Showing papers on "Power system simulation published in 2008"

Security-Constrained Unit Commitment With Volatile Wind Power Generation

Abstract: This paper presents a security-constrained unit commitment (SCUC) algorithm which takes into account the intermittency and volatility of wind power generation. The UC problem is solved in the master problem with the forecasted intermittent wind power generation. Next, possible scenarios are simulated for representing the wind power volatility. The initial dispatch is checked in the subproblem and generation redispatch is considered for satisfying the hourly volatility of wind power in simulated scenarios. If the redispatch fails to mitigate violations, Benders cuts are created and added to the master problem to revise the commitment solution. The iterative process between the commitment problem and the feasibility check subproblem will continue until simulated wind power scenarios can be accommodated by redispatch. Numerical simulations indicate the effectiveness of the proposed SCUC algorithm for managing the security of power system operation by taking into account the intermittency and volatility of wind power generation.

Stochastic Security for Operations Planning With Significant Wind Power Generation

Abstract: In their attempt to cut down on greenhouse gas emissions from electricity generation, several countries are committed to install wind power generation up to and beyond the 10%-20% penetration mark. However, the large-scale integration of wind power represents a challenge for power system operations planning because wind power 1) cannot be dispatched in the classical sense; and 2) its output varies as weather conditions change. This warrants the investigation of alternative short-term power system operations planning methods capable of better coping with the nature of wind generation while maintaining or even improving the current reliability and economic performance of power systems. To this end, this paper formulates a short-term forward electricity market-clearing problem with stochastic security capable of accounting for nondispatchable and variable wind power generation sources. The principal benefit of this stochastic operation planning approach is that, when compared to a deterministic worst-case scenario planning philosophy, it allows greater wind power penetration without sacrificing security.

Stochastic security for operations planning with significant wind power generation

Abstract: In their attempt to cut down on greenhouse gas emissions from electricity generation, several countries are committed to install wind power generation up to and beyond the 10-20% penetration mark. However, the large-scale integration of wind power represents a challenge for power system operations planning because wind power (i) cannot be dispatched in the classical sense; and, (ii) its output varies as weather conditions change. This warrants the investigation of alternative short-term power system operations planning methods capable of better coping with the nature of wind generation while maintaining or even improving the current reliability and economic performance of power systems. To this end, this paper formulates a short-term forward electricity market-clearing problem with stochastic security capable of accounting for non-dispatchable and variable wind power generation sources. The principal benefit of this stochastic operation planning approach is that, when compared to a deterministic worst-case scenario planning philosophy, it allows greater wind power penetration without sacrificing security.

Generalized Integer Linear Programming Formulation for Optimal PMU Placement

Abstract: Based on the integer linear programming formulation proposed for optimal PMU placement, this paper presents a generalized integer linear programming formulation for cases including redundant PMU placement, full observability and incomplete observability. Due to accurate voltage phasor measurement and current phasor measurements provided by PUM units, the accuracy, redundancy and thus the robustness of state estimation will be enhanced with the integration of PMU measurements. The problem of optimal placement of PMU for the redundant PMU placement, full observability and incomplete observability analysis needs to be studied, for various purposes and considerations. The proposed modeling approach by the author in another paper, which models PMU placement as an integer linear programming problem, is extended and generalized to satisfy different needs. Cases with and without zero injection measurements are considered. Simulation results on different power systems show that the proposed algorithm can be used in practice.

GridLAB-D: An open-source power systems modeling and simulation environment

Abstract: GridLAB-D is a new power system modeling and simulation environment developed by the US Department of Energy. This paper describes its basic design concept, method of solution, and the initial suite of models that it supports.

An MILP Approach for Short-Term Hydro Scheduling and Unit Commitment With Head-Dependent Reservoir

Abstract: The paper deals with a unit commitment problem of a generation company whose aim is to find the optimal scheduling of a multiunit pump-storage hydro power station, for a short term period in which the electricity prices are forecasted. The problem has a mixed-integer nonlinear structure, which makes very hard to handle the corresponding mathematical models. However, modern mixed-integer linear programming (MILP) software tools have reached a high efficiency, both in terms of solution accuracy and computing time. Hence we introduce MILP models of increasing complexity, which allow to accurately represent most of the hydroelectric system characteristics, and turn out to be computationally solvable. In particular we present a model that takes into account the head effects on power production through an enhanced linearization technique, and turns out to be more general and efficient than those available in the literature. The practical behavior of the models is analyzed through computational experiments on real-world data.

Multistate Wind Energy Conversion System Models for Adequacy Assessment of Generating Systems Incorporating Wind Energy

Abstract: Wind energy is considered to be a very promising alternative for power generation because of its tremendous environmental, social, and economic benefits. Electrical power generation from wind energy behaves quite differently from that of conventional sources. The fundamentally different operating characteristics of those facilities, therefore, affect the power system reliability in a manner different from that of the conventional systems. This paper is focused on the development of suitable models for wind energy conversion systems, in adequacy assessments of generating systems, using wind energy. These analytical models can be used in the conventional generating system adequacy assessment utilizing analytical or Monte Carlo state-sampling techniques. This paper shows that a five-state wind energy conversion system model can be used to provide a reasonable assessment of the practical power system adequacy studies, using an analytical method, or a state-sampling simulation approach.

Interdependency of Natural Gas Network and Power System Security

Abstract: This paper proposes an integrated model for assessing the impact of interdependency of electricity and natural gas networks on power system security. The integrated model incorporates the natural gas network constraints into the optimal solution of security-constrained unit commitment. The natural gas network is modeled by daily and hourly limits on pipelines, sub-areas, plants, and generating units. The application of fuel diversity (e.g., generating units with fuel switching capability) is presented as an effective peak shaving strategy for natural gas demand which could hedge price volatilities of natural gas and electric power. The proposed model can be used by a vertically integrated utility for the commitment and dispatch of generating units and the allocation of natural gas for the next day utilization. The proposed model can also be used for measuring the security of social services by modeling the interdependency of natural gas and electric power system infrastructures. If the proposed model is used by GENCOs, gas constraints will be submitted to electricity markets as energy constraints. Illustrative examples show the impact of natural gas supply infrastructure on the economic operation of a vertically integrated utility. The examples also discuss the impact of generating units with fuel switching capability on the power system security when the supply of natural gas is limited.

Cost of Reliability Analysis Based on Stochastic Unit Commitment

Abstract: This paper presents a model for calculating the cost of power system reliability based on the stochastic optimization of long-term security-constrained unit commitment. Random outages of generating units and transmission lines as well as load forecasting inaccuracy are modeled as scenario trees in the Monte Carlo simulation. Unlike previous reliability analyses methods in the literature which considered the solution of an economic dispatch problem, this model solves an hourly unit commitment problem, which incorporates spatial constraints of generating units and transmission lines, random component outages, and load forecast uncertainty into the reliability problem. The classical methods considered predefined reserve constraints in the deterministic solution of unit commitment. However, this study considers possible uncertainties when calculating the optimal reserve in the unit commitment solution as a tradeoff between minimizing operating costs and satisfying power system reliability requirements. Loss-of-load-expectation (LOLE) is included as a constraint in the stochastic unit commitment for calculating the cost of supplying the reserve. The proposed model can be used by a vertically integrated utility or an ISO. In the first case, the utility considers the impact of long-term fuel and emission scheduling on power system reliability studies. In the second case, fuel and emission constraints of individual generating companies are submitted as energy constraints when solving the ISO's reliability problem. Numerical simulations indicate the effectiveness of the proposed approach for minimizing the cost of reliability in stochastic power systems.

Impacts of Wind Power Minute-to-Minute Variations on Power System Operation

Abstract: In this paper, minute-to-minute wind power variations are decomposed into slow, fast, and ramp components to assess the influence of each component on power system operation. Using detailed, long-term simulation models, this paper confirms that most power systems can absorb the impacts of wind power variations with little difficulty. Yet, since ramps in wind power and system demand could coincide, systems with limited ramping capabilities are at risk. It is shown that extending simulation models to include load dynamics and automatic generation control (AGC) time delays do not alter these conclusions. This paper also discusses wind penetration approaches and control area performance measures, linking the latter to the placement of the wind farms within the interconnection.

A Novel Coding Scheme for Practical Economic Dispatch by Modified Particle Swarm Approach

Abstract: This paper proposes a new approach and coding scheme for solving economic dispatch problems in power systems through simulated annealing like particle swarm optimization (SA-PSO). This novel coding scheme could effectively prevent obtaining infeasible solutions through the application of stochastic search methods, thereby dramatically improving search efficiency and solution quality. Many nonlinear characteristics of power generators, and their operational constraints, such as generation limitations, ramp rate limits, prohibited operating zones, transmission loss, and nonlinear cost functions, were all considered for practical operation. The effectiveness and feasibility of the proposed method were demonstrated by four system case studies and compared with previous literature in terms of solution quality and computational efficiency. The experiment showed encouraging results, suggesting that the proposed approach was capable of efficiently determining higher quality solutions addressing economic dispatch problems.

Designing an Adaptive Fuzzy Controller for Maximum Wind Energy Extraction

Abstract: The wind power production spreading, also aided by the transition from constant to variable speed operation, involves the development of efficient control systems to improve the effectiveness of power production systems. This paper presents a data-driven design methodology able to generate a Takagi-Sugeno-Kang (TSK) fuzzy model for maximum energy extraction from variable speed wind turbines. In order to obtain the TSK model, fuzzy clustering methods for partitioning the input-output space, combined with genetic algorithms, and recursive least-squares optimization methods for model parameter adaptation are used. The implemented TSK fuzzy model, as confirmed by some simulation results on a doubly fed induction generator connected to a power system, exhibits high speed of computation, low memory occupancy, fault tolerance, and learning capability.

Estimating Electromechanical Mode Shape From Synchrophasor Measurements

Abstract: A theoretical basis and signal-processing approach for estimating a power system's electromechanical mode-shape properties using time-synchronized phasor measurements are presented. The relationship between modal eigenvectors and measurable power system quantities are derived. Spectral correlation analysis is used to implement the approach with demonstrative examples. This includes simulation examples as well as measured data from the western North American power system.

Basic Modeling and Simulation Tool for Analysis of Hydraulic Transients in Hydroelectric Power Plants

Abstract: In this paper, the simulation system of a typical hydroelectric power plant was developed in a MATLAB/Simulink-based software environment, which has a high water head and a long penstock with upstream and downstream surge tanks and is equipped with a Francis turbine. With MATLAB/Simulink, the models of the proposed simulation system are all modularized and visualized, and can be reused easily. No complex codes have been programmed and the proposed simulation system adapts varieties of hydroelectric power plants. The nonlinear characteristics of hydraulic turbine and then inelastic water hammer effect were considered to calculate and simulate hydraulic transients. Moreover, the influences of different parameters, such as hydraulic turbine speed governor proportional-integral-derivative (PID) gains, pressure water supply system, as well as surge tanks, were analyzed for the dynamic performance of hydraulic turbine regulating system. The digital simulations of a sudden full load rejection for an actual hydroelectric power plant in China were performed, and the results indicate that the proposed MATLAB/Simulink-based hydroelectric power plant simulation system is accurate and effective enough to represent and simulate hydroelectric power plant's nonlinear dynamics as well as to design hydraulic turbine speed control system. The proposed simulation system has also been proved to be useful for preliminary designs or assessments of hydropower projects.

Optimal Power Flow Subject to Security Constraints Solved With a Particle Swarm Optimizer

Abstract: This paper presents a novel approach to solve an optimal power flow problem with embedded security constraints (OPF-SC), represented by a mixture of continuous and discrete control variables, where the major aim is to minimize the total operating cost, taking into account both operating security constraints and system capacity requirements. The particle swarm optimization (PSO) algorithm with reconstruction operators (PSO-RO) has been used as the optimization tool. Such operators guarantee searching the optimal solution within the feasible space, reducing the computation time and improving the quality of the solution. Results on systems from the specialized literature are adopted to validate the proposed approach.

Simulation of a Wind Turbine With Doubly Fed Induction Generator by FAST and Simulink

Abstract: In order to fully study the electrical, mechanical, and aerodynamic aspects of a wind turbine with a doubly fed induction generator, a detailed model that considers all these aspects must be used. A drawback of many works in the area of wind turbine simulation is that either a very simple mechanical model is used with a detailed electrical model, or vice versa. Hence, the effects of interactions between electrical and mechanical components are not accurately taken into account. In this paper, three simulation programs - TurbSim, FAST, and Simulink - are used to model the wind, mechanical and electrical parts of a wind turbine, and its controllers. Simulation results obtained from the model are used to observe the interaction of all three factors affecting the operation of a wind turbine system. For example, it is shown how an electrical disturbance can cause dangerous tower vibrations under high speed and turbulent wind conditions, which may not be feasible using a simple model of the wind and wind turbine.

Modeling and Control of AWS-Based Wave Energy Conversion System Integrated Into Power Grid

Abstract: In this paper, the model of Archimedes wave swing (AWS) based wave energy conversion (WEC) system is proposed where a new coordinate transformation for the linear permanent magnet generator between the abc frame of reference and the dq0 frame of reference is proposed and the model of the LPMG in dq0 reference frame suitable for power system dynamic and stability analysis is derived for the first time. Since the output power and the induced voltage both vary, full-scale back-to-back converters are employed to connect the WEC to the power grid in order to maintain a constant active power and terminal voltage at the system side. The controllers for the generator side converter and the grid side converter of the back-to-back converters are also developed. Simulations are performed, when WEC operates under conditions such as no-load, supplying an isolated R-C load and integration with a power system, to simulate the dynamics of the WEC and verify the effectiveness of the model derived and the controllers developed. Comparison between the dynamic responses simulated and those obtained in the field test demonstrates that using the proposed dq0 model, the dynamics of the WEC system can be simulated properly. Using the generator side converter controller, the maximum power can be extracted from the wave while the loss in the LPMG can be minimized. Furthermore, the WEC can keep the output power at the power grid converter side constant and maintain the terminal voltage constant with the grid side converter controller. These are the desired features for the WEC to operate in parallel with the power grid. The effectiveness of the controller proposed is also validated under small disturbance.

A Study of Self-Organized Criticality of Power System Under Cascading Failures Based on AC-OPF With Voltage Stability Margin

Abstract: From the perspective of self-organized criticality, this paper develops a novel model with AC-OPF and AC grid upgrade to study the cascading failures and blackouts in power systems, which overcomes some shortcomings of existing blackout models. The proposed model contains two types of dynamics, one is fast dynamics which simulates the serial blackouts in power systems, the other is slow dynamics which reflects the tendency of the power systems time evolution. This model also has voltage stability analysis function and can reveal critical characteristics from reactive power and voltage viewpoint. Simulation results of the IEEE 118-bus system with this model show that the fast dynamics can capture the cascading process and the criticality property in micro scale. Besides, the macro scale of self-organized criticality of power systems can be revealed from the mean value of fractional overloads and the ratio of total load demand to the total network transfer capability. Furthermore, the voltage stability criticality status could be detected from the eigenvalue with the smallest magnitude through reactive power and voltage relevant modal analysis.

Method of equivalencing for a large wind power plant with multiple turbine representation

Abstract: As the size and number of wind power plants (WPP) increases, power system planners will need to study their impact on the power system in more detail. As the level of wind power penetration into the grid increases, the transmission system integration requirements will become more critical [1-2]. A very large WPP may contain hundreds of megawatt-size wind turbines. These turbines are interconnected by an intricate collector system. While the impact of individual turbines on the larger power system network is minimal, collectively, wind turbines can have a significant impact on the power systems during a severe disturbance such as a nearby fault. Since it is not practical to represent all individual wind turbines to conduct simulations, a simplified equivalent representation is required. This paper focuses on our effort to develop an equivalent representation of a WPP collector system for power system planning studies. The layout of the WPP, the size and type of conductors used, and the method of delivery (overhead or buried cables) all influence the performance of the collector system inside the WPP. Our effort to develop an equivalent representation of the collector system for WPPs is an attempt to simplify power system modeling for future developments or planned expansions of WPPs. Although we use a specific large WPP as a case study, the concept is applicable for any type of WPP.

Power System Risk Assessment Using a Hybrid Method of Fuzzy Set and Monte Carlo Simulation

Abstract: This paper presents fuzzy-probabilistic modeling techniques for system component outage parameters and load curves. The fuzzy membership functions of system component outage parameters are developed using statistical records, whereas the system load is modeled using a combined fuzzy and probabilistic representation. Based on the fuzzy-probabilistic models, a hybrid method of fuzzy set and Monte Carlo simulation for power system risk assessment is proposed to capture both randomness and fuzziness of loads and component outage parameters. An actual example using a regional system at the British Columbia Transmission Corpoation is given to demonstrate the application of the presented fuzzy-probabilistic models for system parameters and new system risk evaluation method.

The operation of diesel gensets in a CERTS microgrid

Abstract: In this paper the operation of diesel engine-driven wound-field synchronous generator sets as distributed generators (DGpsilas) is studied. The objective of this work is to develop the modeling and control framework for such gensets to enable their operation in a distribution system that contains multiple DGpsilas including inverter-based sources. The paper presents experimental results for the interaction of conventional gensets with inverter-based sources in a microgrid test system. From the test results it is observed that there is significant circulating reactive power between the sources as well as frequency oscillations caused by the response of the conventional genset controller. A new controller for the genset is proposed that alleviates these issues and enables the various sources to share power and maintain power quality within the system. The operation of the new controller is demonstrated using simulation results.

A new adaptive control algorithm for maximum power point tracking for wind energy conversion systems

Abstract: This paper presents a new adaptive control algorithm for maximum power point tracking (MPPT) in wind energy systems. A mathematical model of a wind turbine system is also provided. The proposed control algorithm allows the generator to track the optimal operation points of the wind turbine system under fluctuating wind conditions and the tracking process speeds up over time. This algorithm does not require the knowledge of intangible turbine mechanical characteristics such as its power coefficient curve, power characteristic or torque characteristic. It employs a search and reuse concept, a modified Hill Climb Searching (HCS) method and two newly defined loops: change detection loop (CDL) and operation point adjustment loop (OPAL). The adaptive nature of the proposed algorithm eliminates the need for customized algorithms that are optimal for only one particular turbine. It is also a solution to achieve fast optimum power point detection after its initial learning process. A simulated system has been built in PSIM 7.0 for mathematical verification of the wind energy system and for the verification of the proposed algorithm. The algorithm is realized in C++ script and detailed descriptions of the proposed control algorithm are provided for illustration purposes.

Fuzzy MILP Unit Commitment Incorporating Wind Generators

Abstract: Day-ahead unit commitment (UC) solution methods seek to determine the status and output of all available generators. In a world with an increasing integration of renewable energy sources such as wind electric generators (WEG), the UC solution process must model and include WEGs too in the decision-making process. Power output of WEGs in a day-ahead decision-making process are usually modeled using a short-term probabilistic forecast. Inclusion of WEGs introduces uncertainty in the solution that may be quantified through an imbalance risk function. Thus a UC solution method should seek a solution to minimize cost and risk in schedule. Two strategies are proposed in this paper to minimize costs and handle risks introduced due to WEGs. These formulations are posed as fuzzy optimization models and are solved using the mixed integer linear programming (MILP) technique. The proposed strategies are tested on a 26- and a 100-generator systems with associated transmission networks that have three and six wind generators each. The results with two strategies of handling WEGs are discussed.

Dynamic Models of Wind Turbines

Abstract: The impact of wind power generation in the power system is no longer negligible. Therefore, there is an urgent need for wind turbine models that are capable of accurately simulating the interaction between wind turbines or wind farms and the power system. One problem is that no standardized model of wind turbines for power system stability studies is currently available. In response to this problem, generic dynamic models of wind turbines for stability studies are proposed in this thesis. Three wind turbine concepts are considered; fixed-speed wind turbines (FSWTs), doubly fed induction generator (DFIG) wind turbines and full converter wind turbines (FCWTs). The proposed models are developed for positive-sequence phasor time-domain dynamic simulations and are implemented in the standard power system simulation tool PSS/E with a 10 ms time step. Response accuracy of the proposed models is validated against detailed models and, in some cases, against field measurement data. A direct solution method is proposed for initializing a DFIG wind turbine model. A model of a dc-link braking resistor with limited energy capacity is proposed, thus a unified model of an FCWT for a power system stability analysis can be obtained. The results show that the proposed models are able to simulate wind turbine responses with sufficient accuracy. The generic models proposed in this thesis can be seen as a contribution to the ongoing discourse on standardized models of wind power generation for power system stability studies. Aggregated models of wind farms are studied. A single equivalent unit representation of a wind farm is found to be sufficient for most short-term voltage stability investigations. The results show that non-linearities due to maximum power tracking characteristics and saturation of electrical controllers play no important role in characterizing wind farm responses. For a medium-term study, which may include wind transport phenomena, a cluster representation of a wind farm provides a more realistic prediction. Different influencing factors in designing dynamic reactive power compensation for an offshore wind farm consisting of FSWTs are also investigated. The results show that fault ride-through capability of the individual turbines in the wind farm utilizing an active stall control significantly reduces the requirement for the dynamic reactive power compensation.

Generating Random Topology Power Grids

Abstract: Simulation based on standard models is often used as part of the engineering design process to test theories and exercise new concepts before actually placing them into operation. In order to tackle the problem of likely widespread catastrophic failures of electric power grids, an autonomously reconfigurable power system will have to rely on wide-area communication systems, networked sensors, and restorative strategies for monitoring and control. Standard practice is to use simulation of a small number of certain historical test systems to test the efficacy of any proposed design. We believe this practice has shortcomings when examining new communication system ideas. In this paper we develop the means for producing power grids with scalable size and randomly generated topologies. These ensembles of networks can then be used as a statistical tool to study the scale of communication needs and the performance of the combined electric power control and communication networks. The topological and system features of the randomly generated power grids are compared with those of standard power system test models as a "sanity check" on the method.

Wide-Area Signal-Based OptimalNeurocontroller for a UPFC

Abstract: The design and implementation of an optimal neurocontroller for a flexible ac transmission device - the unified power-flow controller (UPFC) - is presented in this paper. Wide area signals in a power system are used to provide auxiliary control to a UPFC in order to achieve enhanced damping of system oscillations. The neurocontroller provides auxiliary signals to the real and reactive power references of a UPFC series inverter. The design of the optimal neurocontroller is based on an adaptive critic design approach - the heuristic dynamic programming. A system identifier, referred to as the wide-area monitor), and a critic network (performance evaluator) are designed for optimizing the neurocontroller. Real-time implementation of the optimal UPFC neurocontroller for a multimachine power system is carried out successfully on a digital signal processor. The power system is simulated on a real-time digital simulator. The performance of this neurocontroller is compared with a conventional linear damping controller. Results show enhanced damping of both inter-area and intra-area modes in the power system under different operating conditions and disturbances with the neurocontroller. The improvement in the damping is also quantified using the Prony method.

Evaluation of First Swing Stability of a Large Power System With Various FACTS Devices

Abstract: This paper presents a simple method of evaluating the first swing stability of a large power system in the presence of various flexible ac transmission system (FACTS) devices. First a unified power flow controller (UPFC) and the associated transmission line are considered and represented by an equivalent pi-circuit model. The above model is then carefully interfaced to the power network to obtain the system reduced admittance matrix which is needed to generate the machine swing curves. The above pi-circuit model can also be used to represent other FACTS devices (SSSC and STATCOM) by selecting appropriate values of control parameters of the UPFC. The complex voltage at two end buses of the pi-circuit model is also evaluated during simulation to implement various existing control strategies of FACTS devices and to update the reduced admittance matrix. The effectiveness of the proposed method of generating dynamic response and hence evaluating first swing stability of a power system in the presence of various FACTS devices is tested on the ten-machine New England system and the 20-machine IEEE test system. The results obtained with various FACTS devices are also compared and discussed.

Optimal placement of FACTS devices by a Group Search Optimizer with Multiple Producer

Abstract: This paper presents a group search optimizer with multiple producer (GSOMP) for reactive power dispatch incorporating with flexible AC transmission system (FACTS) devices, which is formulated as a nonlinear constrained multi-objective optimization problem. The optimal location of multi-type FACTS devices and their control parameters are optimized by GSOMP to minimize the real power loss and also to improve voltage profile. The performance of GSOMP has been evaluated on the standard IEEE 14-bus and New England 39-bus test systems respectively. Simulation results show that the performance of the power systems is improved with multi-type FACTS devices optimally placed in the reactive power planning model.

Reliability Assessment of the Brazilian Power System Using Enumeration and Monte Carlo

Abstract: Two methods have been largely studied and used in power systems reliability assessment: contingency enumeration and nonsequential Monte Carlo simulation. Both have their advantages and drawbacks. Contingency enumeration is conceptually simple and usually requires low computational effort. Conversely, Monte Carlo simulation is computationally harder, but much more versatile to model random aspects. This paper depicts some important practical aspects regarding the application of both methods, emphasizing how they can be used in a complementary way. The Brazilian interconnected electrical system is used to illustrate the risk assessment of an actual large scale power system, utilizing both techniques.