PQ Buses Research Articles

Complete adjoint-based incremental power flow equations

This paper derives a new complete set of incremental power flow equations based on adjoint networks and Tellegen's theorem. The adjoint networks model the power system passive network, the loads or PQ buses, the generators or PV buses, and the reference bus. The adjoint solutions are used as coefficients to the new equations. The new equations are exact. The power system can be submitted to changes in network configuration, changes in loads, and changes in the values specified for generation. The equations presented in this paper relate those changes with the corresponding changes in voltages. A five-node system example chosen so as to illustrate some specific details of the adjoint-based power flow solution allows the replication of final and intermediate results by the reader. The performance of the equations for a realist transmission network is also presented.

Voltage security assessment and optimal load shedding of power system using the case-based reasoning approach

This paper presents the case-based reasoning (CBR) technique, a novel approach for voltage security assessment and optimal load shedding plan in a real time environment. CBR extracts the information of voltage security from large sets of possible operating conditions of the power system, which are screened off-line by randomly varying the real and reactive loads at PQ buses. In a real time environment, a database may be created by keeping the record of operating states by state estimation. The severity of the contingency is assessed by the number of insecure operating states caused by that contingency, which is predicted by CBR. Security classes are defined by the threshold value of the maximum loadability margins (MLM), calculated using the continuation power flow (CPF) method. For insecure states, the presented technique also gives an optimal load shedding plan to bring the system into secure mode.

Power Systems Voltage Security Assessment and Optimal Load Shedding by CBR Approach

This paper presents a case-based reasoning (CBR) technique, a novel approach for voltage security assessment and optimal load shedding in real-time environment. The CBR extracts the information of voltage security from large sets of possible operating conditions of the power system, which are screened off-line by randomly varying the real and reactive loads at PQ buses. The severity of contingency is then assessed by the number of insecure operating states, which are predicted by the CBR system under that contingency. Security classes are defined by threshold value of maximum loadability margins (MLM), calculated using continuation power flow (CPF) method. For insecure states, the presented technique also gives optimal load shedding plan to bring the system from insecure to secure region. Decision trees (DT) are used for case indexing to reduce the search time to obtain the set of relevant cases, which are in thousands of numbers. In addition, decision trees also provide the information about those case features, which mostly influence the severity of a given contingency of the power system. Unlike other non-deterministic approaches, the proposed method is easy to understand for operators, easy to modify under the change of topology of the power system and has continuous learning capability. The effectiveness of the proposed approach is tested on IEEE test systems. The proposed CBR approach provides a fast and accurate voltage security assessment for unknown load patterns and a load shedding plan for insecure cases to mitigate the voltage collapse. Hence it found to be suitable for on-line applications of energy management systems.

Direct solution method for initialising doubly-fed induction wind turbines in power system dynamic models

The modelling of a doubly-fed induction generator (DFIG) wind turbine in large power system dynamic simulation software is discussed, and the steady state equivalent circuit and reduced order dynamic DFIG models are described. A direct solution method for obtaining injected rotor voltages, which satisfy the dynamic model control objectives, is derived from the approximate steady state model. An initialisation procedure is given for the reduced order dynamic DFIG machine model. Simulation results are presented from initialised dynamic DFIG wind turbine models. PQ and PV bus representations of the DFIG for load flow studies are compared and simulated with typical turbine and network data for wind farm installations.

A sequential feature selection-based neural network approach to dynamic voltage stability estimation

Two sequential self-organizing hierarchical neural network (SHNN) models are utilized to estimate power system voltage stability. The first SHNN determines whether the power system is dynamically stable or not. The second one is used for the dynamically stable system to estimate the voltage magnitudes at all PQ buses. Tests results at different loading conditions for two test systems, WSCC nine-bus system and New England 39-bus system, are reported.

Modeling of wind farms in the load flow analysis

Two methods are proposed, for the simulation of wind farms with asynchronous generators in the load flow analysis. Both methods are based on the steady-state model of the induction machine. The first involves improving the conventional PQ bus, and the second involves modeling the generators in steady-state in the bus where the wind farm is located. The two sets of results are then compared.

Comparison of feature selection techniques for ANN-based voltage estimation

Abstract Fast estimation of bus voltage magnitude is essential for security monitoring and analysis of power system. An approach based on a parallel self-organising hierarchical neural network (PSHNN) is proposed to estimate bus voltage magnitudes at all the PQ buses of a power system in an efficient manner. PSHNN is a multi-stage neural network in which stages operate in parallel rather than in series during testing. The revised back-propagation algorithm is used for learning input non-linearities along with forward-backward training of stage neural networks. A method based on Euclidean distance clustering is proposed for feature selection. Effectiveness of the proposed method is compared with two existing methods of feature-selection entropy based and angular distance based clustering methods for bus voltage magnitude estimation at different loading conditions in the IEEE 30-bus system and a practical 75-bus Indian system. The PSHNN based on Euclidean distance based clustering method is found to be superior in terms of training time and error performance.

MEASURES OF VOLTAGE INSTABILITY AND VOLTAGE COLLAPSE, PART II: COMPUTATIONAL ASPECTS

Based on the boundary theorems developed in [1], a method of voltage stability analysis referred to as the Eigen-Structure Analysis method, is developed that does not require the complicated nonlinear programming calculations for evaluation of the closest boundary condition corresponding to a given power network operating point with voltage controlled and PQ buses. An algorithm for determining the stability margin and its sensitivity to bus voltages and bus injections is proposed which is capable of handling large scale power systems by utilizing the sparse matrix techniques for saving computation time and memory space. The Eigen-Structure Analysis method is applied to a number of test system models. The simulation results confirm the theory and show that the proposed stability margin decreases monotonically to zero when the system approaches voltage collapse. Simulation results for 30-bus New England Test System are included in this paper.

A NEW CLUSTERING TECHNIQUE FOR POWER SYSTEM VOLTAGE STABILITY ANALYSIS

Abstract Bus clusters are usually formed by forming groups of PQ and PV buses which are coherent. All the buses in a cluster behave in a coherent manner and therefore a bus can be taken as representative of a group of buses in a cluster. Bus clusters are useful in voltage stability analysis because they not only can be used to identify the weak and strong areas in a network but also help to speed up the control actions taken to improve voltage stability. This paper presents an LQPN method which uses the line stability factors to identify the weak lines in a network. The weak lines are eliminated and the bus clusters are formed based on the coherent nature of buses in a cluster. The LQPN method is compared with an earlier method developed by Schlueter which forms voltage control areas or bus clusters. The results of the bus clusters formed by the two methods are found to be in close agreement.

Tellegen theorem and modelling of power systems — PV buses and nonlinear formulas

Tellegen's theorem has often been used to derive network sensitivities for a variety of systems, including power systems. Recently, Tellegen's theorem has been used to derive approximate nonlinear formulas for evaluating the response of a power system to large network perturbations. Those formulas are efficient and yield accurate results, but the efficiency deteriorates dramatically for systems with PV buses. The reason for the deterioration is that the coefficients of the formulas are computed under the assumption of PQ buses; hence, the resulting formulas have to be iteratively corrected. In the paper, approximate noniterative nonlinear formulas are developed which include PV and PQ buses with equal ease. The modelling behind these formulas is presented. It is shown that, whereas a PQ bus leads to a voltage controlled current source, a PV bus leads to a current controlled voltage source. It is also shown that the corresponding adjoint solutions can be obtained by solving a system of linear equations. A complete numerical example is provided to enable the replication of the results by the reader.

Static bifurcations in electric power networks: Loss of steady-state stability and voltage collapse

This paper presents an analysis of static stability in electric power systems. The study is based on a model consisting of the classical swing equation characterization for generators and constant admittance, PV bus and/or PQ bus load representations which, in general, leads to a semi-explicit (or constrained) system of differential equations. A precise definition of static stability is given and basic concepts of static bifurcation theory are used to show that this definition does include conventional notions of steady-state stability and voltage collapse, but it provides a basis for rigorous analysis. Static bifurcations of the load flow equations are analyzed using the Liapunov-Schmidt reduction and Taylor series expansion of the resulting reduced bifurcation equation. These procedures have been implemented using symbolic computation (in MASYMA). It is shown that static bifurcations of the load flow equations are associated with either divergence-type instability or loss of causality. Causality issues are found to be an important factor in understanding voltage collapse and play a central role in organizing global power system dynamics when loads other than constant admittance are present.

A structure preserving energy function for power system transient stability analysis

A new model is proposed for the study of transient stability where the load is modeled as a PQ bus. Flux decay of the generator field winding is included. The original network topology is maintained explicitly. An energy function is proposed which differs from the traditional one in that it includes additional terms corresponding to the energy stored in the loads and field winding. A characterization of the stability region is derived based on this energy function.

Quantitative Analysis of Steady State Stability in Power Networks

A quantitative analysis of the steady state stability of a general network with arbitrary PV, PQ and slack buses is presented. Steady state stability is that property of the power network defining the constraints on the bus injections under which a steady state equilibrium exists. Necessary and sufficient conditions for steady state stability as well as an algorithm to verify these conditions are derived. The degree of steady state stability of the injections (operating points) is quantified through a computable scalar stability margin. Such a stability margin serves as a design measure with which to compare the steady state stability of different operating points or networks. This result is extended to include the important case where the injections are restricted to certain subspaces. Another result is a simple-to-verify sufficient conditions for steady state stability-in the vicinity of a feasible injection vector

On-line secure and economic dispatch

This paper describes the application of an on-line economic dispatch control program with security constraints including outage-contigency constraints. The program is designed to run on average every 30 s with a small power system and gives feasible solutions with respect to constraints on control variables (real power generation, except in the slack bus, and voltage magnitudes in the PV and slack buses), to constraints on state variables (voltage magnitude in PQ buses) and also to constraints on output variables (line current magnitudes, swing generation and reactive generation in the PV and swing buses). The program has been extensively tested on the Imperial College Power System Simulator. Depending on the solution, the program sends a set of actions to the raise/lower speeder gear and the automatic voltage regulator of each generator unit. For test purposes several well-determined sets of load variations were used and the total generation costs were recorded and compared with the minimum costs (ideal control) and the normal costs (no control). As in a real power system, the simulator ran during these tests with a load/frequency control program in operation. This program, acting upon the raise/lower speeder gear of the generator units, was given priority for its actions, so that the economic actions were only taken when the generation-demand of the system was balanced.