Load Flow Results Research Articles

Investigation of distribution factors for bilateral contract assessment

In deregulated power systems, several market models are prevalent as alternatives to the traditional vertically integrated utilities. Consequently transmission networks are subjected to various bilateral service contracts between customers and suppliers. These transactions adversely affect power system security, and are thus executed only as far as the system design and operating conditions permit. Therefore, fast assessment of the impact of such transactions is one of the prime responsibilities of any system operator. This paper presents a scheme for comprehensive assessment of the impact of multiple, simultaneous bilateral transactions on the operating state of the transmission network. It employs improved distribution factors derived from the base case Jacobian matrix, for computation of voltage and real power flow (and real power loss). Results are presented for three standard test systems, and a comparison with the AC load flow results (and results obtained using DC power flow based distribution factors) shows that the method is fairly accurate. The paper is organized in the particular context of bilateral transactions, but possible applications of the proposed approach are also enumerated.

Comparative Studies on Methods of Modeling Generator Var Limit for Power-Flow Calculations

In power flow calculations, usually a generator is represented as a P V bus, and a simplified method is used to model its reactive power limit. The P Q modeling approach, which converts the generator from P V bus to P Q bus when the reactive power limit is reached, is widely accepted and used by professional load flow programs; however, in reality, a generator on the limit behaves as a constant field voltage instead of a constant reactive output. This fact has raised frequent discussions on the literature about the accuracy or errors introduced by the conventional P Q model on power flow computations. Unfortunately, the real differences between the two modeling approaches for power flow studies have not been researched by these previous efforts. The purpose of this paper is to carry out comprehensive investigation on the impact of the two modeling methods for power flow studies. They are compared from three different perspectives: impact on load flow results, impact on voltage stability margin, and convergence behavior. Based on the results, advantages and dis advantages of the two modeling approaches are discussed, and conclusions are made on the appropriate approach for representing generator var limit for load flow studies.

Emission constrained secure economic dispatch

This paper describes a methodology for secure economic operation of power system accounting emission constraint areawise as well as in totality. Davidon-Fletcher-Powell's method of optimization has been used. Inequality constraints are accounted for by a penalty function. Sensitivity coefficients have been used to evaluate the gradient vector as well as for the calculation of incremental transmission loss (ITL). AC load flow results are required in the beginning only. The algorithm has been tested on IEEE 14- and 25-bus test systems.

Load flow solution of distribution systems with voltage dependent load models

The classical constant-power load model is usually used to solve the load flow problem of a transmission or distribution system. However, the actual load of a system is not independent of voltage magnitude. Incorporation of voltage dependent load models in the load flow algorithm is essential to get better and accurate results. This paper compares the load flow results of a distribution system for various voltage dependent load models. The load flow problem of a distribution system is also formulated in terms of three sets of recursive equations so that very sophisticated voltage dependent load models can easily be incorporated in these equations. A 12.66 kV, 33-bus distribution system was used to observe the effects of load models on the load flow results. The convergence patterns of the load flow method for various load models were also compared.

An algorithm for the allocation of distribution system demand and energy losses

This paper describes a new approach to the evaluation of loss adjustment factors for distribution systems. Such factors are required for 'use of system' and wheeling calculations and reflect the amount by which purchases of energy at entry points to the system must exceed consumption at the point of use to account for the losses which occur in between. Renewed interest in cost-reflective methods of charging for losses has resulted from the deregulation of the electricity supply industry in many parts of the world. An algorithm is described which combines the use of graph theory with readily available load flow results, to assign the losses in each line or transformer within the system to the consumers supplied by it. The resulting allocation is shown to account for the voltage level, location and consumption pattern of the consumer in a way which is economically efficient. A variety of strategies for apportioning losses between multiple consumers at a given location can be implemented. The algorithm is suitable for allocating both demand and energy losses. Results on a full size distribution network are presented, and are compared with traditional published loss adjustment factors.

APPLICATION OF INERTIAL LOAD TO A LOSS OF GENERATOR POSTMORTEM

ABSTRACT The inertial load flow technique [2] is applied to a dynamic equivalent [1] derived from a NERC (North American Electric Reliability Council) data base to compute maximum tie line power flows for a 1980 MW loss of generation at the Nanticoke station in the Ontario Hydro system. The results were compared with a transient stability simulation and recorded tie line power and frequency measurements. The inertial load flow results were more accurate in capturing the filtered measurements of power flows during the first three to five seconds after a loss of generation contingency than the transient stability simulation. The transient stability simulation was shown to contain both synchronizing oscillations between generators as well as the quasi steady-state behavior captured by the filtered power measurements and inertial load flow. The inertial load flow is an excellent tool for estimating proximity to voltage collapse since the field current limiters on exciters utilize filtered measurements of the inertial response that occurs 3-5 seconds after a loss of generation contingency. The loss of voltage control and reactive generation supply due to action of field current limiters is a principle cause of loss of voltage stability in power systems. The inertial response is shown to capture a filtered estimate of the peak of the deceleration wave that propagates from the point of disturbance and would indicate whether the filtered estimate of these peak real power flows would incur sufficient filtered generator field current levels to cause field current limiters to act. Generator field current levels rise in an attempt to counteract voltage decline and increase in reactive losses caused by the peak power flows that are observed in the inertial response. The action of the field current limiter reduces field current and reactive supply to prevent thermal damage to the generator. The action of field current limiters initiates the voltage decline that can result in voltage collapse.

Investigation of fuzzy real power flow modeling with probabilistic—heuristic based information

A conceptual possibilistic framework is proposed to manage the input uncertainties encountered in steady-state real power flow analysis. This study is devoted to building the robust input framework of the possibilistic load flow (POLF) algorithm under an uncertain environment. Three probability density functions are transformed consistently into the corresponding possibilistic representations. Under the possibilistic framework, a compromise between transformation consistency and human updating experience can be satisfied. The possibility distribution function (podf) derived yields both a mean interval and a reasonable spread interval. Compared with the results of probabilistic load flow (PLF) analysis, the spread interval of the compromise line flow podf can be derived to cover only the reasonable output region and its mean interval contains most of the significant probability information. Numerical simulations for three extreme line flows in the IEEE 25-bus system indicate the feasibility of the proposed approach.

Implicit generator and SVC modelling for contingency scheduling of reactive power dispatch

In the paper, CIGRE models of generating units are used for contingency scheduling of reactive power. These models are based upon the capability curves and the reactive power margin at each automatic voltage regulator (AVR) state (normal operation, threshold or loss of voltage control after AVR reaches the limits), rather than on the commonly used PV or PQ representation for generators in load flow. These models, in effect, add a supplementary generator node behind a reactance for each machine, which simulates the behaviour of the generator AVR at each state. The models are not detailed enough to allow the simulation of transient effects but are adequate to represent the system during a slow change under steady-state operation. The salient advantage of the proposed implicit method is to preserve the factorised triangulated nodal admittance matrix used for the fast decoupled load flow [B'] and [B] for each state. This is achieved by calculating new injected powers and voltages at generating nodes and using these values for updating the solution during iteration for the final load-flow results. Simple illustrative cases for the explicit and implicit generation reactance modelling are presented. The injected power and voltage correction techniques are also used for static VAr compensator (SVC) representation, and a numerical example is given. The method was used for contingency analysis of a 620 busbar, 66 generating unit system. The technique proved to be reliable and efficient.

Bus sensitivity to load-model parameters in load-flow studies

This paper considers the sensitivity of the load-flow solution to model parameters when load models of the exponential form are incorporated. Several test systems are considered. Computational experience with Newton's method applied to solve the resulting load-flow problems is given. The effects of model parameters and system characteristics on the convergence of the method and on the resulting solutions are highlighted. Our results indicate that the higher values of model parameters yield more significant changes in the load-flow results from the conventional load-flow solution. For the same system, the effect of load modelling is more pronounced at heavier loads than at normal loads. For systems with high capacitive loads, the effects of model parameters are more significant. We also conclude that Newton's method fails to converge for cases where the capacitive effect is high combined with a high reactive-power model exponent even though the application of Newton's method to the conventional problem is successful.

SELECTION OF BUSES FOR DETAILED MODELING IN LOAD FLOW STUDIES

ABSTRACT Conventional load flow solutions are carried out assuming that the active and reactive power requirements at all load buses are independent of the voltage magnitude at the corresponding bus. While this approach yields satisfactory results in most practical cases, it has been shown that detailed modeling of the load variation with voltage may be necessary to obtain realistic load flow results. From a theoretical point of view, it appears that detailed modelling at all load buses in an electric network may be the answer. Realizing the impracticality of this proposition, the paper presents a summary, of research work carried out to examine the improvements obtained via detailed modeling of loads in a number of test systems. From our experimentation we have found that it is only necessary to deal with only a few key buses in terms of detailed modeling. The paper deals with the problem of finding criteria for selecting such buses. The concept of significance factors is introduced and provides such a c...

Power systems economic dispatch by a rearranged active-reactive power loss model

The economic dispatch conditions of a power system are evaluated using a rearranged active-reactive power loss model. The active-reactive power loss model is divided into two separate submodels. In this formulation, the network total active and reactive power losses are expressed in terms of the active and reactive powers of the generation buses. The network purely reactive sources are modeled in terms of the total reactive load demand. The advantages gained by this separation are discussed. The parameters of the network submodels are estimated by least squares with a high degree of accuracy from a set of load flow results. Based on the above submodels, the constrained fuel cost function is then minimized to obtain the economic dispatch solutions of the power system under consideration. Results are presented for a standard IEEE test system for a wide range of system load levels. The results obtained by the proposed method are also compared to the economic dispatch solutions based on the active power loss model.

A stability measure for use in power system transient stability studies

Large system transient stability calculations may be carried out using network equivalents, and generator grouping, and by reducing the order and complexity of the system representation. Engineering judgement and, in most cases, prior knowledge of transient system performance is required to implement the models. In this paper a new parameter called ‘stability measure’ is introduced. The stability measure can easily be calculated on the basis of load flow and short-circuit results. Upon calculation of the stability measure set for a given fault condition, an estimate of the likely response of the respective generators to the fault is obtained. The validity and generality of the stability measure has been demonstrated by simulated tests on a sample power system. Application of the method with respect to grouping of generators in transient stability studies is also discussed.

An Advanced Contingency Selection Algorithm

This paper reports on the development of an advanced contingency selection algorithm giving superior results compared to earlier techniques. Problems inherent in the earlier algorithm resulted in occasional misranked contingency cases. The new algorithm gives results which are essentially equivalent to a ranking based on the results of a DC load flow of each case, only at a fraction of the calculation time. A complete derivation, test results and applications are given in the paper.

A matrix method for optimal var siting

The load flow problem is formulated in linearized form in which complex notation is retained. Various criterion functions are proposed for optimal reactive power (VAr) siting, and the linear load flow results are used in a gradient scheme to affect the optimization. Matrix notation is used, and computational advantages are noted over existing VAr siting techniques; among these advantages are accuracy, computation speed, and convenient sub-optimal solution when some system busses are unavailable for VAr placement.

Modified form of Newton's method for faster load-flow solutions

A modified form of Newton's method for load flow is introduced in this paper. The results tabulated, for eight different power systems, indicate a consistent advantage in using this modification over the standard Newton method. The comparisons are made on systems that include several for which load-flow results were previously published by other authors.

Simulation Techniques for Rural Electric Power Systems Planning

This paper introduces an effective method for rural electrical systems planning. All three-phase, two-phase, and single-phase lines are simulated in one computer study. Typical load flow results are obtained from the study. The method emphasizes simplicity and flexibility. Very little computation time is required. Once the data are prepared the amount of work required to incorporate the changing of the system is small and very inexpensive. This type of flexibility is one of the most important contributions of this new method. The method applies to both long-range and short-term system planning.

Effective starting process for Newton-Raphson load flows

The results of a noniterative simplified load flow are used as starting values for the Newton-Raphson algorithm. This scheme improves the reliability of the Newton-Raphson method, to the extent that convergence for any physically feasible problem is envisaged, and gives high-accuracy solutions in two or three iterations. The starting process has a number of other valuable uses and may be employed on its own to give fast approximate a.c. load flows.

Combined Use of the Powell and Fletcher - Powell Nonlinear Programming Methods for Optimal Load Flows

The feasibility solving optimal load flow problems by means of nonlinear programming techniques has been previously demonstrated. Recently, a new method by Powell for constrained minimization has claimed a better performance than existing methods. An investigation was carried out to test Powell's method on optimal load flow problems and results obtained confirm expectations. Powell's method and its accompanying Fletcher-Powell method, which performs the actual minimizations, are presented. The power system optimal load flow problem is discussed, and its equations are presented in the form required by the nonlinear programming approach. Finally, a numerical example on the IEEE 30- bus standard test system is presented in which an economic dispatching is accomplished with the new method. Computation time is small enough to permit the application of the method for dispatching at practical intervals of time.