Generation Shift Factor Research Articles

Tractable Stochastic Unit Commitment for Large Systems During Predictable Hazards

Many foreseeable natural hazards, including extreme weather events, lead to an outage of multiple transmission lines. Although such outages can be predicted in advance, there is a great deal of uncertainty in these predictions. To appropriately use the failure estimations in power system scheduling, this paper formulates a stochastic unit commitment (SUC) problem with explicit modeling of the predicted outages. The formulated problem, however, is extremely computationally-demanding, as the uncertainty is placed on the binary status of transmission lines. This paper, then, develops a computationally efficient algorithm to solve the formulated SUC for large-scale systems. The algorithm employs generation shift factors to enable rapid calculation of power flows. Additionally, flow canceling transactions are used to model multiple line outages without having to recalculate shift factors. Finally, critical constraints are iteratively detected and added to the problem. This approach substantially reduces the size of the problem, which helps computational tractability. The effectiveness of the developed algorithm is demonstrated through simulation studies on the Texas 2000-bus test system. The algorithm is used to minimize the lost load during a hypothetical hurricane. The results show that the algorithm is computationally tractable and can effectively identify a preventive dispatch, leading to a substantial reduction in power outages.

A network science-based k-means++ clustering method for power systems network equivalence

Network equivalence is a technique useful for many areas including power systems. In many power system analyses, generation shift factor (GSF)-based bus clustering methods have been widely used to reduce the complexity of the equivalencing problem. GSF captures power flow on a line when power is injected at a node using bus to bus electrical distance. A more appropriate measure is the one which captures what may be called the electrical line distance with respect to a bus termed as relative bus to line distance. With increase in power transactions across different regions, the use of relative bus to line distance becomes appropriate for many analyses. Inspired by the recent trends in network science on the study of network dynamics based on the topological characteristics of a network, in this paper, we present a bus clustering method based on average electrical distance (AED). AED is independent of changes in location of slack bus and is based on the concept of electrical distance introduced in the context of molecular chemistry and pursued later for applications in social and complex networks. AED represents the AED from a bus to buses of the transmission line of interest. We first propose an AED-based method to group the buses into clusters for power systems network equivalence using k-means clustering algorithm integrated with silhouette analysis. One limitation of this method is that despite its speed, sometimes it may yield clusters of inferior quality compared to the optimal solution. To overcome this limitation, we next present our improved clustering method which incorporates a seeding technique that initializes centroids probabilistically. We also incorporate a technique in our method to find the number of clusters, k, to be given as input to our clustering algorithm. The resulting algorithm called AED-based k-means++ clustering method yields a clustering that is O(logk) competitive. Our network equivalence technique is next described. Finally, the efficacy of our new equivalencing technique is demonstrated by evaluating its performance on the IEEE 300-bus system and comparing that to the performance of our AED-based method (Sharma et al. in Power network equivalents: a network science-based k-means clustering method integrated with silhouette analysis. In: Complex networks and their application VI, Lyon, France. p. 78–89, 2017) and the existing GSF-based method.

Continuous-Time Locational Marginal Price of Electricity

Modern electricity markets with large penetration of renewable energy resources require fair and accurate pricing methods to elicit generation flexibility and foster competition in electricity markets. This paper proposes the fundamental theory and closed-form formulas for continuous-time locational marginal price (LMP) of electricity, which more accurately integrates the spatio-temporal variations of load and operational constraints of power systems in the electricity price calculation. This paper first formulates the network-constrained generation scheduling and pricing problems as continuous-time optimal control problems using two methods for modeling transmission network, i.e., Theta and generation shift factor (GSF) methods. The continuous-time network-constrained scheduling and pricing problems minimize in their objective functional the total operation cost of power systems over the scheduling horizon subject to generation and transmission constraints. The closed-form continuous-time LMP formulas are derived for each transmission network model, which explicitly include terms that reflect the simultaneous spatio-temporal impacts of transmission flow limits and intertemporal generation ramping constraints in LMP formation. A scalable and computationally efficient function space solution method is proposed that converts the continuous-time problems into mixed integer linear programming problems with finite-dimensional decision space. The proposed solution method enables high-fidelity solution of transmission-constrained scheduling and pricing problems in higher dimensional spaces, while including as a special case the current discrete-time solutions. The proposed models are implemented on a three-bus system and the IEEE reliability test system, where the proposed models showcase more accuracy in reflecting the impacts of fast net-load variations over discrete-time counterparts.

Transmission Contingency-Constrained Unit Commitment with High Penetration of Renewables via Interval Optimization

Reliability is an overriding concern for power systems that involve different types of uncertainty including contingencies and intermittent renewables. Contingency-constrained unit commitment (CCUC) satisfying the “N – 1 rule” is extremely complex, and the complexity is now compounded by the drastic increase in renewables. This paper develops a novel interval optimization approach for CCUC with N – 1 transmission contingencies and renewable generation. A large number of transmission contingencies are innovatively described by treating corresponding generation shift factors (GSFs) as uncertain parameters varying within intervals. To ensure solution robustness, bounds of GSFs and renewables in different types of constraints are captured based on interval optimization. The resulting model is a mixed-integer linear programming problem. To alleviate its conservativeness and to further reduce the problem size, ranges of GSFs are shrunk through identifying and removing redundant transmission constraints. To solve large-scale problems, Surrogate Lagrangian Relaxation and branch-and-cut (B&C) are used to simultaneously exploit separability and linearity. Numerical results demonstrate that the new approach is effective in terms of computational efficiency, solution robustness, and simulation costs.

Preventive and Emergency Control of Power System for Transient Stability Enhancement

This paper presents preventive and emergency control measures for on line transient stability (security) enhancement. For insecure operating state, generation rescheduling based on a real power generation shift factor (RPGSF) is proposed as a preventive control measure to bring the system back to secure operating state. For emergency operating state, two emergency control strategies namely generator shedding and load shedding have been developed. The proposed emergency control strategies are based on voltage magnitudes and rotor trajectories data available through Phasor Measurement Units (PMUs) installed in the systems. The effectiveness of the proposed approach has been investigated on IEEE-39 bus test system under different contingency and fault conditions and application results are presented.

Real-time pricing program in a smart grid environment

Improving system efficiency and reliability is motivating countries to design and execute different types of time of use demand response programs. However, certain deficiencies prevent these programs from reaching their goals. Smart meters as a mechanism could help the electric system to reach the highest demand-side management goals which are inaccessible through today’s methods. On the other hand, realization of smart meters in a system would be very costly. In this situation, identifying the most influential buses to implement the infrastructures of a smart grid is of highest importance. In this paper, after a short overview of demand response programs and problems facing them, a smart meter is introduced as a solution to these problems. As a test grid, the IEEE 57-bus network has been chosen to compare the results of the execution of a normal time of use program and real-time pricing program available in a smart grid. In order to execute the mentioned programs in this system, 10 buses have been selected as the most influential buses using a generation shift factor method. The execution of time of use and real-time pricing programs on the selected buses have been simulated using a demand response model. Finally, the time of use program and the real-time pricing program in a smart grid environment have been compared with respect to load shape modification, load factor, price curve, and ‘Expected Power Not Supplied’.

Blocking of Zone 3 Relays to Prevent Cascaded Events

Defense systems are needed to prevent catastrophic failures of a power grid due to cascaded events. Cascaded events can be attributed to improper operations of protective relays. The most challenging problem for the design and implementation of a defense system is the performance in accuracy and speed in a real-time environment. Protective devices are normally designed to operate fast in order to isolate the fault(s). This paper proposes a new methodology to distinguish line overloads from actual faults for distance relays. In order to distinguish between line flow transfers from a line outage and an actual fault, the line outage distribution factor (LODF) and generation shift factor (GSF)-based power flow estimation method, and a secure peer-to-peer (P2P) communication structure are adopted. Computer simulations of cascaded events for a six-bus system and the Korean power grid have been performed to establish the feasibility of the proposed scheme.

Zone 3 relay blocking scheme to prevent cascaded events

Defense systems are needed to prevent catastrophic failures of a power grid due to cascaded events. Cascaded events can be attributed to improper operations of protective relays. The most challenging problem for the design and implementation of a defense system is the performance in accuracy and speed in a real time environment. Protective devices are normally designed to operate fast in order to isolate the fault(s). This paper proposes a new methodology to distinguish line overloads from actual faults for distance relays. In order to distinguish between line flow transfers from a line outage and an actual fault, the line outage distribution factor (LODF) and generation shift factor (GSF) based power flow estimation method, and a secure peer to peer (P2P) communication structure are adopted. Computer simulations of cascaded events for a 6-bus system and the Korean power grid have been performed to establish the feasibility of the proposed scheme.

Fast Linear Contingency Analysis

This paper reports on a linear contingency analysis program that computes linearized real power flow changes resulting from branch outages and generation or load changes. A modern formulation has been adopted based on the relation ΔP = Δθ rather than using current injections and the bus admittance matrix. For maximum speed in processing such a large number of contingencies, the explicit inverse (triangular portion) of H is computed by the back substitution method. Multiple branch contingencies require essentially the same time as would the same number computed individually. Multiple generation or load changes are handled most efficiently by a single repeat solution for Δθ using the sparse factors of H and a sparse ΔP vector. Explicit branch distribution and generation shift factors are computed only for display to the operator.