Power Network Analysis Research Articles

The differentiation of functions of conjugate complex variables: application to power network analysis

The mathematical foundations of the rules used to differentiate functions of conjugate complex variables are examined and their use is illustrated with several power network analysis examples. Using conjugate complex notation in power network analysis, it is possible to obtain directly the real Jacobian matrix of the power-flow equations. The author introduces the concept of bicomplex Jacobian matrix and states the rules to invert it. The expressions which are above often permit an immediate physical interpretation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

M - to N-phase transformer models in phase co-ordinates

M- to N-phase transformers (M ≠ N) are considered in the phase co-ordinate frame of reference. Equivalent circuits are derived for zig-zag, Scott, T-T and star-double-star transformers, and the connection tables are given for use in assembling the nodal-admittance-matrix terms in the usual way for power network analysis. The paper concludes with an example of a polyphase load-flow analysis of a network containing some of these transformers.

Framework for power network analysis

The proposed framework for the analysis of electric power networks is motivated by the emerging concepts of power system security. Quantitative measures of system security can be derived within this framework on the basis of regions of operation in the space of system variables and parameters. Probabilistic aspects of load fluctuations and random faults in the network are included in the derivation of the probability number characterizing the level of security of each operating point. Additional research will be required for the practical application of this framework in planning and operating power systems.

Fault analysis of multinode power systems for designing ultra-high-speed protective relays along with a proposed relaying scheme

For designing and assessing the performance of ultra-high-speed relaying schemes, computation of the relaying quantities during a very short time interval after fault inception is required. Time-domain as well as frequency-domain methods are available for this purpose. In this paper, fault analysis of a multinode power network, which employs the nodal formulation and is useful for frequency-domain analyses, is presented. Also, an ultra-high-speed protective scheme, possessing the special features of very fast operation and fault location, is proposed and its principle of operation described. The paper concludes with the results of a numerical example which illustrates the application of the fault analysis described and brings out the feasibility of the proposed relaying scheme.

Stability analysis of multimachine power networks with linear frequency dependent loads

This paper presents a more complete stability analysis of a new power system model which was presented in [1]. The essential feature of the model is the assumption of frequency dependent loads. This facilitates a dynamic representation directly in terms of the network structure. Consequently, concepts and results from circuit theory can play a strong role in the stability analysis of the model. The multivariable Popov criterion is used to obtain general Lure-Postnikov type Lyapunov functions which rigorously allow for the presence of (frequency dependent) real power loads. This has not been possible with the previously used model. Results are given for both local (dynamic) stability and for determination of regions of asymptotic (transient) stability.

Modular decomposition and reliability computation in stochastic transportation networks having cutnodes

AbstractConsider a flow network having random arc capacities and having associated with each node n a “supply‐demand random variable” Yn whose absolute value equals the supply available at the node when Yn assumes a non‐negative value and the demand required by the node when Yn assumes a nonpositive value. A fundamental problem is the computation of the reliability R, that is, the probability that the random variables will assume values that permit a feasible flow. Upon adapting the graph‐theoretic concepts of “cutnode” and “block,” it is possible to identify a “block‐module,” an independent, nontrivial subnetwork that has one and only one node (the “cutnode”) connected to nodes outside the subnetwork. The reliability of the network will increase by a known factor after a “block‐modular decomposition” that consists of a transformation of the cutnode's supply‐demand random variable and the deletion of the remainder of the block module. Provided the original network possesses at least one block module, R can be determined from a sequence of block‐modular decompositions that reduce the original network to a single node whose reliability is easily computed. Computational experience with a computer implementation of such a decomposition method is reported, and the application of the method to the analysis of electrical power networks is included.

Digital and hybrid computer simulation of power systems

In order to meet the increasing demand for reliable design and expansion of power networks, the use of system simulation must play a leading role in the power industry's future R &amp; D programs. Digital com puters are already widely used in the analysis and design of large power networks. Hybrid computers offer a convenient alternative, especially where fast and accurate simulation of complex nonlinearities is required. In this article, general principles are presented for the computer simulation of interconnected power systems. The technique discussed is directly applicable to an all-digital simulation, but emphasis is also placed on a hybrid implementation in which the transmission por tion of the system is represented digitally, while the integration and nonlinearities associated with termi nal apparatus are represented on the analog. Example studies are performed to illustrate the technique. Results include voltage waveforms for a three-phase line energization, and the modification of switching transients by surge arresters in a single-phase system.

The general form of some common network theorems

Whereas network theorems are widely used for the reduction and simplification of networks of a substantial degree of complexity, they tend to be neglected when complex systems are to be solved on a network analyzer. The network analyzer has proved to be a very satisfactory tool for power network analysis, but a review of the situation is profitable for cases of large problems which may exceed the number of impedance units available. There are two main general aspects to the use of network theorems: 1. The use of theorems for the specific investigation of a portion of a network, or the relationship between two portions of a network, e.g., Thevenin's, or the compensation, theorem. 2. The use of techniques of successive reduction, e.g., mesh-to-star transformation.

The General Solution Method of Power Network Analysis

The general solution method of power network analysis grew from the systematic investigation of the effects of changes in a power system being analyzed by mathematical methods. The investigation led to an improved method of computing load-flow studies by which successive approximations converging upon precise answers could be carried through without the solving of simultaneous equations, a method so flexible that changes in loads, ratios, phase shifts, or even the circuit offer no difficulties. The general solution, by taking advantage of a previously computed solution when computing a new solution, is particularly adapted to the computation of a family of solutions for a particular network. Investigation of the effects of changes indicated that the effect of a change in loading, transformer ratio, or phase shift upon any particular network answer could be closely approximated by multiplying the change by a coefficient. Similarly, the effect of a change in value of a circuit element, or the effect of a new circuit element added, upon any particular network answer could be approximated by multiplying a constant by a coefficient. This paper is concerned with the computation of the complete set of coefficients describing the effects of any loading, transformer ratio, phase shift, or circuit change upon any flow, voltage, or phase angle. The complete set of coefficients is termed in this paper the ``general solution'' to the network.