Quantitative transient voltage dip assessment of contingencies using trajectory sensitivities

https://doi.org/10.1016/j.ijepes.2014.03.063Get rights and content

Highlights

  • We design a new index to assess transient voltage dips quantitatively.

  • The new index can rank contingency severity in terms of transient voltage dips.

  • We use trajectory sensitivity approach to calculate the new index efficiently.

  • The analysis using the new index is consistent with operational experience.

Abstract

A new index, voltage critical clearing time (V-CCT), is presented for quantitative assessment of transient voltage dips subject to various contingencies. Calculation of V-CCT needs estimation using trajectory sensitivities of voltages with respect to fault clearing time. The V-CCT indices indicate the severity of fault-initiated contingencies by comprehensively evaluating transient voltage dips according to dynamic performance criteria. Using trajectory sensitivities to obtain V-CCT minimizes the computational effort by avoiding repetitive trial-and-error time-domain simulations. Performance of the proposed transient voltage dips assessment method has been tested on a 9-bus system, the New England 39-bus system and a 13,000-bus system. For the small test systems, some selected contingencies are compared to verify the consistency of ranking using V-CCT with time-domain simulation analysis. The computational efficiency of the proposed assessment method is analyzed. Then the case studies on the large system build up the relation between analysis results and system operating condition. The results show that the assessment using V-CCT reflects the contingency severity in scope of transient voltage dips.

Introduction

Transient voltage dip (TVD) refers to the short-term voltage magnitude reduction after faults or other disturbances, such as transformer energizing, large motor starting and heavy load switching [1], that result in extreme increase of currents. TVD is an important aspect of power quality. Severe TVD brings high consequences in various industry areas [2], [3], [4], [5]. To avoid TVD, time-domain simulations must be done and preventive actions taken when unacceptable TVD is detected [6]. In this paper, we present a new index to facilitate fast TVD assessment after fault-initiated contingencies.

There is a significant body of literature on assessing TVD. In [7], the IEC and IEEE TVD standards and application areas were reviewed. Ref. [8] presented various TVD indices relating voltage dip duration and energy variation. Ref. [9] developed a TVD index considering compatibility between equipment and supply. The TVD duration assessment criteria were summarized in [10] from various industry resources. Some other TVD assessment standards include voltage dip window criterion [11] and economic cost [12]. In [13], [14], stochastic methods were presented for TVD assessment.

Inspired by critical clearing time (CCT), a familiar metric to indicate power system rotor angle stability [15], [16], this paper proposes an index called voltage critical clearing time (V-CCT). The system dynamic security subject to fault-initiated contingencies is quantified by fast estimation of V-CCT. To obtain V-CCT, voltage trajectory sensitivities with respect to fault clearing time are first calculated. The calculated trajectory sensitivity information is used to estimate V-CCT, which is defined as the maximum fault clearing time for which the limit of TVD dynamic security region is reached. V-CCT is a comprehensive index, because it considers multiple TVD dynamic performance criteria that define the TVD dynamic security region. Using trajectory sensitivities to calculate V-CCT avoids time-consuming repetitive trial-and-error time-domain simulations to obtain those critical values. The calculated V-CCT are used to rank the TVD severity of assessed contingencies.

The rest of the paper is organized as follows. Section ‘Trajectory sensitivities with respect to fault clearing time’ introduces the trajectory sensitivities with respect to fault clearing time, including the calculation, initial condition determination and computational efficiency analysis. Section ‘TVD assessment’ introduces the TVD dynamic performance criteria used by NERC/WECC to define the TVD dynamic security region and presents the concept of V-CCT. Then the procedure of using V-CCT for TVD assessment is described. Section ‘Estimation error index’ introduces an index to quantify the estimation error. Section ‘Case studies’ provides the case study results from the tests on three benchmark systems. Section ‘Conclusions’ summarizes the contributions of this paper.

Section snippets

Trajectory sensitivities with respect to fault clearing time

The dynamics of a power system considering switching actions can be described by a differential algebraic discrete model as in [17]. A special but common case is the model described by differential algebraic equations (DAEs)ẋ=f(x,y,t,λ)0=g-(x,y,t,λ)s(x,y,t,λ)<0g+(x,y,t,λ)s(x,y,t,λ)>0where x are dynamic state variables, y are algebraic variables and λ are system parameters and initial conditions. Examples of system parameters are transmission line impedances, generation levels and load

TVD dynamic performance criteria and dynamic security region

Calculation of V-CCT requires dynamic performance criteria to determine the TVD dynamic security region. Commonly used criteria consider both low voltage and high voltage limits during the oscillations and the time duration when a limit is violated, i.e., violation duration, as shown in Fig. 1. The criteria are used to evaluate the post-fault transient voltage trajectories and define the boundary of TVD dynamic security region. System performance subject to various disturbances can then be

Estimation error index

Because power systems are nonlinear, using trajectory sensitivities to calculate V-CCT will cause estimation error, the degree of which depends on the magnitude of MAX(Δtcl) and the system nonlinearity characteristics around tclbase. Detailed estimation error analysis can be found in [20], [32]. In case of unacceptable estimation error, Ref. [32] presented two strategies: second order trajectory sensitivities and switching operating states method, to reduce the estimation error. In [32], the

Case studies

Three systems are used to evaluate the performance of the proposed assessment method: a 9-bus system [33], the New England 39-bus system [34] and a large 13,000-bus system.

Conclusions

This paper has presented a new index, i.e., V-CCT, for power system TVD quantitative assessment. V-CCT applies the concept of CCT to TVD assessment. It indicates the severity of fault-initiated contingencies based on TVD dynamic performance criteria. Obtaining V-CCT is computationally efficient, due to the use of trajectory sensitivities to estimate V-CCT.

The proposed index has been tested on a 9-bus system, the New England 39-bus system and a 13000-bus system. Computational efficiency has also

Acknowledgment

Dr. Siddhartha Kumar Khaitan and Dr. Chuan Fu are acknowledged for providing the 13,000-bus system and helping test the data validity.

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    This paper was supported by Power System Engineering Research Center through project ‘Next generation online dynamic security assessment’

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