Sensitivity analysis of interconnected power system low frequency oscillation

Transcription

1 ADVANCED APPLICAIONS OF ELECRICAL ENGINEERING Sensitivity analysis o interconnected power system low requency oscillation HUIJIE SHI, CHEN CHEN, YONG JIN Department o Electrical Engineering Shanghai Jiao ong University No. 800 Dongchuan Rd, Minhang District, Shanghai CHINA shj1234@sjtu.edu.cn Abstract: - he damping sensitivity analysis o interconnected power system low requency oscillation is studied. he unction o sensitivity analysis is implemented in the Small Signal Stability Analysis Package (SSAP). he paper mainly analyzes the sensitivities o oscillation modes with respect to the parameters o power system stabilizer (PSS) in the excitation systems o generators or a physical large-scale interconnected power system with AC/DC parallel transmission China Southern Power Grid (CSG). he results show the eectiveness o this unction which could direct the optimization o PSS parameters and improve the low requency oscillation damping o the system. Key-Words: - Power system, Low requency oscillation, Eigenvalue sensitivity, Power system stabilizer, Parameter optimization 1 Introduction With the increase in scale and complexity o interconnected power systems, many transmission lines are more than thousand kilometers long. Inter-area low requency oscillation (LFO) becomes a bottleneck o power system operation. Low requency oscillatory instability occurred around the world during the past decades [1-3]. How to characterize and mitigate the oscillations eectively is a signiicant engineering problem. he main actors which aect the oscillation modes the most and the necessary measures to enhance overall system stability need intensive studies. A variety o controllers were developed to enhance the damping o the oscillations due to the recent advancement in power electronic technology [4-7]. he optimal allocation and strategy o these controllers in power systems aimed at achieving the most eective damping especially or the electromechanical modes attracted so much attention. Magnitudes o the open-loop transer unction residues associated with the critical electromechanical modes between the speciied input and output are oten used as the indication o the most eective location or controller installation [8]. But there are a huge number o controllers in a large-scale power system, and they are reluctant to oer satisied damping o inter-area oscillations i not well coordinated. hereore how to adjust the existing controllers properly and eectively is more practical. he sensitivities o oscillation modes with respect to controller parameters may direct the optimization process, thus eigenvalue sensitivity analysis becomes an important tool or power system dynamic studies and controller designs. In this paper, the basic theory and the algorithm o eigenvalue sensitivity analysis are described in section 2, which was implemented in the Small Signal Stability Analysis Package (SSAP). SSAP is developed by Department o Electrical Engineering at Shanghai Jiao ong University with powerul AC/DC modeling unction and user-riendly graphical interaces. It provides alternative advanced eigenvalue calculation algorithms including QR method (may calculate all the eigenvalues o matrix within 3000 dimension) and Implicit Restarted Arnoldi Method (IRA), which can compute eigenvalues within speciied requency and damping ranges with varying complex shits [9-11]. Computation modules o mode shape and participation actors together with eigenvalue sensitivity analysis are integrated in SSAP. Case o China Southern Power Grid proved that the sensitivity analysis is practical and eective or enhancing the small signal stability o very large AC/DC interconnected power system. Power system stabilizers (PSS) and HVDC supplementary control both are proved to be eective to increase power system damping. Since PSS are widely used in power system practically, this paper mainly ocuses on sensitivity analysis o oscillation modes with respect to the PSS parameters. Large ISSN: ISBN:

2 ADVANCED APPLICAIONS OF ELECRICAL ENGINEERING scale system case study is presented in section 3. Finally, the conclusion is presented in section 4. 2 Eigenvalue Sensitivity 2.1 Sytem state matrix For small signal stability study, nonlinear equations o the power system dynamics are linearized by applying aylor s expansion around a speciic operating point [12]. he mathematical model o system can be obtained by component connection model (CCM) technique and may be described by the ollowing augmented state space representation as: ΔX& JA JB ΔX ΔX = = A (1) a 0 JC JD ΔU ΔU By eliminating the algebraic variables rom (1), the ollowing representation is obtained: -1 ΔX& = J J J J ΔX= A ΔX (2) ( A B D C) where X is the n 1 vector o component state variables, such as generator states, controllers states and dynamic load states. U is the vector o component input variables. Δ is a preix representing perturbed values. A is a n n system matrix. Aa is the augmented system state matrix. Consider an n n system matrix A with eigenvalues λ i =σ i ±ω i,(i=1,...,n), then corresponding let and right eigenvectorψ i, ψ i augmented let and right eigenvector ψ ia, ф ia may be written as: ψ ia = ψi ψ iv, ia = i iv (3) J A J B ψi ψ iv = λ i ψi JC JD 0 (4) JA JB i i = λi C D iv 0 J J (5) When including a subsection you must use, or its heading, small letters, 12pt, let justiied, bold, imes New Roman as here. 2.2 Eigenvalue sensitivity analysis he stability o a large system is determined by the knowledge o the eigenvalues o the system state-space matrix A. he system eigenvalues are, in general, unctions o all control and design parameters. Whenever there is a disturbance on a parameter q, the system matrix A and the eigenvalues will vary accordingly. o determine the eect o the variation o the parameter on the eigenvalue, the irst-order eigenvalue sensitivity is considered and can be expressed as [13]: JA JB ψ ia ia A J a C JD ψia ia λ q q i = = (6) ψi i ψi i Since the parameter q may range rom very large to very small, it makes more sense to calculate the relative sensitivity, deined by [14]: λ SRS = q = SRRS + js (7) IRS λ SRRS = Re{ q} (8) λ SIRS = Im{ q} (9) he main purpose o sensitivity analysis is to push σ i as negative as possible or the weakly damped system to increase damping. Whenever S RRS is positive (negative), q should be decreased (increased) by suitable adjustment to achieve the goal. heoretically q is said to be at its optimum value when S IRS approaches zero. he computation o relative eigenvalue sensitivity was implemented in SSAP. 2.3 Sensitivity analysis or PSS parameters in SSAP Power system stabilizer (PSS) is a wildly used control device to improve the system dynamic stability. he basic unction o a PSS is to produce an electrical torque component in phase with the rotor speed variation and to add damping to the rotor oscillations by introducing an auxiliary stabilizing signal to automatic voltage regulator (AVR). It is most cost-eective in providing power system damping and may implement more lexible system control strategies. In this paper, the analysis o eigenvalue sensitivity with respect to PSS parameters is presented. Speed-based (Δω) stabilizers, requency-based (Δ) stabilizers and accelerating power-based (ΔP G ) stabilizers are three alternative types o PSS in SSAP. Fig.1 shows the block diagram o them, mainly consists o the gain block, the wash-out block, and three lead-lag compensation blocks, etc. he eigenvalue sensitivities with respect to those nine parameters in the blocks can be calculated by SSAP. 3 Sensitivity analysis or CSG o veriy the eectiveness o the eigenvalue sensitivity analysis o SSAP, a large-scale interconnected power system with AC/DC parallel ISSN: ISBN:

3 ADVANCED APPLICAIONS OF ELECRICAL ENGINEERING transmission China Southern Power Grid (CSG) is investigated. According to the inormation oered by modal analysis and eigenvalue sensitivity analysis, some PSS parameters are selected to be modiied to enhance the overall stability o the system. 3.1 Description o the system he main part o CSG consists o our provincial power grids: Guangdong (GD), Guangxi (GX), Guizhou (GZ) and Yunnan (YN). One HVDC link connects the CSG with the central China power grid asynchronously, and several ac lines connect the CSG with HongKong (HK). he main structure o CSG in the year 2007 is shown in Fig.2. At summer peak demand o loads in 2007, more than 11 GW o bulk power is transmitted rom YN, GZ, and GX to remote load center in GD. he longest transmission distance is approximately 2000 km. In such a wide-area power grid with AC/DC parallel bulk power transmission, inter-area oscillation among the our provincial power grids occurs at times and becomes a problem concerned in the system operation. he studied system includes 439 generators, 3754 buses, 4710 AC transmission lines, our ±500kv HVDC links and 789 loads. In the analysis o system oscillation 17 generators are described by classical model, the other 422 generators are modeled in detail, among which 419 generators are equipped with exciter systems represented as several standard IEEE ω P G K QS 1 + s 1 + s QS Q Q ' Q1 type models, and 154 existing PSSs are modeled including speed-based (142) and accelerating power-based (12) types. Four HVDC links are represented by the Quasi-Steady-State (QSS) model specially deined in SSAP, and load static characteristics is taken into account by ZIP model. 1 + s 3.2 Small signal characteristics o the system Eigenvalues o electromechanical modes with requency ranged in Hz and damping ratio less than 10% are scanned by the IRA part o SSAP. he results are summarized in able 1, where ζ denotes the damping ratio and denotes the requency o the mode. Mode shape analysis indicates that mode 1 is an inter-area mode. he machines in YN swing against the group o machines in GZ. Fig.3 shows the mode shape scatter diagram o the generator speed state variables o mode 1, and Fig.4 shows the relevant bar diagram o the participation actors. Mode 2 represents the machines in the east region o GD swinging against those in the rest region o GD. Mode 3 and mode 4 are local modes relecting the swing among machines in YN. he major participants o each mode are also shown in able 1. It is expected or the inter-area oscillation modes with requency lower than 1.0 to have damping ratios larger than 10% to ensure small-signal stability o the Q1 ' Q s Q 2 Fig.1 Block diagram o PSS ' Q S Q 3 V S max V S min V Fig.2 Structure diagram o CSG in 2007 ISSN: ISBN:

4 ADVANCED APPLICAIONS OF ELECRICAL ENGINEERING able 1 Electromechanical oscillation modes between 0.1 and 1.0 Hz, with damping ratio less than 10% Mode Eigenvalues (HZ) ζ (%) Oscillation pattern Major participants (generator No.) ± YN vs. GZ YN: G387, G388, GZ: G238, G ± East o GD vs. the rest o GD GD: G94, G95, G98, G ± machines in YN YN:G352, G353, G389, G385, G ± machines in YN YN: G389, G395, G352, G Fig.3 Mode shape scatter diagram o generator speeds or mode Fig.4 Participation actors diagram o generator speeds or mode 1 system. For the past years, PSSs have been installed on major generators in the CSG to improve damping o system oscillation, which make the dampings o mode 1~3 larger as shown in able 1. Among the major participants listed in able 1, generators G94, G95, G98, G91 and G389, G395 are not equipped with PSSs. Dampings o mode 2 and mode 4 can be enhanced by installing PSSs on these machines, that is omitted in this paper. he emphasis is laid on improving damping o oscillation modes by tuning the parameters o existing PSSs. 3.3 Parameter optimization or PSS based on eigenvalue sensitivity analysis able 2 shows the eigenvalue sensitivity results calculated by SSAP. For convenience, only the eigenvalue sensitivities with respect to the gain (K QS ) ISSN: ISBN:

5 ADVANCED APPLICAIONS OF ELECRICAL ENGINEERING o PSS with larger values are presented. It seems that the magnitudes o the real parts o the eigenvalue sensitivities o mode 1 with respect to the PSS gains o G387, G388, G238 and G239 are larger. It is conormable to the result o major participant analysis. he corresponding signs o values imply that, the reduction o PSS K QS o G387 and the increment o PSS K QS o G388, G238 and G239 will enhance the damping o mode 1. Besides, decreasing PSS K QS magnitudes o G87, G88, G201, G202, G347 and increasing those o G83, G84, G203, G204 will increase damping o mode 2; decreasing PSS K QS magnitudes o G385, G386, G387, G388 and increasing that o G347 will improve damping o mode 3; decreasing PSS K QS magnitudes o G387, G388, G385 and G386 will reinorce the damping o mode 4. It also shows that the tendency and eect o a gain variation on eigenvalues are dierent. For example, a small increment o the gain o G388 will much reinorce the damping o mode 1, but jeopardize the damping o mode 4. his observation implies that we should take a comprehensive consideration o all dierent eects in order to adjust parameters properly and improve overall system stability. According to the direction o increasing damping oered by the eigenvalue sensitivities, the tuning o the parameters o PSS are conducted by steps. able 2 Eigenvalue sensitivity with respect to PSS gain constant K QS PSS area Mode 1 Mode 2 Mode 3 Mode 4 G387 YN j j j j G238, G239 GZ j j j j G388 YN j j j j G88 GD j j j j G83, G84 GD j j j j G87 GD j j j j G201G202 GD j j j j G347 YN j j j j G204 GD j j j j G203 GD j j j j G385 YN j j j j G386 YN j j j j According to the oregoing analysis above, the parameters K QS o several PSSs are selected to be tuned in the irst step as shown in able 3. able 3 he modiied settings o PSS gains PSS Initial Modiied Initial Modiied PSS setting setting setting setting G G G238, G G G G G83, G G G G G201, G Ater the modiied parameters are set on these PSSs, the small signal analysis is carried out again, and inormation on the new oscillation modes is listed in able 4. Clearly, the damping ratio o the system or mode 1 increases signiicantly, and those or mode 2~4 increase moderately. However, a new oscillation mode 5 appears at the requency o 0.79 HZ with damping ratio less than 10%. Mode shape analysis indicates that mode 5 belongs to the local mode relecting among machines in YN with G387 generator as the major participant. he eigenvalue sensitivity with respect to the parameter K QS o G387 PSS or mode 5 has larger magnitude and negative real part, which explains the result o small signal analysis. able 4 Oscillation modes o system with the modiied PSS settings in step 1 Mode (HZ) ζ(%) In order to improve the damping ratios o each mode urther, eigenvalue sensitivity analysis is carried out again with the modiied PSS gains. he real part signs o sensitivities with respect to parameters Q1 and Q2 o G387 PSS (only have two lead-lag blocks) or each mode are all positive as shown in able 5. able 5 Eigenvalue sensitivity with respect to the lead time constant Q1 and Q2 o G387 PSS Mode S RS Mode S RS j j j j j In the second step, the parameter Q1 and Q2 o G387 PSS are both reduced rom initial setting 0.2s ISSN: ISBN:

6 ADVANCED APPLICAIONS OF ELECRICAL ENGINEERING to 0.16s. he inormation on the oscillation modes ater applying the new parameter setting is listed in able 6. able 6 Oscillation modes o system with the modiied PSS settings in step 2 Mode (HZ) ζ(%) he damping ratios o all ive modes are more or less improved ater the parameter modiied in step 2, and mode 4, 5 are enhanced more clearly, which can be explained by the magnitude o sensitivities in able 5. Furthermore, the imaginary part o eigenvalue sensitivity or mode 5 in able 5 is negative and has a larger magnitude, which make the requency o mode 5 increased signiicantly. Ater urther analysis, no new electromechanical oscillation mode with requency ranged in 1-2.5Hz and damping ratio less than 3% appears, and damping ratios o initial modes in that range are not deteriorated ater applying the modiied PSS parameters. In other words, a satisactory balance between improvement in the mode o interest and deterioration o other modes is attained. In act, the parameters o PSSs can be optimized by adjusting them in this way step by step, and the overall system stability can be enhanced urther. 4 Conclusion Eigenvalue sensitivity analysis is applied to improve damping o the low requency oscillation in AC/DC interconnected power system. his unction in SSAP sotware is introduced. Low-requency oscillation characteristics o a typical operation condition o the China Southern Power Grid are analyzed and some PSS parameters are adjusted in the direction o increasing damping according to the inormation provided by the corresponding eigenvalue sensitivity analysis. he results show that the dampings o oscillation modes concerned are improved and the overall system stability is enhanced. Eigenvalue sensitivity analysis unction o SSAP can provide orientation or controller parameter optimization. Reerences: [1] Schlei, F.R., and White, J.H., Damping or the northwest-southwest tieline oscillations - an analog study, IEEE rans. Power Appar. Syst., Vol.85, No.12, 1966, pp [2] Kosterev, D.K., aylor, C., and Mittelstadt, W.A., Model validation or the August 10, 1996 WSCC system outage, IEEE rans. Power Syst., Vol.14, No.3, 1999, pp [3] Lou, G.J., Xu, X.H., Long, S.Q., and Li, Q.C., Low requency oscillations on the Interconnectors between Hong Kong and Guagndong, Proc. o the Chinese Society o Electrical Engineering, Vol.6, No.1, 1986, pp [4] Messina, A.R., Ramirez, J.M., and Canedo C., J.M., An investigation on the use o power system stabilizers or damping inter-area oscillations in longitudinal power systems, IEEE rans. Power Syst. Vol.13, No.2, 1998, pp [5] Larsen, E.V., Sanchez-Gasca, J.J., and Chow, J.H., Concepts or design o FACS controllers to damp power swings, IEEE rans. Power Syst., Vol.10, No.2, 1995, pp [6] Gama, C., Brazilian north-south interconnection control-application and operating experience with a CSC, Power Engineering Society Summer Meeting, IEEE, vol.2, July 1999, pp [7] Smed,., and Andersson, G., Utilizing HVDC to damp power oscillations, IEEE rans. Power Deliv., Vol.8, No.2, 1993, pp [8] Arcidiacono, V., Ferrari, E., Marconato, R., Dos Ghali, J., and Grandez, D., Evaluation and improvement o electromechanical oscillation damping by means o eigenvalue-eigenvector analysis. Practical results in the Central Peru Power System, IEEE rans. Power Appar. Syst., Vol.99, No.2, 1980, pp [9] Gu, H.Y., and Chen, C., Using Implicitly Restarted Arnoldi Method or Eigenvalue Analysis o Power Systems, IFAC World Conerence, Beijing, China, July 1999, pp [10] Li, G., Su, J., and Chen, C., Object-oriented multi-spectrum transormation Implicit Restarted Arnoldi Algorithm, Automation o Electric Power Systems, China, Vol.25, No.8, 2001, pp [11] Li, G., Small signal stability analysis and object oriented sotware developing, PhD thesis, Shanghai Jiaotong University, [12] Kundur, P., Power system stability and control, New York: McGraw-Hill, [13] VanNess, J.E., Boyle, J.M., and Imad, F.P., Sensitivities o Large, Multiple-loop Control Systems, IEEE rans on Automatic Control, July 1965, pp [14] se, C.., and so, S.K., Design optimization o power system stabilizers based on modal and eigenvalue- sensitivity analyses, IEE Proc., Pt. C, Vol.135, No.5, September 1988, pp ISSN: ISBN: