A study of the homogeneous algorithm for dynamic economic dispatchwith network constraints and transmission losses

This paper presents a study of the homogeneous interior point (HIP) method for the economic dispatch problem that combines both independent blocks of constraints (generation demand balance, network flows) and coupling constraints (ramping) into a single optimization problem. By approximating the network constraints through the DC load flow, and the transmission losses through the B-matrix loss formula, the problem is reduced to a convex optimization problem that possesses nonlinear inequality constraints and free variables. The HIP algorithm is specialized in solving this problem, it yields either an approximate global optimum solution or detects possible infeasibility or unboundedness of the problem. The algorithm is tested on the IEEE 14, 30, 57, and 118 bus test systems dispatched over 10 half-hour intervals. The results show that the algorithm is practically efficient     

A PC based state estimator interfaced with a remote terminal unitplacement algorithm

In this paper a new remote terminal unit (RTU) placement algorithm is presented. The objective of this algorithm is to place a minimum set of RTUs which satisfies three important constraints of the problem-observability, absence of critical measurements, and reliability requirements defined in terms of RTU loss. The problem is solved in a single stage. The results of this algorithm are interfaced with a linear programming (LP) state estimator. This estimator only uses the voltage measurements, and the active and reactive power flows in the lines for the development of the coupled state-estimation Jacobian H-matrix. The injection measurements are not currently included, though in practice they can be easily added to the estimator model. The inclusion of the injection measurements will enlarge the use of the presented algorithm. The RTU placement algorithm and its link with the LP estimator are tested on IEEE standard bus systems. Using the proposed RTU set, the test results presented show that the LP estimator has very good filtering capabilities when operated with or without bad data, and that the loss of any RTU does not have any significant impact on the solution     

Self-scheduling under ellipsoidal price uncertainty: conic-optimisation approach

Power producers have to take decisions concerning their bidding strategy in the presence of uncertain prices. The paper addresses the problem of generator self-scheduling when locational marginal prices are subject to ellipsoidal uncertainty. A robust counterpart of the uncertain self-scheduling problem is formulated as a second-order cone program and solved using a commercially available interior-point package. The safety parameter, which trades between profit and risk, is determined based on a prespecified chance that the realised loss would be greater than the corresponding value at risk. Simulation results are presented on the IEEE 30-bus test system. A Monte Carlo simulation is used to compare the stability properties of the schedules obtained.     

A Primal-Dual Interior-Point Method to Solve the Optimal Power Flow Dispatching Problem

This paper presents a primal-dual path-following interior-point method for the solution of the optimal power flow dispatching (OPFD) problem. The underlying idea of most path-following algorithms is relatively similar: starting from the Fiacco-McCormick barrier function, define the central path and loosely follow it to the optimum solution. Several primal-dual methods for OPF have been suggested, all of which are essentially direct extensions of primal-dual methods for linear programming. Nevertheless, there are substantial variations in some crucial details which include the formulation of the non-linear problem, the associated linear system, the linear algebraic procedure to solve this system, the line search, strategies for adjusting the centring parameter, estimating higher order correction terms for the homotopy path, and the treatment of indefiniteness. This paper discusses some of the approaches that were undertaken in implementing a specific primal-dual method for OPFD. A comparison is carried out with previous research on interior-point methods for OPF. Numerical tests on standard IEEE systems and on a realistic network are very encouraging and show that the new algorithm converges where other algorithms fail.     

A primal-dual interior point method for optimal power flow dispatching

In this paper, the solution of the optimal power flow dispatching (OPFD) problem by a primal-dual interior point method is considered. Several primal-dual methods for optimal power flow (OPF) have been suggested, all of which are essentially direct extensions of primal-dual methods for linear programming. The aim of the present work is to enhance convergence through two modifications: a filter technique to guide the choice of the step length and an altered search direction in order to avoid convergence to a nonminimizing stationary point. A reduction in computational time is also gained through solving a positive definite matrix for the search direction. Numerical tests on standard IEEE systems and on a realistic network are very encouraging and show that the new algorithm converges where other algorithms fail.     

Leakage flux saturation effects on the transient performance of wound-rotor induction motors

The prediction of induction machine performance has traditionally been based on the constant parameter models. This approach was later replaced by considering saturation in the main flux paths. However, such models have not been sufficiently accurate for certain transient conditions such as on-line starting and short-circuit. So, an accurate study of their performance should necessarily consider the magnetic saturation effect both in the main and leakage flux paths. In this paper, an experimental procedure to determine the machine parameters and saturation characteristics is adopted. The adopted experimental procedure facilitates the measurement of both stator and rotor leakage reactance saturation characteristics. Two models of saturated induction motors are developed to predict the transient performance of a laboratory wound-rotor induction motor. The results calculated by the proposed models considering and ignoring the leakage flux saturation are compared with the experimental results. The model that considers saturation in the leakage flux paths produces more accurate transient responses.     

Conic programming approach for static voltage stability analysis in radial networks

That the problem of computing the capacity limit of a radial distribution system can be formulated as a second-order cone program is shown. The implications of the conic programming formulation are 2-fold. First, the load capability of the radial system can be obtained using existing efficient implementations of polynomial time interior-point algorithms, thus avoiding the need for running a sequence of load flow solutions. Secondly, the conic objective function yields a voltage stability indicator (SI). This indicator quantifies the maximum percentage by which the current load profile can be uniformly increased before voltage collapse occurs. The proposed method is validated by computing the load capability and voltage SIs of 11 different distribution systems. Comparisons are carried out with five previously published voltage SIs     

Choice of estimator for distribution system state estimation

In this study, a statistical framework is introduced to assess the suitability of various state estimation (SE) methodologies for the purpose of distribution system state estimation (DSSE). The existing algorithms adopted in the transmission system SE are reconfigured for the distribution system. The performance of three SE algorithms has been examined and discussed in standard 12-bus and 95-bus UK-GDS network models.     

Generation self-scheduling with partial information on the probability distribution of prices

Recent research has shown that generation self-scheduling in electricity markets can be approached using conditional value-at-risk (CVaR). This study considers a worst-case CVaR methodology applicable to cases where only partial information on the underlying probability distribution of prices is given. In particular, the probability distribution is considered under box and ellipsoidal uncertainty structures. It is shown that both structures result in self-scheduling problems that can be formulated as a quadratic cone program. The cone program can be used to (i) compute the worst-case conditional robust profit with probability level β and (ii) optimise the self-schedule for a pre-specified probability β of the corresponding worst-case conditional robust profit. Simulation results are used to demonstrate the self-scheduling model based on the worst-case CVaR. The usefulness of the proposed model is established by contrasting it with the CVaR approach.     

Application of geometric programming to transformer design

This paper considers the transformer design optimization problem. In its most general form, the design problem requires minimizing the total mass (or cost) of the core and wire material while ensuring the satisfaction of the transformer ratings and a number of design constraints. The constraints include appropriate limits on efficiency, voltage regulation, temperature rise, no-load current, and winding fill factor. The design optimization seeks a constrained minimum mass (or cost) solution by optimally setting the transformer geometry parameters and the relevant electrical and magnetic quantities. In cases where the core dimensions are fixed, the optimization problem calls for a constrained maximum volt-ampere or minimum loss solution. This paper shows that the above design problems can be formulated in geometric programming (GP) format. The importance of the GP format stems from two main features. First, GP provides an efficient and reliable solution for the design optimization problem with several variables. Second, it guarantees that the obtained solution is the global optimum. The paper includes a demonstration of the application of the GP technique to transformer design. It also includes a comparative study to emphasize the advantage of including the transformer core dimensions as variables in the design problem.