Damping of power system oscillations using SSSC in real-time implementation

Electrical Power and Energy Systems 26 (2004) 357–364 www.elsevier.com/locate/ijepes

Damping of power system oscillations using SSSC in real-time implementation Jianhong Chen, Tjing T. Lie*, D.M. Vilathgamuwa Centre for Advanced Power Electronics, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore Received 12 November 2002; revised 13 June 2003; accepted 7 November 2003

Abstract This paper deals with damping of power system oscillations using the SSSC. A robust damping controller based on Fuzzy Logic is proposed after its operation principles are fully analyzed. The only input signal for the damping controller is the real power measurement at the location of the SSSC to generate the modulation index for controlling the injected voltage of the VSC while its phase angle is required to remain constant with respect to a local reference voltage vector. Real-time simulations at the switch level are conducted to demonstrate the validity of the proposed damping controller using the RTDS interfaced with an external DSP-based digital control system. q 2004 Elsevier Ltd. All rights reserved. Keywords: Damping; DSP; Fuzzy Logic; Power system oscillations; Real-time simulation; Static synchronous series compensator

1. Introduction Low frequency oscillations are very harmful for power systems, especially in the deregulated electric utility industry where steady increase in long-distance power transfers makes the situation grave. Conventional methods, such as Power System Stabilizers (PSSs), however, may not be so effective to deal with various oscillation modes emerging in large scale, complex and deregulated electricity industries [1]. Speedy advancement of semiconductor technology offers promising future for the applications of switching power converters in power systems. The three-phase Voltage Source Converter (VSC) is the fundamental building-block of the new generation in the FACTS family based on switching power converter technology. The Static Synchronous Series Compensator (SSSC) [2], which consists of a VSC being connected in series with a transmission line through a coupling transformer, can inject a controllable voltage at the line frequency to regulate the line reactance irrespective of the line current. Although its original motivation is for the steady-state power flow control, the SSSC also shows bright future in enhancement of power system stability and damping of power system oscillations * Corresponding author. Tel.: þ 65-790-4519; fax: þ65-793-3318. E-mail address: [email protected] (T.T. Lie). 0142-0615/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2003.11.004

[3]. However, only few research results have been reported on the SSSC although it has a simpler hardware configuration and similar capability of series voltage injection compared with the hot-topic Unified Power Flow Controller (UPFC). In this paper, the operation characteristics of the SSSC are fully addressed. According to its power flow regulating capability, a robust damping controller based on Fuzzy Logic is proposed for the SSSC to enhance damping of power system oscillations. Only the real power measurement at the location of the SSSC is needed as the input signal for the damping controller to control the modulation index of the VSC while its phase angle is assumed to remain constant with respect to a certain local reference voltage vector. However, numerous research results have been reported on the effectiveness of various kinds of FACTS controllers to control power flows, enhance power system stability and damping of power system oscillations [4 –6] employing offline simulation software tools, hardly has any work been carried out in real time at the switch level, especially using external control systems to generate gate signals for power semiconductor devices. Unfortunately, it is crucial to test the whole system before it is implemented in the practical power systems since the off-line simulation results may not be so accurate compared with practical events. In this paper, various simulation tests are implemented in the Real-Time

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Digital Simulator (RTDS) interfaced with an external DSPbased digital control system that generates gate signals for the SSSC modeled in the RTDS.

2. Operation Characteristics Of SSSC In this section, the characteristics of the SSSC are fully addressed. A stand-alone SSSC, which consists of a VSC being connected in series with a transmission line through a coupling transformer, aims to regulate the line reactance through injecting a controllable AC voltage. Since it does not have the capability of real power exchange between the transmission line and the DC link, its injected voltage has to be 908 phase lead or lag to the line current. However, to selfmaintain the DC link voltage, a certain phase shift is implemented to control the DC link voltage. Fig. 1 shows a single line diagram of a two-fixed-bus system with an SSSC ðVi ¼ V/0; Vj ¼ V/ 2 dÞ: The R and X include the line impedance and those of the coupling transformer. 2.1. Operating range of SSSC

2V sinðd=2Þ Vpq cosðd=2 þ rÞ X

ð1Þ

As a result, the following conclusions can be attained: † The operating point of the SSSC should follow the trajectory of the Line MN ðr ¼ p=2 2 d=2 or r ¼ 2p=2 2 d=2Þ as shown in Fig. 2 on which no real power exchange experiences; † In the case that the operating point is located in the left side of the Line MN, the DC link absorbs real power from the transmission line; on the contrary, it supplies real power when the operating point in the opposite side; † However, to self-maintain the DC link voltage, a certain phase shift has to be implemented to absorb real power from the transmission line. That is to say, the operating

Fig. 1. Single line diagram.

point of a stand-alone SSSC must be in the left side of the Line MN. Provided that the effect of the line resistance is included, the real power exchange can be derived as follows: Pex ¼

Line current flow through a series connected VSC will cause a certain amount of real power exchange between the transmission line and the DC link Without considering the effect of the line resistance, the real power exchange can be approximated as follows: Pex ¼

Fig. 2. Vector diagram of SSSC.

2 Vpq R 2

lZl

þ

2V sinðd=2Þ Vpq cosðd=2 þ r 2 qÞ lZl

ð2Þ

where Z ¼ R þ jX; q ¼ p=2 2 arc cosðR=lZlÞ: The linearity property is not valid any more. However, due to R being much smaller than lZl2 in practical power systems, one can make the similar conclusions as above except that the Line M0 N0 becomes the watershed which is derived by rotating the Line MN by q anti-clockwise as shown in Fig. 2. 2.2. Relationship between the transmission line and the dc link Due to the switching loss and conducting loss of the VSC, the injected voltage vector must be shifted by a certain degree to the left side of the Line MN (or the Line M0 N0 ) as shown in Fig. 2 to absorb a certain amount of real power from the transmission line in order to maintain the dc link voltage. Assuming that all the losses are modeled by a resistor in parallel with the dc link capacitor as shown in Fig. 3, the relationship between the dc link voltage and the system

Fig. 3. A simplified model for loss.

J. Chen et al. / Electrical Power and Energy Systems 26 (2004) 357–364

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In other words, the SSSC cannot control both the real power and the reactive power simultaneously. Furthermore, the following conclusions can be drawn: † When the operating point of the SSSC is located along the Line EF as shown in Fig. 2, the injected voltage does not change the real power at the Bus j. However, the real power is increased when its operating point lies above the Line EF; on the contrary it is decreased in the opposite side; † In the case that the operating point is located on the Point M, the maximal real power at Bus j may be attained; on the contrary, on the Point N, the minimal real power at Bus j may be attained.

Fig. 4. Damping controller.

parameters can be derived as follows: Pex ¼ 4

2 Vdc r

ð3Þ

Hence, given a certain transmission system, the attainable DC link voltage can be derived as follows without or with consideration of the line resistance respectively: Vdc #

where

3 Vr sinðd=2Þ 2 X

Z ¼ R þ jX; q ¼ p=2 2 arccosðR=lZlÞ:

or Vdc #

3 Vr sinðd=2Þ 2 lZl

With consideration of the line resistance, the power flows at the Bus j can also be calculated as follows: 8 VVpq V2 V 2R > > > < Pij ¼ lZl sinðd þ qÞ 2 lZl2 þ lZl sinðd þ r þ qÞ > > VVpq V2 V 2X > : Qij ¼ cosðd þ qÞ 2 cosðd þ r þ qÞ þ 2 lZl lZl lZl

ð4Þ

ð6Þ

Similar conclusions can also be reached except that the Line E0 F0 becomes the watershed that is derived by rotating the Line EF by q clockwise as shown in Fig. 2.

Thus, the following can be concluded: 2.4. Remarks † To make the proper operation of a stand-alone SSSC, the transmission line current must be large enough to provide sufficient emf to charge the dc link capacitor to the desired level. 2.3. Power flow control capability of SSSC Through injecting a controllable ac voltage by the SSSC, the power flows at the Bus j can be approximated as follows with the effect of line resistance being ignored: 8 > VVpq V2 > > P sind þ sinðd þ rÞ ¼ < ij X X > > VVpq V2 > : Qij ¼ ðcosd 2 1Þ þ cosðd þ rÞ X X Since the SSSC has to maintain its DC link voltage by itself, there is only one degree of control freedom for the SSSC

In practical power systems, the ratio between the resistance and the reactance is quite small, thus the angle q is small enough to be ignored. In short, the operating range of the SSSC consists of two parts: the sector ETM and ETN as shown in Fig. 2 where the real power at the Bus j is increased and decreased, respectively.

3. Control designs In this section the damping controller based on Fuzzy Logic is developed. The basic idea is through the adjustment of the injected voltage to oppose the growth of the real power through the transmission line as much as possible [6,7], namely the series injected voltage vector is following through the particular routine of the Line MN as shown in

Fig. 5. Membership functions.

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Table 1 Inference rules Ð DPe DPe NB

NM

NS

Z

PS

PM

PB

NB NM NS Z PS PM PB

NB NB NB NB NM NM NS

NB NB NM NS Z PS PM

NB NM NS Z PS PM PB

NM NS Z PS PM PB PB

PS PM PM PB PB PB PB

PB PB PB PB PB PB PB

NB NB NB NB NB NB NB

Fig. 6. Configuration of the real-time implementation system.

Fig. 2 for the SSSC with a certain phase shift to maintain the DC link voltage by itself. Furthermore, to make full use of the series converter, the control output is saturated to make the magnitude of the injected voltage maximal whenever the control inputs are linguistic ‘Big’. In this proposed control strategy shown in Fig. 4, the phase angle of the series injected voltage is always set at p=2 with respect to the reference voltage vector Vi þ Vj for the SSSC. However, to self-maintain the DC link voltage at a desired level, a certain phase shift is controlled by a conventional PI controller as shown in Fig. 4. Only the real power flow measurement is required at the location of the SSSC for the damping controller to generate gate signals for the VSC [1]. Two derived inputs, namely power deviation and its integral, are applied to the damping controller where the output is the modulation index Mi [8]. Normally, Mi should be greater than zero. But in this article, since the phase angle of the injected voltage is always kept constant at p=2; Mi is confined in the range [2 1,1] in order to make full use of the capability of the VSC while maintaining the safe operation of the system. The gate signals are generated using Sinusoidal Pulse Width Modulation (SPWM) technique through comparing the derived sinusoidal control signals with a unit triangle carrier signal at 900 Hz.

The membership functions, for both inputs and output of the Fuzzy Logic damping controller, are chosen as triangular with 50% overlap, as shown in Fig. 5. There are seven linguistic variables for each input variable and output variable, namely, negative big (NB), negative medium (NM), negative small (NS), zero (Z), positive small (PS), positive medium (PM), positive big (PB). Therefore, there are totally 49 linguistic rules as listed in Table 1 based on practical experience and the Direct Lyapunov Stability Criterion [5–7]. Such linguistic inference rules are chosen so that the output is always saturated to make full use of the series converter once the integral of the real power deviation as the first input is linguistic ‘big’. Furthermore, the SSSC can be disconnected from the power system when no more power system oscillations exist. In principle, the width of membership functions should not be set too large in order to saturate the Mi and hence to mitigate the first swing while in order to avoid controller oscillation when the inputs become small, the width of the second input should not be set too small. By employing MIN-MAX inference and Center of Gravity (COG) defuzzification method [9], the output of the Fuzzy Logic damping controller can be determined as follows: 4 X

ucrisp ¼

bi

i¼1 4 X

ð

ð

mðiÞ

mðiÞ

i¼1

where bi is the center of membership function, denotes the area under the membership function mðiÞ :

Ð

mðiÞ

4. Real-time implementation system Since the formation of the concept of FACTS controllers, numerous research results about FACTS controllers’ applications in power systems have been reported employing various software tools such as EMTP, PSCAD/EMTDC, MATLAB, and NETOMAC. Although power system models and power semiconductor devices can readily be represented and control algorithms can easily be realized, all those off-line simulation results may not be so accurate in terms of practical phenomena. In this context, there is still a huge gap between the research and practical implementation.

Fig. 7. SMIB test system.

J. Chen et al. / Electrical Power and Energy Systems 26 (2004) 357–364 Table 2 Machine data of SMIB SN

480 M/A

Xd

0.770 p.u.

H Xq Xd 00 Xd 00

3.117 s 1.014 p.u. 0.314 p.u. 0.280 p.u.

Xq 00 Td 00 Td 00 Td 00

0.375 p.u. 6.55 s 0.039 s 0.071 s

However, the RTDS provides a powerful tool to study power systems along with power semiconductor devices in real time. A quite attractive way is to have the RTDS interfaced with an external digital controller. The RTDS represents the power system and the power semiconductor devices while the digital controller provides the necessary gate signals to the power semiconductor devices modeled as ideal switches in the RTDS. In this way, much more reliable results can be expected. The configuration of the whole system is illustrated in Fig. 6. The power system components are modeled in Tandem Processor Cards (TPCs) and the SSSC is modeled in a Triple-Processor Card (3PC) in the RTDS. Three signals are extracted from the RTDS, namely the real power measurement at the location of the SSSC, the error of the DC link voltage, and the local reference voltage vector after D/A conversion and necessary scaling of those signals originally in digital form. The digital controller is implemented by employing a DS1102 DSP card resided in a PC ISA slot. The DSP card receives those three signals and converts them back into digital form using the A/D module embedded in the DSP card. Six gate signals are generated using SPWM technique and sent back to the SSSC modeled in the 3PC of the RTDS through a Digital Input Time Stamp (DITS) card and opto-isolation.

5. Real-time simulation results To test the effectiveness of the SSSC together with the proposed damping controller, real-time simulations employing the real-time implementation system described above have been conducted on a SMIB as shown in Fig. 7 [4] with system parameters as given in Table 2 and a two-machine test system as shown in Fig. 8 [5] with system parameters

361

as given in Table 3 with deliberate faults applied. The effects of generator exciters and governor-turbines are also modeled in the test systems while no PSS signal is included. The loads are modeled as constant impedances. 5.1. SMIB test system Case 1: Three-phase fault is applied at point F with 100 ms, then it is cleared by opening the line. The line is reconnected after 200 ms; Case 2: Three-phase fault is applied at point F with 300 ms, then it is cleared by opening the line. The line is reconnected after 200 ms; Case 3: Three-phase temporary fault is applied at point G with 100 ms. The characteristics of the deviation of the rotor angle and the modulation index as the control signal for Cases 1, 2, and 3 are shown in Figs. 9– 11, respectively. 5.2. Two-machine test system Case 4: Three-phase fault is applied at point F with 100 ms, then it is cleared by opening the line. The line is reconnected after 200 ms; Case 5: Three-phase fault is applied at point F with 300 ms, then it is cleared by opening the line. The line is reconnected after 200 ms; Case 6: Three-phase temporary fault is applied at point G with 100 ms. The characteristics of the deviation of the rotor angle difference and the modulation index as the control signal for Cases 4, 5, and 6 are shown in Figs. 12– 14, respectively. 5.3. Discussions The real-time simulation results shown in Figs. 9 – 14 shows the effectiveness of power system oscillations

Fig. 8. Two-machine test system.

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Table 3 Machine data of two-machine system

G1 G2

SN (M/A)

H (s)

Xd (p.u.)

X 00d (p.u.)

Xq (p.u.)

T 00d (s)

2700 5400

4 4

1.00 2.00

0.30 0.25

0.60 1.90

5.00 6.00

damping using the SSSC with the proposed damping controller. Once there is a disturbance, the SSSC can be activated to mitigate power system oscillations. The DC link voltage can be charged to the reference value within a time short enough to make the VSC fully being utilized because the modulation index is always saturated in the case that

Fig. 9. Real-time simulation results for Case 1. (a) Deviation of rotor angle (b) Modulation index.

Fig. 10. Real-time simulation results for Case 2. (a) Deviation of rotor angle. (b) Modulation index.

Fig. 11. Real-time simulation results for Case 3. (a) Deviation of rotor angle. (b) Modulation index.

J. Chen et al. / Electrical Power and Energy Systems 26 (2004) 357–364

Fig. 12. Real-time simulation results for Case 4. (a) Deviation of rotor angle. (b) Modulation index.

Fig. 13. Real-time simulation results for Case 5. (a) Deviation of rotor angle. (b) Modulation index.

Fig. 14. Real-time simulation results for Case 6. (a) Deviation of rotor angle. (b) Modulation index.

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commissioning. Future work will be concentrated on larger and more practical power systems with multiple SSSCs.

Appendix A A

B C Fig. A1. A typical curve of the DC link voltage in Case 1.

D

(1) The DC capacitor value is 5000 uF (2) The reference value for the DC link voltage is 20 kV (3) he winding voltage ratings of the series transformer are 10/20 kV. The characteristics of the DC link voltage (Fig. A1) Reset filter (Fig. A2) Width of membership functions For the first input it is set as 0.3 while for the second input, it is set as 5.

References Fig. A2. Block diagram of reset filter.

the inputs are linguistic ‘Big’. After oscillations are completely mitigated, the SSSC can be disconnected safely.

6. Conclusions This paper has presented the detail analysis of the SSSC and proposed a damping controller based on Fuzzy Logic method. Only the local measurable real power signal is needed for the control design. Furthermore, it is quite robust irrespective of the system parameters and configuration. Various simulations have been conducted on the developed real-time implementation system. All the real-time simulation results have strongly demonstrated the effectiveness of the SSSC together with the proposed damping controller. Moreover, the real-time implementation system has bridged the gap to some extent between theoretical analysis and practical

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