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This paper demonstrates how a probabilistic criterion could be explicitly integrated in the unit commitment (UC) formulation. Both spinning reserve and interruptible load are taken into account as the operating reserve facilities. Incorporating the interruption notice time of interruptible load involves some complexities in the evaluation procedure and problem formulation which is considered in this paper. The expected energy not supplied (EENS) is considered as a probabilistic criterion and a new method is proposed to calculate this index in the presence of interruptible load. The reliability-constrained unit commitment (RCUC) problem is formulated based on the mixed-integer programming (MIP) method that can be solved using large-scale commercial solvers. The effectiveness of the proposed formulation is examined using the IEEE-RTS. Numerical results are presented and the implementation issues are discussed. A number of analyses are examined to evaluate the impact of some important factors on the problem solution. [ABSTRACT FROM AUTHOR]

This paper proposes the planning method for capacitor installation in a distribution system to reduce the installation costs and minimize the loss of electrical energy. The expected life-time of devices with moving parts depends on the total number of operations, which affects the replacement period and replacement decisions for aging equipment under a limited budget. In this paper, the expected device lifetimes are included in the formulation, and the optimal operation status of the devices is determined using a genetic algorithm. The optimal numbers and locations for capacitor installation are determined based on the optimal operation status. Simulation results in a 69-bus distribution system show that the proposed technique performs better than conventional methods. [ABSTRACT FROM AUTHOR]

This paper presents a multiobjective performance index-based size and location determination of distributed generation in distribution systems with different load models. Normally, a constant power (real and reactive) load model is assumed in most of the studies made in the literature. It is shown that load models can significantly affect the optimal location and sizing of distributed generation (DG) resources in distribution systems. The simulation technique based on genetic algorithms is studied. The studies have been carried out on 16-bus and 37-bus distribution systems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel nonlinear approach to solve the short-term hydro scheduling problem under deregulation, considering head-dependency. The actual size of hydro systems, the continuous reservoir dynamics and constraints, the hydraulic coupling of cascaded hydro systems, and the complexity associated with head-sensitive hydroelectric power generation still pose a real challenge to the modelers. These concerns are all accounted for in our approach. Results from a case study based on one of the main Portuguese cascaded hydro systems are presented, showing that the proposed nonlinear approach is proficient. [ABSTRACT FROM AUTHOR]

This paper describes and analyzes the Spanish AGC system. The differences with respect to a standard hierarchical structure are explained. A simple model useful for simulation is proposed. Using this model, the performance of the system and the influence of several parameters in system response is evaluated. The paper also suggests some changes in the configuration and parameter settings of the system to improve its performance. [ABSTRACT FROM AUTHOR]

This paper describes a method of developing wide-band multi-port system equivalents for use with real-time digital power system simulators. The proposed equivalent combines a frequency dependent network equivalent (FDNE) for the high frequency electromagnetic transients and a transient stability analysis (TSA) type simulation block for the electromechanical transients. The frequency dependent characteristic for FDNE is obtained by curve-fitting frequency domain admittance characteristics using the vector fitting method. The paper also introduces an approach for approximating the frequency dependent characteristic of large power networks from readily available typical power-flow data. The paper shows how the TSA algorithm can be adapted to a real-time platform. The validity of this method is confirmed with examples, including the study of a multi infeed HVDC system based network. [ABSTRACT FROM AUTHOR]

The power oscillation damping (POD) controllers implemented in the two thyristor controlled series compensators of the Brazilian North-South (NS) interconnection, in the year 1999, were solely intended to damp the low-frequency NS oscillation mode. These controllers are still under operation and are derived from the modulus of the active power flow in the NS line that is phase-lagged at the frequency of the NS mode and may experience relatively large excursions generated by exogenous disturbances. This paper utilizes the same 1999 data to compare the performance of a proposed robust POD controller design with those of two conventional designs. A recent robust control synthesis algorithm used in this work is based on a nonsmooth optimization technique and has the capability to handle various controller structures, including reduced-order, and to deal with time-domain constraints on both controlled and measured outputs. Moreover, the nonsmooth design technique encompasses multiple operating conditions subject to various test signals, hence building a truly time-domain multi-scenarios approach. According to the results discussed hereafter, this is a key advantage in the industrial context of increasing demand for performance and robustness. The described results relate to a large-scale system model used in the feasibility studies for that interconnection. [ABSTRACT FROM AUTHOR]

Traditional online security assessment determines whether the system is secure or not, but how secure or insecure is not explicitly indicated. This paper develops probabilistic indices, risk, to assess real-time power system security level. Risk captures not only event likelihood, but also consequence. System security level associated with low voltage and overload can be optimally controlled, using the NSGA multiobjective optimization method. A security diagram is used to visualize operating conditions in a way that enables both risk-based and traditional deterministic views. An index for cascading overloads is used to evaluate the Pareto optimal solutions. This paper shows that the multiobjective approach results in less risky and less costly operating conditions, and it provides a practical algorithm for implementation. The IEEE 24-bus RTS-1996 system is analyzed to show that risk-based system security control results in lower risk, lower cost, and less exposure to cascading outages. [ABSTRACT FROM AUTHOR]

In power distribution networks the load varies within any given time frame. It may, therefore, seem that a good approach to reduce losses would be the solving of a network reconfiguration problem to suit each of the significant load variations. However, frequent changes in configuration can trigger outages or cause transient problems; they are best avoided. A recent formulation of this problem explicitly considers load variations and proposes to restrain frequent reconfigurations by assuming that network topologies will remain unchanged for a given planning period. This formulation leads to a much larger optimization problem than that traditionally used for network reconfiguration; moreover, it requires a new approach to optimization which is capable of dealing with energy flows instead of only instantaneous power flows. Such an approach is proposed in this paper, which discusses the design of an adaptive hybrid genetic algorithm that fulfills these new requirements. Key concepts in evolutionary computation and analysis of distribution systems are explored to develop this new algorithm. Application to real case studies certifies its benefits. [ABSTRACT FROM AUTHOR]

Deregulation of the electric power industry has introduced new uncertainties for market participants and made planning of transmission expansion more difficult. More flexible transmission expansion plans are needed, to cope with the increased risks. In this paper, a novel planning approach is proposed to meet the above challenge. In our approach, the planning process is modeled as a mixed integer nonlinear programming (MINLP) problem, so that conflicting objectives can be optimized simultaneously. To minimize planning risks, our method identifies several scenarios based on statistics and expert knowledge; the most flexible expansion plan is selected as the plan that has least adaptation cost. The proposed method is tested with the IEEE 14-bus system. Promising results are obtained to demonstrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present a new fuzzy logic method for midterm energy forecasting. The proposed method properly transforms the input variables to differences or relative differences, in order to predict energy values not included in the training set and to use a minimal number of patterns. The input variables, the number of the triangular membership functions and their base widths are simultaneously selected by an optimization process. The standard deviation is calculated analytically by mathematical expressions based on the membership functions. Results from an extensive application of the method to the Greek power system and for different categories of customers are compared to those obtained from the application of standard regression methods and artificial neural networks (ANN). [ABSTRACT FROM AUTHOR]

This paper describes use of a multiobjective optimization method, elitist nondominated sorting genetic algorithm version II (NSGA-II), to the generation expansion planning (GEP) problem. The proposed model provides for decision maker choice from among the different trade-off solutions. Two different problem formulations are considered. In one formulation, the first objective is to minimize cost; the second objective is to minimize sum of normalized constraint violations. In the other formulation, the first objective is to minimize investment cost; the second objective is to minimize outage cost (or maximize reliability). Virtual mapping procedure is introduced to improve the performance of NSGA-II. The GEP problem considered is a test system for a six-year planning horizon having five types of candidate units. The results are compared and validated. [ABSTRACT FROM AUTHOR]

In this paper, a primary frequency control strategy based on fuzzy logic, designed for variable-speed wind generators, is proposed and tested on a 2.2-kW test bench. The fuzzy logic supervisor ensures a regular primary reserve for a large range of wind speeds without any wind speed measurement. This supervisor controls simultaneously the generator torque and the pitch angle to keep the primary reserve; it determines in real time the generator power reference value. The fuzzy logic supervisor is compared to a simpler strategy, based only on the control of the generator torque. This classical strategy ensures a regular power reserve only when the wind generator operates at full load, and the generator power reference needs to be determined previously or by the network manager. A procedure for implementing a fuzzy logic supervisor in real time is proposed. The experiments indicate the regularity of the power reserve and the ability to contribute to frequency control. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for finding the sequence of events that may lead to catastrophic failure in a power system. The probable sequences (of events) leading to catastrophic failures are identified using risk indices which incorporate the severity as well as the probability of the contingencies. Probable collapse sequences are identified offline for different possible loading conditions using a modified fast decoupled load flow method which considers the voltage and frequency dependence of loads and generator regulation characteristics and stored in a knowledge base. Pattern recognition method and fuzzy estimation are used for online identification of collapse sequences for any operating condition from the stored database (knowledge base). [ABSTRACT FROM AUTHOR]

This paper proposes a new control approach for a unified power flow controller (UPFC) for power system oscillation damping. This control is simple to implement, yet is valid over a wide range of operating conditions. It is also effective in the presence of multiple modes of oscillation. The proposed control is implemented in several test systems and is compared against a traditional PI control. [ABSTRACT FROM AUTHOR]

In this paper, dead band control algorithms using a performance index of the load tap changing (LTC) tap position are proposed to reduce the tap changing operation times. The performance index is defined as the customer voltage quality with the tap position of LTC transformer. In addition, dead band control algorithms using the load diversity values of the feeders are proposed. The mathematical formulations of the proposed dead band control algorithms are introduced. A sample case study is shown to verify the effectiveness of the proposed dead band control algorithms. [ABSTRACT FROM AUTHOR]

In order that the supply of electric power remain stable and sustainable, a certain level of power quality must be maintained while securing energy resources and resolving environmental issues. The distributed generation (DG) has become an essential and indispensable element of such distribution systems from both an environmental and an energy security perspective. However, the installation of DGs in distribution systems may cause variations of voltage on distribution feeder because the DG power outputs may change randomly and dramatically. Generally, the sending voltage at substation in distribution systems can be regulated by an under load tap changer (ULTC) designed to maintain customers' receiving voltages within a predetermined range. Voltage regulation performed by ULTC calls for two parameters: the equivalent impedance and the load center voltage. Therefore, in distribution networks with DG interconnections, these parameters should be designed with attention not only to load variations but also to DG outputs. This paper proposes a method for designing ULTC parameters with reference to variations in DG output. The proposed algorithm is tested with IEEE 13-node system and Korean model network. The results demonstrate the validity of the proposed design method for varying DG distribution. [ABSTRACT FROM AUTHOR]

In a competitive electricity market, price forecasts are important for market participants. However, electricity price is a complex signal due to its nonlinearity, nonstationarity, and time variant behavior. In spite of much research in this area, more accurate and robust price forecast methods are still required. In this paper, a combination of a feature selection technique and cascaded neuro-evolutionary algorithm (CNEA) is proposed for this purpose. The feature selection method is an improved version of the mutual information (MI) technique. The CNEA is composed of cascaded forecasters where each forecaster consists of a neural network (NN) and an evolutionary algorithm (EA). An iterative search procedure is also incorporated in our solution strategy to fine-tune the adjustable parameters of both the MI technique and CNEA. The price forecast accuracy of the proposed method is evaluated by means of real data from the Pennsylvania-New Jersey-Maryland (PJM) and Spanish electricity markets. The method is also compared with some of the most recent price forecast techniques. [ABSTRACT FROM AUTHOR]

As power systems becoming more closely interconnected and are being deregulated in energy markets, distributed simulations among different dispatch centers are highly required for online full system analysis and control applications. In this paper a new algorithm for distributed transient stability simulation of interconnected power systems is presented. Based on a Jacobian-free Newton-GMRES(m) method, this algorithm requires only exchanges of states of boundary buses among different regions. Therefore, it has strong scalability in distributed computing environments built on heterogeneous computing resources. Moreover, several accelerating methods are developed to enhance its efficiency, including continuous preconditioning with adaptive preconditioners, predicting boundary conditions and multistep coordination. The standard IEEE 39-bus system and a real power system with 1165 buses were used as test systems. The test results show that these accelerating methods greatly enhance the convergence rate of the proposed algorithm and reduce communication costs remarkably, which proves the novel algorithm is feasible and can be adopted in wide area networks with high-latency. [ABSTRACT FROM AUTHOR]

Electromagnetic transient program (EMTP) simulators are being widely used in power system dynamics studies. However, their capability in real-time simulation of power systems is compromised due to the small time step used and relatively slow simulation speed. The shifted frequency analysis (SFA) is then proposed to accelerate the EMTP simulations for power system dynamics. The objective of this paper is to extend the SFA method [7] to model the induction machines in EMTP. By analyzing the relationship between rotor and stator physical variables, a phase-coordinate model with lower number of equations is first derived. Based on this, an SFA model is proposed as a general purpose model capable of simulating both fast transients and slow dynamics. Case study results have confirmed the SFA induction machine model is a valuable component for real-time EMTP simulations. It is observed that the SFA model is in excess of 70 times faster than the standard EMTP model when simulating dynamics with frequency spectra close to the fundamental power frequency. [ABSTRACT FROM AUTHOR]

This paper describes a methodology to identify potential conflicts among power flow control devices that may slow down or impair convergence. The proposed methodology is based on the eigenvalue analysis of the sparse Jacobian matrix associated with the Newton power flow with controls. Practically identical results are obtained from a smaller control sensitivity matrix. The implementation in a power flow program has been tested using both small- and large-scale systems. The results presented validate and clearly indicate the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

The ability of using dispersed generation (DG) in the distribution system restoration service in the context of smart networks is presented in this paper. The objectives are to reduce the consequences due to a major blackout in terms of the out-of-service load volume, and the duration of restoration process. Based on knapsack problem formulation and network represented graph modeling, a new restoration procedure for distribution network is proposed. An adapted branch-and-bound algorithm is then used to solve the problem. It maximizes the restored loads in distribution by using the DG availability. Simulation results on a study case will be shown to illustrate the proposed procedure and quantify the benefit of using DG in critical situations. [ABSTRACT FROM AUTHOR]

In the paper, Markov chains in conjunction with Monte Carlo simulation are used to predict the power system security level. The new approach uses a Markov chain for each identified security range to track the development of security level through time. Based on the forecasted and recorded data, the proposed procedure offers a useful tool to the system operator to predict a future power system security level. The method has been tested on the Bosnian power system using the recorded data on security levels during a one-year period. The forecasted results show a striking coincidence with the real security levels. By means of a simple and computationally fast method, the system operator can estimate the probability of a power system blackout. The presented method could be incorporated in the wide-area monitoring system in control centers. [ABSTRACT FROM AUTHOR]

In nowadays deregulated market, total transfer capability (TTC) calculation, which is the basis for evaluating available transfer capability (ATC), has been becoming more significant. During the last decade, transient stability constraints have been included in the optimal power flow approach to maximize TTC. However, no previous work on investigating the effect of generation shedding action to TTC has been reported. Therefore, in this paper, we propose a TTC maximization by means of transient stability constrained optimal power flow considering the generation shedding action. Proper selection of the generator to shed is based on its Lagrange multiplier value of transient stability constraint. Our simulation results show how TTC can be increased to anticipate possible generation shedding. [ABSTRACT FROM AUTHOR]

A generic operations framework for a distribution company (disco) operating in a competitive electricity market environment is presented in this paper. The operations framework is a two-stage hierarchical model in which the first deals with disco's activities in the day-ahead stage, the Day Ahead Operations Model (DAOM). The second deals with disco's activities in real-time and is termed Real-Time Operations Model (RTOM). The DAOM determines the disco's operational decisions on grid purchase, scheduling of distributed generation (DG) units owned by it, and contracting for interruptible load. These decisions are imposed as boundary constraints in the RTOM and the disco seeks to minimize its short-term costs keeping in mind its day-ahead decisions. A case-study is presented considering the well-known 33-bus distribution system and three different scenarios are constructed to analyze the disco's actions and decision-making in this context. [ABSTRACT FROM AUTHOR]

The task of controlling a power system is generally accomplished by several entities, each responsible for a distinct part of the system. For the enhancement of the system security, controllable devices such as FACTS devices are installed and operated by these entities. But in order to avoid conflicting behavior coordination is needed, leading to the concept of multiarea control. In this paper, it is assumed that the areas are determined independently from each other according to the influence of the control devices. As a consequence, overlapping areas may result necessitating an extension of the applied multiarea control method based on approximate Newton directions. In addition, it is taken into account that part of the grid might not be included in any of the areas. [ABSTRACT FROM AUTHOR]

This paper proposes a probabilistic small signal stability assessment (PSSSA) methodology based on the application of Monte Carlo approach for iterative evaluation, via modal analysis of small signal stability (SSS). Operation states represented by random values of generation and demand are analyzed. A probabilistic instability risk index based on cumulative probability distribution function of damping ratios of oscillatory modes is calculated, as well as a power system stabilizer (PSS) devices location index based on eigenvectors and participation factors, which are considered random variables. Moreover, the impact of long-distance power flows on oscillatory modes (OM) and how the damping of OM depends on the orientation and magnitude of power flows is investigated. Further, an additional index concerns qualitatively the determination of transfer capability as affected by small signal stability. PSSSA is tested on a reduced order model of New England-New York's interconnected system considering uncertainties around three different system conditions separately: highly loaded, fairly loaded, and lowly loaded. The results highlight the main advantages of PSSSA over deterministic SSS studies such as instability risk assessment, small signal stability enhancement through adequate PSS location, and the proposal of possible restrictions for transfer capability in order to avoid poorly damped oscillations in the face of the diversity in power system operation. [ABSTRACT FROM AUTHOR]

The voltage at the point of common coupling (PCC) in a weak network is very sensitive to load changes. A sudden change in active load will cause both a phase jump and a magnitude fluctuation in the bus voltage (voltage at the PCC), whereas reactive load changes mainly affect the voltage magnitude. With the addition of energy storage to a static synchronous compensator (StatCom), it is possible to compensate for the active power change as well as providing reactive power support. In this paper effective active power compensation schemes are proposed. Simulation and experimental results verify the compensation schemes by showing that a StatCom with energy storage can significantly reduce phase jumps and magnitude deviations of the bus voltage under load disturbances. [ABSTRACT FROM AUTHOR]

In this paper the design of power system stabilizers for small-signal stability using phasor measurements is considered. An approach based on optimal control with structural constraints is proposed to design a two-level control structure. Time delays are included in the design. The method is combined with order reduction to ensure faster convergence of the design algorithm and to facilitate the choice of the weighting matrices for damping inter-area modes. The control scheme is discussed and modal analysis and time-domain simulations of two Brazilian equivalent systems are performed to assess the control performance. The robustness to loss of communication links, topological changes, and variations of time delay is evaluated. [ABSTRACT FROM AUTHOR]

This paper presents a new method to enhance the participation of variable-speed wind energy conversion systems (WECS) in existing frequency regulation mechanisms. The proposed approach, based on a modified inertial control scheme, takes advantage of the fast response capability associated with electronically-controlled WECS, allowing the kinetic energy stored by rotational masses to be partly and transiently released in order to provide earlier frequency support. An additional improvement is achieved by communicating the WECS response to conventional generators so that these can eventually take care of the full load imbalance. Several simulations using a two-area test system are performed to demonstrate the benefits of the proposed scheme. [ABSTRACT FROM AUTHOR]

Standard computations reveal that locational marginal prices (LMPs), being Lagrange multipliers in an optimization problem, must lie in the null space of a Jacobian matrix evaluated at the optimal power flow solution, augmented by columns associated with active line flow limits. The impact of network power flow and active line limit constraints is to confine the LMPs in a subspace that satisfies necessary conditions for optimality. Optimal market clearing can then proceed as a minimization over offer curves confined to admissible LMPs in this subspace. When no line limits are active and losses neglected (e.g., in a dc power flow representation), the matrix in question has a generalized Laplacian structure, and admits only a vector of all equal elements in its null space (verifying the well-known equal incremental cost condition). As line flow limits become active, the null space grows in dimension. Among the phenomena of interest as the dimension of admissible LMPs grows is that of "load pockets"; that is, admissible LMP vectors that can show patterns in which buses partition into zones of approximately equal LMPs, with significant differences between zones. This paper explores an approach to admissible LMP calculation that isolates the topological role of active line flow constraints, independent of offer curve prices. Identification of this admissible subspace can then greatly facilitate computations such as clustering to identify potential zones of differentiated LMPs. [ABSTRACT FROM AUTHOR]

This paper analyzes the impact of system frequency variations on the steady-state operation point of fixed speed induction generators used in wind turbine generation systems (WTGS). An analytic method to predict the values of angular speed, torque and current during and after a frequency disturbance is presented. The proposed method as well permits to establish the operation limits in order to keep the WTGS connected during frequency variations and therefore to adjust protection relay settings. [ABSTRACT FROM AUTHOR]

This paper presents a concept overview of an automatic operator of electrical networks (AOEN) for real-time alleviation of component overloads and increase of system static load-ability, based on state-estimator data only. The control used for this purpose is real-power generation rescheduling, although any other control input could fit the new framework. The key performance metrics are the vulnerability index of a generation unit (VIGS) and its sensitivity (SVIGS), accurately computed using a realistic ac power flow incorporating the AGC model (AGC-PF). Transmission overloads, vulnerability indices and their sensitivities with respect to generation control are translated into fuzzy-set notations to formulate, transparently, the relationships between incremental line flows and the active power output of each controllable generator. A fuzzy-rule-based system is formed to select the best controllers, their movement and step-size, so as to minimize the overall vulnerability of the generating system while eliminating overflows. The controller performance is illustrated on the IEEE 39-bus (New England) network and the three-area IEEE-RTS96 network subjected to severe line outage contingencies. A key result is that min- imizing the proposed vulnerability metric in real-time results in increased substantial loadability (prevention) in addition to overload elimination (correction). [ABSTRACT FROM AUTHOR]

During 2005 and 2006, the Western Electricity Coordinating Council (WECC) performed three major tests of western system dynamics. These tests used a Wide-Area Measurement System (WAMS) based primarily on phasor measurement units (PMUs) to determine response to events including the insertion of the 1400-MW Chief Joseph braking resistor, probing signals, and ambient events. Test security was reinforced through real-time analysis of wide-area effects, and high-quality data provided dynamic profiles for interarea modes across the entire western interconnection. The tests established that low-level optimized pseudo-random ±20-MW probing with the Pacific DC Intertie (PDCI) roughly doubles the apparent noise that is natural to the power system, providing sharp dynamic information with negligible interference to system operations. Such probing is an effective alternative to use of the 1400-MW Chief Joseph dynamic brake, and it is under consideration as a standard means for assessing dynamic security. [ABSTRACT FROM AUTHOR]

The computation of the unstable equilibrium point (UEP) is a key step involved in the direct methods of power system transient stability analysis. A new continuation-based method to compute the UEPs is proposed. The mechanical powers of the generators are changed to form a parameterized equation. Then the solution curve of the equation is traced by the continuation method from the stable equilibrium point to a UEP. The direction of power increase is determined to get a UEP relevant to the fault. The obtained UEPs are mostly type-1 and the method is applicable to detailed generator models. The method is tested in several systems and satisfactory results are obtained. [ABSTRACT FROM AUTHOR]

We address the problem of finding optimal medium-term generation policies for a specific generation company by modeling the supply side of a liberalized electricity market. The model assumes a noncooperative oligopoly and determines the joint optimal generation policies of all market generators, taking into account hydro, market, and system uncertainties. We propose an endogenous function of market price with respect to load duration where the choice of fuel and technology influences both the average and range of variation of the medium-term market price. We assume an inelastic demand represented by the load-duration curve, which is matched using the Bloom and Gallant formulation. This accounts for unit outages without using scenarios, which are reserved for modeling other uncertainties such as a latent price variable and the hydro inflows. The equilibrium is solved using the Nikaido-Isoda relaxation algorithm, which enables a series of multistage cubic stochastic programming models to be solved. In order to deal with the large number of load matching constraints, we use a heuristic which allows us to generate only those constraints that will presumably be active at the optimal solution. The model is calibrated to the Spanish electricity market using historical price and generation data. [ABSTRACT FROM AUTHOR]

This letter presents a control method for grid-connected PWM voltage source inverters (VSIs) featuring fast load voltage regulation and effective mitigation of fast voltage disturbances. The control scheme is based on a hybrid linear with variable-structure control (VSC) voltage controller and a deadbeat current regulator. The proposed scheme is applied to a VSI-based distributed generation (DG) interface to regulate the voltage at the point of common coupling (PCC). [ABSTRACT FROM AUTHOR]

This letter describes an approach using Benders decomposition to decompose security-constrained optimal power flow (DSCOPF). It provides a complexity analysis to give insight into the improved computing speeds obtained using the approach. The method is illustrated on two six-bus test systems and on the IEEE reliability test system. [ABSTRACT FROM AUTHOR]