Small Signal Stability Analysis: Experiences, Achievements, and Challenges

P. Kundur, Fellow IEEE Lei Wang, Member IEEE

Powertech Labs Inc. Surrey, BC, Canada

Abstract - This paper presents an overview on the recent trend of small-signal stability analysis of power systems, focusing mainly on the experience, applications and achievements, and the challenges facing the power industry in this area. Issue:$ discussed include experiences and lessons learnt from real-life incidents, modelling and study requirements, analysis tools available and their performances, and the possible future developments. The paper shows the importance of addressing small signal stability of power systems in all stages of planning and operation, as well as the viability of analysing and mitigating these problems with the advanced tools available to the industry today.

1. INTRODUCTION

Small signal (rotor angle) stability, along with transient stability, voltage stability and frequency stability, is the basic requirement for a power system to maintain secure operation [l].

The theory and analysis methods for small signal stability problem are well established [ 13. Research and development efforts over the past two decades have also resulted in effective computation algorithms and successful applications of control theory to mitigate many problems related to power system oscillations [2-51. Several computer programs specifically designed for small signal stability analysis have been developed and used [4,5]. These theoretical and developmental breakthroughs havt: greatly helped the understanding and advancement of the small signal stability analysis. They form a solid foundation for practical applications. Despite these impressive developments, however, small signal stability is not yet being adequately addressed by the electric power industry. Most utilities do not carry out small signal stability analysis routinely as a part of planning and operating studies.

However, due to the changing ways power system; are being planned and operated in the new industry environment, this problem has not only emerged as one of the primary concerns for secure system operation but also poses new challenges for developing better analysis and mitigating methods.

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In presenting this paper, we are motivated by the lack of sufficient appreciation by the industry as a whole for properly addressing the small signal stability problems in the planning and operation of power systems. Our objective is to provide a broad overview of the subject by discussing the following aspects:

Past experiences illustrating the importance of small signal stability analysis;

Recent achievements and development of tools for small signal stability analysis;

0 Challenges and possible fWre developments,

2. EXPERIENCES

2.1 Utility experiences

Small signal stability problems in power systems date back to several decades, with many reported incidents [2]. This problem often appears as poorly damped, sustained, or even growing (unstable) oscillations due to insuficient damping. The oscillations may appear in only a small part of the system (local mode oscillations), or spread over a large region of an interconnected system (inter-area mode oscillations) [ 11.

A typical example of the local problem is the Rush Island incident which occurred in 1992 in the AmerenUE system of Mid US [6]. A contingency, previously not analysed, occurred on the system making the Rush Island units weakly connected to the main grid, triggering a sustained oscillation involving the Rush Island units. An unstable local mode oscillation under the post,eontingency condition was later confirmed in the post-mortem analysis. The problem was solved by use of a conventional power system stabilizer (PSS).

The August 1996 disturbance on the WSCC system (North American Western Interconnected system) is a classic example of the inter-area oscillation problem [7]. Several circuit outages made a low-

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frequency (0.23Hz) inter-area mode unstable, leading to the break-up of the entire WSCC system. A similar oscillation occurred again on the WSCC system on August 4, 2000, triggered by the separation of Alberta system from the WSCC interconnection 181. Figure 1 shows the California-Oregon inter-tie flow during the oscillation. For both incidents, post- mortem analysis, including eigenvalue analysis, was able to replicate the events [8,9]. Some factors causing these oscillations and the measures required to predict and control them have been developed and partially implemented.

E 340 2 320 E

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Figure 1: California-Oregon intertie flow during the August 4,2000, incident

Due to the potential adverse effects of the oscillation problems, many utilities have introduced reliability or security requirements to ensure sufficient damping (commonly as a damping criterion) when new generation or transmission facilities are added, or when operating guides are set. This creates demands for good analysis tools and methods to deal with the small signal stability problems.

Nonlinear time-domain simulation used to be the only approach in the analysis of the oscillation problems. Although this method is very mature and straightforward, it does not have the capabilities that are critical in determining the modal characteristics and in designing appropriate controllers. The modal (eigenvalue) analysis approach overcomes these limitations. It gives usel l information on the inherent characteristics of modes (mode shapes, participation factors, transfer functions, etc.) which can be used in control design for damping enhancements. The complementary use of eigenvalue and nonlinear time-domain analyses is a sound approach to resolve system oscillation problems [VI. 2.2 Modelling issues

Many studies have been performed to identify the critical modelling requirements for the small signal stability analysis, and to understand the impact of various power system components and controls on

the characteristics of different types of oscillations. Generally, the following have been proven or observed:

For local mode oscillations, the overwhelming factor affecting the modal characteristics is the excitation controls of the generators involved. The accurate modelling of the exciter, AVR, and other supplementary controls (such as PSS) is essential for analyzing this type of problems.

For inter-area mode of oscillations, the situation is usually much more complicated [lo]. However, certain factors are known:

Since an inter-area mode usually involves a large region of an interconnected system, a detailed representation of the full system is required to study such phenomena. The accuracy and consistency of the models are important; therefore, extensive model and data sanity checking and validation are necessary before performing the studies.

9 Excitation systems are again the most critical controls affecting inter-area modes. Under some conditions, speed governor characteristics may also have an impact [8]. Other controls such as HVDC modulation and FACTS controllers could have a significant contribution to the damping of inter-area modes.

Load characteristics can play a very important role in an inter-area mode [lo]. Not only correct load level and distribution but also appropriate model type mix must be represented in the study in order to simulate realistic behaviour of inter- area modes. Usually, dynamic characteristics of loads (mostly induction motors) need to be included as well.

. System operating conditions (load levels, major power transfers, etc.) can significantly affect the Characteristics of inter-area modes, particularly their mode shapes and damping. Therefore, certain practices of using “worst case” transfer scenarios in planning studies may not represent critical conditions for inter-area oscillation studies.

2.3 Planning and operation considerations

The small signal stability problem is essentially a problem of damping control. This requires special consideration in the “deregulated” industry environment. Deregulation creates great generation

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development opportunities for independent power producers (IPP), but many of these IPP units are being built at locations that are ideal from the generation point of view but their power often has to be delivered through a weak transmission system. In such situations, small signal stability can often be a limiting factor for adding new generation facilities. This is amply illustrated in [ 1 11. Without appropriate consideration of small signal stability and the required controls, the new generation facilities could have unacceptable damping performance.

On the operation side, demands for large power transactions in an open-access market can severely stress a system up to the edge of its stability limits. With the changing characteristics of the present d a y power systems, such limits are increasingly being imposed by small signal stability considerations [2:1. Figure 2 shows a typical example of power transfer limited by small signal stability. In this figure, the responses of a medium-sized test system are simulated for a critical contingency at different power transfer levels across an important interface. The system is stable with acceptable damping for its primary inter-area mode when the transfer is below 2600 MW (damping ratio s is above 3.9%). As transfer is increased to 3000 MW and 3400 MW, the damping of this mode is decreased to 1.6% and 0.9% respectively. The system would eventually lose angle stability at a transfer of about 3800 MW, but wa:y before this transfer the damping is so low that the operation would not be acceptable (if a damping criterion of 3% is used, the stability limit would be about 2730 MW). This example illustrates the importance of establishing a damping performance criterion for systems with damping problems and determining the transfer limits accordingly. Such problems have already been observed in the Pacific Northwest and Southeast systems of the US.

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Time in seconds

Figure 2: System performance at different transfer levels

3. RECENT DEVELOPMENTS

3.1 New analysis tools

The reason that small signal stability analysis has not been routinely performed by many utilities is partly due to lack of p o w e m yet user-friendly computer analysis tools. Many of the computer programs developed in the past two decades were research- grade, focusing mainly on theory and algorithm development with less emphasis on utility applications. Applying these programs for practical system studies was often not a straightforward task for a number of reasons, such as data and model incompatibility with traditional transient stability analysis tools, lack of convenient features and capabilities for comprehensive analysis, and difficulties in interpreting computed results.

This situation is changing, with the introduction of the new generation of small signal stability analysis tools. Two such tools, both developed recently by the authors' company Powertech Labs Inc., are briefly described below.

Small Signal Ana&& Tool (SSAq [12]

This is a comprehensive software tool for analysis and mitigation of small signal stability problems of large interconnected power systems. It includes not only a variety of eigenvalue computation options for determination of different types of modes, but also a suite of use l l system study capabilities such as:

Input data customization and representation options Contingency analysis Eigenvalue sensitivity analysis Root locus (mode trace) analysis Frequency response computation Small signal stability limit determination Output result analysis and visualization tools User-friendly program interface

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Figure 3 shows two ways of visualizing a mode shape in SSAT for a major inter-area mode (0.48 Hz and 8.4% damping) in North America, obtained from a fiill US-Canada Eastern Interconnection model (39,873 buses and 6,652 generators). Figure 3(a) illustrates the geographical distribution of the mode, in which the oscillation of the mode is seen to be mainly between those units in Southeast US (excluding Florida) plus Canada (denoted by circles in blue) and those units in rest of the system (denoted by crosses in red), The intensity (contrast) of each

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symbol indicates the magnitude of the oscillation in the associated generator. Figure 3(b) shows the mode shape (magnitude and phase) arranged by control areas (denoted by different colours). This kind of result visualization significantly helps study engineers to understand the physical phenomena related to the mode and thus to apply the suitable mitigation method if necessary.

(a) Geographical mapping of the mode (different symbols, colours, and colour contrasts indicate respective modal characteristics)

(b) Mode shape scatter plot (magnitudes and phases of individual mode shape entries are shown with colour- coded area representation)

Figure 3: Two different views of a mode shape in SSAT

Control System Tuning Toolbox (CSTlJ

This is a development in’ response to industry’s call for tools enabling systematic determination and tuning of parameters of controllers (particularly PSS) for damping enhancement.

CSTT uses optimization techniques to determine or tune the parameters of controllers in a power system for target performance requirements (mainly damping criteria). There have been a number of similar developments in this area [5 ] , but what makes CSTT unique are the following unique capabilities:

CSTT is built on both linear and non-linear analysis techniques, with SSAT and TSAT (a commercial time-domain simulation program) as its computation engines. This, in addition to ensuring sufficient verification of the robustness of tuned controllers, provides for adequate modelling and computation capabilites.

Tuning can be performed with an approach that is either highly customized or fully automatic. Multiple controllers can be tuned simultaneously. This offers flexibilities for different application objectives and thus provides best possible results.

An application of CSTT to a sample system of 686 buses and 219 generators shows that by going through an automatic tuning process for 4 PSS, an unstable inter-area mode in the system can be stabilized with a damping ratio of 7.6% for a set of realistic PSS parameters.

3.2 Computation performances

Another fact that has often been misunderstood is the computation performances related to the small signal stability analysis. It is true that eigenvalue calculation used to have such a high burden of computation and memory requirements that only relatively small systems could be analyzed. This has changed dramtically with the use of advanced computation and programming techniques adopted in the new generation of software. Table 1 shows the computation times for the conventional time-domain simulation and eigenvalue analysis of a very large system model (34,381 buses, 3,870 generators, 41,382 dynamic states). Computation times were obtained using TSAT for time-domain simulation and SSAT for eigenvalue computation (111 modal characteristics including mode shapes and participation factors were computed for each mode). It is clear that the orders of computation times are comparable for these two types of analyses. Since the eigenvalue computation problem can usually be decoupled into many parallel sub-problems, it is possible to fiuther boost the computation performance by using parallel or distributed computation techniques.

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Table 1 : Computation time comparison

Computation task One 1 O-second time-domain simulation

Computation time (min)

7.9 Mode scan in the frequency range of 0.2 and 0.8 Hz and damping range of 0% and 10% (24 modes were computed)

’ 3.3 Applications in operation studies

As described in Section. 2.3, when small signal stability is the primary security constraint, power transfers are limited by damping criterion. Reference [13] reports a method of increasing power transfer in such a situation by using the sensitivity-based method. The idea is as follows: when power trancifer needs to be increased or decreased, the groups of candidate generators in the source and sink regions; of the transfer are dispatched in an order determined by the sensitivities of the critical mode with respect to the outputs of these generators, so as to achieve the increased power transfer level, without the addition of new damping controls.

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Figure 4 shows the comparison of this scheme with other generator dispatch methods for a sample system. As indicated, for a given small signal stability criterion (3% damping), the sensitivity-based method can achieve a stability limit of 2450 MW, which is 160 MW greater than the uniform-scalxng method or 500 MW greater than the econornic dispatch method.

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0 ‘1950MW I ’ 2450MW I

1800 2000 2200 2400 2600 2800 3000

Figure 4: Comparison of power transfer limits ’ with different generator dispatch methods

4. CHALLENGES

Although very significant advancements have been made in small signal stability analysis techniques and powerfil tools have been developed, the following important issues are yet to be satisfactorily addressed.

4.1 Modelling

An adequate system model is essential for the successful assessment of small signal stability. Assembling a system model appropriate for such studies is not an easy task. Past experiences have indicated that in most cases the models created for planning purposes are unlikely to give results consistent with the actual system measurements [8,9]. Improvements are required in several areas:

Modelling accuracy and details of major equipment such as excitation systems and speed governors. One of the ways to ensure good models for such equipment is the model validation and refinement through extensive field testing, such as the mandatory compliancy process that has been in place in WSCC since the 1996 blackouts.

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Addition of models not usually represented in conventional stability studies. One typical example is the representation of induction motor loads which often turns out to be important to replicate measured characteristics of inter-area modes [8,9].

Choice of system operating conditions such as load levels and power transfers. Use of the “worst case” scenario approach is usually not adequate; considering a range of realistic feasible operating conditions could improve the quality of results significantly.

4.2 Controls

Control of local mode of oscillations is a relatively simple task and in most cases it can be solved by applying power system stabilizers. In some situations, however, local oscillation problems can also become difficult to control. Figure 5 shows such an example which is based on a real case study involving a gas turbine with digital governor. In this case, a local oscillation problem is simulated under two conditions: with the speed governor blocked and enabled. As seen in the figure, when the speed governor of the gas turbine is blocked, the oscillation is reasonably damped, but when it is enabled, the damping becomes very poor. This indicates a strong negative contribution of the governor to the damping. Application of a conventional PSS was found to be

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ineffective in this case. This problem requires W h e r investigation but is indicative of some of the challenges in controlling local mode oscillations

acta scta 4000 8000 acta io

Time in seconds

Figure 5: Local oscillations associated with governors

Control of inter-area modes presents greater challenges, and has been the focus of many research projects; however, widely accepted and effective universal approaches are yet to be developed. This is an area that requires M e r investigation and industry experience.

4.3 On-line security assessment

As mentioned earlier, operating limits of many power systems are constrained by small signal stability, as the transmission systems are becoming increasingly stressed. This would eventually call for on-line small signal security assessment (SSA).

SSA of a power system refers to the small-signal stability analysis of the system under a set of credible contingencies for a range of feasible operating conditions. The system is small-signal secure if the damping of all critical modes in the system are within a required threshold. Further, a small signal stability limit can be defined as a power transfer limit beyond which the damping of at least one mode becomes insecure. SSA is the sibling of the other two forms of the dynamic security assessment, namely transient security assessment (TSA) and voltage security assessment (VSA)[ 141. Technically, the requirements for on-line SSA are similar to those of TSA and VSA, including the following:

0 Contingency screening Detailed security analysis of critical contingencies

0 Small signal stability limit determination 0 Remedial measure to improve small signal security

0 On-line computation speed requirements 0 Connectivity to the EMS system

Most of these computation capabilities are already available in the new generation of small signal stability analysis software. It is therefore technically feasible to incorporate on-line SSA, particularly where on-line TSA has been implemented, since SSA could share most of the data with TSA.

5. CONCLUSIONS

This paper discusses the past experience and new challenges in the small signal stability analysis of power systems. Some of the recent applications and achievements for a range of small signal stability problems are described with illustrative examples. The paper demonstrates the importance of addressing small signal stability of power systems in all stages of planning and operation, as well as the viability of analysing and mitigating these problems with the advanced tools available to the industry today.

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6. REFERENCES .

P. Kundur, Power System Stability and Control, McGraw-Hill, 1994

IEEE PES System Oscillation Working Group, “Inter- area Oscillations in Power Systems,” IEEE PES Special Publication 95 TP 101, October 1994.

CIGRE Task Force 38.01.07, “Analysis and Control of Power System Oscillations,” CIGRE Technical Brochure, December 1996.

P. Kundur, G.J. Rogers, D.Y. Wong, L. Wang, and M.G. Lauby, “A Comprehensive Computer Program for Small Signal Stability Analysis of Power Systems,” IEEE Trans., Vol. PWRS.J, pp.1076-1083, November 1990.

CIGRE Task Force 38.02.16, “Impact of Interactions Among Power System Controls,” CIGRE Technical Brochure, May 2000.

K.S. Shah, G.R. Berube, and R.E. Beaulieu, “Testing and Modelling of the Union Electric Generator Excitation Systems,” Missouri Valley Electric Association Engineering Conference, Kansas City, April 5-7,1995.

D.N. Kosterev, C. Taylor, and W.A. Mittelstadt, “Model Validation for the August 10, 1996 WSCC System Outage,” IEEE Trans. Vol. PWRS-14, No. 3, pp. 967-979, August 1999.

D.N. Kosterev, W.A. Mittelstadt, M. Viles, B. Tuck, J. Burns, M. Kwok, 3. Jardim, and G. Garnett, “Model

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Validation and Analysis of WSCC System Oscillations Following Alberta Separation on August 4, 2000,” Final Report by Bonneville Power Administration and BC Hydro, January 200 1.

EPRl Report TR-108256, “System Disturbance Stability Studies for Western System Coordinating Council (WSCC),” Prepared by Powertech Labs Inc., September 1997.

[lo] M. Klein, G.J. Rogers, and P. Kundur, “A Fundamental Study of Inter-area Oscillations in Power Systems,” IEEE Trans. Vol. PWRS-6, No. 3, pp. 914- 921, August 1991.

[11] S. Arabi, P. Kundur, P. Hassiak, and D. Matthews, “Small Signal Stability of a Large Power System as Effected by New Generation Additions,” Presented at IEEE PES Summer Meeting Panel Session on Recent Applications of Small Signal Analysis Techniques, Seattle, July 2000.

[12] L. Wang, F. Howell, P. Kundur, C.Y. Chung, and ’W. Xu, “A Tool For Small-Signal Security Assessment ‘Of Power Systems,” PICA 2001, Sydney, Australia. May 2 1-24,2001.

[13] L. Wang and C.Y. Chung, “Increasing Power Transfer Limits at Interfaces Constrained by Small-Signal Stability,” Presented at IEEE PES Winter Meeting Panel Session on Recent Applications of Small Signal Analysis Techniques, New York, January 2002.

E141 P. Kundur, G.K. Morison, L. Wang, and H. Hamadanizadeh, “On-line Dynamic Security Assessment of Power Systems,” Fifth International Workshop on Electric Power Control Centres, Hevzz, Hungary, June 1999.

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