Quantitative transient voltage dip assessment of contingencies using trajectory sensitivities☆
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)where 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 . 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.
References (37)
- et al.
Under voltage load shedding in power systems with wind turbine-driven doubly fed induction generators
Electr Power Syst Res
(2013) - et al.
Oscillatory stability analysis with high penetrations of large-scale photovoltaic generation
Energy Convers Manage
(2013) - IEEE PES Power Quality Subcommittee. Draft standard glossary of power, quality terminology;...
- Carlsson F. On impacts and ride-through of voltage sags exposing line-operated AC-machines and metal processes. Ph.D....
- Yin S, Lu C, Liu E, Huang Y, Huang C. A survey on high tech industry power quality requirements. In: IEEE/PES...
- et al.
Reliability worth assessment of high-tech industry
IEEE Trans Power Syst
(2003) - Bhattacharyya S, Cobben G, Kling L. Assessment of the impacts of voltage dips for a MV customer. In: International...
- et al.
Determination of effectiveness of transient stability controls using reduced number of trajectory sensitivity computations
IEEE Trans Power Syst
(2004) - Alves M, Ribeiro T. Voltage sag: an overview of IEC and IEEE standards and application criteria. In: IEEE transmission...
- et al.
Voltage-sag indices – recent developments in IEEE PI564 task force
A voltage sag index considering compatibility between equipment and supply
IEEE Trans Power Delivery
A method for estimating the frequency and cost of voltage sags
IEEE Trans Power Syst
A new method for obtaining critical clearing time for transient stability
IEEE Trans Power Syst
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This paper was supported by Power System Engineering Research Center through project ‘Next generation online dynamic security assessment’