Rajeev Kumar Gajbhiye

Optimal Multistage Scheduling of PMU Placement: An ILP Approach

This paper addresses various aspects of optimal phasor measurement unit (PMU) placement problem. We propose a procedure for multistaging of PMU placement in a given time horizon using an integer linear programming (ILP) framework. Hitherto, modeling of zero injection constraints had been a challenge due to the intrinsic nonlinearity associated with it. We show that zero injection constraints can also be modeled as linear constraints in an ILP framework. Minimum PMU placement problem has multiple solutions. We propose two indices, viz, BOI and SORI, to further rank these multiple solutions, where BOI is bus observability index giving a measure of number of PMUs observing a given bus and SORI is system observability redundancy index giving sum of all BOI for a system. Results on IEEE 118 bus system have been presented. Results indicate that: (1) optimal phasing of PMUs can be computed efficiently; (2) proposed method of modeling zero injection constraints improve computational performance; and (3) BOI and SORI help in improving the quality of PMU placement.

Min-Max Fair Power Flow Tracing for Transmission System Usage Cost Allocation: A Large System Perspective

Power flow tracing has been suggested as an approach for evaluating 1) transmission system usage (TSU) cost and 2) loss (MW) cost for generator and load entities in the system. Recently, optimal power flow tracing methods have been proposed to “explicitly” model fairness constraints in the tracing framework. This paper, further, strengthens the tracing-compliant min-max fair cost allocation approach. The min-max model proposed in this paper is robust. It addresses concerns like scalability, numerical stability and termination in a finite number of steps while searching the optimal solution. We also propose a methodology to model DISCOMs and GENCOs as coalition within min-max framework. Case studies on an all India network of 1699 nodes and comparison with average participation and marginal participation methods bring out the better conflict resolution feature of the proposed approach. A method to model HVDC lines within the marginal participation scheme is also proposed. Quantitative and qualitative comparison of various TSU cost allocation methods on such a large system is another noteworthy contribution of the paper.

An Expert System Approach for Multi-Year Short-Term Transmission System Expansion Planning: An Indian Experience

This paper proposes an expert system approach to short-term expansion planning (STEP). The rules which drive STEP can be classified into MW, MVAR, and ampacity management rules. MW and ampacity management rules are for alleviating transmission line congestion. Reactive power management is required for voltage control at load busses, conformity to the capacity curve of the generators, and containing the MW losses within acceptable limits. Embedding reactive power management in STEP is a challenging task since ac load flow may not converge in absence of proper reactive power planning and load modeling. Therefore, we also propose enhancements to the fast decoupled load flow algorithm for on-the-fly reactive power management. The enhanced algorithm not only can detect divergent load flow scenarios but also self-correct it by restarting the whole process with greater degree of freedom in reactive power controls. The proposed approach leads to development of an automated tool for STEP which has the capability to work, even with incomplete information. A simple method for evaluating location and requirement of shunt reactor is also proposed. By analysis and comparative evaluation, we show that the proposed system can arrive at a solution which is close to optimal. Results on the Western Regional Grid of India with an approximate load of 28 000 MW and 1200 nodes are presented to demonstrate effectiveness of the proposed approach.

Computationally Efficient Methodology for Analysis of Faulted Power Systems With Series-Compensated Transmission Lines: A Phase Coordinate Approach

A capacitor in series with a transmission line is protected from overvoltage due to a large fault current by a nonlinear metal-oxide varistor (MOV) connected in parallel. Fault analysis, as well as the evaluation of performance of the transmission protection system, in the presence of MOV action becomes complex because (1) v-i characteristics of the MOV are nonlinear; (2) un- symmetrical MOV action for unsymmetrical faults will introduce coupling in sequence networks; and (3) MOV action will influence voltage or current inversion phenomenon. This paper presents a computationally efficient and simple methodology for fault analysis wherein the linear part of the network is modeled by an equivalent multiport Thevenin network. The proposed approach handles nonlinearity in fault analysis efficiently. It also provides an elegant approach to model unbalance in a network due to MOV action. The proposed approach can be used to determine relays prone to voltage or current inversion. Results on a real-life 716-bus Indian system illustrate the efficiency of the proposed approach.

Computation of Optimal Break Point Set of Relays—An Integer Linear Programming Approach

We propose an integer linear programming (ILP) formulation for the minimum relay break point set (BPS) computation. Subsequently, in the ILP framework, we propose an alternate maximum-independent relay BPS formulation with the intention of minimizing dependency within the BPS. We show that 1) in practice, the relaxed version of the ILP suffices to obtain an integral vertex and 2) the relaxed version of the ILP can be efficiently solved by the dual-simplex method. The performance of the proposed algorithm is compared and contrasted with existing algorithms. Case studies on various test systems show the efficacy of the proposed approach.

Analysis of faulted power systems in three phase coordinates - a generic approach

Analysis of faulted power systems in 3-phase coordinates is desirable when dealing with unbalanced networks and complex faults. Thevenins model in 3-phase domain is well-known for shunt faults. However, lack of generic circuit model for series and simultaneous faults is an impediment, as it sacrifices both simplicity and computational efficiency. In this paper, we extend this approach to arbitrarily complex faults. Case studies with complex faults on two example systems demonstrate the claims made in the paper

A simple and efficient approach to determination of minimum set of break point relays for transmission protection system coordination

Coordination of relays in a meshed system is an iterative process. It involves finding a set of break point relays. In this paper, we propose a new polynomial time approximation algorithm for computation of the minimum break point relay set. In turn, procedure for computation of minimum break point relays requires systematic enumeration of all possible simple loops in the system. Therefore, we also propose a simple method for enumerating all possible loops. The advantages of proposed approach are (1) simplicity and (2) reduced computational complexity. Case studies on various topologies demonstrate the utility of the proposed approach

Short term portfolio optimization for load serving entity considering multiple exchanges and ramping constraints

The typical requirement of supply-demand balance in electricity market necessitates for an LSE to incorporate corrective measures in short term. In case of surplus, either few of the contracts may have to be backed down and/or excess power has to be sold in short term market(s). In contrast, deficit scenario has to be managed by procuring additional requirement again from short term market(s). The volatility, and hence risk, associated with prices in such market motivates LSEs to look for an optimal strategy based on portfolio management. While doing so, in addition to conventional approach, one has to comply by regulations as well as factor for technical constraints. In this paper, we model prevention of arbitrage and ramping constraints akin to unit commitment problem.

New bid structures for power exchange with modelling in ILP framework

Block bid were introduced in power exchanges to allow generators with high fixed cost component (start-up and shut-down cost) participate in the market. However, block bid has been designed with very simple structure. Rigid structure in block bid often leads to them being rejected paradoxically. With this factor as motivation, we present new bid structures which retains objective of block bid, but brings in more flexibility, resulting in more liquidity in market.

Facilitating emission trade within power exchange: Development of conceptual platform

Electricity sector is one of the major contributor of emission. Hence, any policy which restricts emission level will have significant impact on its functioning. As a consequence, electricity traders will have to actively participate in emission market. What it means is that electricity traders will have to trade in two separate markets, namely power and emission (or carbon). However, to be able to derive maximum benefit, trader should be able to accurately forecast prices in either of the markets. Alternatively, we propose a new scheme where emission trading is facilitated within power exchange (PX). This not only provides single trading platform for the traders but also ensures that maximum benefit is achieved for individually as well as collectively by utilizing available carbon credits optimally.