Real Power Dispatch Research Articles

Improving an interior-point-based OPF by dynamic adjustments of step sizes and tolerances

This paper presents an efficient interior point algorithm for optimal power flow (OPF) problems, in particular, the real power dispatch and the reactive power dispatch problems. The nonlinear OPF problem is solved by a predictor-corrector primal-dual log-barrier (PCPDLB) method as a sequence of linearized sub-problems. Besides discussing the problem formulation, the paper offers a detailed description of the PCPDLB algorithm; it also addresses several implementation issues such as the determination of barrier parameter and the customization of initial points for OPF problems. In addition, practical issues on how to choose linear step sizes and convergence criteria are investigated to evaluate their impact on the performance of the algorithm. Some heuristics of dynamically adjusting step sizes and tolerance are proposed which significantly improve OPF solution speed. Computational results on power systems of 118 and 1062 buses are presented and discussed. Comparisons with other variants of primal-dual log-barrier methods are also provided to demonstrate the superiority of the proposed predictor-corrector interior point algorithm.

SENSITIVITY FACTOR BASED SHORT TERM DYNAMIC OPTIMAL POWER FLOW

ABSTRACT In general, conventional Optimal Power Flow(OPF) solutions utilize some optimization techniques at a single case. In the OPF solution method, all the available variables are used to solve the problem. In practical operation, such a solution is not a practical consideration because the control actions would be too many to be implemented. In this paper, sensitivity factors combined with dynamic programming technique are used to solve short term (one day) dynamic optimal power flow. A two-step real time real power dispatch method considering inconforming load change is used to solve real power dispatch, and then, the sensitivity factors are used to solve reactive power dispatch with some constraints. Finally, the dynamic programming technique is used to minimize the control actions to as little as possible. The advantages of this method are simple and easy to implement, and it would greatly enhance the operators' planning.

A real-time closed loop controller for security dispatch

The objective of the proposed controller is to ensure that the system is always in a secure state with no system component being overloaded, even under changing load conditions. In addition the controller ensures that the conventional requirements such as Automatic Generation Control (AGC) and Economic Load Dispatch (ELD) are met. The controller makes use of the system measurements obtained through Supervisory Control and Data Acquisition (SCADA) systems and evaluates incremental changes to the control variables as and when necessary. The incremental changes are such that the system operating state will move towards the optimal state in which the objectives of the controller are achieved. Unlike the conventional Optimal Power Flow (OPF) methods which inherently solve the power system model to determine the optimal operating point, the proposed controller solves only a set of controller equations. The scheme is implemented for real power dispatch and is tested for its efficacy on a dynamic power system simulator.

A New Approximate Sub-Optimum Formulation for Real and Reactive Power Optimization

This paper presents a new formulation for optimal real and reactive power dispatch for economic operation of electric power systems. As in other recent formulations, the problem is decomposed into a Q-optirnization module and a P-optimization module to minimize real power transmission losses and hourly fuel costs of thermal generating units, respectively. The formulation is based upon the approximations due to the well-known power system coupling principles.

A UNIFIED APPROACH TO OPTIMAL POWER FLOW SOLUTIONS USING GRG

ABSTRACT This paper presents a new formulation of the optimal power flow problem suggesting a single objective function for real and reactive power dispatch. This objective function is nothing but the sum of the cost of active generation and system losses satisfying the network constraints. The objective function and constraints are expressed in terms of real and imaginary parts of bus voltages and line parameters. The generalized reduced gradient technique has been used to solve this problem. Effectiveness of this formulation is demonstrated by taking examples of actual networks.

Multiple objective optimal load flow. a new perspective

In the past a great deal of work has been reported on optimal load flow (OLF). However, in most of the works only one aspect of the power system has been optimised. The OLF problem (optimal real and reactive power dispatch) has been attempted sequentially, rather than simultaneously. In this paper a new formulation of the OLF problem has been attempted to minimise both the cost of generation and transmission loss simultaneously through a multiple objective programming technique (priority goal programming technique).

Different time-scale approaches to the real power dispatch of thermal units

Different time-scale approaches to the dispatch problem are proposed for the centralized control of real power. In particular, the problem of optimally sharing a time-varying load among the committed thermal units of an electrical power system is addressed. It is shown that the real power dispatch of the thermal units is handled at different time scales as a dynamic problem where rate of change limits , environmental constraints, and the security constraints of the traditional static approach are taken into account. The adoption of the same general model guarantees the coherency of the results in the three phases of day-before scheduling, advance dispatch, and online dispatch. A modified gradient projection algorithm, which suitably exploits some good second-order information, has been adopted for the solution of the large-scale problem arising from the discretization of the dynamic model. The resulting procedure is capable of solving the very large day-before scheduling (more than 2000 variables and 4000 constraints for the Italian EHV system) in a few minutes, as well as providing the solution of the advanced dispatch problem in no more than 10 s even when a corrective rescheduling is required.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An elegant approach to optimal real and reactive power dispatch

This paper presents a new reactive VAR and real power dispatch method for the economic operation of a power system. The analysis is twofold, involving successive evaluation of the optimum voltage and the real power generation. The former is obtained by reactive VAR control, avoiding non-linear programming techniques, and the latter by a closed-form expression of λ, a linear function of the penalty factors. Transmission losses are considered as a function of the system voltage and are minimized by adjusting the transformer tap positions, the reactive power injection of VAR sources, and the generator voltage magnitude dependent on excitation. The feasibility of the technique is demonstrated by means of a standard system.

Security constrained dynamic dispatch of real power for thermal groups

A dynamic approach to the real power dispatch of thermal generating units, suitable for time periods characterized by high rates of load variation, is presented. A discrete formulation of the dispatch problem is adopted, with step variations of the loads. Dynamic constraints on the rate of change of the present loading output of thermal units are added to the ordinary constraints of the static approach. Costs associated with the act of quickly changing the thermal generation are included in the model. The solution of the problem uses a modified version of the Han-Powell algorithm in a compact-reduced model formulation. A sparsity technique used in the construction and in the updating of the Hessian matrix of the Lagrangian function, allows the solution of large-scale problems arising from a minute subdivision of the dispatch interval in large electrical systems. >

Large-scale application of the Han-Powell algorithm to compact models of static and dynamic dispatch of real power

In this study some second-order algorithms derived from the Han-Powell method are applied to real power optimization both in a static and in a dynamic dispatch procedure with security constraints. These procedures employ suitable compact reduced models for large-scale applications. In the dynamic approach a time-varying load is shared among the control units by adopting a discrete formulation of the dispatch problem. This involves the subdivision of the optimization interval into a certain number of sub-intervals with constant loads and the addition, to the ordinary constraints of the static approach, of dynamic constraints on rate of change of MW output of thermal units. In particular, security constraints are modified in order to take into account their dependence on the load variability during the optimization interval. Also in the paper, a dynamic approach is shown to be needed for preventive scheduling of the thermal generation during the time periods characterized by a high rate of load variation (pick-up or drop-down hours) as well as during the online rescheduling. The robustness and the efficiency of the adopted procedures have been demonstrated by several tests on a sample network of small dimension as well as on large-scale systems. In the dynamic approach a suitably modified version of the Han-Powell algorithm is adopted which employs an alternative technique in the construction and in the updating of the Hessian matrix of the Lagrangian function. This allows us to handle large-scale problems arising from the optimization of a large system on the framework of a minute subdivision of the dispatch interval. This technique exploits and conserves in the updating phase the sparseness property of the matrix, without using the usual Broyden-Fletcher-Shanno-Goldfarb formulae.

A United Approach to Optimal Real and Reactive Power Dispatch

This paper presents a unified method for optimal real and reactive power dispatch for the economic operation of power systems. As in other methods, the problem is decomposed into a P-optimization module and a Q-optimization module, but in this method both modules use the same generation cost objective function. The control variables are generator real power outputs for the real power module; and generator reactive power outputs, shunt capacitors/reactors, and transformer tap settings for the reactive power module. The constraints are the operating limits of the control variables, power line flows, and bus voltages.

A United Approach to Optimal Real and Reactive Power Dispatch

A United Approach to Optimal Real and Reactive Power Dispatch

Optimal real and reactive power dispatch

Abstract This paper presents a method for optimal real and reactive power dispatch for the economic operation of power systems. As in other methods, the problem is decomposed into a P-optimization module and a Q-optimization module, but in this method both modules use the same generation cost objective function. The control variables are generator real power outputs for the real power module; and generator reactive power outputs, shunt capacitors/reactors, and transformer tap settings for the reactive power module. The constraints are the operating limits of the control variables, power line flows, and bus voltages. The optimization problem is solved using the gradient projection method (GPM) which is used for the first time in the power systems study. Among other advantages, the GPM allows the use of functional constraints without the need for penalty functions or Lagrange multipliers. Mathematical models are developed to represent the sensitivity relationships between dependent and control variables for both (real and reactive power) optimization modules, and thus eliminate the use of B-coefficients. Results of two test systems are presented and compared with conventional methods.

Optimum Dispatch of Active and Reactive Generation by Quadratic Programming

Optimum scheduling of generation subject to constraints on maximum and minimum levels and rates of change of generation, spare capacity and line flow limits, is studied. A linear programming formulation for system constraints is used with a quadratic cost function for generation and transmission line loss. An optimal solution for real power dispatch is obtained by quadratic programming, and optimum allocation of reactive power is based on a gradient technique which minimises transmission loss subject to nodal voltage and reactive power limits. An ac load flow analysis is incorporated together with a load prediction program based on a spectral analysis of past load data. The feasibility of simulating the overall system problem, including load-frequency control of equivalent generation, using a combined analogue-digital process computer system linked to a large scientific digital computer by data link is investigated.

Multicomputer Configurations and Diakoptics: Dispatch of Real Power in Power Pools

It is the major objective of this paper to present the use of multicomputer configurations in the dispatch of real power in power pools. It is shown that the area dispatch computers, upon the formation of power pools, can form a multicomputer configuration. The characteristics of such a configuration are outlined and a computer hierarchy presented. Both the single-area as well as the multiarea approaches to the power dispatch problem are formulated and their associated modeling described. A number of novel methods for the instant-by-instant dispatch of real power are given. Three multiarea methods are described in detail which have been called 1) pool boundary cost iteration method, 2) pool ?ratio method, and 3) pool base point and participation factor method.

A Method for Optimum Scheduling of Power and Voltage Magnitude

A general formulation of the economic dispatch problem is presented, based on the Lagrange multipliers approach. The necessary conditions are established and upon these conditions an algorithm is developed for real power and voltage magnitude dispatch (i.e., reactive power dispatch). Feasible solutions are always attained during the optimizing procedure. Basically the coordination equations have the same form of the Jacobian matrix for which efficient solution methods have already been developed. Very small additional work beside the necessary calculations for a load flow solution by Newton's method is required. All the equality constraints dual variables (Lagrangian multipliers) are calculated in the iterative procedure, but once the optimal solution is attained (within a specified precision) the additional dual variables of the Kuhn-Tucker theorem for the effective inequality constraints can be calculated. The feasibility of the method is shown by means of a sample system.