A graph theoretic approach to accelerate natural cutset prediction during an out-of-step condition

Highlights

• The focus of the proposed scheme is on identifying the natural boundary of separation during an out-of-step condition.

• A fast, adaptive and accurate PMU based cutset prediction scheme is proposed.

• Faster than known PMU based cutset prediction schemes.

• Utilizes graph theory and clustering technique.

• Improves the lead time available for executing controlled islanding.

Abstract

When an out-of-step (OOS) condition occurs in a power system, it splits into multiple islands. This uncontrolled separation happens due to distance relay operation on the lines where electrical centers appear. Real-time phasors obtained from Phasor Measurement Units (PMUs) can be used to track the evolution of electrical centers and identify the natural boundary of separation (cutset). Interestingly, electrical centers do not appear simultaneously on the cutset lines; instead, they evolve at different rates. Hence, the cutset is identified only when the signature of the last electrical center appears. We aim to accelerate the cutset prediction so that the complete cutset is identified when the first electrical center is predicted. For this, we propose a computationally efficient algorithm based on the application of graph theory and clustering technique. Thus, the proposed scheme addresses the significant delay in cutset prediction and thereby increases the time available for controlled islanding. Test results on standard IEEE systems and the All India test system validate the scheme.

Introduction

India witnessed two major blackouts on July 30th and 31st, 2012, due to inadvertent tripping of a distance relay on the 400 kV, 230 km Gwalior-Bina line. This mal-operation resulted in an out-of-step condition (or transient instability), and a complete blackout occurred in the northern and eastern parts of the country. Tie-line flows on the North-West corridor were from West to North, i.e., western region (WR) was generation-rich. Incidentally, there was no fault on the Gwalior-Bina line, but the first tripping occurred due to load encroachment seen by a distance relay. Subsequently, it was found that load encroachment and power swing blocking features were not set correctly. The tripping induced severe electromechanical oscillations, and surprisingly, single tripping led to the loss of the entire North-West AC corridor. The axis of separation (cutset) on July 30, 2012, is shown in Fig. 1. Later on, it was realized that many 765 kV and 400 kV lines were kept out to contain overvoltages in the night as the overvoltage problem is more severe with 765 kV and 400 kV lines than 220 kV lines. Further, on the West-East and North-East interconnections, distance relays picked up on severe power swings and tripped. As no out-of-step tripping (OST) or controlled islanding scheme was in place, the grid collapsed with a loss of approximately 48 GW of load. Western region survived because, after uncontrolled islanding (or natural separation), it had excess generation. Total generation of approximately 2300 MW tripped on over frequency, which resulted in the restoration of load-generation balance and hence its survival. At that point in time, the southern region (SR) was only asynchronously connected to western and eastern regions (ER) through back-to-back and long-distance HVDC lines, and as such, it did not face a blackout. However, import from the eastern region was lost. Therefore, load-shedding had to be resorted to in this region as well. The complete saga is documented in the postmortem analysis report [1].

Since these blackouts, two significant developments have happened in the grid. First is the AC interconnection between SR and WR region through a 400 kV/765 kV corridor, leading to one All India AC grid. The second significant development is a wide-scale deployment of PMUs in the grid under an initiative from PowerGrid India (Central Transmission Utility) as well as state transmission utilities like GETCO. In this initiative [2], PowerGrid has installed more than 1400 PMUs and 59 Phasor Data Concentrators (PDCs) in the grid. Two important analytics envisaged from this project are vulnerability analysis of distance relays [3] and emergency control schemes, in particular, OST.

The authors have been involved in conceptualizing and developing an adaptive, setting-free, system integrity protection scheme (SIPS) which could have minimized the adverse impact of transient instability by resorting to controlled islanding or what is commonly known as OST ([4], [5]). Early prediction of an OOS condition from PMU input has already been addressed in [6] and determination of the best locations for controlled islanding in [7].

This paper is a sequel to the above two papers, and its primary purpose is to speed up OST decision-making by improving the lead time in predicting the cutset where the uncontrolled (or natural) separation of the system will occur. A cutset prediction scheme using PMU data is presented in [8]. The scheme first detects an OOS condition using the time series of bus voltage angle and its rate of change. Subsequently, dynamic equivalencing of coherent generators is performed to obtain a two-terminal equivalent of the power system. Then, a grouping criterion is used to identify the buses in each island. The lines which have their ends in different islands are determined to be the cutset. In the work of [6], the evolution of electrical centers on transmission lines was tracked using PMU data. An electrical center [9] is a transient zero voltage phasor on a transmission line that arises during an OOS condition. It can be tracked by monitoring the minimum voltage on the transmission line, and angular difference across the line. During electrical centre formation, the minimum voltage approaches zero, and the angular difference across the line approaches 180°. PMUs located at both ends of the transmission line can directly measure the angular difference, and the minimum voltage can be estimated from the distributed transmission line model. The work of Swati et al. [6] introduces a normalized ${V_{\mathit{min}}}_{\mathit{pu}}-{\delta }_{\mathrm{sr}}$ plane on which a distance relay characteristic can be mapped. In this plane, not only is it easy to separate a fault from a swing but, it is also possible to reliably predict the time to zone 3, 2, and 1 encroachment by an unstable power swing. Being a PMU based algorithm, it automatically adapts to any changes in the power system (such as generator addition, transmission line addition), and does not require transient stability studies. Hence, the scheme provides a significant advantage over the existing R-Rdot relay [10] or blinder-based schemes [5] in which there is a possibility of misclassification of an OOS condition. Both the situations viz., either classifying stable oscillations as unstable or unstable oscillations as stable, have high costs. As such, it is better to design schemes using real-time PMU data.

In [7], it was shown that the zone 1 infringement prediction algorithm [6] could be used to determine the lines which will trip and cause an uncontrolled system separation during an OOS condition. Henceforth, we refer to these lines as the “natural” cutset. Each area separated by the natural cutset contains coherent groups of generators [11]. Hence, by predicting the natural cutset, the coherent groups of generators are implicitly determined without the need for a separate algorithm. However, a lacuna of out-of-step prediction schemes ([6], [11]) is that all the natural cutset lines are not predicted at the same instant. For example, it was shown in [11] that when a 3-$\varphi$ fault is simulated at bus 33 of the 10-generator system, the time between instability predictions on the first and the last lines of the natural cutset is 16 cycles. Similarly, in the simulations on the 16-generator system reported in [7], it was shown that the time between predictions of electrical center formation on the first and last lines of the natural cutset was 240 ms. As such, it is apparent that while an OOS condition is predicted well in advance, the natural cutset is only known 240 ms later. Such a delay is significant during OST. This phenomenon is due to the fact that electrical centers evolve at different speeds on different lines of the natural cutset. Time is of the essence during OST; every millisecond earned counts. Hence, if all the lines of the natural cutset can be predicted right at the instant of first electrical center prediction, then it increases the time available for OST.

This paper aims to show that by application of data science and graph theory, we can predict the natural cutset at the instant of first electrical center prediction. Unlike the method of [8], it does not require identification of coherent groups of generators and determination of their dynamic equivalents. The proposed scheme predicts the natural cutset by employing a clustering algorithm on the time series of bus voltage angle difference across each line, and recursive application of max-flow min-cut algorithm (from graph theory) on a reduced graph of the power system. The reduced graph is a consequence of the dynamics of the system during an OOS condition. The scheme is generic and can be used in conjunction with controlled islanding schemes proposed in the literature, e.g., [7], [12], [13], [14]. Being a PMU based method, it is fast, adaptive, and appropriate for real-time control applications.

The organization of the rest of the paper is as follows. Section 2 describes the two stages of the proposed scheme. Section 3 presents the results of simulations performed on the 10-generator system with 39 buses, 46 branches (includes transmission lines and transformers), and 6125 MW load [11], 16-generator system with 68 buses, 86 branches, and 18034 MW load [15], [16], and the All India test system with 7242 buses, 12474 branches, and 117 GW load [17]. Section 4 concludes the paper.