Jin-Cheng Wang

Optimal capacitor placements in distribution systems. I. A new formulation and the overall problem

A novel formulation of the general capacitor placement problem taking into consideration practical aspects of capacitors, the load constraints, and the operational constraints at different load levels is presented. This formulation is a combinatorial optimization problem with a nondifferentiable objective function. A solution methodology based on an optimization technique (simulated annealing) is proposed to determine the locations where capacitors are to be installed, the types and sizes of capacitors to be installed, and the control settings of these capacitors at different load levels. The solution methodology can offer the global optimal solution for the general capacitor placement problem. >

Dynamic load models in power systems using the measurement approach

Accurate dynamic load models allow more precise calculations of power system controls and stability limits, which are critical in the planning and operation of power systems. The development of dynamic load models using the measurement approach for the Taipower system are described. Two dynamic load model structures are developed. A procedure for applying a set of measured data from an online transient recording system to develop dynamic load models for the Taipower system is described. A technique based on the concept of confidence interval is used to validate the developed high-order load model structure. Case studies are also presented. >

An efficient algorithm for real-time network reconfiguration in large scale unbalanced distribution systems

Real-time applications demand fast computation, and this paper proposes an efficient algorithm for real-time network reconfiguration on large unbalanced distribution networks. A novel formulation of the network reconfiguration to achieve loss minimization and load balancing is given. To reduce computational requirements for the solution algorithm, well justified power flow and loss reduction formulae in terms of the on/off status of network switches are proposed for efficient system updating. The algorithm relies only on a few full power flow studies based on system states attained by explicit expressions using backward-forward sweeps for efficient computation of power system states at the critical system operating points. The solution algorithm runs in an amount of time linearly proportional to the number of tie switches and the number of sectionalizing switches in the system. The solution algorithm has been implemented into a software package and tested on unbalanced distribution systems including a system with 292 buses, 76 laterals, 7 transformers, 45 switches and 255 line sections under diverse system conditions.

Optimal capacitor placements in distribution systems. II. Solution algorithms and numerical results

For pt.I see ibid., vol.5, no.2, p.634-42 (1990). A general solution algorithm based on simulated annealing for optimal capacitor placements in distribution systems is proposed and analyzed. The solution algorithm can provide the global optimal solution for the capacitor placement problem. The solution algorithm has been implemented into a software package and tested on a 69 bus system with very promising results. >

Optimal capacitor placement, replacement and control in large-scale unbalanced distribution systems: modeling and a new formulation

This paper undertakes the problem of optimal capacitor placement, replacement and control in large-scale unbalanced, radial or loop distribution networks. The problem is how to optimally determine the locations to install (or replace, or remove) capacitors, the types and sizes of capacitors to be installed (or replaced) and, during each load level, the control schemes for each capacitor in the nodes of a general three-phase unbalanced distribution system such that a desired objective function is minimized while the load constraints, network constraints and operational constraints (e.g. the voltage profile) at different load levels are satisfied. The objective function considered consists of two terms: cost for energy loss; and cost related to capacitor purchase, capacitor installation, capacitor replacement and capacitor removal. Comprehensive modelings of different components are presented which include primary power networks, three-phase transformers (different winding connections, off-nominal tap ratio, core and copper losses), cogenerators, voltage sensitive load models for single-phase, two-phase and three-phase loads, shunt capacitors and reactors. The new problem is formulated as a combinatorial optimization problem with a nondifferentiable objective function. The configuration space essential in the design of a annealing-based solution methodology for the new problem is derived. >

Development of a frequency-dependent composite load model using the measurement approach

In control and stability studies, load models should realistically represent the aggregate load behavior of all kinds of individual components. In this paper, the development of a composite load model, where the load is represented as a combination of an RC circuit in parallel with an induction motor equivalent circuit, is presented. A procedure is developed for identifying a frequency-dependent composite load model using digital measurements from an on-line transient recording system, taking account of system frequency variation. A nonlinear model parameter estimation technique is described to derive the frequency-dependent load model. A computer program called LMSP has been developed. The program consists of five major phases: user-interface, data manipulation, load model identification; model conversion and system model response evaluation. A case study is presented to illustrate, in particular, the accuracy of the developed model for the representation of dynamic load behaviors of an actual power system. >

Capacitor placement and real time control in large-scale unbalanced distribution systems: loss reduction formula, problem formulation, solution methodology and mathematical justification

A comprehensive study of capacitor placement and real-time control in general unbalanced distribution systems is undertaken. New developments in a loss reduction formula, problem formulations, solution methodology and mathematical justification are presented. The problem is decoupled into two subproblems: the capacitor placement subproblem; and the real-time control subproblem. An effective solution algorithm for placing capacitors and determining their real-time control schemes for general unbalanced distribution systems is proposed. To meet the need for efficient implementation in real-time environments, a fast pseudo gradient-type mechanism for deriving capacitor control settings is incorporated into the solution algorithms. A quadratic integer programming based approach is proposed to determine the number, locations and sizing of capacitors to be placed in the distribution systems. The subproblem of determining capacitor control settings under varying loading conditions is formulated as another quadratic integer programming problem. Mathematical justification is provided to show that the proposed algorithms are guaranteed to yield local optimal solutions.

Development of a dynamic ZIP-motor load model from on-line field measurements

Abstract We developed, using on-line field measurements, a dynamic ZIP-motor load model which attempts to capture the dynamic behavior of loads. The dynamic ZIP-motor load model consists of two parts: a static part and a dynamic part, where the static load is represented by a combination of constant impedance, constant current and constant power while the dynamic load is represented by an induction motor model. A procedure for building the model structure of the dyanmic ZIP-motor load model is developed. An effective solution algorithm for estimating the associated model parameters is presented. A notable feature of the algorithm is that the model parameters are estimated based upon pseudo-gradient information instead of exact gradient calculation. The proposed algorithm is easy to implement and can be used to identify nonlinearities associated with ZIP-motor models, such as models accounting for magnetizing and leakage reactances. The results developed in this paper are tested and evaluated using real field measurements from a real power system. It is shown numerically in the case study that the developed dynamic load model can accurately capture the dynamic behaviors of loads.

Identification of excitation system models based on on-line digital measurements

Accurate and sufficient detailed excitation system models are essential to the precise calculations of power system stability limits. This paper presents, in detail, a procedure for identifying excitation system models based on the online digital measurements from a plant transient recorder system. A solution algorithm for identifying parameters of the excitation system models is devised and implemented. The gradient averaging stochastic approximation method is employed to handle nonlinearity of the power system models. Detailed numerical results based on the online measured data of the Taipower system are included. >

On-line measurement-based model parameter estimation for synchronous generators: model development and identification schemes

Accurate generator modeling allows for more precise calculations of power system control and stability limits. In this paper, a procedure using a set of measured data from an online plant transient recording and analysis system to develop the synchronous generator model for the Taipower system is described. A continuous-time transfer function matrix is derived for a popular sixth-order synchronous generator model. In order to accommodate the nature of online digital measurements, the transfer function matrix is transformed into a simple discrete-time linear regression model. A measure of discrepancy between the generator model outputs and the online measurements from generators is employed. A modified conjugate gradient method suitable for identifying generator parameters is developed to minimize the measure of discrepancy, from which a set of accurate generator parameter values can be obtained. The merits of the modified conjugate gradient method include its computational efficiency and numerical reliability. The proposed procedure allows simultaneous estimation of all generator parameter values. >