Voltage Dependent Load Models Research Articles

Linear Power-Flow Formulation Based on a Voltage-Dependent Load Model

The power-flow (PF) solution is a fundamental tool in power system analysis. Standard PF formulations are based on the solution of a system of nonlinear equations which are computationally expensive due to the iterations needed. On the other hand, distribution-system (DS) automation algorithms should be fast enough to meet real-time performance. The conventional load representation, as constant <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$P$</tex></formula> – <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Q$</tex></formula> , becomes less accurate as we get closer to the actual load's level. In this paper, a new load model is proposed which represents the loads' voltage dependency. A simple curve-fitting technique is used to derive a voltage-dependent load model which splits the load as a combination of an impedance and a current source. With this representation and some numerical approximations on the imaginary part of the nodal voltages, it is possible to formulate the load-flow problem as a linear power-flow (LPF) solution which does not require iterations. The approximation has been tested in systems up to 3000 nodes with excellent results. The LPF formulation is particularly important in the context of optimization algorithms for automated smart distribution systems. The extension of the technique to unbalanced distribution systems will be presented in future work.

Online Tracking of Voltage-Dependent Load Parameters Using ULTC Created Disturbances

This paper presents a field-test verified method for continuous tracking of voltage-dependent load model parameters. The basic idea is to use the natural or automatic movement of the under load tap changer (ULTC) as the source of voltage disturbance. Load parameters are estimated from each taping activity. While the idea of using manual ULTC tapping disturbances for load parameter estimation is not new, this paper has demonstrated, through laboratory tests and field measurements, that load parameters can be estimated from the automatic ULTC movements. Since a ULTC often has many movements in any given day, the load parameters can be collected in a consistent, frequent, and predictable manner and, consequently, online estimation and tracking of load parameters becomes feasible. The paper presents the implementation of the proposed method and its field measurement experiences, especially the characteristics of tap movements and the associated load responses. Experiments and a large number of field measurements presented in this paper have shown that the proposed method is a practical and effective method for determining load parameters online.

A profit-centric strategy for distributed generation planning considering time varying voltage dependent load demand

This paper proposes a new algorithm to determine the best connection of multiple distributed generations (DGs) on distribution networks according to type of customers. The considered DG technology is combined heat and power (CHP) in various sizes which can be extended to other technologies. Different types of demand, such as industrial, residential and commercial are defined by the load model that is voltage dependent and the load patterns from real life hourly demand data. This method which is based on multi-year multi-period power flow is useful for Distribution Network Operators (DNOs) when they are faced with voltage dependent load models in their networks. However it can be used in constant load models with multi-period or single demand. The proposed optimization is from the DNO’s perspective and aims to maximize their present value of profit against the supplying costs of the network. It is shown that by definition of an appreciated economic based objective function, the customer type can significantly affect the optimal DG options in distribution network planning. Finally, this method is tested using the 69-bus radial system. Furthermore, a comparative study for different customer demand types is shown for various cases and results are discussed in this paper.

Multi-Objective Day-Ahead Real Power Market Clearing with Voltage Dependent Load Models

In this paper, we investigate the influence of voltage dependent load models on day ahead real power market clearing (DA-RPMC). The investigations clearly bring out the unsuitability of conventional single objectives such as production cost minimization (PCM) (or social welfare maximization (SWM)), due to reduction of load served. Hence, the multi-objective optimization is essential in this context. The paper proposes several objectives such as production cost minimization (PCM) (or social welfare maximization (SWM)), load served maximization (LSM), and Voltage Stability Enhancement Index (VSEI); which can be judiciously combined as per the needs of the operating condition. Multi-objective Strength Pareto Evolutionary Algorithm (SPEA) has been used to solve the DA-RPMC problem. The effectiveness of the proposed approach is tested on IEEE 30 bus system and the detailed simulation studies have been carried out by considering different operating conditions with voltage dependent load modeling.

Effect of load models on assessment of energy losses in distributed generation planning

Distributed Generation (DG) is gaining in significance due to the keen public awareness of the environmental impacts of electric power generation and significant advances in several generation technologies which are much more environmentally friendly (wind power generation, micro-turbines, fuel cells, and photovoltaic) than conventional coal, oil and gas-fired plants. Accurate assessment of energy losses when DG is connected is gaining in significance due to the developments in the electricity market place, such as increasing competition, real time pricing and spot pricing. However, inappropriate modelling can give rise to misleading results. This paper presents an investigation into the effect of load models on the predicted energy losses in DG planning. Following a brief introduction the paper proposes a detailed voltage dependent load model, for DG planning use, which considers three categories of loads: residential, industrial and commercial. The paper proposes a methodology to study the effect of load models on the assessment of energy losses based on time series simulations to take into account both the variations of renewable generation and load demand. A comparative study of energy losses between the use of a traditional constant load model and the voltage dependent load model and at various load levels is carried out using a 38-node example power system. Simulations presented in the paper indicate that the load model to be adopted can significantly affect the results of DG planning.

Reactive power price clearing using multi-objective optimization

This paper presents a new multi-objective optimization based reactive power price clearing (RPPC) mechanism, considering voltage stability. Use of realistic voltage dependent load models is important in power system analysis and optimization. The influence of the same on RPPC is investigated in this paper. Investigations have also been carried out to ascertain the effectiveness of objectives such as, Total Payment Function (TPF), Loss Minimization (LM), Load Served (LS) and Voltage Stability Enhancement Index (VSEI). The unsuitability of LM/TPF minimization as independent or joint objective(s) for this problem, due to load served reduction is emphasized. The effect of loading condition on judicious combination of these objectives is further probed. The multi-objective RPPC problem is solved using Strength Pareto Evolutionary Algorithm (SPEA). Some of the results are also compared with the Multi-Objective Particle Swarm Optimization (MOPSO). The utility of the proposed approach is demonstrated through detailed investigation on IEEE 30 bus system considering base and stressed cases with constant and voltage dependent load modeling.

Effect of Load Models on Probabilistic Characterization of Aggregated Load Patterns

This paper presents a comprehensive approach to probabilistic characterization of aggregated load pattern of low-voltage consumers. Different from previous methods, consumer load patterns obtained from load survey are converted to empirical cumulative density functions. The functions are then used to address stochastic nature of load pattern in any given point of distribution network. The proposed approach is adopted to investigate the effect of load models on the characterization of aggregated load patterns. In addition, a goodness-of-fit analysis has been carried out to show that the load models can significantly affect the accuracy of aggregated load modeling. It is demonstrated that the constant power (real and reactive) load model which is normally adopted in most distribution network management studies may lead to misleading results compared to the actual network. Case studies are presented and discussed with reference to a real distribution network. The results verify that the proposed method is accurate and flexible, and the voltage-dependent load model is the most promising solution for the aggregated load modeling.

DSPFAP: Distribution systems power flow analysis package using Matlab graphical user interface (GUI)

AbstractThis paper describes a software package whose purpose is to provide a tool to be used for load flow analysis in Power System Analysis courses. The software package which is called Distribution Systems Power Flow Analysis Package (DSPFAP) uses the graphical user interface (GUI) capabilities of Matlab. The main advantage of the developed package is that the load flow analysis can be achieved in both transmission and distribution levels. The package facilitates different forward/backward sweep‐based algorithms to be used for the distribution systems and conventional Newton–Raphson, Gauss–Seidel algorithms for the transmission system load flow analysis. In addition to that, effect of voltage dependent load models and effects of DGs on the distribution systems load flow solution can be investigated using the program. It is also possible to use conventional algorithms for distribution system load flow analysis in the package. The package can freely be downloaded from the website: http://www.gyte.edu.tr/Dosya/102/power/. © 2009 Wiley Periodicals, Inc. Comput Appl Eng Educ 18: 1–13, 2010; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20209

06/01670 A new power flow method for radial distribution systems including voltage dependent load models: Eminoglu, U. and Hocaoglu, M. H. Electric Power Systems Research, 2005, 76, (1–3), 106–114

06/01670 A new power flow method for radial distribution systems including voltage dependent load models: Eminoglu, U. and Hocaoglu, M. H. Electric Power Systems Research, 2005, 76, (1–3), 106–114

A new power flow method for radial distribution systems including voltage dependent load models

This paper presents a simple and efficient method to solve the power flow problem in radial distribution systems. The proposed method takes into account voltage dependency of static loads, and line charging capacitance. The method is based on the forward and backward voltage updating by using polynomial voltage equation for each branch and backward ladder equation (Kirchoff's Laws). Convergence ability and reliability of the method is compared with the Ratio-Flow method, which is based on classical forward–backward ladder method, for different loading conditions, R/ X ratios and different source voltage levels, under the wide range of exponents of loads. Results demonstrate that the proposed power flow algorithm has a robust convergence ability when compared with the improved version of the classical forward-backward ladder method, i.e., Ratio-Flow.

Fuzzy power flow solutions with reactive limits and multiple uncertainties

Importance of simultaneous modeling of diverse sources of non-statistical uncertainty in power system analysis and optimization is being increasingly realized. Keeping this in view, an attempt is made to obtain fuzzy power flow solution considering reactive power limit violations at voltage controlled buses, uncertainties in voltage-dependent load models, load forecast and system parameters. Corresponding to the given range of uncertain variables, a range of dependent variables and functions is provided by the proposed approach. Results of two sample test systems demonstrate utility of this approach.

Improvement of precise P∕V curve considering effects of voltage-dependent load models and transmission losses for voltage stability analysis

The P/V (power/voltage) curve of a power system has been often used for the analysis of voltage stability. If the P/V curve is evaluated with improved precision, then it can have an important role in the analysis of voltage stability. An approach is presented to improve the precision of the P/V curve of a power system, considering the effect of voltage dependency of electric loads and power transmission losses. For electric loads, the use of the voltage-dependent load model, expressed in quadratic form of the bus voltage, has been adopted. For the losses, the re-allocation of transmission losses to each generation bus has been used in the process of power flow calculation for obtaining the P/V curve. Case studies demonstrate the performance of the approach.

A New Approach for Power Flow Analysis of Balanced Radial Distribution Systems

Power flow analysis is perhaps the most useful technique in the design and operation of a power system. This paper reports on a new method of power flow analysis for solving balanced radial distribution systems. The proposed method models the radial distribution system as a series of interconnected ladder networks. Using Kirchoff's laws, a set of iterative power flow equations was developed to conduct the power flow studies. It is very efficient and has excellent convergence characteristics. The radial topology of distribution networks has been fully exploited such that a unique branch and node numbering scheme is utilized to achieve storage and computational economy. Due to the voltage dependency of loads in distribution systems, various static load models are incorporated in the power flow algorithm to obtain better and more accurate results. The computer software implemented in this power flow method was then developed using C++ and successfully applied to several practical radial distribution networks. The results were then validated with those obtained from using existing power flow analysis software. The performance of this method was found to be superior in terms of solution time and convergence characteristics to existing power flow methods. This paper also compares the power flow results of a distribution system for the different voltage-dependent load models. The convergence patterns of this power flow method for the various load models were also compared. In addition, the effects of system characteristics on the convergence of the method are highlighted.

96/05050 Load flow solution of distribution systems with voltage dependent load models

96/05050 Load flow solution of distribution systems with voltage dependent load models

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.

A Practical Transient Stability Program Using Modified Transient Energy Function with HVDC and Load Models

In this paper a practical transient stability program modified transient energy method is introduced. PEBS method is used to compute transient energy to avoid the need to calculate UEP, when generator saliency (constant Eq') and voltage dependent load models incorporated to improve the accuracy. A simplified HVDC model is also included in the program. The proposed method has been tested on a 64 machine, 433 node power system. It has been shown by test results that the computation speed and accuracy is satisfactory for on-line applications.

A vector energy function approach for security analysis of AC/DC systems

The authors examine dynamic behavior in system models that reflect reasonably detailed third-order high-voltage DC (HVDC) dynamics along with AC system models that include reactive flows, and frequency and voltage-dependent load models. A vector Lyapunov function approach is used to define a system-wide energy function that can be used for general security analysis. They describe the derivation of individual component Lyapunov functions for simplified models of HVDC links connected to infinitely strong AC systems, along with a standard AC only system Lyapunov function. A novel method of obtaining weighting coefficients to sum these components for the overall system energy function is proposed. Use of the new energy function for transient stability and security analysis was illustrated in a test system. >

FSH-P ® batch variation

This paper presents a new state estimation (SE) method including equality constraints to model voltage dependent loads and zero injections. Formulation of conventional SE, assuming simple constant power model for the system's loads, is modified to incorporate voltage dependent load models. Assuming reliable load models and zero injections, it is analytically proved that modeling the equality constraints leads to better SE accuracy. To numerically validate the analytical findings, the proposed SE method is implemented on the IEEE 118-bus test system and the large-scale real-world Iran’s power system, and its obtained results are compared with the results of conventional SE. Also, it is shown that considering voltage dependent load model in SE formulation leads to better performance of bad data detection. Moreover, it is illustrated that the accuracy of the proposed SE has low sensitivity to load model identification error.