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DC interconnected power system
Electric Power Systems Research 61 (2002) 221 /226 www.elsevier.com/locate/epsr
Fuzzy logic controller for enhancing oscillatory stability of AC/DC interconnected power system T.S. Chung a,*, Fang Da-zhong b a b
Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Department of Electric Power and Automation, Engineering, Tianjin University, Tianjin, People’s Republic of China Received 29 August 2001; accepted 7 January 2002
Abstract A novel control strategy is developed for High Voltage DC (HVDC) links to improve oscillatory stability of interconnected power systems. An ‘area’ principle is proposed for controller design to damp AC tie power oscillations by increasing the oscillatory ‘deceleration area’. Exploiting fast control capability of HVDC link, a fuzzy-rule is adopted to smooth the power transition for reducing power ‘shock’ to power system. The strategy also incorporates adaptive control techniques to prevent tie-link power ‘chattering’. Simulation results using the proposed control scheme on two typical power systems are presented. The results demonstrate that significant improvements in both oscillatory and transient stability are obtained. # 2002 Published by Elsevier Science B.V. Keywords: HVDC; Fuzzy logic control; Adaptive control; Oscillatory stability; Transient stability
1. Introduction High Voltage DC (HVDC) links are often used to transmit large amount of power over long distance in parallel with an AC link. Fig. 1 shows a typical two-area power system in which AC and DC links are used to transmit power between two areas or from remote plants to load centers. For such interconnected power systems, transient stability and oscillatory stability problems may limit the amount of available transfer capacity. This paper addresses the issue of developing novel control approach for HVDC links for damping postdisturbance oscillations and enhancing transient stability. Conventionally, supplementary control is usually used in HVDC modulation to damp AC/DC system oscillations [1]. A pole placement technique is used for designing the supplementary controller. The difficulty in analysis of eigenvalues and eigenvectors for a very large linearized power system limits this technique to be used in controller design for realistic large power systems. In * Corresponding author. E-mail address: [email protected] (T.S. Chung).
this paper, an alternative approach is proposed to modulate power order input to HVDC master control for such AC/DC power system shown in Fig. 1. Based upon the characteristics of the AC tie power versus the line phase angle, an ‘area’ control principle is presented to explain the physical process of AC tie power oscillations. A bang-bang control strategy is utilized to increase the stability ‘deceleration area’ for stability improvement. Fuzzy rules are adopted in the strategy to control the HVDC power smooth transition for reducing power shocks caused by bang /bang controls. The fuzzy logic approach has an advantage over the conventional control method in that it does not require precise numerical values of control inputs and system parameters [2,4]. The proposed controller also incorporates adaptive techniques to avoid AC tie line power chattering while the tie oscillation is being damped to small amplitude, and to modify the oscillatory center angle identically converging to steady operation point of post-fault system. Simulation results on 4-generator, two-area system AC/DC system [1] show that the HVDC control strategy provides satisfactory performance both in oscillatory and transient stability enhancement.
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Fig. 1. Typical 2-area power system with AC and DC tie links.
2. Stability control 2.1. Electromechanical oscillations between areas Consider the two area AC/DC system shown in Fig. 1. Let the AC tie line have an impedance of 0.0055/j0.055 (p.u. ) and the voltages of buses A1 and B1 maintain at 1.0 (p.u. ). Thus the characteristic of the power through bus A1 sent to area B is plotted in Fig. 3 where line angle dA1B1 denotes dA1 /dB1, difference of voltage angles of bus A1 and B1. Here point ‘O’ is the steady operation point of the AC line. Assume that there exists electromechanical oscillation between area A and area B after a disturbance. For the AC link A1 /B1, the oscillation is exhibited both on the phase angle, dA1B1, and on the power transferred through the AC link. Relative motions of generator rotors between the two areas [7] usually cause an area mode oscillation. To explain the nature of the area mode oscillation, we consider the motion of the Center of Inertia (COI ) of generators in area A (called generator A for simplicity) and the motion of COI of generators in area B (called generator B for simplicity) [3]. The elative motion between the two COIs dominates the oscillation behavior. Under the assumption that the total generations and consumption of the power in both areas maintain constant during the oscillation, the motion equations of the two COIs can be expressed by: MA v˙ A PA0 PAD PA1 ; MB v˙ B PB0 PBD PB1 ;
d˙A vA vR d˙B vB vR
(1) (2)
where variables of dA, dB, vA and vB are for the angles and speeds of the generators A and B; vR denotes AC synchronous speed; PA0 and PB0 are the mechanical powers of generators A and B, that represent the differences between the total generations and the total consumption of the two areas; PAD, PBD, PA1 and PB1 are the DC and AC link powers at each their terminal; PAD0 and PBD0 express the constant of PAD and PBD if they do keep un-change during an oscillation. The parameters MA and MB denote inertia constants of the two COIs [3]. During oscillations the power PA1 will change in value along the plot shown in Fig. 2. To shown the physical process, one circle of oscillation is divided into four phases. As shown in Fig. 2, phase 1 is for the swing from
Fig. 2. AC link power plot at bus A1 vs. difference of bus voltage angles.
Fig. 3. Swing curves of angles and speeds obtained on the 4-generator, two-area AC /DC system by software simulation without damping control.
point ‘O’ to ‘B’. This phase is characterized by vAB /0 Considering equations Eqs. (1) and (2), as PA0 /PAD0 / PA1 B/0 and /PB0 /PBD0 /PB1 B/0, it is easy to show that v˙ A B0 and v˙ B 0; i.e. v˙ AB B0; in this phase. At point ‘B’ the speed reaches zero (/v˙ AB 0): Phase 2 is for the swing back from ‘B’ to ‘O’. Similarly, it can be shown that the motion in this phase is characterized by vAB B0 and v˙ AB B0: Phases 3 and 4 are for the swings from point ‘O’ to ‘F’ and ‘F’ to ‘O’, respectively. Since PA0 /PAD0 /PA1 /0 and /PB0 /PBD0 /PB1 /0 in the two stages, the motions for them are characterized by v˙ AB 0: AS the oscillation power must transmit through the AC/DC tie link, the variations of dA1B1 should be in the same mode with that of dAB, i.e. at point ‘B’ (and ‘F’) both angles dA1B1 and dAB reach their maximum (and minimum) value synchronously. The above point has been verified on the 4-generator test AC/DC test system [1]. Fig. 4 shows the simulation results on the 4-generator system (see Fig. 7) for the verifications. In Fig. 4 dAB and vAB denote the difference of the angle and speed between the generators A and B [3]. d5,9 is for the line angle between tie buses 5 and 9 and v5,9 denotes its derivative to time.
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Fig. 4. Configuration of SFLAC.
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damping will be effective. However, when DPAD is large, the bang /bang control nature may cause a big shock to the generator turbine shafts in areas A and B near the HVDC convertors, because of sudden changes of output power to the generators. This can in turn cause a reduction in the shaft life. On the other hand, a fixed DPAD may cause chattering of AC tie line power while the oscillation is being stabilized to small amplitude. In the next paragraph, some techniques are developed to overcome these problems.
2.2. Bang /bang control strategy
2.3. Development of HVDC controller
As dA1B1 and dAB swing in the same mode, the characteristics of PA1 versus dA1B1 shown in Fig. 2 can also be used to represent characteristics of PA1 versus dAB. Hence, in phase 1 the area of ABO with respect to generator A is backward deceleration energy and with respect to generator B is forward deceleration energy. In phase 2 the area of ABO is forward acceleration energy for generator A and backward acceleration energy for generator B. Similarly, in phase 3 the area of EFO is forward deceleration energy for generator A and backward deceleration energy for generator B. In phase 4 the area of EFO is backward acceleration energy for generator A and forward acceleration energy for the generator B. Under the assumptions of section 3.1, the tie oscillations will be continuously repeated, because, of the same acceleration and deceleration areas for the four phases in one circle. For realistic AC tie line oscillations, besides voltage phase angles, voltage amplitudes is also involved in the oscillations. This will make the characteristic shown in Fig. 3 vary from time to time associated with oscillations. Hence, the sum of the deceleration areas may not be just equal to the sum of acceleration areas for a realistic power system. If the deceleration areas are larger than acceleration areas the oscillation will be decreased, otherwise it will be amplified. Based upon the basic principle presented above, a strategy of bang-bang control of HVDC power for damping an post-fault area-mode oscillation is proposed here. As shown in Fig. 2, assume that in phase 1 the HVDC power at rectifier and the inverter is controlled to maintain PAD0/DPAD and PBD0/DPBD, respectively. In phase 3 the HVDC power at rectifier and the inverter is controlled to maintain PAD0 /DPAD and PBD0 /DPBD, respectively. In phase 2 and 4 the HVDC power remain unchanged. Thus, in one circle the area of AOADC/AOEHG in Fig. 3 denotes the kinetic energy at point ‘O’ of generator A decreased (of generator B increased if the AC/DC tie power loss is ignored). Hence after one oscillation at point ‘O’, vAB is decreased. The HVDC control can damp the AC tie oscillation identically if the conditions of vAB /0 and the reduction of vAB at point ‘O’ maintain. If DPAD is large, the
The controller presented in this section is referred to as the stability fuzzy logic adaptive controller (SFLAC). The configuration of the SFLAC is shown in Fig. 4. In Fig. 4, the notations of d , d0, PDC0 and DP are for the ones of dA1B1, d0, PAD0 and DPAD used before. Here the signal PDC0, the DC power flow arrangement, come from the AC/DC system control center. The phase angle d is the input signal that can be measured by detecting the crossover points of the respective voltage waveforms with respect to synchronized pulse trains [5]. With the development of new technology, precise time-synchronized phasor measurements unit [6,8] are available to us today, which provide an alternate way in the measurement of signal d . The output of the SFLAC is the power order signal to the HVDC master control as shown in Fig. 2. High pulses in the signal Dd or Dv may interfere the proper work of the SFLAC. Hence two low-pass filters are used here to wash out the components of high frequency in the signals of Dd or Dv which is usually brought in by measurement errors or sudden change of system conditions, such as switching on or tripping out of a large load (or a line). The signals come out from the filters are denoted by Ddˆ and Dv: ˆ The signal of d0 initially takes the pre-disturbance value of d, and to be adaptively modified by the value of Ddˆ once Dvˆ passes its maximum or minimum value. This adaptive modification of d0 makes the SFLAC is independent on the operating point of post-fault system. To apply fuzzy logic approach in smoothing the transition of HVDC link power, the variable pair (/Ddˆ and Dv) ˆ in the form of Cartesian phase are transformed to a pair of polar co-ordinate variables by: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g Ddˆ2 Dvˆ 2 (3) Dvˆ a tan 1 (4) Ddˆ Thus an AC tie link oscillation can be studied on the phase plane shown in Fig. 6. The phases 1, 2, 3 and 4 of a oscillation mentioned in section 3.1 correspond to the trajectory of state of (/Ddˆ and Dv) ˆ passing through the quadrants 1, 4, 3 and 2, respectively. For the bang-bang control strategy shown in section 3.2, the HVDC link
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T.S. Chung, F. Da-zhong / Electric Power Systems Research 61 (2002) 221 /226 Table 1 Fuzzy rules Sector A
Sector B
DPmax(p .u .)
DPmin(p .u .)
ciated membership grades of the linguistic variables DPmax and DPmin. The membership functions are particularly designed in the overlapping regions of sectors A and B, a T1 and a T2, to make output of FLC gradually change between the two sectors. In mathematics the relationship between DPpre and a is: Fig. 5. Phase plane for control strategy.
DPpre mmax (a)DPmax mmin (a)DPmin
(5)
For example, if a belongs to sector A with a membership of 0.4 then the output fuzzy set will consist of {{DPmax, 0.4} and {DPmin, 0.6}}. Then the output of the defuzzifier, DPpre, is calculated by: DPpre (0:4 0:6)DP0
Fig. 6. Angular membership functions.
power is switched between the maximum P0/DP and minimum P0 /DP . In terms of fuzzy logic this means that the output of a fuzzy logic controller (FLC) has two linguistic variables referred to as DPmax and DPmin. The input-output relationship of the FLC is given in terms of a very simple fuzzy rule set in Table 1. For damping an area mode oscillation, as show in Fig. 4 the angle a is fuzzified using the membership function shown in Fig. 6. The angle a is to fire the fuzzy rules in Table 1 to result output, DPreq, of the FLC. Here the output fuzzy set is denoted by {DPreq, mp} for {(DPmax, mpmax), (DPmin, mpmin)}. The mpmax and mpmin, the membership functions in Fig. 7, denote the asso-
(6)
if DPmax /DP0 and DPmin / /DP0. Here DP0 is the expected increment of the HVDC power controlled. The variable g 2 (Fig. 5) gives a measurement of the oscillation magnitude. Hence, in designing SFLAC, g 2 is used to adjust the increment of the HVDC power order adaptively. Suitable constant parameter k (Fig. 5) makes the SFLAC operation satisfactory. For large disturbance the DPpre is amplified greatly, but confined by the limit unit. On the other hand, for small oscillation the DPpre is reduced to control Dd approaches to zero identically.
3. Simulation tests To evaluate the effect of SFLAC on stability enhancement, the controller was extensively tested using computer software simulations on the 11-bus, 4-generator, two area AC/DC system [1]. Configurations of the system are shown in Fig. 7. The HVDC internal dynamic models adopted here are similar to that used in
Fig. 7. The 11 bus, four-generator, two area AC/DC system.
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the supplementary control of HVDC link in reference [1], but the maximum short-time current limit is allowed to reach 1.3 times of its normal full load current for transient stability enhancement [1]. The signal of power order from the SFLAC is transformed to current order signal limited by the maximum current, minimum current and voltage-dependent current in the master control [1]. The system data of the 4-generator AC/DC system is just the same as that used in the example of HVDC link supplementary control in Chapter 17 of [1]. All four generators have self-excited DC exciter. The DC link is represented as a monopolar link with a voltage rating of 56 kV and current rating of 3.6 kA. At the assumption of short time maximum current 4.68 kA (1.3 times of the rating current), simulation results for a 3f short circuit at bus 6 cleared in 0.25 s without line tripping (3f -SC-6(tcl /0.25 s)-0) is shown in Fig. 8. Simulation results for a 3f short circuit at bus 6 cleared in 0.25 s with one line 6 /9 tripping (3f-SC-6-(tcl /0.25 s)-(1, 6/9)) are shown in Figs. 9 and 10. It is observed that after about 6 s the post-fault inter-area mode oscillation on the AC tie are stabilized down for the two fault conditions. The oscillation, after 6 s, exhibited on the plot dG3 /dG1 in Fig. 8 is induced by the local mode oscillations in each area and after 10 s the local mode oscillations are also stabilized down by the SFLAC. Plot of d0 in Fig. 8 and the plot P59/PDC in Fig. 10 show that the methods of adaptive modification of d0 and DPpre are effective in stabilizing oscillations down. Comparing with the simulation results of conventional HVDC link supplementary controller in page 1159 of reference [1], the following aspects are outstanding. (1) The SFLAC have a stronger effect on damping the inter area mode post-fault oscillation. (2) The SFLAC is an adaptive controller, that means it is effective for inter-area mode oscillation with different frequencies. (3) In controller design of SFLAC, eigenvalues and eigenvectors analysis is not required which is not an easy work for a large AC/DC power system. Extensive tests were also performed to examine the enhancement of transient stability by SFLAC. As
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Fig. 9. Variations of generator angle of dG3 dG1, and d59, for fault 3f -SC-6-(tcl 0.25 s)-0 in the four-generator AC /DC test system.
Fig. 10. Variations of AC line power (P59) and total AC /DC line power (P59PDC) for fault 3f -SC-6-(tcl 0.25 s)-(1, 6 /9) on the fourgenerator AC /DC test system.
examples, tests are done for faults of 3f short circuit at bus 6 without line tripping (3f-SC-6-0)) on the 4generator test system. Test results presented in Table 2 demonstrate that SFLAC can enhance transient stability for severe disturbances near AC/DC tie links.
4. Conclusions A novel HVDC control strategy for oscillatory and transient stability enhancement is developed. An area analysis approach is proposed to explain the physical process of AC tie oscillations. Using the capability of HVDC in rapid control of transmission power, the control strategy is to increase the deceleration area. Some techniques such as fuzzy logic and adaptive control are verified to be effective on controlling the HVDC tie power in smooth transition and on avoiding AC tie line power chattering. Simulation results show that the control strategy provides significant effect in Table 2 Comparison of critical fault clearing time with and without SFLAC
Fig. 8. Variations of d59, and the angle d0 using SFLAC for fault 3f SC-6-(tcl 0.25 s)-(1, 6 /9) on the four-generator AC /DC test system.
Fault type
tcl without SFLAC (s)
tcl with SFLAC (s)
(3f -SC-6-0)
0.32 /0.33
0.37 /0.38
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damping area mode oscillations. The simplicity and robustness of the SFLAC are the attractive features. Further research to extend the control strategy to FACTS device control for system stability enhancement is currently being carried out.
[6] S.E. Stanton, C. Slivinsky, K. Martin, J. Nordstrom, Application of phasor measurement and partial energy analysis in stabilizing large disturbances, IEEE Trans. Power Syst. 10 (1) (1995) 297 /302. [7] V. Vittal, N. Bhatia, A.A. Fouad, Analysis of the inter-area mode phenomenon in power system following large disturbances, IEEE Trans. Power Syst. 6 (4) (1991) 1515 /1521. [8] E.W. Kimbark, Direct Current Transmission, Wiley-Interscience, 1971.
Acknowledgements Biographies The funding support from CRG of Hong Kong Polytechnic University for this research project is gratefully acknowledged.
References [1] P. Kundur, Power System Stability and Control, MCGraw-Hill, 1993. [2] M. Jamshidi, N. Vadiee, T.J. Ross, Fuzzy Logic and Control: Software and Hardware Application, Prentice Hall, 1993. [3] F. Da-zhong, T.S. Chung, Z. Yao, S. Wennan, Transient stability limit conditions analysis using a corrected transient energy function approach, PE338PRS(05-99), IEEE Summer Power Meeting, in Edmonton in July 1999. [4] T. Hiyama, K. Miyazaki, H. Satoh, A Fuzzy, Logic excitation system for stability enhancement of power system with multi-mode oscillations, IEEE Trans. Energy Conversion 11 (1) (1996) 125 / 131. [5] G. Missout, J. Beland, G. Beland, Y. Lafleur, Dynamic measurement of the absolute voltage angle on long transmission line, IEEE Trans. PAS100 (11) (1981) 4428 /4434.
Dr T.S. Chung is presently Professor and Power Group Leader in Electrical Engineering Department of The Hong Kong Polytechnic University. He received his B.S. from Hong Kong University, M.S. from Imperial College, London University and Ph.D. from Strathclyde University, UK. He had a post-graduate training at Hawker Siddeley Electric, UK and worked as T and D Engineer at Hong Kong Electric Co. Ltd. His current research interests are in power system security control, stability, optimization, power system deregulation and AI applications. Dr Fang Da-zhong, Professor of Tianjin University, China, received a B.S. from the Beijing Mechanical Institute, Beijing PR China, an M.S. from Tianjin University, Tianjin PR China and a Ph.D. from The Hong Kong Polytechnic University. His current research interests are in power system stability and security control.
Fuzzy logic controller for enhancing oscillatory stability of AC/DC interconnected power system T.S. Chung a,*, Fang Da-zhong b a b
Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Department of Electric Power and Automation, Engineering, Tianjin University, Tianjin, People’s Republic of China Received 29 August 2001; accepted 7 January 2002
Abstract A novel control strategy is developed for High Voltage DC (HVDC) links to improve oscillatory stability of interconnected power systems. An ‘area’ principle is proposed for controller design to damp AC tie power oscillations by increasing the oscillatory ‘deceleration area’. Exploiting fast control capability of HVDC link, a fuzzy-rule is adopted to smooth the power transition for reducing power ‘shock’ to power system. The strategy also incorporates adaptive control techniques to prevent tie-link power ‘chattering’. Simulation results using the proposed control scheme on two typical power systems are presented. The results demonstrate that significant improvements in both oscillatory and transient stability are obtained. # 2002 Published by Elsevier Science B.V. Keywords: HVDC; Fuzzy logic control; Adaptive control; Oscillatory stability; Transient stability
1. Introduction High Voltage DC (HVDC) links are often used to transmit large amount of power over long distance in parallel with an AC link. Fig. 1 shows a typical two-area power system in which AC and DC links are used to transmit power between two areas or from remote plants to load centers. For such interconnected power systems, transient stability and oscillatory stability problems may limit the amount of available transfer capacity. This paper addresses the issue of developing novel control approach for HVDC links for damping postdisturbance oscillations and enhancing transient stability. Conventionally, supplementary control is usually used in HVDC modulation to damp AC/DC system oscillations [1]. A pole placement technique is used for designing the supplementary controller. The difficulty in analysis of eigenvalues and eigenvectors for a very large linearized power system limits this technique to be used in controller design for realistic large power systems. In * Corresponding author. E-mail address: [email protected] (T.S. Chung).
this paper, an alternative approach is proposed to modulate power order input to HVDC master control for such AC/DC power system shown in Fig. 1. Based upon the characteristics of the AC tie power versus the line phase angle, an ‘area’ control principle is presented to explain the physical process of AC tie power oscillations. A bang-bang control strategy is utilized to increase the stability ‘deceleration area’ for stability improvement. Fuzzy rules are adopted in the strategy to control the HVDC power smooth transition for reducing power shocks caused by bang /bang controls. The fuzzy logic approach has an advantage over the conventional control method in that it does not require precise numerical values of control inputs and system parameters [2,4]. The proposed controller also incorporates adaptive techniques to avoid AC tie line power chattering while the tie oscillation is being damped to small amplitude, and to modify the oscillatory center angle identically converging to steady operation point of post-fault system. Simulation results on 4-generator, two-area system AC/DC system [1] show that the HVDC control strategy provides satisfactory performance both in oscillatory and transient stability enhancement.
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Fig. 1. Typical 2-area power system with AC and DC tie links.
2. Stability control 2.1. Electromechanical oscillations between areas Consider the two area AC/DC system shown in Fig. 1. Let the AC tie line have an impedance of 0.0055/j0.055 (p.u. ) and the voltages of buses A1 and B1 maintain at 1.0 (p.u. ). Thus the characteristic of the power through bus A1 sent to area B is plotted in Fig. 3 where line angle dA1B1 denotes dA1 /dB1, difference of voltage angles of bus A1 and B1. Here point ‘O’ is the steady operation point of the AC line. Assume that there exists electromechanical oscillation between area A and area B after a disturbance. For the AC link A1 /B1, the oscillation is exhibited both on the phase angle, dA1B1, and on the power transferred through the AC link. Relative motions of generator rotors between the two areas [7] usually cause an area mode oscillation. To explain the nature of the area mode oscillation, we consider the motion of the Center of Inertia (COI ) of generators in area A (called generator A for simplicity) and the motion of COI of generators in area B (called generator B for simplicity) [3]. The elative motion between the two COIs dominates the oscillation behavior. Under the assumption that the total generations and consumption of the power in both areas maintain constant during the oscillation, the motion equations of the two COIs can be expressed by: MA v˙ A PA0 PAD PA1 ; MB v˙ B PB0 PBD PB1 ;
d˙A vA vR d˙B vB vR
(1) (2)
where variables of dA, dB, vA and vB are for the angles and speeds of the generators A and B; vR denotes AC synchronous speed; PA0 and PB0 are the mechanical powers of generators A and B, that represent the differences between the total generations and the total consumption of the two areas; PAD, PBD, PA1 and PB1 are the DC and AC link powers at each their terminal; PAD0 and PBD0 express the constant of PAD and PBD if they do keep un-change during an oscillation. The parameters MA and MB denote inertia constants of the two COIs [3]. During oscillations the power PA1 will change in value along the plot shown in Fig. 2. To shown the physical process, one circle of oscillation is divided into four phases. As shown in Fig. 2, phase 1 is for the swing from
Fig. 2. AC link power plot at bus A1 vs. difference of bus voltage angles.
Fig. 3. Swing curves of angles and speeds obtained on the 4-generator, two-area AC /DC system by software simulation without damping control.
point ‘O’ to ‘B’. This phase is characterized by vAB /0 Considering equations Eqs. (1) and (2), as PA0 /PAD0 / PA1 B/0 and /PB0 /PBD0 /PB1 B/0, it is easy to show that v˙ A B0 and v˙ B 0; i.e. v˙ AB B0; in this phase. At point ‘B’ the speed reaches zero (/v˙ AB 0): Phase 2 is for the swing back from ‘B’ to ‘O’. Similarly, it can be shown that the motion in this phase is characterized by vAB B0 and v˙ AB B0: Phases 3 and 4 are for the swings from point ‘O’ to ‘F’ and ‘F’ to ‘O’, respectively. Since PA0 /PAD0 /PA1 /0 and /PB0 /PBD0 /PB1 /0 in the two stages, the motions for them are characterized by v˙ AB 0: AS the oscillation power must transmit through the AC/DC tie link, the variations of dA1B1 should be in the same mode with that of dAB, i.e. at point ‘B’ (and ‘F’) both angles dA1B1 and dAB reach their maximum (and minimum) value synchronously. The above point has been verified on the 4-generator test AC/DC test system [1]. Fig. 4 shows the simulation results on the 4-generator system (see Fig. 7) for the verifications. In Fig. 4 dAB and vAB denote the difference of the angle and speed between the generators A and B [3]. d5,9 is for the line angle between tie buses 5 and 9 and v5,9 denotes its derivative to time.
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Fig. 4. Configuration of SFLAC.
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damping will be effective. However, when DPAD is large, the bang /bang control nature may cause a big shock to the generator turbine shafts in areas A and B near the HVDC convertors, because of sudden changes of output power to the generators. This can in turn cause a reduction in the shaft life. On the other hand, a fixed DPAD may cause chattering of AC tie line power while the oscillation is being stabilized to small amplitude. In the next paragraph, some techniques are developed to overcome these problems.
2.2. Bang /bang control strategy
2.3. Development of HVDC controller
As dA1B1 and dAB swing in the same mode, the characteristics of PA1 versus dA1B1 shown in Fig. 2 can also be used to represent characteristics of PA1 versus dAB. Hence, in phase 1 the area of ABO with respect to generator A is backward deceleration energy and with respect to generator B is forward deceleration energy. In phase 2 the area of ABO is forward acceleration energy for generator A and backward acceleration energy for generator B. Similarly, in phase 3 the area of EFO is forward deceleration energy for generator A and backward deceleration energy for generator B. In phase 4 the area of EFO is backward acceleration energy for generator A and forward acceleration energy for the generator B. Under the assumptions of section 3.1, the tie oscillations will be continuously repeated, because, of the same acceleration and deceleration areas for the four phases in one circle. For realistic AC tie line oscillations, besides voltage phase angles, voltage amplitudes is also involved in the oscillations. This will make the characteristic shown in Fig. 3 vary from time to time associated with oscillations. Hence, the sum of the deceleration areas may not be just equal to the sum of acceleration areas for a realistic power system. If the deceleration areas are larger than acceleration areas the oscillation will be decreased, otherwise it will be amplified. Based upon the basic principle presented above, a strategy of bang-bang control of HVDC power for damping an post-fault area-mode oscillation is proposed here. As shown in Fig. 2, assume that in phase 1 the HVDC power at rectifier and the inverter is controlled to maintain PAD0/DPAD and PBD0/DPBD, respectively. In phase 3 the HVDC power at rectifier and the inverter is controlled to maintain PAD0 /DPAD and PBD0 /DPBD, respectively. In phase 2 and 4 the HVDC power remain unchanged. Thus, in one circle the area of AOADC/AOEHG in Fig. 3 denotes the kinetic energy at point ‘O’ of generator A decreased (of generator B increased if the AC/DC tie power loss is ignored). Hence after one oscillation at point ‘O’, vAB is decreased. The HVDC control can damp the AC tie oscillation identically if the conditions of vAB /0 and the reduction of vAB at point ‘O’ maintain. If DPAD is large, the
The controller presented in this section is referred to as the stability fuzzy logic adaptive controller (SFLAC). The configuration of the SFLAC is shown in Fig. 4. In Fig. 4, the notations of d , d0, PDC0 and DP are for the ones of dA1B1, d0, PAD0 and DPAD used before. Here the signal PDC0, the DC power flow arrangement, come from the AC/DC system control center. The phase angle d is the input signal that can be measured by detecting the crossover points of the respective voltage waveforms with respect to synchronized pulse trains [5]. With the development of new technology, precise time-synchronized phasor measurements unit [6,8] are available to us today, which provide an alternate way in the measurement of signal d . The output of the SFLAC is the power order signal to the HVDC master control as shown in Fig. 2. High pulses in the signal Dd or Dv may interfere the proper work of the SFLAC. Hence two low-pass filters are used here to wash out the components of high frequency in the signals of Dd or Dv which is usually brought in by measurement errors or sudden change of system conditions, such as switching on or tripping out of a large load (or a line). The signals come out from the filters are denoted by Ddˆ and Dv: ˆ The signal of d0 initially takes the pre-disturbance value of d, and to be adaptively modified by the value of Ddˆ once Dvˆ passes its maximum or minimum value. This adaptive modification of d0 makes the SFLAC is independent on the operating point of post-fault system. To apply fuzzy logic approach in smoothing the transition of HVDC link power, the variable pair (/Ddˆ and Dv) ˆ in the form of Cartesian phase are transformed to a pair of polar co-ordinate variables by: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g Ddˆ2 Dvˆ 2 (3) Dvˆ a tan 1 (4) Ddˆ Thus an AC tie link oscillation can be studied on the phase plane shown in Fig. 6. The phases 1, 2, 3 and 4 of a oscillation mentioned in section 3.1 correspond to the trajectory of state of (/Ddˆ and Dv) ˆ passing through the quadrants 1, 4, 3 and 2, respectively. For the bang-bang control strategy shown in section 3.2, the HVDC link
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T.S. Chung, F. Da-zhong / Electric Power Systems Research 61 (2002) 221 /226 Table 1 Fuzzy rules Sector A
Sector B
DPmax(p .u .)
DPmin(p .u .)
ciated membership grades of the linguistic variables DPmax and DPmin. The membership functions are particularly designed in the overlapping regions of sectors A and B, a T1 and a T2, to make output of FLC gradually change between the two sectors. In mathematics the relationship between DPpre and a is: Fig. 5. Phase plane for control strategy.
DPpre mmax (a)DPmax mmin (a)DPmin
(5)
For example, if a belongs to sector A with a membership of 0.4 then the output fuzzy set will consist of {{DPmax, 0.4} and {DPmin, 0.6}}. Then the output of the defuzzifier, DPpre, is calculated by: DPpre (0:4 0:6)DP0
Fig. 6. Angular membership functions.
power is switched between the maximum P0/DP and minimum P0 /DP . In terms of fuzzy logic this means that the output of a fuzzy logic controller (FLC) has two linguistic variables referred to as DPmax and DPmin. The input-output relationship of the FLC is given in terms of a very simple fuzzy rule set in Table 1. For damping an area mode oscillation, as show in Fig. 4 the angle a is fuzzified using the membership function shown in Fig. 6. The angle a is to fire the fuzzy rules in Table 1 to result output, DPreq, of the FLC. Here the output fuzzy set is denoted by {DPreq, mp} for {(DPmax, mpmax), (DPmin, mpmin)}. The mpmax and mpmin, the membership functions in Fig. 7, denote the asso-
(6)
if DPmax /DP0 and DPmin / /DP0. Here DP0 is the expected increment of the HVDC power controlled. The variable g 2 (Fig. 5) gives a measurement of the oscillation magnitude. Hence, in designing SFLAC, g 2 is used to adjust the increment of the HVDC power order adaptively. Suitable constant parameter k (Fig. 5) makes the SFLAC operation satisfactory. For large disturbance the DPpre is amplified greatly, but confined by the limit unit. On the other hand, for small oscillation the DPpre is reduced to control Dd approaches to zero identically.
3. Simulation tests To evaluate the effect of SFLAC on stability enhancement, the controller was extensively tested using computer software simulations on the 11-bus, 4-generator, two area AC/DC system [1]. Configurations of the system are shown in Fig. 7. The HVDC internal dynamic models adopted here are similar to that used in
Fig. 7. The 11 bus, four-generator, two area AC/DC system.
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the supplementary control of HVDC link in reference [1], but the maximum short-time current limit is allowed to reach 1.3 times of its normal full load current for transient stability enhancement [1]. The signal of power order from the SFLAC is transformed to current order signal limited by the maximum current, minimum current and voltage-dependent current in the master control [1]. The system data of the 4-generator AC/DC system is just the same as that used in the example of HVDC link supplementary control in Chapter 17 of [1]. All four generators have self-excited DC exciter. The DC link is represented as a monopolar link with a voltage rating of 56 kV and current rating of 3.6 kA. At the assumption of short time maximum current 4.68 kA (1.3 times of the rating current), simulation results for a 3f short circuit at bus 6 cleared in 0.25 s without line tripping (3f -SC-6(tcl /0.25 s)-0) is shown in Fig. 8. Simulation results for a 3f short circuit at bus 6 cleared in 0.25 s with one line 6 /9 tripping (3f-SC-6-(tcl /0.25 s)-(1, 6/9)) are shown in Figs. 9 and 10. It is observed that after about 6 s the post-fault inter-area mode oscillation on the AC tie are stabilized down for the two fault conditions. The oscillation, after 6 s, exhibited on the plot dG3 /dG1 in Fig. 8 is induced by the local mode oscillations in each area and after 10 s the local mode oscillations are also stabilized down by the SFLAC. Plot of d0 in Fig. 8 and the plot P59/PDC in Fig. 10 show that the methods of adaptive modification of d0 and DPpre are effective in stabilizing oscillations down. Comparing with the simulation results of conventional HVDC link supplementary controller in page 1159 of reference [1], the following aspects are outstanding. (1) The SFLAC have a stronger effect on damping the inter area mode post-fault oscillation. (2) The SFLAC is an adaptive controller, that means it is effective for inter-area mode oscillation with different frequencies. (3) In controller design of SFLAC, eigenvalues and eigenvectors analysis is not required which is not an easy work for a large AC/DC power system. Extensive tests were also performed to examine the enhancement of transient stability by SFLAC. As
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Fig. 9. Variations of generator angle of dG3 dG1, and d59, for fault 3f -SC-6-(tcl 0.25 s)-0 in the four-generator AC /DC test system.
Fig. 10. Variations of AC line power (P59) and total AC /DC line power (P59PDC) for fault 3f -SC-6-(tcl 0.25 s)-(1, 6 /9) on the fourgenerator AC /DC test system.
examples, tests are done for faults of 3f short circuit at bus 6 without line tripping (3f-SC-6-0)) on the 4generator test system. Test results presented in Table 2 demonstrate that SFLAC can enhance transient stability for severe disturbances near AC/DC tie links.
4. Conclusions A novel HVDC control strategy for oscillatory and transient stability enhancement is developed. An area analysis approach is proposed to explain the physical process of AC tie oscillations. Using the capability of HVDC in rapid control of transmission power, the control strategy is to increase the deceleration area. Some techniques such as fuzzy logic and adaptive control are verified to be effective on controlling the HVDC tie power in smooth transition and on avoiding AC tie line power chattering. Simulation results show that the control strategy provides significant effect in Table 2 Comparison of critical fault clearing time with and without SFLAC
Fig. 8. Variations of d59, and the angle d0 using SFLAC for fault 3f SC-6-(tcl 0.25 s)-(1, 6 /9) on the four-generator AC /DC test system.
Fault type
tcl without SFLAC (s)
tcl with SFLAC (s)
(3f -SC-6-0)
0.32 /0.33
0.37 /0.38
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damping area mode oscillations. The simplicity and robustness of the SFLAC are the attractive features. Further research to extend the control strategy to FACTS device control for system stability enhancement is currently being carried out.
[6] S.E. Stanton, C. Slivinsky, K. Martin, J. Nordstrom, Application of phasor measurement and partial energy analysis in stabilizing large disturbances, IEEE Trans. Power Syst. 10 (1) (1995) 297 /302. [7] V. Vittal, N. Bhatia, A.A. Fouad, Analysis of the inter-area mode phenomenon in power system following large disturbances, IEEE Trans. Power Syst. 6 (4) (1991) 1515 /1521. [8] E.W. Kimbark, Direct Current Transmission, Wiley-Interscience, 1971.
Acknowledgements Biographies The funding support from CRG of Hong Kong Polytechnic University for this research project is gratefully acknowledged.
References [1] P. Kundur, Power System Stability and Control, MCGraw-Hill, 1993. [2] M. Jamshidi, N. Vadiee, T.J. Ross, Fuzzy Logic and Control: Software and Hardware Application, Prentice Hall, 1993. [3] F. Da-zhong, T.S. Chung, Z. Yao, S. Wennan, Transient stability limit conditions analysis using a corrected transient energy function approach, PE338PRS(05-99), IEEE Summer Power Meeting, in Edmonton in July 1999. [4] T. Hiyama, K. Miyazaki, H. Satoh, A Fuzzy, Logic excitation system for stability enhancement of power system with multi-mode oscillations, IEEE Trans. Energy Conversion 11 (1) (1996) 125 / 131. [5] G. Missout, J. Beland, G. Beland, Y. Lafleur, Dynamic measurement of the absolute voltage angle on long transmission line, IEEE Trans. PAS100 (11) (1981) 4428 /4434.
Dr T.S. Chung is presently Professor and Power Group Leader in Electrical Engineering Department of The Hong Kong Polytechnic University. He received his B.S. from Hong Kong University, M.S. from Imperial College, London University and Ph.D. from Strathclyde University, UK. He had a post-graduate training at Hawker Siddeley Electric, UK and worked as T and D Engineer at Hong Kong Electric Co. Ltd. His current research interests are in power system security control, stability, optimization, power system deregulation and AI applications. Dr Fang Da-zhong, Professor of Tianjin University, China, received a B.S. from the Beijing Mechanical Institute, Beijing PR China, an M.S. from Tianjin University, Tianjin PR China and a Ph.D. from The Hong Kong Polytechnic University. His current research interests are in power system stability and security control.