A new formulation for FACTS allocation for security enhancement against voltage collapse

This paper proposes a new formulation for reactive power (VAr) planning problem including the allocation of flexible ac transmission systems (FACTS) devices. A new feature of the formulation lies in the treatment of security issues. Different from existing formulations, we directly take into account the expected cost for voltage collapse and corrective controls, where the control effects by the devices to be installed are evaluated together with the other controls such as load shedding in contingencies to compute an optimal VAr planning. The inclusion of load shedding into the formulation guarantees the feasibility of the problem. The optimal allocation by the proposed method implies that the investment is optimized, taking into account its effects on security in terms of the cost for power system operation under possible events occurring probabilistically. The problem is formulated as a mixed integer nonlinear programming problem of a large dimension. The Benders decomposition technique is tested where the original problem is decomposed into multiple subproblems. The numerical examinations are carried out using AEP-14 bus system to demonstrate the effectiveness of the proposed method.     

Sensitivity Methods in the Dispatch and Siting of FACTS Controllers

Flexible AC transmission systems (FACTS) play an important role in improving the transfer capability and stability of a power system. In the application of voltage-sourced converter (VSC)-based FACTS controllers, it is important to study how a VSC impacts the flows in a power system. In this paper, we investigate this flow control problem using two sensitivity approaches, one using an injected voltage source formulation and the other an equivalent impedance formulation. The applications of sensitivity analysis for line active power redispatch and for new series VSC siting in a 1673-bus system are presented.     

Fast linear programming state estimation using the dual formulation

The authors present a fast and efficient technique for solving the power system state estimation problem using linear programming (LP). The dual formulation of the original problem is described. This formulation improves the solution time significantly. Four LP state estimators are presented and test results on the IEEE 30, 57, and 118 bus standard systems are included. Both the full and decoupled dual problems were solved. Test results indicate that the dual estimators are superior to the primal estimators     

Environmentally constrained economic dispatch using the LaGrangianrelaxation method

This paper presents a general formulation of the environmentally constrained economic dispatch (ECED) problem based on the requirements of Clean Air Act Amendments of 1990 and others which may be imposed by local air quality regulations. The formulation considers multiple NO_x constraints and incorporates the utilization of the affected units (those named in the legislation) along with SO₂ constraints. It also proposes a new algorithm to solve the problem for large power systems. This algorithm has the ability to handle a large number of various types of linear and nonlinear environmental constraints. It is reliable, and viable for both offline and online applications. Test results on a large size power system demonstrate the possible savings which can be realized by using the algorithm. Details of the problem formulation and the solution technique are given in the paper     

A more efficient formulation for computation of the maximum loadingpoints in electric power systems

This paper presents a more efficient formulation for computation of the maximum loading points of power systems. A distinguishing feature of the new formulation is that it is of dimension (n+1), instead of the existing formulation of dimension (2n+1), for n-dimensional load flow equations. This feature makes computation of the maximum loading points very inexpensive in comparison with those required in the existing formulation. A theoretical basis for the new formulation is provided. The new problem formulation is derived by using a simple reparameterization scheme and exploiting the special properties of the power flow model. Moreover, the proposed test function is shown to be monotonic in the vicinity of a maximum loading point. Therefore, it allows one to monitor the approach to maximum loading points during the solution search process. Simulation results on a 234-bus power system are presented     

Transmission expansion planning: a mixed-integer LP approach

This paper presents a mixed-integer LP approach to the solution of the long-term transmission expansion planning problem. In general, this problem is large-scale, mixed-integer, nonlinear, and nonconvex. We derive a mixed-integer linear formulation that considers losses and guarantees convergence to optimality using existing optimization software. The proposed model is applied to Garver's 6-bus system, the IEEE Reliability Test System, and a realistic Brazilian system. Simulation results show the accuracy as well as the efficiency of the proposed solution technique.     

Efficient integer optimization algorithms for optimal coordinationof capacitors and regulators

The optimal coordination of switched capacitors and tap-changing transformers in a radial distribution system is considered. The formulation incorporates voltage constraints. The coordination problem is approximated by a constrained discrete quadratic optimization using the results from the corresponding unconstrained continuous problem. The discrepancy between the actual and approximating problem is discussed. Two algorithms are proposed to seek solutions to the approximating optimization problem. The first is a randomized algorithm that runs fast but for which there is no guarantee of optimality. The second is a deterministic algorithm, the run time of which is polynomially bounded in the problem size. For large systems the run times of these algorithms may be significantly less than the run times of explicit search or branch and bound algorithms. Test results on a 70 node system confirm the theoretical predictions     

Combined genetic algorithm/simulated annealing/fuzzy set approachto short-term generation scheduling with take-or-pay fuel contract

This paper first develops a new formulation for short-term generation scheduling with take-or-pay fuel contract. In the formulation, a fuzzy set approach is developed to assist the solution process to find schedules which meet as closely as possible the take-or-pay fuel consumption. The formulation is then extended to also cover the economic dispatch problem when the fuel consumption is higher than the agreed amount in the take-or-pay contract. The extended formulation is combined with the genetic algorithms and simulated-annealing optimization methods for the establishment of new algorithms for the present problem. The new algorithms are demonstrated through a test example, in which the generation loadings of 13 generators in a practical power system are scheduled in a 24-hour schedule horizon     

Supply Shortage Hedging: Estimating the Electrical Power Margin for Optimizing Financial and Physical Assets With Chance-Constrained Programming

This paper deals with estimating the maximal production capacity of a hydrothermal system. We will show why this is of interest and how such a problem arises in a context of hedging against supply shortage, using financial and physical assets. Therefore, we will formulate the supply shortage hedging as a stochastic optimization problem with chance constraints and show on an example why introducing physical assets in the hedging problem is of economical interest. We then highlight the inherent mathematical difficulties, introduced by optimizing physical assets. Using maximal production capacities of the hydrothermal system improves tractability of the hedging problem. However, focusing on the hydraulic production maximal capacity, we illustrate the combinatorial and nontrivial nature of this subproblem. Finally, we show how our problem formulation may lead to embedded chance constraints.     

An Improved Harmonic Load Flow Formulation

Abstract

The paper contributes an improved harmonic load flow formulation with fewer convergence problems but the same accurate results as traditional formulations. The proposed formulation approaches the harmonic load flow problem as a single nonlinear equation system where the harmonic bus voltage influence on nonlinear load behavior is considered and harmonic bus voltages at linear buses are not included as unknowns. This formulation allows any sort of nonlinear load to be considered and uses the Newton-Raphson method with true Jacobian matrix to reduce the inherent increase in the number of iterations caused by the presence of highly distorted bus voltages. The numerical results obtained when solving a three-bus network operating under highly distorted bus voltages using traditional harmonic load flow formulations and the improved formulation are comparatively discussed.     

Stochastic mid-term generation scheduling incorporated with wind power

A challenge now facing system operator is how to schedule optimally the generation units in a wind integrated power system over a one year time horizon considering the effects of wind forecasting and variability; also, regarding the effects of load uncertainty. By the same token, this paper first develops a new formulation for Stochastic Mid-term Generation Scheduling (SMGS). In the formulation, 2m + 1 point estimate method is developed to accurately estimate the output variables of Mid-term Generation Scheduling (MGS) problem. Then, the formulation is combined with adaptive modified gravitational search algorithm and a novel self-adaptive wavelet mutation strategy for the establishment of new robust algorithm for the present problem. It is noteworthy to say that the classical methods considered certain wind information in the deterministic solution of the MGS problem which is not the realistic approach. However, this study improves modeling of wind–thermal system in the MGS problem by considering possible uncertainties when scheduling the generators of power system. The proposed model is capable of taking uncertainty of load and wind into account. The proposed method is applied on two test cases and the numerical results confirmed the efficiency and stability of the proposed algorithm.     

A reinforcement learning approach to automatic generation control

This paper formulates the automatic generation control (AGC) problem as a stochastic multistage decision problem. A strategy for solving this new AGC problem formulation is presented by using a reinforcement learning (RL) approach. This method of obtaining an AGC controller does not depend on any knowledge of the system model and more importantly it admits considerable flexibility in defining the control objective. Two specific RL based AGC algorithms are presented. The first algorithm uses the traditional control objective of limiting area control error (ACE) excursions, where as, in the second algorithm, the controller can restore the load-generation balance by only monitoring deviation in tie line flows and system frequency and it does not need to know or estimate the composite ACE signal as is done by all current approaches. The effectiveness and versatility of the approaches has been demonstrated using a two area AGC model.     

HYDRO-THERMAL POWER SYSTEM LOSS MINIMIZATION: A PROBABILISTIC PERTURBATION APPROACH

ABSTRACT

We present a formulation of the power system loss minimization problem that includes power demand uncertainty. We assume that the perturbations in the system power demand and its resultant effects on the system voltages as random variables with zero mean and some variance.

The equality constraints associated with the formulation are characterized by the power flow equations in polar form utilizing the nodal admittance matrix approach. The algorithm is applied to 4 different IEEE hypothesized test system, using Newton's method and Powell's penalty function approach, and computational results are obtained. A comparison of the probabilistic approach with deterministic based solutions for three systems are offered. The difference in voltage profiles and other variables may be minimal for smaller systems. However, these differences appear to be substantial as the system increases both in size and capacity.     

Optimal dynamic economic dispatch of generation: A review

This paper presents a review of the research of the optimal power dynamic dispatch problem. The dynamic dispatch problem differs from the static economic dispatch problem by incorporating generator ramp rate constraints. There are two different formulations of this problem in the literature. The first formulation is the optimal control dynamic dispatch (OCDD) where the power system generation has been modeled as a control system and optimization is done in the optimal control setting with respect to the ramp rates as input variables. The second one is a later formulation known as the dynamic economic dispatch (DED) where optimization is done with respect to the dispatchable powers of the committed generation units. In this paper we first outline the two formulations, then present an overview on the mathematical optimization methods, Artificial Intelligence (AI) techniques and hybrid methods used to solve the problem incorporating extended and complex objective functions or constraints. The DED problem in deregulated electricity markets is also reported.     

Planning of multi-type FACTS devices in restructured power systems with wind generation

Many electrical power systems are changing from a vertically integrated entity to a deregulated, open-market environment. This paper proposes an approach to optimally allocate multi-type flexible AC transmission system (FACTS) devices in restructured power systems with wind generation. The objective of the approach is to maximize the present value of long-term profit. Many factors like load variation, wind generation variation, generator capacity limit, line flow limit, voltage regulation, dispatchable load limits, generation rescheduling cost, load shedding cost, and multilateral power contracts are considered in problem formulation. The proposed method accurately evaluates the annual costs and benefits obtainable by FACTS devices in formulating the large-scale optimization problem under both normal condition and possible contingencies. The overall problem is solved using both Particle Swarm Optimization (PSO) for attaining optimal FACTS devices allocation as main problem and optimal power flow as sub optimization problem. The efficacy of the proposed approach is demonstrated for modified IEEE 14-bus test system and IEEE 118-bus test system.     

Optimized Restoration of Unbalanced Distribution Systems

A novel formulation for service restoration algorithm for unbalanced three phase distribution systems is described. This problem is a constrained multiobjective optimization formulated as a mixed integer non-linear programming problem. A comparison of the solutions with and without switch pairs has been made. The formulation was first validated using already developed three-phase unbalanced power flow software. The three-phase unbalanced power flow equations were embedded in the formulation, and hence separate calculations were not needed. Simulation results are presented for modified IEEE 13-node and IEEE 37-node test cases     

THE HYDRO-THERMAL OPTIMAL POWER FLOW PROBLEM IN RECTANGULAR COORDINATES

Abstract

This paper considers the formulation and computational solution of the optimal power flow problem in hydro-thermal electric system. The problem is formulated using the cartesian coordinate form of the power flow equations. Here the hydro generation is energy limited. As a result, a dynamic optimization problem involving the daily scheduling of the system is encountered. This dynamic optimal power flow problem requires the solution of a large scale set of non-linear simultaneous equations. In this paper, Newton's method is used to solve the problem. Due to the large scale nature of the problem, we have exploited the sparsity of the Jacobian and developed three different versions of the algorithms and implementation of these versions have been detailed in this paper. In all cases, the algorithm has been successfully tested with six standard IEEE test systems varying in size from 5 bus to 118 bus. Computational results and the CPU times required by all of the methods are given. Results are compared with the results obtained by the earlier version using polar form for load flow constraints and it is shown that the sparse implementation using rectangular coordinates offers superior computational speed.     

Optimum Hvac-Transmission Expansion Planning - A New Formulation

A new flexible mixed-integer formulation is presented in this paper for solving the single-stage ac-transmission expansion planning problem. This new formulation handles exactly the discrete nature of equipment additions without resorting to linearized incremental approaches, but still uses integer linear programming. The interconnection of a disconnected system is handled directly without resorting to an initial connected system. The optimal configuration at the end of the planning step under consideration minimizes an annually amortized cost function including the investment cost for equipment additions and the operating cost in terms of real-power transmission losses. Using a new efficient linear load-flow model, this new formulation is characterized by a complete decoupling between real and reactive equations. Examples have been incorporated to illustrate the potentials of this new optimum planning formulation.     

Analysis of FACTS devices on Security Constrained Unit Commitment problem

This paper focuses on solving Security Constrained Unit Commitment (SCUC) problem using ABC algorithm incorporating FACTS devices. The objective of the SCUC problem is to obtain the minimum operating cost simultaneously maintaining the security of the system. The SCUC problem is decomposed into Unit Commitment (UC), the master problem and Security-Constrained Economic Dispatch (SCED) as the sub-problem. The existing generation constraints, such as hourly power demand, system reserves, and minimum up/down time limits, ramp up/down limits are included in the SCUC problem formulation. The ability of FACTS devices to control the power flow through designated routes in transmission lines and thereby reducing the overloading of lines are studied. The solution of SCUC problem is also analyzed during a single line outage contingency. The SCUC is carried out incorporating FACTS devices such as SVC, TCSC, STATCOM, SSSC, UPFC and IPFC. The modeling of the FACTS devices within the power system network and finding a suitable location are discussed. The SCUC has been solved and validated on an IEEE 118-bus test system and a practical South Indian 86 bus utility.     

A fuzzy-based optimal reactive power control

A mathematical formulation of the optimal reactive power control problem using fuzzy set theory is presented. The objectives are to minimize real power losses and improve the voltage profile of a given system. Transmission losses are expressed in terms of voltage increments by relating the control variables to the voltage increments in a modified Jacobian matrix. This formulation does not require Jacobian matrix inversion, and hence it will save computation time and memory space. The objective function and the constraints are modeled by fuzzy sets. Linear membership functions of the fuzzy sets are defined and the fuzzy linear optimization problem is formulated. The solution space is defined as the intersection of the fuzzy sets describing the constraints and the objective functions. Each solution is characterized by a parameter that determines the degree of satisfaction with the solution. The optimal solution is the one with the maximum value for the satisfaction parameter. Results for test systems reveal the advantages of the approach