torsional oscillations in alternators7

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Published in IET Generation, Transmission & Distribution

Received on 29th August 2011

Revised on 10th January 2012

doi: 10.1049/iet-gtd.2011.0625

ISSN 1751-8687

Damping of subsynchronous oscillations in powersystem using static synchronous series compensatorM. Farahani

Department of Electrical Engineering, Bu-Ali Sina University, Hamedan, Iran

E-mail: [email protected]

Abstract: In this study, a static synchronous series compensator (SSSC) is used to damp the subsynchronous oscillation in a

power system compensated by the series capacitor. In order to achieve an effective damping, a supplementarysubsynchronous damping controller (SSDC) is added to the SSSC. The only input signal for the SSDC is the rotor speeddeviation to generate the modulation index for controlling the injected voltage of the voltage-sourced converter (VSC). Also,the chaotic optimisation algorithm is employed to tune the parameter of SSDC. The design objective is to suppress thesubsynchronous resonance (SSR) caused by the series capacitor. By using the SSDC, the SSSC connected at the transmissionline is able to damp the SSR. The first system of IEEE second benchmark model is used to evaluate the effective of SSDC onthe torsional oscillations. The several simulations are used to demonstrate the ability of SSDC in damping the SSR.

1 Introduction

The use of series capacitor is a conventional method for

reducing high reactance of long transmission lines. Thismethod has some advantages such as increase in transientstability, improvement of load carrying of transmission linesand by controlling this reactance, they allow better controlover load sharing between parallel transmission lines.However, despite these benefits, these series capacitors canincrease the risk of interaction between electrical powersystems and turbine generators rotor torsional system.This problem is known as subsynchronous resonance (SSR)or subsynchronous oscillations. Subsynchronous oscillationis an electric power system condition where the electricnetwork exchanges significant energy with a turbinegenerator at one or more of the natural frequencies of thecombined system below the synchronous frequency of thesystem following a disturbance from equilibrium [1].

The researchers have used many techniques to overcomethis problem and proposed many controllers in the literatures.In general, most of these techniques can be divided into twomain groups. The first one contains the controllers based onthe excitation system of generator [24]. The second oneconsists of the flexible AC transmission systems (FACTS)devices.

The FACTS devices provide a powerful mechanism inorder to control the reactive power and voltage in powersystems. Besides these abilities, the different types of thesedevices can be used in improving the stability of system. Alot of articles have been published about the use of these

devices in damping the SSR [513].In this paper, a static synchronous series compensator

(SSSC) along with the supplementary subsynchronousdamping controller (SSDC) connected at the transmission

line is used to damp the SSR. The parameters of SSDC aretuned by the chaotic optimisation algorithm to achieve aneffective damping. The SSSC is used as a voltage source in

series with a fixed capacitor. So, this combination canprevent the subsynchronous oscillations that may be causedby conventional fixed capacitor. This factor, along with thesimple control method, makes the proposed configurationhighly effective in damping the SSR.

2 System under study

In this study, the first system of IEEE second benchmarkmodel shown in Fig. 1 is used to evaluate and analyse therisk of SSR [14]. In this model, a 600-MVA synchronousgenerator via two 500-kV transmission lines is connected toa large grid which is approximated by an infinite bus. Theturbinegenerator system as shown in Fig. 2 is modelled byfour masses.

As seen in Fig. 1, the SSSC injects a voltage Vs in serieswith the transmission line where it is connected. Voltage-sourced converter (VSC) using insulated gate bipolartransistor (IGBT)-based pulse width modulation (PWM)inverters is used in this study. However, as details of theinverter and harmonics are not represented in the SSRstudies, the same model can be used to represent a gate turnoff (GTO)-based model. The overall performance of SSSCis completely explained in [1011].

3 Proposed approach

3.1 Structure of control for the SSSC

An SSSC has an inherent damping capability and that onlyunder certain circumstances it may be not sufficient [11],

IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 6, pp. 539 544 539

doi: 10.1049/iet-gtd.2011.0625 & The Institution of Engineering and Technology 2012

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thereby to achieve an effective damping, an SSDC must bedesigned and added to the SSSC. The structure shown inFig. 3 is selected in this study in order to control the powerflow. In this structure, there are two basic controllersimplemented in SSSC, a Vq voltage regulator and a DCvoltage regulator. The principal strategy in controllingSSSC for damping the SSR oscillations is to use simplestabilising signals. The rotor speed deviation of generator

Dv contains components of all the torsional modes.Consequently, if the rotor speed deviation is used to controlSSSC, all the torsional modes, in addition to the modecorresponding to the generator mass will be affected. Asseen in Fig. 3, the SSDC input selected is the rotor speeddeviation of generator. The input after passing through awashout filter excites the derivative gain Kd. The outputsignal of derivative gain signifies the existence of the SSR

in the system power. Therefore the SSDC uses the rotorspeed deviation to modulate the SSSC-injected voltage Vqto improve the damping of the unstable torsional modes. InFig. 3, Vqref represents the reference injected voltage asdesired by the steady-state power flow control loop. Thesteady-state power flow loop acts quite slowly in practiceand hence, in the present study Vqref is assumed to beconstant during the disturbance period. In the control

system block diagram, Vd_conv and Vq_conv designate thecomponents of converter voltage Vconv which are,respectively, in phase and in quadrature with current.

The control system consists of

A phase-locked loop (PLL) which synchronises on thepositive-sequence component of the current I. The output ofthe PLL (angle u vt) is used to compute the direct-axisand quadrature-axis components of the AC three-phasevoltages and currents (labelled as Vd, Vq or Id, Iq on thediagram shown in Fig. 3). Measurement systems measuring the q components of AC

positive-sequence of voltages V1 andV2 (V1q andV2q) as wellas the DC voltage Vdc. AC and DC voltage regulators that compute the twocomponents of the converter voltage (Vd_conv and Vq_conv)are required to obtain the desired DC voltage (Vdcref) andthe injected voltage (Vqref). The Vq voltage regulator isassisted by a feed-forward-type regulator which predicts theVconv voltage (the injected voltage on the VSC side of thetransformer) from the Id current measurement.

3.2 Problem formulation

The transfer function of SSDC is

y =

TWs

1 + TWsDvKds (1)

Although local control signals can easily be obtained, theymay not consist of the oscillation modes. By consideringthe recent advances in optical fibre communication andglobal positioning system, the rotor speed deviation can bemeasured and deliver to the control centre [10].

Fig. 1 IEEE second benchmark model along with SSSC

Fig. 2 Modelling of the turbinegenerator system

Fig. 3 Block diagram of power flow control of the SSSC along with SSDC

540 IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 6, pp. 539544

& The Institution of Engineering and Technology 2012 doi: 10.1049/iet-gtd.2011.0625

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In the SSDC, the signal washout block serves as a high-pass filter, with the time constant TW, high enough to allowsignals associated with oscillations in input signal to passunchanged. The washout time constant TW is usually pre-specified [10]. In this paper, TW is taken as 10 s. In order toachieve a satisfactory damping, the derivative gain Kd must

be determined. Under steady-state conditions, the SSDCoutput and Vqref are constant values. During the dynamic

and transient conditions the series injected voltage Vq ismodulated to suppress the subsynchronous oscillations.

3.3 Optimisation problem

It is worth mentioning that the SSDC is designed to minimisethe modes oscillation. So, the objective can be formulated asthe minimisation of objective function fgiven by

f=

t=tsimt=0

t|Dv| dt (2)

where tsim is the simulation time and Dv is the rotor speed

deviation. For objective function calculation, the time-domainsimulation of the system model incorporating all saturationlimits of control signals is carried out for the simulation

period. The purpose is to minimise this objective function todamp the torsional oscillations. The design problem can beformulated as the following constrained optimisation

problem, where the constraint is the SSDC parameter bounds

Kmind Kd K

maxd (3)

In this paper, the chaotic optimisation algorithm (COA) is usedto solve this optimisation problem and search for the optimal

parameter. The implementation of optimisation algorithm is

summarised in Fig. 4.

3.4 Chaotic optimisation algorithm

In this paper, the COA based on the Lozi map is implementedand used. The Lozi map is as follows [15]

y1(k) = 1 a|y1(k 1)| +y(k 1) (4)

y(k) = b y1(k 1) (5)

z(k) =y(k) a

b a(6)

where k is the iteration number. In this work, the values of yare normalised in the range [0, 1] to each decision variable inthe n-dimensional space of optimisation problem. Thus,

y [ [20.6418, 0.6716] and [a, b] (20.6418, 0.6716).Many unconstrained optimisation problems with continuousvariables can be formulated as the following functionaloptimisation problem.

FindX to minimise f(X), X [x1, x2, . . ., xn], where fandX are the objective function and the decision solution vector,respectively. The decision solution vector consists of n

variables xi that are bounded by lower (Li) and upper limits(Ui). The COA based on the Lozi map is shown as follows[15] (Fig. 5):

Where Mg, Ml, f and X are number of iterations of the

chaotic global and local searches, the best objective functionand the best solution of the current run of the chaotic search,respectively. The impact of the current best solution on thegenerating of a new trial solution is controlled by the stepsize l. A small l tends to perform exploitation to refineresults by local search, whereas a large one tends to facilitatea global exploration of search space. In this study, we haven 1 and X [x1] [Kd]. The COA based on the Lozimap is completely explained in [15].

4 Simulations and results

The optimisation of SSDC parameter is carried out based onthe following initial operating condition and assumptions:

1. The generator delivers 1 p.u. power to the transmissionsystem and the magnitude of the generator and infinite busvoltages are adjusted at 1.00 p.u.2. The compensation level provided by the series capacitor isset at 55%3. It is assumed that three-line-to-ground fault is occurred atthe beginning of the line 2.

In order to acquire better performance, 2000 and 500iterations are considered for the global search and the localsearch, respectively. It should be noted that the COA is runseveral times and then the optimal parameter of SSDC ischosen. The final value of SSDC parameter is Kd 0.839.To show the effectiveness of SSSC with the proposedSSDC, three simulations are carried out using MATLAB/SIMULINK.

4.1 Increase in input mechanical power

As the first test case, a 10% decrease in input mechanicalpower is applied to the generator at t 0.5 s and removed

at t 1 s. Also, the compensation of the line 1 and theoperating conditions are 55% and P 0.85 p.u.,Vt 1 p.u., respectively. The rotor speed deviation ofgenerator Dv as shown in Fig. 6 is well controlled and theFig. 4 Flowchart of optimisation



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Fig. 5 COA based on the Lozi map



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oscillations amplitude is clearly decreased by the SSSC.Fig. 7 illustrates the torsional oscillation on the shaft ingenerator-low pressure turbine (Gen-LP) section. It is

observed that in the absence of SSSC, increase of theoscillation amplitude indicates that the generator have agrowing torsional vibration, which would probably lead togreat damage on the shaft. When the SSSC is applied to thesystem, the subsynchronous oscillation is successfullydamped out.

4.2 Disconnection of the line 2

For the second simulation, it is assumed that the transmissionline 2 is tripped out at t 1 s and again reclosed at t 4 s.Also, the compensation of the line 1 and the operatingconditions are 55% and P 0.9 p.u., V

t 0.95 p.u.,

respectively. Fig. 8 shows the rotor speed deviation. It is

clear that in this disturbance, the SSSCs performance isstill satisfactory. The torsional oscillations on the shaft inGen-LP section is depicted in Fig. 9. As the SSDC

parameter is tuned under heavy operating conditions andwith a large disturbance, the SSSC with the SSDC show a

proper performance in other operating conditions and withdifferent disturbances.

4.3 Three-line-to-ground fault

For completeness, the performance of SSSC is alsoinvestigated under a large disturbance. To demonstrate therobustness of SSSC with the proposed SSDC, the

performance of SSSC is evaluated in different operatingconditions. For this purpose, it is assumed that a seriousthree-phase short-circuit fault occurs at the beginning of

line 2 and the compensation of the line 1 and the operating

Fig. 6 Rotor speed deviation during and after a small disturbance

Fig. 7 Torque of Gen-LP section during and after a small disturbance

Fig. 8 Rotor speed deviation during and after the disconnection of

line 2

Fig. 9 Torque of Gen-LP section during and after the

disconnection of line 2



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conditions are 55% and P 0.95 p.u., Vt 1.05 p.u.,

respectively. The rotor speed deviation is depicted inFig. 10. It is clear that the proposed controller is robust and

provides efficient damping even under large disturbanceconditions. The torsional oscillation on the shaft in Gen-LPsection is shown in Fig. 11. For short time after the fault(about ,1 s), the magnitude of the oscillations is large,

because of the severe impact of the fault. The SSSC withthe proposed SSDC is clearly able to decrease during theshort time so that the severe vibration on the shaft isquickly debilitated.

In addition to these simulations, sufficient simulations havebeen carried out for other operating conditions and with largebut different disturbances. Totally, SSSCs performance is

good in damping all the torsional modes and cansatisfactorily weaken the vibrations caused by SSR indisturbances.

5 Conclusion

In this paper, an SSSC is proposed to dampen the SSR. Inorder to achieve an effective damping, an auxiliary

controller called SSDC is designed and added to the SSSC.A simple structure is proposed for the SSDC. The COA isused to tune the parameter of SSDC in order to minimisethe oscillation amplitude. A simple signal is chosen as theinput of SSDC. This signal contains all the torsional modesso that the SSSC with the proposed SSDC can improve thestability of system. The SSSC is used as a voltage source inseries with a fixed capacitor. So, this combination can

prevent the subsynchronous oscillations that may be causedby conventional fixed capacitor. This factor along withsimple control method, make the proposed configurationhighly effective in damping the SSR. Some simulations areused to demonstrate the ability of the SSSC with the

proposed SSDC.

6 References

1 IEEE Subsynchronous Resonance Working Group: Terms, definitionsand symbols for subsynchronous oscillations, IEEE Trans. PowerAppar. Syst., 1985, PAS-104, (6), pp. 13261334

2 Ganjefar, S., Farahani, M.D.: Damping of subsynchronous resonance

using self-tuning PID and wavelet neural network, Int. J. Comput.Math. Electr. Electron. Eng., 2012, 31, (4), pp. 12591276

3 Widyan, M.S.: On the effect of AVR gain on bifurcations ofsubsynchronous resonance in power systems, Electr. Power EnergySyst., 2010, 32, (6), pp. 656663

4 Zhang, D., Xie, X., Liu, S., Zhang, S.: An intelligently optimized SEDCfor multimodal SSR mitigation, Electr. Power Syst. Res., 2009, 79, (7),pp. 1018 1024

5 Jusan, F.C., Gomes, S. Jr., Taranto, G.N.: SSR results obtained with adynamic phasor model of SVC using modal analysis, Electr. PowerEnergy Syst., 2010, 32, (6), pp. 571582

6 Pahlavani, M.R.A., Mohammadpour, H.A.: Damping of sub-synchronous resonance and low-frequency power oscillation in aseries-compensated transmission line using gate-controlled seriescapacitor, Electr. Power Syst. Res., 2011, 81, (2), pp. 308317

7 Padiyar, K.R., Prabhu, N.: Design and performance evaluation of

subsynchronous damping controller with STATCOM, IEEE Trans.Power Deliv., 2006, 21, (3), pp. 13981405

8 Alomari, M.M., Zhu, J.G.: Bifurcation control of subsynchronousresonance using TCSC, Commun. Nonlinear Sci. Numer. Simul.,2011, 16, (3), pp. 23632370

9 Sindhu, T.K.C., Nandakumar, M.P., Cheriyan, E.P.: Adaptive RTRLbased neurocontroller for damping subsynchronous oscillations usingTCSC, Eng. Appl. Artif. Intell., 2011, 24, (1), pp. 6076

10 Panda, S.: Multi-objective evolutionary algorithm for SSSC-basedcontroller design, Electr. Power Syst. Res., 2009, 79, (6),pp. 937 944

11 Pillai, G.N., Ghosh, A., Joshi, A.: Torsional interaction studies on apower system compensated by SSSC and fixed capacitor, IEEETrans. Power Deliv., 2003, 18, (3), pp. 988993

12 Moursi, M.El, Sharaf, A.M., El-Arroudi, K.: Optimal control schemesfor SSSC for dynamic series compensation, Electr. Power Syst. Res.,2008, 78, (4), pp. 646656

13 Chen, J., Lie, T.T., Vilathgamuwa, D.M.: Damping of power systemoscillations using SSSC in real-time implementation, Electr. PowerEnergy Syst., 2004, 26, (5), pp. 357364

14 IEEE Subsynchronous Resonance Working Group: Second benchmarkmodel for computer simulation of subsynchronous resonance, IEEETrans. Power Appar. Syst., 1985, 104, (5), pp. 10571066

15 Coelho, L.D.S.: Tuning of PID controller for an automatic regulatorvoltage system using chaotic optimization approach, Chaos SolitonsFractals, 2009, 39, (4), pp. 15041514

Fig. 11 Torque of Gen-LP section during and after a large

disturbance

Fig. 10 Rotor speed deviation during and after a large

disturbance



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