorem is drawn and stated again [6]: Theorem 1: If all the solutions of a nonlinear system

(1) X I = x2 { X 2 = f (W4

satisfy

lim z l ( t ) = 0 and lim za(t) = 0 t+oo t+oo

Then to any bounded integratable function v(t) and con- stant T > 0, the solution of the system:

z1 = 22

22 = R2 f (21 - U, %2/R) (2)

( 3 )

will satisfy

T+IX lim 1 Izl(t) - v( t ) ld t = 0

where R is a constant (R > 0). The details of the proof of this theorem are given in the closure of [6]. Remark 3. I : This means that zl(t) will uniformly converge to v(t) and z2(t) to dvldt. Therefore z , ( t ) is considered as a tracker of v(t) and z2(t) is an approximation of the deriva- tive of v(t). Remark 3.2: The advantages of application of TD: a The derivative signal of v(t) is obtained by integral block, instead of directly obtained from signal v(t). b Tracking efficiency and derivative quality will be deter- mined by different selection of function Axl, x2). The nonlinear PID controller is described by Fig. 3. A TD is such a dynamic system that can produce two output signals vl(t) and v2(t). v,(t) is given to track input signal v(t), while v2(t) is the derivative signal of vl(t). The func- tions of TD are (i) to govern appropriate transient response v1 of input signal v, based on the performance specifications of object, and to produce the derivative v2 of input signal;

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Y object -

alogorithm

parameters

middle control

system

(low-level control)

I

current forcing SPWM control

( GTO'S triggering ) Fig. 4 Overview o j UPFC control

To realise all the functions, each part of the devices needs to be separately controlled. In addition, the control signal generated by each part must be synchronised with the system signal. For example, the shunt branch is controlled to maintain DC voltage constant while the series branch plays a role in injecting the variable voltage, with its contin- uous magnitude and phase angle control, this injection is achieved by the booster transformer.

A hysterisis current-forced (HCF) control is used as a switch scheme for the converter in the shunt branch, to maintain DC voltage constant, and provides the necessary real power required by the series branch. Sinusoidal pulse- width modulation (SPWM) is used as a switch scheme for the inverter in the series branch. Control of magnitude and phase angle of injected voltage in the series branch is real- ised by controlling the magnitude and phase angle of the control signal. The magnitude is controlled by a state feed- back control, while NLPID is applied to the phase-angle control of the series-voltage injection.

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As an initial study, the authors have designed the tracker of differential but ESO is not considered.

3.3 Development and application of NLPID Based on Theorem 1 of Section 3.1, the tracker of differen- tial is adopted as shown in Fig. 5. The input signal is the difference between reference and measured quantities of generator rotor angle 6, [SI, and it is represented as 6, = ares- 6, where, 6 is rotor angle of generator.

' 6 . L...--d

Fig.5 Trucker of di@zntial

Although the availability of the rotor angle as the input is assumed in this paper, it may not be readily available, especially as the UPFC may be installed at the middle of the transmission line. However, the state observer could be designed to obtain the rotor angle from the measurable rotor speed [SI.

8, is considered as a tracker of a,, ad an approximation of the derivative of Se, R is constant:

f(z1,zz) = kllzll"lsign(zl) + k2/221"2sign(z2)

(4) J(xl, x2) is selected to satisfy Theorem 1. /cl, k2, al, a2 are parameters of TD and are determined from simulation studies.

The nonlinear PID controller is used as the phase angle control of series injected voltage with its output signal used as the phase angle of the control signal of the UPFC series converter (see Fig. 6).

. %---dfeedbackB state magnitude controlv

Fig. 6 NLPID controlfor the comtrol of injected voltuge

Based on the proposed tracker of differential, the nonlin- ear algorithm using sign and exponential functions has been developed as follows:

s ign(ed) ( 5 )

U is the controller output or the injected phase angle of the series voltage. S,, 6, are the integral and derivative of the original input signal Se, respectively, S, is an approximation of 6,.

A nonlinear function is used to constitute the output signal of the NLPID controller. The coefficients /z , k,, kc,, ai and a d are constants. m e n a, and a d are equaf' to one, the controller becomes a linear PID controller. To increase the damping ability of error signal and reject disturbances, a, < 1 and a d < 1 are necessary conditions. Eqn. 5 has two benefits: (a) The exponential function in each term can introduce some nonlinearity. For example, if a, < 1, then the small signal e, will be amplified, whereas the larger signal of e, will look as though it is saturated as compared with the

U = k p 16t Isign(ep)+k,16, 1"s sign(e,)+kdlbd I

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linear PID controller. This feature is desired because of the nonlinearity of the power system. (0) The other feature of the NLPID controller is that it is not so sensitive to the operating conditions and system parameters as compared with a power system stabiliser

With the appropriate selection of the coeficients in eqns. 4 and 5, the NLPID controller can be expressed in following form:

(PSS).

'U = f u ( h-1, a1 , k 2 , a2 k p ; k t , kd, ai, a d )

Again, all the controller parameters can be found through the simulation studies and are listed in Appendix 7.2. The magnitude of the injected voltage is controlled through state feedback and is limited to 0.1 p.u.

4 Simulation results

The feasibility of the proposed control scheme for the UPFC, including the GTOs switching scheme and system, are demonstrated with the aid of digital simulation studies performed on the three-phase model of the test system. Detailed parameters of the model are presented in Appen- dix 7.1.

The system performance under large disturbance was studied by applying a transient symmetrical 3-phase short- circuit fault at the middle of the transmission line (Fig. l), with the following sequence: Stage I : the system is in a steady state Stage 2: the fault occurs at t = 1.0s Stage 3: the fault is cleared at t = 1.095s. The system operating condition prior to the application of the fault is taken as Pln0 = 167MW, and So = 70".

Comparisons of transient performances of the power sys- tem with NLPID against those with (i) no control and (ii) linear PI control are shown in Figs. 7 and 8, respectively.

It is observed from Figs. 7n and c that the NLPID control can help improve transient stability quite well. The first swing peak value of the generator rotor angle is 79" compared with the 93" without control. It is seen from Fig. 8 that conventional PI control also performs quite well with the first swing peak limited to 83". However, this is the operating condition used to design the PI controller.

The variation of the sending end voltage is shown in Fig. 7e. The voltage performance has been improved. In addition, the DC busbar voltage is very well regulated at the reference level, which proves that the current control of the exciter branch is robust to the supply oscillations.

The DC busbar voltage does not need to be considered as a state in designing the feedback control. It means that the UPFC can be constructed to have very fast internal dynamics with a constant DC busbar voltage.

To demonstrate the robustness of the proposed NLPID controller, the authors have conducted the simulation stud- ies under various operating conditions, without making any adjustment on the controller parameters. The system performance following a large disturbance, when the initial operating condition is SO", is shown in Fig. 9. Solid lines indicate the performance with NLPID, dashed lines repre- sent the behaviour of the system with PI control. i t is clear that the system performance with NLPID following a large disturbance is not affected by the change of operating condition. However, the performance of linear PI control deteriorates drastically under the new operating condition.

Owing to the robust behaviour of the proposed NLPID, the control technique has been investigated for application

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0 0.5 1.0 1.5 2.0 2.5 3.0 time. s

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Fig. 7 System hduvioiir when S, = 70"fbNowitzg U large distiii.bcit~ce with NLPID __ with NLPID .......... without control o Rcal power, MW h Reactive power, Mvar c Rotor angle of generator (So)

tl Rotor speed of generator (raNs) e Voltage vadation at sending end f DC side performance

in multimdchine systems and the results have been reported elsewhere.

Some oscillations have been observed at some parame- ters in the simulation studies. Application of UPFC involves the application of power electronics devices, which will introduce harmonics into the power system because of its high-frequency switching and nonlinear behaviour. Some measures needed to alleviate these oscillations have been studied, but this aspect is not elaborated in this paper.

5 Conclusion

This paper presents the application of the NLPID control- ler to UPFC control and the development of the new tracker of differential (TD) in a power system. The authors have investigated the design procedure of the NLPID controller on the application of UPFC control. A dynamic block to obtain the derivative signal dynamically, namely the differential tracker, is proposed to obtain an accurate and low-noise derivative signal. A nonlinear algorithm is employed to realise the nonlinear control of UPFC for the purpose of enhancing transient stability. This nonlinear

IEE Proc.-Gerier. Tronsni. Distrih., V d 148. No. 6, N<~veiiiher 2001

algorithm includes an exponentially damped coefficient and a sign function. Therefore, the proposed controller has a strong damping ability to its error input, and has the ability to reject the disturbances.

The digital simulation study results have shown that the proposed controller is effective and efficient in improving transient stability of the power system. Its robustness and adaptability at different operating conditions have been demonstrated.

The robustness of the proposed NLPID controller of the FACTS devices may be attributed to the fact that it does not require full information and an exact model of the power system.

References

SHRESTHA, G.B., KANG, Y.L., and LIE, T.T.: 'Incorporation of a general model of static phase shifter in power systems'. Proceedings of 1999 International Power Engineering conference (IPEC '99), Singa- pore, 24-26 May 1999 WANG, H.F.: 'Damping function of unified power flow controller', IEE Proc., Gena: Transm. Distrib., 1999, 146, (l), pp. 81-87 WANG, H.F.: 'Application of modeling UPFC into multi-machine power systems', IEE Proc., Gener. fiunsm. Distrib., 1999, 146, (3), pp. 306-3 12

521

500 350-

300 -

a b

l O O r

1.0-

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! > 0.4

0.2

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4 WANG. H.F., LI, F., and CAMERON, R.G.: 'FACTS control design based on power system nonparametric models', IEE Proc. Gener., Transm. Distrib., 1999, 146, (5), pp. 409415

5 TOUFAN, M., and ANNAKKAGE, U.D.: 'Simulation of the uni- fied power flow controller performance using PSCADEMTDC', Electr. Power. Syst. Res., 1998, 46, pp. 67-75

6 HAN, J.: 'A new controller: Nonlinear PID control', Control and Decision (China), 1994, 9, (6), pp. 401407

7 NI, Y., JIAO, L., CHEN, S., and ZHANG, B.: 'Application of a nonlinear PID controller on STATCOM with a differential tracker'. Proceedings of 1998 Energy Management and Power Delivery (EMPD '98), 1998, Vol. 1, pp. 29-34 DEMELLO, F.P.: 'Measurement of synchronous machine rotor angle

Inrush decay time constant 0.01 s Knee voltage 1.25p.u. Time t' Base operation frequency = 60.0Hz TD, = 1.0 sec (see

Table 1,

flux 'lipping 0'

'1.

8 from analysis of zero sequence harmonic components of machine ter- minal voltage', IEEE Trans. Power Deliv., 1994, 9, (4), pp. 1770-177 Line-to-line Magnising Positive-sequence

Type voltage kV, current, leakage reactance, (RMS) p.u. p.u.

Winding 1 delta 20 0.02 0.1 7 Appendix

7.7 Equipment data and system parameters Winding 2 star 242 0.02

7.1. I Step-up transformer: 3-phase, 2-winding transformer: 380 MVA Saturation is placed on winding 1 Aircore reactance 0.2p.u.

7.1.2 Boosting transformer: 3 single-phase transformer: 22.0MVA Base operation frequency = 60.0Hz (see also Table 2).

528 IEE Proc-Geiier. Trnnsm. Disnih., Vol. 148. No. 6. November 2001

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Table 2

Line-to-line Magnising Positive-sequence Type voltage kV, current, leakage reactance,

(RMS) p.u. p.u.

Winding 1 star 45 0.0 0.1

Windina2 star 11.25 0.0

7.1.3 Exciter transformer: 3-phase, 2-winding transformer 2-winding transformer: 5OMVA Base operation frequency = 60.OHz (see also Table 3).

Table 3

Line-to-line Magnising Positive-sequence Type voltage kV, current, leakage reactance,

(RMS) p.u. p.u.

Winding 1 star 242 0.01 0.1

Winding 2 delta 11.0 0.01

7.1.4 Synchronous machine parameters: Rated RMS line-to-neutral voltage UN$ = 11.55 kV Rated RMS line current IN = 10.19kV Rated real power PG = 300MW Base angular frequency o = 376.99 radls Initia constant H = 3.055MWlMVA Stator resistance R, = 0.0p.u. Stator leakage reactance X, = 0.13p.u. Power factor 0.85 cosq = 0.85

0 0.5 1.0 1.5 2.0 2.5 3.0 time, s

d

d-axis unsaturated reactance X, = 2.36p.u. d-axis unsaturated transient reactance X ; = 0.319p.u. d-axis unsaturated transient time (open) T:m = 7.96s d-axis unsaturated subtransient reactance Xffd = 0.191 p.u. d-axis Unsaturated subtransient time (open) Tffcm = 0.134s q-axis unsaturated reactance XC, = 0.319p.u. q-axis unsaturated transient reactance X:, = 0.219p.u. q-axis unsaturated transient time (open) Tf@ = 0.85s q-axis unsaturated subtransient reactance Fq = 0.289p.u. q-axis unsaturated subtransient time (open) Tffq = 0.034s

7.1.5 Transmission line parameter: L = 0.0728 h

7.1.6 Power electronic switch: GTO, snubber circuit is in parallel with GTO, loss compensation enabled. Thyristor on, resistance Ron = 0.005Q Thysitor off, resistance Rojy= 1.0 x lO*Q Forward voltage drop EFVD = 0.0 kV Forward breakover voltage EBo = 1 .O x lo5 kV Reverse withstand voltage ERw = 1.0 x 105kV Minimum extinction time Text = 0 . 0 ~ Snubber resistance R D = 5000.0Q Snubber capacitance C, = 0.05F

7.2 Controller parameters Tracker of differential (TD):

Nonlinear equation coefficients: I c ~ = -0.2; k2 = -0.5; C X ~ = 0.01; C X ~ = 0.6

kll = -0.002; ki = 0.25; kc/ 5.0; 1 0.1; aj = 0.001

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