Reactive Power Generation Limits Research Articles

A Novel FFHE-Inspired Method for Large Power System Static Stability Computation

This article proposes a novel method termed HEAP for fast and reliably computing nose points, tracing the entire PV curve, and assessing static stability limits. Here, the prefix “HE” in HEAP refers to (fast and flexible) <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</u> olomorphic <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</u> mbedding, and “AP” is short for <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</u> rc-length <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</u> arametrization. This novel method uses an arc-length parametrization and piecewise approximants that enable it to have the favorable feature of Continuation Power Flow that can pass through the nose point without numerical difficulties. Another outstanding feature of the proposed method HEAP is its computational efficiency by enabling the accurate approximation over a long interval of the parameter (i.e., a large step size). This is because of the large convergence region of HEAP. The existing methods for similar tasks usually suffer from several issues such as empirical criteria for detecting nose points, small convergence regions of correctors, numerous intermediate points, and large memory space consumption. These issues are well addressed by HEAP. To examine its numerical performance, HEAP is tested on various power system models with as many as 70,000 buses, and numerical results substantiate the outstanding features of HEAP. Depending on intended applications (e.g., only locating the nose point or fully tracking the curve), two tailored approaches are devised to effectively derive numerical solutions. In comparison with the continuation-based power flow method, HEAP attains speedups of 3x to 300x and notably attains speedups of at least 19x for all large test cases with 10,000 or more buses. The continuation-based power flow method fails in several large test cases, however, all of which are successfully solved by HEAP. After enforcing the generator reactive power limit, HEAP also produces the same accurate results as the continuation-based power flow method.

Novel models of power system components for implicit solution of the adjusted power flow problem

AbstractThe solution of the adjusted power flow problem involves handling power system components whose control characteristics possess operational limits. Examples include generator reactive power limits, tap-changing and phase-shifting transformers, and FACTS devices. While the conventional method involves checking for limit violations in an outer loop drawn around the unadjusted power flow problem being solved by the Newton-Raphson (NR) method, for iterative processes, it is desirable to have smooth, continuously differentiable models implicitly handled within a single loop. A novel formulation for a subset of devices is presented for implicit handling within power flow. The steady state characteristics of tap-changing and phase-shifting transformers, and FACTS devices SVC and STATCOM, can be described using the “cut function”, a piecewise linear function traditionally employed in neural networks. A new approximation of the cut function is used for formulating novel equations describing the steady state characteristics. An augmented set of equations is formed and solved by the NR method, eliminating the need of an outer loop. The efficacy of the proposed method is demonstrated by employing it for plotting bus voltage profiles and determining maximum loadability of test systems. Comparisons with the conventional method show that significant savings in computation can be achieved.

Measurement-Based Transmission Capability Estimation of Power Grid Using Load Response-Based Equivalent Model

In this paper, the load response-based equivalent model is proposed to develop a more sturdy method for the transmission capability estimation of the power grid. Based on real-time phasor measurement unit (PMU) measurements, the power grid is modelled as the multi-port equivalent model based on the coupled single-port models. The associated critical equivalent branch in the multi-port model is identified and modified by the shaping factor to construct the proposed model. According to the modification, the dissimilarity of the load response index between the critical equivalent branch and the approximate profile of the actual load voltage can indeed be reduced to obtain the perfect matching between the critical load voltage and the actual load voltage. Accordingly, the accurate and sturdy transmission capability estimation can be achieved in the proposed model. Moreover, the proposed model is further extended to design a complete solution algorithm for the limit-induced transmission capability estimation considering generator reactive power limits. Simulations on IEEE 14-bus and IEEE 118-bus test systems are presented to validate the accuracy and the sturdiness of the proposed method.

An Interval Arithmetic-Based Power Flow Algorithm for Radial Distribution Network with Distributed Generation

This paper presents a primary distribution system power flow analysis in the presence of uncertainties in distributed generation and loads. The algorithm is based on a backward/forward sweep power flow algorithm with power flow updates. The uncertainties are modelled by real compact intervals based on interval arithmetic. A simple and interactive method is used to consider the generator bus voltage controls and reactive power limits. Simulations are presented on a 69-bus, a 104-bus and a 282-bus test distribution system to verify the effectiveness of the proposed method. The power flow solution bounds obtained by the proposed algorithm are compared to those calculated using a Monte Carlo simulation. The results confirm the efficiency of the proposed method which makes it promising to solve real problems of power flow analysis in distribution feeders.

Automatic schemes for including generator Q and transformer tap limits in the fast decoupled load flow method

This study proposes a modified formulation for the popular fast decoupled load flow method to facilitate automatic incorporation of reactive power flow related constraints, i.e. generator reactive power and in-phase transformer tap limits. This formulation has been developed by viewing each device constraint as a set of complementary conditions and adopting the complementarity framework to define one equation to represent this set. The original set of load flow equations is augmented with this set of new equations representing the device constraints and solved to get the adjusted solutions directly. This approach is a significant departure from all the earlier approaches. The earlier approaches generally adopt a two-stage scheme. In the first stage, an approximate unadjusted solution is obtained and in the next stage, adjustments are attempted by ad hoc schemes. The new formulation presented here permits handling both the reactive power related constraints simultaneously. However, it can also be used in situations where only one type of adjustment is needed. Two alternate algorithms in complementarity framework based on mixed complementarity problem and non-linear complementarity problem formulations are presented here. Simulation results are presented to provide evidence of the impressive performance of the new algorithms as compared with the existing ones.

A generalized short-term unit commitment approach for analyzing electric power and natural gas integrated systems

This paper proposes a generalized short-term unit commitment approach for optimizing the hourly thermal generation scheduling by considering the existing interdependence between natural gas and electricity infrastructures. This generalized approach is formulated as a mixed-integer nonlinear optimization problem where a multi-period optimal gas and alternating current power flow model is incorporated into the thermal unit commitment problem. Contrary to all other proposals that ignore the reactive power dispatch and alternating current electricity network constraints for solving the unit commitment problem that considers the integrated electricity-natural gas system, the proposed solution approach simultaneously co-optimizes the active and reactive power scheduling and dispatch, while taking into account the set of physical and operational constraints associated with each infrastructure. This set of constraints includes reactive power generation limits, nodal voltage magnitude limits and dynamic gas flow constraints. The solution is obtained by decomposing this generalized optimization problem into two mutually connected optimization subproblems: one spatially separable related to the unit commitment problem and the other temporally separable associated with the unified co-optimization of both energy systems, which are sequentially solved until the same hourly generation dispatch in both subproblems is obtained. Hence, this solution is optimal for the unit commitment problem and the optimal gas and power flow problem. Study cases on two multi-energy systems are presented to numerically illustrate the suitability and main characteristics of the proposed approach.

A new perspective on wind integrated optimal power flow considering turbine characteristics, wind correlation and generator reactive limits

The operation of power system is facing newer challenges due to inherent uncertainty in wind generation. The current study fills the gap in the available literature by combining the nature of uncertainty of wind power in terms of varying wind speed correlation, turbine characteristics and generator reactive power limits. Wind speed correlation is modelled using Weibull distribution and Gaussian copula; the turbine characteristics considered are rated power and turbine performance index (TPI); the generators considered are doubly fed induction generators (DFIG) whose reactive power limits are varied based on converter current limits and grid voltage conditions. The above variations are combined to simulate a large number of dependent wind power scenarios which are then incorporated as two wind farms replacing the conventional generators at bus 11 and bus 13 in a modified IEEE 30 bus 6 generator system. Optimal power flow solution is obtained for each of the scenarios and the impact on generation cost, emission, losses, capacity factor and voltage profile is investigated. Another novelty in this work is computation of voltage violation index (VVI) for varying correlation and turbine characteristics when the system is subjected to contingency states of load increase, line outage and their combination.

Tools for handling steady‐state under‐frequency regulation in isolated microgrids

This study presents two approaches to handling under-frequency regulation in isolated microgrids. The first one is a governor power flow (PF) model in which the generators steady-state governor equations are modeled into a full Newton PF formulation resulting in an augmented sparse linearised system of equations to be solved at each iteration. As a result, it is possible to evaluate the under frequency problem in the case of microgrid islanding as well as to set the reference bus angle to evaluate the possibility of reconnection to the main grid. The second approach presents an optimal PF (OPF) formulation in which the generators governor equations are considered as additional equality constraints to determine the minimum amount of load shedding to keep the system frequency between specified limits. In both methods, it is also used an equation that provides voltage regulation in a droop-based control. The reactive power generation limits in the OPF approach are bounded by a proposed complementarity constraint-based method adapted for the generators' droop-controlled terminal voltage. The proposed approaches are evaluated and validated through the study of the EHV1 Network, a 61-bus 33/11-kV radial distribution system, and the New England test system.

Global Approximation of Static Voltage Stability Region Boundaries Considering Generator Reactive Power Limits

Power system static voltage stability region boundary (SVSRB) is a complicated hypersurface in parameter space. Due to inequality constraints such as generator reactive power limits, different critical points on the SVSRB may be related to different groups of active constraints and can be associated with different types of loadability limit, which makes it difficult to approximate the whole SVSRB at once or assemble many local approximations of the SVSRB. To overcome the difficulty, this paper proposes an approach for globally approximating the whole SVSRB considering generator reactive power limits at one go. First, a parametric optimization model incorporating all inequality constraints is formulated to describe the SVSRB, where the optimal solutions are the critical points on the SVSRB. The optimality condition, i.e., parametric Karush–Kuhn–Tucker conditions (KKT conditions), is also derived. Then, by applying the Galerkin method to the parametric KKT conditions in an interior-point-method-like manner, the whole SVSRB is approximated and represented using a single polynomial expression. Case studies in a 10-bus system and IEEE 300-bus system verify the effectiveness and accuracy of the proposed method.

GECM-Based Voltage Stability Assessment Using Wide-Area Synchrophasors

Voltage instability is a crucial issue in the secure operation of power grids. Several methods for voltage stability assessment were presented. Some of them are highly computationally intensive, while others are reported not to work properly under all circumstances. This paper proposes a new methodology based on the generator equivalent circuit model (GECM) and the phasor measurement unit (PMU) technology for online voltage stability monitoring of a power grid. First, the proposed methodology utilizes synchronized phasor (synchrophasor) measurements to determine the impedance parameters of a transmission grid by means of the recursive least squares (RLS) algorithm. Furthermore, it incorporates the dynamic models of generators to handle the cases with generator reactive power limit violations. After that, an enhanced voltage stability index with GECMs incorporated is developed for reliable and accurate voltage stability assessment. The proposed methodology was first demonstrated on several standard IEEE power systems, and then applied to a practical power system, the Taiwan power (Taipower) system. The test results demonstrate the flexibility and effectiveness of the proposed methodology.

ATC using FACTS Devices in Deregulated Power Systems

A Repeated Power Flow with FACTS devices including ATC is used to evaluate the feasible ATC value within real and reactive power generation limits, line thermal limits, voltage limits and FACTS operation limits. An IEEE-30 bus system is used to demonstrate the effectiveness of the algorithm as an optimization tool to enhance ATC. A Genetic Algorithm technique is used for validation purposes. Introduction of FACTS devices in a right combination of location and parameters could enhance ATC and Ant Colony optimization can be efficiently used for this kind of nonlinear integer optimization.

Alternative LP and SOCP Hierarchies for ACOPF Problems

The alternating current optimal power flow (ACOPF) problem optimizes the generation and the distribution of electric energy taking into account the active and the reactive power generation limits, demand requirements, bus voltage limits, and network flow limits. The ACOPF problem can be formulated as a nonconvex polynomial program that is generally difficult to solve due to the nonlinear power flow constraints. A recently proposed approach to globally solve the ACOPF problem is through the formulation of a hierarchy of semidefinite programs that are computationally challenging to solve for large-scale problems. In this paper, we explore a solution approach that alleviates this computational burden by using hierarchies of linear and second order cone programs and by exploiting the network structure of the transmission grid. Furthermore, we show that the first level of the second order cone hierarchy is equivalent to solving the conic dual of the approximation that was recently proposed in the literature, which provides the optimal solution of the ACOPF problem for special network topologies.

Efficiency Improvements in Meta-Heuristic Algorithms to Solve the Optimal Power Flow Problem

AbstractThis paper proposes the efficient approaches for solving the Optimal Power Flow (OPF) problem using the meta-heuristic algorithms. Mathematically, OPF is formulated as non-linear equality and inequality constrained optimization problem. The main drawback of meta-heuristic algorithm based OPF is the excessive execution time required due to the large number of power flows needed in the solution process. The proposed efficient approaches uses the lower and upper bounds of objective function values. By using this approach, the number of power flows to be performed are reduced substantially, resulting in the solution speed up. The efficiently generated objective function bounds can result in the faster solutions of meta-heuristic algorithms. The original advantages of meta-heuristic algorithms, such as ability to handle complex non-linearities, discontinuities in the objective function, discrete variables handling, and multi-objective optimization, etc., are still available in the proposed efficient approaches. The proposed OPF formulation includes the active and reactive power generation limits, Valve Point Loading (VPL) and Prohibited Operating Zones (POZs) effects of generating units. The effectiveness of proposed approach is examined on IEEE 30, 118 and 300 bus test systems, and the simulation results confirm the efficiency and superiority of the proposed approaches over the other meta-heuristic algorithms. The proposed efficient approach is generic enough to use with any type of meta-heuristic algorithm based OPF.

Estimating the Voltage Stability Margin Using PMU Measurements

This paper presents a new method based on phasor measurement units (PMUs) for the estimation of voltage stability margin in a power system to increase operator's situational awareness. The method assumes a PMU measurement preprocessing technique as a priori in order to eliminate data inconsistency and uncertainty caused by random load disturbances. The measurements are then used in the computation of voltage stability margin based on the coupled single-port Thevenin equivalent model and the cubic spline extrapolation technique. Moreover, some practical operating constraints such as the generator reactive power limits are taken into account for practical assessment of the method's performance. Extensive case studies conducted on several standard IEEE test systems are used to demonstrate the effectiveness of the proposed method.

Efficiency improvements in meta-heuristic algorithms to solve the optimal power flow problem

This paper presents three efficient approaches for solving the Optimal Power Flow (OPF) problem using the meta-heuristic algorithms. Mathematically, OPF is formulated as non-linear equality and inequality constrained optimization problem. The main drawback of meta-heuristic algorithm based OPF is the excessive execution time required due to the large number of load flows/power flows needed in the solution process. The proposed efficient approaches uses the concept of incremental power flow model based on sensitivities, and lower, upper bounds of objective function values. By using these approaches, the number of load flows/power flows to be performed are substantially, resulting in the solution speed up. The original advantages of meta-heuristic algorithms, such as ability to handle complex non-linearities, discontinuities in the objective function, discrete variables handling, and multi-objective optimization, are still available in the proposed efficient approaches. The proposed OPF formulation includes the active and reactive power generation limits, Valve Point Loading (VPL) effects and Prohibited Operating Zones (POZs) of generating units. The effectiveness of proposed approaches are examined on the IEEE 30, 118 and 300 bus test systems, and the simulation results confirm the efficiency and superiority of the proposed approaches over the other meta-heuristic algorithms. The proposed efficient approaches are generic enough to use with any type of meta-heuristic algorithm based OPF.

Distributed Monitoring of Voltage Collapse Sensitivity Indices

The assessment of voltage stability margins is a promising direction for wide-area monitoring systems. Accurate monitoring architectures for long-term voltage instability are typically centralized and lack scalability, while completely decentralized approaches relying on local measurements tend towards inaccuracy. Here we present distributed linear algorithms for the online computation of voltage collapse sensitivity indices. The computations are collectively performed by processors embedded at each bus in the smart grid, using synchronized phasor measurements and communication of voltage phasors between neighboring buses. Our algorithms provably converge to the proper index values, as would be calculated using centralized information, but but do not require any central decision maker for coordination. Modifications of the algorithms to account for generator reactive power limits are discussed. We illustrate the effectiveness of our designs with a case study of the New England 39 bus system.

A modified Newton–Raphson load flow scheme for directly including generator reactive power limits using complementarity framework

A modified Newton–Raphson (NR) load flow scheme which automatically incorporates generator reactive power limits is proposed. Traditionally, handling generator reactive power limits is considered as an adjusted load flow solution and this adjustment is carried out through bus type switching method. Incorporating bus type switching in a NR algorithm is not straight forward, as it involves several subjective decisions and hence, there is no commonly used implementation. The modified NR scheme proposed here combines this adjustment feature in the load flow problem formulation directly. This is achieved by augmenting the set of complementary reactive power relations at voltage controlled buses with the conventional set of active power balance equations at all buses and reactive power balance equations at load buses in a Mixed Complementarity Problem (MCP) framework. Effectiveness of the scheme has been demonstrated through extensive simulations considering a number of test systems.

Probabilistic load flow incorporating generator reactive power limit violations with spline based reconstruction method

The increase in the penetration of intermittent generation and uncertainty in load patterns calls for the need to include these uncertainties in the conventional power flow programs. Consideration of the generator reactive power limit violation is an essential aspect in load flow studies for planning. In this paper, a probabilistic load flow method is proposed in which the violation of the reactive power limits of the generators are adequately represented. The seven point estimate method along with the spline based reconstruction technique is proposed for constructing the probability density function of the resulting multimodal distributions. The proposed load flow method has been tested on the IEEE-118 bus and IEEE-300 bus test systems for unimodal and multimodal load distributions, with and without correlation, and the accuracy of the results has been validated by comparing these results with those obtained by Monte Carlo simulation studies. Further, the effect of slack bus power limits has also been studied in this work.

A direct method based on tensor calculation to determine maximum loadability power flow solutions

In this paper, the determination of critical loadability points of the power flow equations is formulated as an optimisation problem. A quadratic parameterisation scheme is used to model the load change, which is equivalent to implicitly including a non-negativity constraint in the load variation. The power flow equations are expressed in rectangular coordinates. This is suitable to exploit the second order information (tensor term) of the equations representing the optimality conditions. The use of this term improves the convergence of the iterative process and facilitates the manipulation of the reactive power generation limits. Simulation results obtained with a number of power systems, including real networks, are used to illustrate the main features of the proposed methodology.

Functional Approximation of Power System Steady-State Voltage Stability Limits by Artificial Neural Networks

The estimation of steady-state voltage stability limits represented by the critical value of a voltage stability index (VSI) in power flow-based electric energy system models may be a very difficult task, which might render their applicability impractical. When voltage collapse is associated with a generation bus reaching one of its reactive power generation limits, critical values of VSIs based on properties of the system Jacobian are difficult to be predicted without actually solving the maximum loading problem. In this context, this paper proposes the functional approximation of power system steady-state voltage stability limits, represented by the critical values of the minimum singular value (MSV) and tangent vector norm (TVN) indices, by means of artificial neural networks (ANNs). To construct a steady-state voltage stability boundary, the maximum loading problem was solved for a normalized even distribution of generation and load increase patterns using an optimal power flow-based approach. With these collapse points, the MSV and TVN indices were calculated and then used in the training and testing processes of the ANNs. A 6-bus system was used for carrying out this study. Results show that the proposed architecture of ANNs can be readily applied to the functional approximation of these VSIs at the voltage collapse.