Constant Impedance Load Research Articles

Voltage stability of radial distribution networks for different types of loads

The paper presents voltage stability analysis of radial distribution networks. A new voltage stability index is proposed for identifying the node, which is most sensitive to voltage collapse. It is shown that the node, at which the value of voltage stability index is minimum, is more sensitive to voltage collapse. For the purpose of voltage stability analysis, constant power, constant current, constant impedance and composite load modelling are considered. It is seen that with the insertion of shunt capacitor, load capability limit of the feeder has increased for all types of loads. By using this voltage stability index, one can measure the level of voltage stability of radial distribution networks and thereby appropriate action may be taken if the index indicates a poor level of stability. The proposed method is compared with the other two existing methods. The effectiveness of the proposed method is demonstrated through two examples.

Congestion management with generic load model in hybrid electricity markets with FACTS devices

The load variations during the entire day specially during the peak hours have substantial impact on the loading pattern of the transmission system. The voltage profile become poor during such situation of peak loading of the network and can lead to congestion during such events. This paper attempts congestion management considering the impact of constant impedance, current, and power (ZIP) load model along with the load variation pattern in a day-a-head hybrid electricity market. The main contribution of the proposed work is: (i) Optimal rescheduling based congestion management for a hybrid market model with three bid offer from generators, (ii) study of the impact of ZIP load model and load variations on rescheduling and congestion cost, (iii) impact of third generation FACTS devices on congestion management, (iv) comparison of results obtained for hybrid market model without and with ZIP load model. The generators offer three block bid structure to the ISO in a day-a-head market for congestion management. The base case economic load dispatch has been obtained for generators and is taken as base case generation output data during the congestion management to obtain new generation schedule. The three block bid structure submitted to the ISO has been modeled as a linear bid curve which is a function of increment/decrement (inc./dec.) of generation within the upper and lower bounds offered for congestion management. The results have been obtained for IEEE 24 bus test systems.

Power signature-based non-intrusive load disaggregation

For more efficient energy consumption, it is crucial to have accurate information on how power is being consumed through a single power measurement. It benefits both market participants such as retailers, network businesses and also power consumers. This means that the metering device must not only be able to distinguish between different loads on a common circuit, but also decipher their respective power consumption. This paper gives our investigation on power load signature and power decomposition. In particular, the paper focuses on the development of power decomposition algorithm based on support vector machine (SVM), i.e., estimating the power proportion of constant power (CP) loads to constant impedance (CI) loads. The power decomposition algorithm in this paper is working on steady-state power load signal.

State Estimation and Power Flow Analysis of Power Systems

State estimation and power flow analysis are important tools for analysis, operation and planning of a power system. In this paper, a new state estimation method based on the extended weighted least squares (WLS) method for considering both measurement errors and model inaccuracy is presented. Two bus, three bus, and IEEE 14 bus test cases are employed to evaluate the accuracy of the method. The comparison results show that the extended WLS method may outperform traditional WLS approach when the model is not accurate. In addition, this paper investigates a method based on Z matrix to implement power flow in a transmission system with multiple types of loads (e.g. constant PQ, constant impedance and constant current magnitude loads or mixed loads). The load flow results demonstrate that the method is effective and easy to implement when composite load types exist in the system. Our studies also show that it may be possible that multiple solutions exist for a power flow problem.

Study on Load Model of PV Generation Planning

In distribution system planning with photovoltaic generations (PVGs), if load is not properly modeled in the simulation, the accuracy of results will be affected. A large number of studies show that load characteristics play a impotrant role in the system analysis. This paper presented the resultant load model, and on this basis, studied the impacts of the constant power load model and constant impedance load model on PV generation planning. Simulation results show that the selection of load models has an important impact on PV generation planning.

Parameter Estimation of Dynamic Load Model in Power System by using Measured Data

In this paper, we propose a dynamic load model considering change of flux inside induction motor for transient stability analysis and we present a new method for estimating unknown parameters of the dynamic load model. The model is a parallel composite of a constant impedance load and an induction motor load behind a series constant reactance. An adequate dynamic load model is essential for evaluating power system stability and this model can represent the behavior of actual load by using appropriate parameters. However, the problem of this model has a large amount of parameters and it is not easy to estimate a lot of unknown parameters. Therefore we propose an estimating method based on Particle Swarm Optimization (PSO), which is a non-linear optimization method, by using measured instantaneous voltage sag data. We estimated parameters of the actual load by PSO to minimize error between calculated and measured power of load after a load drop due to voltage sag by the accident. It was confirmed that the proposed method was successful and PSO is effective in parameter estimation.

An accurate voltage solution method for radial distribution systems

This paper formulates a set of equations (SOE) to describe a radial distribution system with high R/X ratio. The SOE comprises 3(N - 1) second-order equations and an equal number of variables for an N-bus system. The proposed method solves this SOE using the first-order Newton-Raphson technique. The SOE model accounts for elements such as transformers, transmission lines, shunt capacitors, constant PQ loads, and constant impedance loads. Irrespective of the R/X ratio values of the lines in the system, the SOE preserves a strong diagonal characteristic. As well, this SOE is devoid of bus phase angles, unlike the 2(N - 1) ac power flow equations used to describe transmission systems. The proposed method is compared with other methods reported in the literature for distribution systems, such as Newton-based methods and recursive methodologies that use forward and reverse sweeps. Tests conducted on radial distribution systems with 43, 69, and 5002 buses show the new method to be more accurate than other methods reported in the literature.

An Approach to Determine a Pair of Power-Flow Solutions Related to the Voltage Stability of Unbalanced Three-Phase Networks

This paper proposes an approach to determine a pair of power-flow solutions associated with the voltage stability of unbalanced three-phase networks. The approach is derived from the observations of the multiple three-phase power-flow solutions of a two-bus network. It is found that there are two pairs of solutions at the load bus. The plot of the voltage magnitude of each pair against the power demand at the load bus shows that two possible PV curves can be constructed for each phase. Each of the two curves is a combination of the two pairs of solutions. One of these curves is associated with the voltage stability of the system whereas the other is associated with the imbalance of the three-phase network. Based on the above observations, a constant impedance load model is utilized to calculate the solution associated with the voltage stability of the study system. Then the equivalent complex power load demand is used to calculate the two pairs of solutions, i.e., the multiple three-phase power-flow solutions. Simulation studies have been carried out for the multiple solutions. The results show that there is a point which is directly proportional to the imbalance in the power demand at the load bus. This point is used to set a criterion to differentiate between the two PV curves. Hence, the PV curve which is related to the voltage stability can be determined without the assumption of the linear load model at the start of the study.

Reducing Identified Parameters of Measurement-Based Composite Load Model

A load model is one of the most important elements in power system simulation and control. Recently, the constant impedance, constant current, and constant power load in combination with the induction motor load have been widely used as the composite load model, whose parameters are all identified from the field measurements in measurement-based load modeling practices so far. However, there is virtually no research conducted on whether all these parameters could really be identified. This paper investigates the possibility on reducing the number of composite load model parameters to be identified from field measurements. This paper first shows that direct application of the IEEE load motor parameters in the composite load model may be inadequate on describing the load dynamics over different operating status. Then the perturbation method is used to derive the trajectory sensitivities of the equivalent motor parameters, based on which the reduction on the identified parameters of the composite load model is presented. Two cases of measurement-based load modeling in North China and Northeast China are studied to illustrate the validity of the reduction method. It is shown that the reduction does not lose the model's capability on describing the load dynamics. The reduction on the number of identified parameters not only provides a possible way to solve the multi-valued load model problem based on the current practices on measurement-based load modeling, but it also facilitates building of the load model with more components included in it. Meanwhile, reducing the identified parameters reduces the identification time; thus, the proposed strategy significantly enhances the efficiency of the load modeling work.

分散型電源大量導入時における動的負荷の安定性解析

The load stability in bulk power system may be seriously affected when a large amount of distributed generators (DG) stop simultaneously due to voltage sag. It is important to understand the mechanism of load instability, which cannot be analyzed by well-known P-V curve only. For analyzing load stability without detailed simulations, this paper presents torque-speed characteristic curves of induction motor considering power system condition and constant impedance loads. As the results of examining the curves in various conditions (model order reduction methods, load dropping out), this paper also presents some cautions for bulk power system modeling with DG. A bulk power system model whose lower voltage subsystems are reduced by an accurate model order reduction method is introduced in order to check out the problems by DG-stopping. As to the numerical simulation, a great number of DG-stopping leads to voltage instability in bulk power system, and the instability is greatly improved by DG-voltage regulation.

Transmission Line Performance with Voltage Sensitive Loads

In this paper, transmission line performance with voltage sensitive loads is studied. Three types of load, namely constant power, constant current and constant impedance loads are considered, individually as well as in a mixed combination, and it is shown that the transmission line loss is highest with the constant power load and lowest with the constant impedance load. The line loss for mixed load is higher than that for constant power load when the constant power component is more pronounced in the mixed load.

Handling three-winding transformers and loads in short circuit analysis by the admittance summation method

The admittance summation method is efficient in short circuit analysis of radial and weakly meshed networks. It is especially powerful if all node loads can be represented as any combination of constant impedance and constant current load component. However, in the existing literature one cannot find any explanation how to handle power transformer in that approach. For that reason, the corresponding equations have been developed in this paper along with a procedure for development of a three-winding transformer admittance matrix. In addition, a procedure for handling an arbitrary load was proposed. A large number of tests were performed and results were compared with that obtained by the previously published method. As an illustration, some of the results for single fault currents are presented. It can be concluded that the proposed approach makes the admittance summation method capable to take into account all network elements in a proper way.

Voltage Stability Analysis of Radial Distribution Networks

The paper presents voltage stability analysis of radial distribution networks. A new stability index is proposed to identify the nodes that are on the verge of voltage collapse. The value of the proposed voltage stability index is calculated at each node of the network. A modified load flow method is used for voltage stability analysis. The modified load flow method incorporates composite load modeling and variations in load pattern at each node. The results are compared with the other known methods of voltage sensitivity indices and found satisfactory. A comprehensive comparison with the recently proposed voltage stability index by Chakravorty and Das [1] is presented in this paper. A detailed analysis of effects of different load models on voltage computation and voltage stability are carried out, and it is observed that for voltage stability analysis, a constant impedance load model can be used without losing the sensitivity of load modeling.

Reactive power compensation for radial distribution networks using genetic algorithm

In the present work, genetic algorithm is applied to select the optimum values of fixed and switched shunt capacitors required to be placed on a radial distribution network under varying load conditions so as to minimize the energy loss while keeping the voltage at load buses within the specified limit by taking the cost of the capacitors into account. Both fixed and marginal costs of the capacitors are considered to obtain the best overall performance. The voltage constraint is included as penalty term in the objective function. Further, instead of only assuming the capacitors as a constant reactive power load, it is also been considered as a constant impedance load in optimization problem itself and comparison of performances for both considerations are also presented. Also possible convergence criteria of genetic algorithm based on ‘the difference between best fitness and average fitness’ of population is suggested to reduce the CPU time required to a great extent with a very small sacrifice in overall savings.

Particle-in-cell simulations of electron flow in the post-hole convolute of the Z accelerator

The three-dimensional, particle-in-cell code QUICKSILVER [J. P. Quintenz et al., Lasers Part. Beams 12, 283 (1994)] is now being used to simulate the inner region of the Z accelerator [R. B. Spielman et al., Phys. Plasmas 5, 2105 (1998)] at Sandia National Laboratories. The simulations model electron flow and anode losses in the double post-hole convolute, which couples four radial, magnetically insulated transmission lines (MITLs) in parallel to a single MITL that drives a Z-pinch load. To efficiently handle the large range in the magnetic field, 0<B<200 T, the particle pusher is modified to subcycle the electron advance relative to the field solver. Results from a series of simulations using a constant-impedance load are presented. The locations of electron losses to the anode in the convolute are in qualitative agreement with damage to the Z hardware. The electron energy deposited in these anode regions rapidly heats the surface to temperatures above 400 °C—the threshold at which anode plasma formation is expected.

TORQUES IN MULTI-MACHINE GENERATOR SHAFTS DUE TO HVOC RECTIFIER RIPPLE CURRENTS SUPERIMPOSED ON THE DC CURRENT IN ASYNCHRONOUS LINKS

ABSTRACT This paper analyses torsional vibrations in steam turbine-generator-exciter shafts of machines in multi-machine power systems in close proximity to the inverter station due to rectifier ripple currents superimposed on the DC current in asynchronous DC links. It extends earlier work to include an in-depth analysis of system scaling factors for modulation product harmonic currents impressed on generators not examined in the literature heretofore by an inverter in an asynchronous link. Frequency at which shaft torsional vibrations would be excited by modulation product harmonics in 50Hz/50Hz asynchronous links as a function of deviation in system frequency is first reviewed. Amplitude of shaft torque due to steady resonant torque excitation which is a function of initial rate of increase of vibration at adjacent cells where the steady resonant torque excitation is applied, the time constant for decay of the vibration and stiffness between adjacent cells is then discussed. The paper then shows that torque in shafts of machines in multi-machine networks may be estimated by proportioning HVDC Link inverter modulation product harmonic disturbance current appropriately to each machine at risk. A three phase fault studies programme to proportion converter harmonic current to each machine is discussed. System scaling factors are evaluated for different scenarios : (i) neglecting system loads, (ii) using a lumped load at the inverter, and (iii) employing distributed system loads for (a) constant impedance loads and (b) subtransient reactance dynamic loads. The effect of tappings of transformers is also discussed. On the basis of these evaluations, generators are identified which are most at risk. Torques in shafts of the machines in Ireland due to rectifier ripple currents superimposed on the DC current of the proposed North Wales/Ireland Link are then analysed and discussed.

Investigation of impacts of different three-phase transformer connections and load models on unbalance in power systems by optimization

This paper investigates the impacts of different three-phase transformer connections and load models on unbalance in power systems. New three-phase transformer models are presented. These models are derived from a new primitive impedance matrix incorporated with positive, negative and zero sequence elements. The constant power and constant impedance load models are discussed. The three-phase models are implemented in a general-purpose optimization software package. Two power systems are used to illustrate the test results. The test results provide assistance to engineers in understanding the effect of different connections on the transformers. This paper also emphasizes that a proper load model should be used; otherwise, an incorrect solution will be obtained.

EFFECTS OF VOLTAGE SENSITIVE LOADS ON THE VOLTAGE STABILITY OF COMPENSATED EHV-TRANSMISSION LINES

ABSTRACT In this paper, effects of voltage sensitive loads, namely, constant power, constant current and constant impedance type loads on the voltage collapse phenomenon of EHV transmission lines with different types of compensation schemes are studied and discussed. Exponential modelling is used for the three types of loads and exact long line equations are used in the analysis. It is seen that the power transfer capability of a long line for any type of compensation scheme is the highest for a constant impedance load, and the lowest for a constant power load. The power transfer capability for a constant current load has an intermediate value compared to those for constant impedance and constant power loads respectively. Further, the transformer tap control has an adverse effect on the voltage stability for constant current and constant impedance type loads. Improved power factor improves the voltage stability condition for all types of compensation schemes. In all compensation schemes, an increased degr...

Voltage stability as affected by static load characteristics

Voltage stability is analysed as a dynamic phenomenon associated with the excitation field dynamics of synchronous machines. It is shown that, for constant impedance loads, a single machine powersystem is voltage stable for all reasonable operating conditions. For constant power loads, however, a simple system has a voltage controllability limit that can be close to nominal voltage. The voltage stability region as a function of real and reactive load dependence on voltage is calculated for a single machine system with and without automatic voltage regulation. The analysis is then extended to the multimachine case, for which approximate voltage stability criteria are developed using the extended linearisation coefficient matrices. The linearised model analysis is found to be absolutely consistent with the results obtained by nonlinear simulation of a multimachine power system.< >

General purpose fast decoupled power flow

A general purpose fast decoupled power flow model (GFDPF) is presented that exhibits more or less best convergence properties for both well-behaved and ill-conditioned systems. In the proposed model, all network shunts such as line charging, external shunts at buses, shunts formed due to π representation of off-nominal in-phase transformers etc. are treated as constant impedance loads. The effect of line resistances is considered while forming the [B′] matrix and are ignored in forming the [B″] matrix. This model is tested on several systems for both well-behaved and ill-conditioned situations. Simple, efficient compensation technique is proposed to deal with Q-limit enforcements associated with bus-type switchings at voltage-controlled buses. The results demonstrate that the proposed GFDPF model exhibits more or less stable convergence behaviour for both well-behaved and ill-conditioned situ ations.