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The book is composed of 12 chapters and three appendices, and can be divided into four parts. The first part includes Chapters 2 to 7, which discuss the concepts, models, methods and data in probabilistic transmission planning. The second part, Chapters 8 to 11, addresses four essential issues in probabilistic transmission planning applications using actual utility systems as examples. Chapter 12, as the third part, focuses on a special issue, i.e. how to deal with uncertainty of data in probabilistic transmission planning. The fourth part consists of three appendices, which provide the basic knowledge in mathematics for probabilistic planning.

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... Monte Carlo simulation and state enumeration have been the traditional methodologies used to assess the availability of bulk power systems [3,[24][25][26][27]. Some commercial software have reliability assessment tools based on these techniques. ...

... The proposal of this paper is to apply the concepts of the Point Estimate Method (PEM) in order to take into account uncertainties model of WPP and correlated behavior of a set of WPP. Although many PEM schemes have been suggested [12][13][14][15][16] and have been used to solve the problem of probabilistic power flow [15,26], this paper proposes the use of the 2m+1 PEM proposed by Hong in [16]. The purpose is to compute the common reliability (availability) indices: Loss of Load Probability (LOLP) and Expected Energy Not Supplied (EENS) as are defined at [26,27], using the state enumeration method. ...

... Although many PEM schemes have been suggested [12][13][14][15][16] and have been used to solve the problem of probabilistic power flow [15,26], this paper proposes the use of the 2m+1 PEM proposed by Hong in [16]. The purpose is to compute the common reliability (availability) indices: Loss of Load Probability (LOLP) and Expected Energy Not Supplied (EENS) as are defined at [26,27], using the state enumeration method. ...

The use of renewable non-conventional energy sources, as wind electric power energy and photovoltaic solar energy, has introduced uncertainties in the performance of bulk power systems. The power system availability has been employed as a useful tool for planning power systems; however, traditional methodologies model generation units as a component with two states: in service or out of service. Nevertheless, this model is not useful to model wind power plants for availability assessment of the power system. This paper used a statistical representation to model the uncertainty of power injection of wind power plants based on the central moments: mean value, variance, skewness and kurtosis. In addition, this paper proposed an availability assessment methodology based on application of this statistical model, and based on the 2m+1 point estimate method the availability assessment is performed. The methodology was tested on the IEEE-RTS assuming the connection of two wind power plants and different correlation among the behavior of these plants.

... Transmission network planning involved prediction of clusters of aggregated loads, and how to generate enough power in the most efficient and cost-effective way to feed these loads. This must be done considering the existing meshed transmission infrastructure, technical-economical limits, and localised generating plants available [1]. Losses play an important role in these studies as there are multiple paths for power flow depending on the load-generation state [2]. ...

... While generality is given in (1), this work will focus on the most studied constraints in the distribution level: voltage deviations for each node, and loading limits for each line, depending on their physical characteristics. ...

... It is hypothesised that once the NAEC of a grid is known, individual users can make an informed decision about their DER capabilities. Three paths to use the NAEC are visualised: (1) installing the NAEC as a conservative HC, (2) depending on the demand profile and generation technology, a NAEC-to-HC enhancement method allows a larger HC installation, or (3) participants can choose to install as much resource as they want, provided they can afford to turn off their installation or store energy in moments were the NAEC is exceeded. ...

A novel distributed energy resources (DER) allocation method focused on grid constraints that avoids topological bias is proposed for distribution networks. A technology-agnostic approach is used, where a non-bias allocation of export capacity (NAEC) not specific to generation type is calculated. Moreover, the proposed NAEC is extended from an export capacity into a hosting capacity (HC) using a statistical approach. The methods are tested using the IEEE 33-bus distribution system, and two typical Irish distribution feeders -one urban, one rural- as case studies. Using a high-resolution year-long quasi-static time series simulation (QSTS) and three different generation profiles, the proposed NAEC method is validated against current practices and state of the art allocation methods in terms of active balancing, security of supply, interactions between users, operational concerns, and fairness. Results show that an equivalent or higher level of DER penetration is achieved using the proposed methodology. There are no additional constraint violations using the NAEC methodology, moreover, time slots with violations are reduced, improving security of supply. Furthermore, results suggest that avoiding topological bias makes the network accessible for more users, and prioritises self-consumption.

... Some studies [2,5,14,15] have computed or estimated failure rates and MTTR of the elements that compose a converter stations; and give the guide for computing the equivalent failure rate λ Stat and the equivalent repair rate (μ Stat ) for the converter stations. Based on these parameters the FOR of a converter station is calculated as follows [16]μ ...

... where q i is the probability of the ith component working, p i is the probability of the ith component being in a state of failure, n is the number of components, m is the number of working components and n -m is the number of failed components. The frequency of system state f i is given by [16] ...

... The requirements for assessing DC transmission system reliability are similar to those of AC transmission systems [16]; therefore, common reliability indices for AC transmission grids (such as LOLP, ENLC, DNS and EENS) are adapted for the availability assessment of HVDC grids. The proposed reliability indices of VSC-HVDC transmission grids are classified in two setsμ (i) loss of power and energy extracted from the DC grid to the AC grid or AC zones and (ii) loss of power and energy injected to AC zones from the DC grid. ...

This study proposes a methodology for assessing the availability of voltage source converter high-voltage direct current (HVDC) grids based on the enumeration methodology of contingency analysis with N − 2 criteria and makes contributions in the computation of remedial actions and the definition and computation of reliability indices applied for HVDC grids. Thus, this study proposes the computation of remedial actions based on an optimal power flow, looking to maintain power exchanges between HVDC and high-voltage alternating current grids, when a contingency occurs on the HVDC grid and converter stations or HVDC lines are out of their operating limits. On the other hand, an HVDC grid has the function of injecting and extracting power from AC interconnected zones, and then traditionally used nodal reliability indices must be modified to indices that reflect the performance of the HVDC network to fulfil its function of interconnection of systems. This study defines two sets of availability indices applicable to HVDC grids: (i) loss of power and energy extracted from the DC grid to the AC zones and (ii) loss of power and energy injected to AC zones from the DC grid. The proposed methodology is applied to perform the availability assessment of the CIGRE B4 DC grid test system and the results are presented.

... Good expansion alternatives should be able to ensure a compromise between investment and operating costs of the system, while keeping an adequate quality level in the energy supply and also maximizing the use of the current available resources. Moreover, proper investments in the transmission grid result in an adequate environment for interaction between consumers, generators, and traders of electricity [1][2][3][4]. ...

... In general, TEP is a tough optimization problem, which can be classified as nonlinear mixed integer programming with non-convex solution space [2,[4][5][6]. The current dimensions of power systems together with the uncertainties associated with load growth and availability of energy sources and equipment make TEP solution assessment a complex task [7]. ...

... In the formulation of the static TEP problem for long-term planning horizons, simplified mathematical models are commonly used to represent the power system network. Among them, the DC network linear model is the most accepted [1][2][3][4][10][11][12]. This section presents the formulation of the TEP problem adopted in this work, which uses a DC model, including ohmic losses [8,9], and considers the "N-1" security criterion [7,11] to assess the configurations during the solution process. ...

This paper proposes an enhanced genetic algorithm model, named EGA-TEP, to solve the transmission expansion planning (TEP) problem of electric power system networks. Heuristic information is integrated into the evolutionary process of metaheuristic to improve the expansion plans (solutions). This heuristic information is translated in the form of sensitivity indices, based on the circuit loading/overloading and observed load shedding, considering both the intact network and the “N-1” contingency operating conditions (security criteria). In addition, an iterative process of evolutionary runs (ERs) is adopted as the basis for designing the EGA-TEP. These contributions make the optimization tool more robust and ready to handle different types of systems. The efficiency of the proposed EGA-TEP tool is consistently evaluated through performance statistical indices. Results obtained with systems with different characteristics and dimensions are presented and widely discussed.

... Para usar el método de simulación Monte Carlo en la construcción de la base de datos se requieren varios datos de entrada, esto depende generalmente del objetivo de la simulación. Estos datos de entrada son usualmente representados por medio de funciones de distribución de probabilidad (PDF, de sus siglas en inglés) (Billinton & Li, 2013;Li, 2011). ...

... Se busca diseñar una metodología que se pueda actualizar diariamente por el operador del sistema. Para el análisis de la incertidumbre propuesta se considera únicamente el horizonte del planeamiento de corto plazo; por lo cual, se deben construir modelos probabilísticos de las variables aleatorias del sistema de potencia, como también los cambios de topología en la red que deben reflejar el comportamiento del sistema lo más cercano posible a la realidad (Li, 2011). La información inicial para construir la base de datos usando el método de simulación Monte Carlo es: ...

... La selección de las contingencias depende de la probabilidad de salida forzada de los componentes del sistema. La probabilidad de ocurrencia de un evento de contingencia puede ser estimado usando la distribución de Poisson con una tasa de ocurrencia constante (Billinton, 2013;Li, 2011). Usando la fórmula de la distribución de Poisson se tiene que la probabilidad de ocurrencia de una contingencia (N-1) en un periodo de tiempo esta dada por la siguiente ecuación: ...

En la actualidad, la característica competitiva de los mercados de energía eléctrica
desregulados, los limitados planes de expansión del sistema, las restricciones ambientales y la inserción de generación renovable han provocado que los sistemas eléctricos de potencia sean operados habitualmente muy cerca de sus límites de estabilidad. Uno de estos límites es el de estabilidad de tensión, que resulta excedido cuando el sistema de potencia ya no tiene la capacidad de mantener estables las tensiones en todos o algunos de sus nodos
después de un disturbio. En este trabajo de investigación se desarrolló un método para la
evaluación de la estabilidad de tensión de largo alcance en tiempo real en sistemas de potencia.
Inicialmente, se dividió el sistema de potencia en sub-áreas que permitieran una mejor vigilancia del fenómeno de inestabilidad debida a nodos propensos a la inestabilidad y fuentes de generación que los pudieran controlar. La evaluación de la estabilidad de tensión se realizó mediante mediciones fasoriales sincronizadas y usando técnicas de inteligencia artificial. A través de las mediciones fasoriales sincronizadas se adquirió la información de la condición actual del sistema; y posteriormente, por medio de técnicas de inteligencia artificial e índices tradicionales, se desarrolló un esquema para la evaluación de la estabilidad de tensión. Este método permite vigilar la inestabilidad de tensión ocasionada por limitaciones en la transmisión de potencia reactiva en los corredores de las líneas, y también vigila cuando en un área del sistema se experimenta un déficit de potencia reactiva en las fuentes de suministro. Se realizó la validación del método propuesto en un sistema de prueba de 39 nodos para el cual se realizaron mediciones fasoriales sincronizadas simuladas. Estas pruebas corroboran que el método propuesto funciona correctamente ante diferentes escenarios y condiciones del sistema, siempre garantizando un monitoreo adecuado de la estabilidad de tensión independiente de la causa que lo produce.

... In other words, the research aimed at obtaining probable and secure normal operating mode conditions for future loadings, considering bulk load expectations or uncertainties at the delivery points. Although random variables, as power system loads, imply that one cannot predict its value, the distribution can be determined from the observed historical loads pattern over a given period of time [15][16][17]. ...

... The purpose is to plan ahead and account for various hypotheti-cal situations [18,19]. In situations where network does not perform satisfactorily under probable loadings, appropriate TN-reinforcing elements are determined and applied [17]. ...

... According to [17,18], the real and reactive power supplied to the system at bus i is given in Eq. (4). ...

The paper presents a 10-year expansion model for Nigerian 330 kV 38-bus transmission network that adequately accommodates probabilistic growing loads using heuristic time-step power flow simulations approach. Past network operation planning was based on assigned and deterministic load projections that created transmission system performance inadequacy and load-shedding conditions under normal demands. The network simulator was created using NEPLAN software for electrical networks, and specific probabilistic loading model and contingency were applied to obtain the present and prospective system performance responses and expansion requirements. From an analysis of the obtained results, required transmission system reinforcements under the probabilistic loading model were established. The research findings are useful guides for effective transmission grid development in Nigeria.

... Literature [2] proposed a filter function capable of reflecting the characteristics of the magnetic storm. Li [3] proposed that the failure rate of transformer can be approximated by the failure frequency. A time-varying model of transformer and the evaluation method about operation reliability of transformers based on Monte-Carlo Simulation is proposed in [4]. ...

... The failure rate can be estimated as the mean annual number of failures of the component over a certain period of time [3], then the correction value can be involved in the calculation as: ...

With the increment of grid complexity and voltage level, the effect of geomagnetic induced current (GIC) on the grid is also increasing. There is no complete system to assess the impact of GIC on the reliability of the grid at present. This paper discusses the relationship between geomagnetic data and transformer failure rate. Referring to the existing mathematical model between GIC indices and failure rate, Monte–Carlo method is used to calculate the reliability of a given system under the influence of geomagnetic storm. The case study shows the validity of the assessment and this paper contributes to the establishment of a complete reliability evaluation system.

... Two approaches are known for the analysis of power system operation: deterministic and probabilistic [2,3]. The deterministic analysis is based on calculating network parameters under strictly defined conditions [2,4]. ...

... The probabilistic approach uses random variables instead of determined values [3,5]. In this case, the calculations are performed for values whose occurrence has a specific nature, based on the event, with an assigned probability. ...

Power systems can be analyzed using either a deterministic or a probabilistic approach. The deterministic analysis centers on studying the quantities and indicators that characterize the operating states of the power system under strictly defined conditions. However, the long-term horizon of planning analyses, the changes of marketing mechanisms, the development of renewable electricity sources, the leaving from large-scale generation, the growth of smart technology and the increase in consumer awareness make the development of transmission networks a non-deterministic problem. In this article, we propose a planning procedure that takes the probabilistic elements into account. This procedure was developed to take into account the high variability of power flows caused by the generation of renewable sources and international exchange. Such conditions of the power system operation forced a departure from deterministic planning. The new probabilistic approach uses the existing tools and experience gained during subsequent development projects. As part of the probabilistic approach, simulations were carried out using the Latin Hypercube Sampling and Two Point Estimation Method algorithms. These methods effectively reduce the computation time and, at the same time, give satisfactory results. The verification was carried out on a test grid model developed in accordance with the technical standards used in the Polish Power System. Effects were assessed using a deterministic and probabilistic approach. This analysis confirmed the practical possibility of using the probabilistic approach in planning the development of transmission network in Poland. When using a probabilistic approach to predict power flow, the criteria of technical acceptability for a given development variant and the manner in which the strategy is determined are of particular importance.

... The method for cleansing outliers includes the following steps: (1) load curve data are represented using a smoothing curve, which captures the general trend of the data; (2) a confidence interval on the smoothing curve is built to identify localized y-outliers; (3) the smoothing curve is modeled by a sequence of valleys and peaks, called ∪ shapes and ∩ shapes, which are the potential places where x-outliers could occur; (4) x-outliers are identified as the valleys, peaks, or both that do not repeat; and (5) the detected outliers are approximately repaired [8,9,10]. ...

... Once load curves at all considered buses are cleansed, it is straightforward to calculate the BLCFs. The BLCF is an important concept in power system analyses, particularly in power flow studies [4]. The load forecast generally provides annual peak values for the whole system, each region, and individual substations. ...

... In addition to the N-1 criterion, probabilistic risk indices have been developed and used for power system planning [1,20,21]. However, the this risk indices used in selecting planning alternatives do not include long-term voltage instability risk. ...

... The the method of sequential network reduction [21] was proposed for equivalent reliability indices calculation for the meshed network. According to it the block diagram, which represents an analog of real elements connections of power supply scheme: transformers (T), circuit breakers (CB), overhead lines (PL), generators (G) and cables, is composed. ...

Research objective: The reliable power supply at a reasonable cost is fundamental for the development of any country. Special attention should be paid to the power supply system of industrial enterprises. In the designing, the operation and the mode planning of these systems it is required to account not only the power supply reliability but also the risks associated with operation interruptions. The task of risk assessment is complicated because of such a characteristic feature of industrial power supply system as the uncertainty of information about possible emergency modes, operational loads, etc. Methods. The combination of two methods: the sequential network reduction and Newton's method is proposed for the calculation of equivalent reliability indices of complex systems. On the basis of reliability calculation, the damage from power supply interruption is determined. The game theory criteria are proposed to use for decision making in case of uncertainty. The Wald, Minimin, Hurwicz, Bayes, Hodge-Lehmann, Savage, Laplace, Multiplication, Germeier-Hurwitz criteria are calculated and analyzed. Scientific novelty and practical significance. The proposed algorithm for reliability evaluation allows to determine the probability of no-failure, failure intensity and recovery time. The algorithm can be used to evaluate the reliability of an existing distribution system and to provide useful planning information regarding improvements to existing systems and the design of new distribution systems. This algorithm with the Iron and Steel Works in Russia. Application of game theory criteria allows to select the optimal strategy for the power supply system development and to compare the different variants of normal and repair maintenance schemes of the network in uncertainty conditions. Introduction. In terms of the modern market economy, the financial impact of the unreliable power supply is of great importance. Particular attention should be paid to the reliability of power supply systems of the energy-intensive industries such as Iron and steel works. The power supply system of a large Iron and steel work has a number of features: the high level of redundancy, chosen on the design stage; the significant transformer power that considers the development of production; the combination of explicit and implicit redundancy at all voltage levels; insufficient statistical information on certain elements outages in 35-220 kV networks. So the accounting of reliability of power supply systems is necessary for both the design and the operation of power supply systems of industrial enterprises.

... The adequacy assessment is carried out in the long-term planning of the development of electric power systems (EPS). We used the Monte Carlo method (method of statistical tests) [1][2][3] to assess the adequacy of large EPSs. The methodology for adequacy assessment based on this method has been developed a long time ago; at present, various components of this method are being enhancement to improve the adequacy of the obtained indicators and make more informed decisions based on them. ...

... The considered models are suitable for a rough estimate of the power shortage of EPS for the long-term development of power systems (more than 10-15 years), when the uncertainty in the forecast of the initial data is significant. Subsequently, the model for minimizing the power shortage was added the power losses during its transmission through inter-zone communications [3][4][5][6][7][8][9]. Initially, the power losses were set linearly dependent on the transmitted power through interconnections. ...

The article presents an analysis of the models for minimizing the power shortage used in adequacy assessment by the Monte Carlo method. We analysed two models: a model with quadratic losses in power lines and a model using network coefficients (first-order sensitivity coefficients), that are showing the dependence of the change in power flows through power lines on the balance of generation / consumption in the reliability zones. As a result of the analysis, a conclusion is made about the applicability of the investigated models for adequacy assessment in the long-term planning of the development of electric power systems.

... Based on Li, transmission expansion planning (TEP) is traditionally grounded in probabilistic assessments, while this is not always the case for GEP [11]. In almost all optimization approaches, security of supply is covered implicitly through hourly profiles of energy demand and renewable power generation, an explicit assumption of an RM and/or expected energy not served (EENS). ...

Globally, renewable energy sources (RES) are getting more and more competitive even without subsidies. In general, optimization methods are used to identify the most economic setup of individual power systems. This study contributes to the discussion on how much reserve capacity a power system should have to ensure reliable electricity supply in assessing the explicit and probabilistic system reliability metric loss of load hours (LOLH) as well as expected energy not served (EENS) within a dynamic programming approach. Multi-year RES profiles from different locations are used to identify the minimum reserve margin (RM) requirements using LOLH and EENS as planning criterions. The findings indicate, that using RM as the only reliability constraint within optimization is not appropriate as a too high assumption on RM would increase the required conventional generation capacity unnecessarily and a too low assumption would risk reliable power supply. Using LOLH as the single metric for reliable power system planning, the EENS would grow with increasing RES contribution. This is the result due to the concept of LOLH as the amount of electricity not supplied is not part of the metric, only the hours of power undersupply are. On the other hand, a constant assumption of EENS is misleading as well as the concept of EENS does not consider the number of hours the power service can’t be fulfilled. Therefore, the recommendation is to use LOLH and EENS simultaneously in a single optimization framework as shown within this study.

... Several forecast techniques have been developed and discussed in the literature (Li, 2011). These include: linear regression, non-linear regression, probabilistic time series, and neural network methods. ...

Load forecast is very important in the energy industry. Deterministic energy consumption forecast has a lot of limitations since it does not take care of randomness and uncertainties. This study employs probabilistic energy consumption forecast in Ekiti State using standard normal distribution as a tool. It focuses on the energy consumption in Ekiti State using the available data from Benin Electricity Distribution Company (BEDC), Ado-Ekiti office. The study shows energy consumption in the state has a tendency of rising above 8601.5MWh (the maximum for year 2017) by 4.65% in 2018. It was established that the probability of the energy consumption falling below 4970MWh is 8.38%. The consumption of energy in year 2018 in the state may fall between 4970MWh and 8601.5MWh monthly at a probability of 86.97%. Energy consumption in year 2018 will mostly fall between 5500MWh and 8000MWh particularly. It is unlikely it falls between 3500MWh and 4000MWh (0.98%) and 9000MWh and 9500MWh. The result of this work can be used by stakeholders in the power industry for planning activities.

... This type of analysis ultimately is used to assist in sustaining economic activity and quality of life through reliable Identification of critical N-2 or N-1-1 contingencies is a computationally challenging problem, especially with complex and large-scale networks, and a large amount of research has been conducted on his topic. Risk-based planning methods are one group of alternatives to evaluate electric power systems [46,47]. For example, in [7] and [8] a cumulant-based Probabilistic Power Flow (PPF) and a hybrid algorithm are employed to correlate the parametric input of random variables. ...

Increased generation capacity from non-dispatchable energy resources such as wind and solar has created challenges to ensuring the reliable delivery of electric power. This research develops a systematic three-step method of assessing the reliability of electric power systems under a variety of different possible fault conditions to ensure that overall system stability is preserved in a manner the meets regulatory requirements. The first step is a risk-based reliability method (RBRM) that accounts for the probability of a line outage versus the severity of impact. This allows system planners to judiciously allocate expenses for reliability improvements based on the greatest economic benefit. The second approach is the synchrophasor validation method (SVM) which allows system planners and analysis to develop accurate models of electric power system behavior. This improves the decision making capability for implementing new system designs and equipment choices. The third new area is the development of norm-based wide-area control methods that optimize system stability and reliability based on the statistical characteristics found in the first two steps. This norm-based approach includes calculating optimal values for parameters of flexible ac transmission system (FACTS) devices and high voltage direct current (HVDC) links in order to have results within the regulatory requirements of the North American Electric Reliability Corporation (NERC). Power flow and frequency criteria are used to verify conformance with the regulations. These criteria are evaluated under N-1-1 conditions in two reduced order models to demonstrate the ability of the norm-based wide-area controller to maintain performance of these systems within acceptable ranges. The obtained simulation results confirm the benefits of the proposed technique in meeting regulatory requirements under conditions of N-1-1 contingencies in electric power systems with large amounts of renewable energy resources.

... where the mean value µ P of P L is provided by load forecaster, and σ P denotes the forecasting error. Generally, only the active power is predicted, whereas the reactive power is calculated under the assumption of constant power factor [27]. ...

In this paper, a mathematical formulation of the probabilistic available transfer capability (PATC) problem is proposed to incorporate uncertainties from the large-scale renewable energy generation (e.g., wind farms and solar PV power plants). Moreover, a novel non-intrusive low-rank approximation (LRA) is developed to assess PATC, which can accurately and efficiently estimate the probabilistic characteristics (e.g., mean, variance, probability density function (PDF)) of the PATC. Numerical studies on the IEEE 24-bus reliability test system (RTS) and IEEE 118-bus system show that the proposed method can achieve accurate estimations for the probabilistic characteristics of the PATC with much less computational effort compared to the Latin hypercube sampling (LHS)-based Monte Carlo simulations (MCS). The proposed LRA-PATC method offers an efficient and effective way to determine the available transfer capability so as to fully utilize the transmission assets while maintaining the security of the grid.

... Following this, various situations are simulated, and the power deficits in the system are calculated. Ultimately, according to the received data, we determine the reliability of certain objects in the system [32,33]. We modified the methodology that was used to assess the reliability of the interconnected electricity systems of the three countries. ...

In our research, we focus on the reliability of the interconnected electricity supply system of three countries of the Eurasian Economic Union (EAEU)—Russia, Kazakhstan, and Kyrgyzstan. We apply a mathematical model to evaluate the reliability of the electricity supply system under the threat of earthquakes. Earthquakes can damage elements of electricity grids and, considering the interconnectivity of electricity supply systems in the EAEU, effects in the aftermath of earthquakes can be far-reaching and even transboundary. This necessitates the development of coordinated policies and risk management strategies to deal with electricity outage risks in the EAEU. In our study, the earthquake probability is derived from seismic zone maps, while damage events are computed using maps of energy power systems. In addition, we determine which elements of the system are susceptible to failure due to an earthquake of a given magnitude. We conduct a scenario analysis of earthquakes and their impacts on the reliability of the power supply system, considering potential energy losses and threats to energy security. An analysis of the resilience of electricity transmission grids allows us to determine the critical interconnection lines in terms of exposure to earthquake risk, as well as exposure to total systemic loss. We also identify the most critical interconnection lines where power outages can lead to the destabilization of the entire power supply system. Some examples of such lines are at the border of Kazakhstan and Kyrgyzstan, where power outages can lead to serious economic costs and electricity outages.

... The existing literatures related to TOU strategies primarily focused on two aspects, i.e., the period partitioning and the TOU electricity pricing optimization. The traditional k-means algorithm [10], [11] and the bisecting k-means algorithm [12], [13] are widely used in the period partitioning, the load forecasting and the probabilistic power flow. But the k-means based algorithms have an obvious shortcoming, namely, the clustering results are always fluctuant due to the random initial values. ...

Because the time of use (TOU) strategies can directly affect the power flow distribution of electrical distribution system, this paper investigates the optimal TOU electricity pricing model and its functions for improving the power quality and reducing the power loss of electrical distribution system. Firstly, an optimal period partitioning algorithm based on a moving boundary technique is proposed for dividing an entire day to the different periods. Secondly, an optimal TOU electricity pricing model is proposed through minimizing the peak-valley difference, the voltage fluctuation, and the power loss. The particle swarm optimization (PSO) algorithm is adopted to solve the proposed optimization problem, and the multi-objective constrained optimization problem is transformed into a single objective unconstrained optimization problem. Thirdly, two novel indices of describing the voltage variation and the power loss are defined for considering the impact of TOU strategies and improving the power quality and reducing the power loss. Finally, an IEEE 14-bus system is applied to verifying the correctness and effectiveness of the proposed method. The results prove that the algorithm which proposed in this paper has a great significance in improving the power quality and the economic benefits of electrical distribution system.

... However, this deterministic criterion may lead to over investments in the network while it does not ensure acceptable reliability indices for the entire network, as it does not consider the probabilistic nature of network equipment outage events. In a different way, the outage information representing the life cycle of system components is used in the evaluation of probabilistic system reliability indices, as the EENS [16]. ...

Transmission Expansion Planning (TEP) is traditionally carried out based on long-term forecasts for the peak load, which is viewed as the worst-case scenario. However, with the increasing renewable penetration, the peak load may not be longer the only worst-case to quantify new investment requirements. In fact, high off-peak load scenarios combined with low renewable generation can originate unforeseen bottlenecks. Besides, as TEP is a time-consuming problem, relaxed decision-making processes are often proposed in the literature to address the problem, however there is no guarantee that optimal planning has been achieved when some costs in the decision-making process are neglected. In this sense, this paper proposes a novel methodological framework to ensure that the system is sufficiently robust to overcome conditions with high electricity demand and low renewable energy, furthermore, this paper also presents a broad comparison between the common decision-making processes adopted in the TEP literature aiming at providing a more insightful understanding of its impact on the total system cost. The optimization model, which is based on a multi-stage planning strategy, considers an AC-OPF model to enforce operational constrains, including the N-1 contingency criterion. The proposed model is tested through an evolutionary algorithm on a large test system with 118 bus. The uncertainties inherent to wind-solar-hydrothermal
systems, demand and the life cycle of generation and transmission equipment are duly considered in the simulations. The results demonstrate the effectiveness of the proposed methodology in providing solution plans able to meet the demand even in scenarios with
high off-peak load and low renewable generation, unlike the planning carried out considering only the peak load. Besides, the results also demonstrate that relaxed decision-making models may generate insufficient expansion plans.

... It is assumed that component failures outside of the defined boundary have no impact on the reliability performance of the substation of interest. The proposed approach incorporates load duration curve (LDC) and load forecast uncertainty (LFU) [37][38][39] in the evaluation. Reliability data contains the failure rate (both active and passive failure rates), maintenance rate and average outage duration for all components associated with the substation of interest including transmission lines, transformers, bus sections and generating units. ...

A new enhanced probabilistic approach for substation reliability assessment is presented. The proposed technique evaluates substation reliability using a combinative approach that considers not only the impact of substation equipment failures but also the effect of the system conditions in which the substation resides. The approach uses the analytical contingency enumeration technique and uses a commercial program to perform power flow analysis in order to assure the accuracy of the reliability evaluations. The application of the proposed approach is illustrated by performing probabilistic reliability assessment on an actual utility substation. The technique presented will enable more realistic assessment of the reliability performance of substations and/or switching stations using probabilistic approaches.

... Despite significant contributions to date, there remains a number of key challenges, e.g. incorporating very high shares of volatile renewables [9] [71], considering simultaneous generation expansion and transmission planning and operation considering MES [72] [73] [74], and uncertainty [75]. ...

Historically, energy system tools were predominantly proprietary and not shared with others. In recent years, there has been an increase in developing open source tools by international research and development organizations. More than half of the open energy modeling (openmod) initiative listed tools are based on the freely available scripting language Python. Previous comparisons of energy and power system modeling tools focused on comparisons such as which tool category (e.g. optimization, simulation) or energy demand (e.g. electricity, cooling, and heating) can be considered. Until now, the assessment of incorporated functions such as unit commitment (UC) or optimum power flow (OPF) has been ignored. Therefore, this work assesses 31 mostly open source tools based on 81 functions for their maturity. The result shows that available open source tools such as Switch, TEMOA, OSeMOSYS, and pyPSA are mature enough based on a function comparison with commercial or proprietary tools for serious use. Nevertheless, future commercial, as well as open source energy system analysis tools, have to consider more functions such as the impact of ambient air conditions and part-load behavior to allow better assessments of including high shares or renewable energy sources and other flexibility measures in existing and new energy systems.

... Cette courbe, illustrée à la figure 5.33, est parfois appelée la courbe du nez pour sa forme. [137] A la limite de charge, ou la pointe de la courbe du nez, la matrice jacobienne du système des équations de l'écoulement de puissance va devenir singulière comme la pente de la courbe du nez devient infinie. Ainsi, la méthode de Newton-Raphson traditionnelle qui permet d'obtenir la solution de flux de puissance ne fonctionne pas. ...

L'UPFC comme élément FACTS présente l'avantage d’être l'unique dispositif capable de contrôler simultanément la répartition des puissances actives et réactives dans les lignes de transport d'énergie en plus de sa capacité de réguler la tension dans les différents nœuds interconnectés. L'UPFC joue un rôle primordial dans l'amélioration de la qualité de l'énergie et la stabilité des réseaux électriques puisqu'il permet aux lignes de transport de véhiculer l'énergie jusqu'à leur limites thermiques. Ainsi l'opérateur des réseaux électriques disposera d'une grande flexibilité quant à la satisfaction des demandes en énergie. L'objectif de cette thèse est de développer un model d'UPFC qui peut être facilement incorporé dans un programme de résolution de répartition des puissances.

... The TEP can also be characterized into short-term, midterm and long-term planning, as shown in Fig. 3. There is no fixed rule for this categorization, but generally, long-term planning has a time-scale of decades (usually 20-30 years); medium-term planning deals with time scales of 10-20 years, and short-term planning deals with issues that must be addressed within 10 years [5][6]. TEP problem can be represented using DC or AC power flow (AC PF) model. ...

The increasing demand and the corresponding rising penetration of renewable energy generation has brought various challenges for the power system. In this regard, expansion planning of the system is exceedingly significant. Commonly, power system expansion is categorized into generation, transmission, and distribution domains. As the investment involved in transmission expansion planning (TEP) is usually greater than the other two domains, thus, this paper focuses on TEP. The main aim of TEP is to install new devices on a transmission grid to optimize a variable, based on an objective function, while fulfilling some pre-defined technical and economic constraints. The non-linear and non-convex nature of TEP, along with system uncertainties (load, renewable generation, etc.), makes it a stimulating issue. Moreover, the combinatorial explosion of investment replacements, bundled with (N-1) security constraints, generally necessitates a huge computational effort to solve it. The security-constrained transmission expansion planning (SCTEP) has various challenges. Thus, the main objective of this research is to review and present some challenges associated with SCTEP problem.

... However, the process of introducing probability factors into system planning scheme is still complicated. Different from introducing probability factors in the formation stage of planning schemes, it was pointed out in [13] that introducing probability factors in the comprehensive economic comparison stage is simple and more practical, which inspires us to study the expansion planning method of modern power systems by considering the uncertainty of wind power in the comprehensive economic comparison stage of system planning. To sum up, there are few existing papers that carry out expansion planning for alleviating transmission congestion. ...

Transmission congestion identification and expansion planning methods for power systems with wind power are proposed in this paper. First, wind farm model is established based on Copula theory considering the uncertainty and correlation of wind speed and wind turbine’s failure. Next, generation rescheduling model with wind farm and TCSC is established and a transmission congestion identification method based on reliability evaluation is proposed. Then, alternative schemes of expansion planning have been proposed according to the results of congestion identification, and the final scheme is determined by probabilistic economic analysis method. Finally, case studies have been carried out on modified RBTS test system. For the mRBTS system, when wind farms are integrated into system from bus 1 and 2, the best expansion solution is to build new transmission line; while when wind farms are integrated from bus 3 and 5, the best expansion solution is to install TCSC. Results of case studies verify the effectiveness of the proposed congestion identification and expansion planning methods of transmission system, and reveal that the location of wind power affects the decision making of transmission system expansion planning scheme.

... Therefore, further research on various situations is needed. According to previous studies of transmission planning or security analysis based on the probabilistic approaches, from a security perspective, probabilistic voltage and transient stability assessment are key issues toward probabilistic transmission planning [27]. For transmission expansion planning, scenario-specific fault, load flow, reactive power, and stability analysis (dynamic analysis) should be performed [28]. ...

As the importance of renewable generating resources has grown around the world, South Korea is also trying to expand the proportion of renewable generating resources in the power generation sector. Among the various renewable energy sources, wind generating resources are emerging as a key alternative to conventional power generations in the electricity sector in Korea accounted for 17.7 GW of total capacity by 2030. As wind generating resources are gradually replacing traditional generating resources, the system security and reliability are negatively affected because of the variability, due to intermittent outputs. Therefore, existing power grids will need to be correctly re-measured to cover the large scale of renewable energy, including wind generation. To expand the grid, we must understand the characteristics of renewable energy and the impact of its adoption in the grid. In this paper, we analyze various characteristics of wind power generation, and then we propose a probabilistic power output modeling method to consider the uncertainty of wind power generation. For the probabilistic approach, Monte-Carlo simulation is used in the modeling method. The modeled wind power outputs can help planning for the reinforcement and expansion of power systems to expand the capacity for large-scale renewable energy in the future. To verify the proposed method, some case studies were performed using empirical data, and probabilistic power flow calculation was performed by integrating large-scale wind power generation to the Jeju Island power system. The probabilistic method proposed in this paper can efficiently plan power system expansion and play a key strategy of evaluating the security of the power system through the results of stochastic power flow calculation.

... To cope with these limitations, there is a body of work that recommends replacing deterministic standards with probabilistic (or stochastic) approaches to ensure a secure design and operation of power networks [3,[11][12][13][14][15][16][17][18][19]. Under a probabilistic approach, outage risks can be appropriately measured and balanced against the costs of designing and operating the grid in a manner that could reduce such risks [13]. ...

Natural hazards cause major power outages as a result of spatially-correlated failures of network components. However, these correlations between failures of individual elements are often ignored in probabilistic planning models for optimal network design. We use different types of planning models to demonstrate the impact of ignoring correlations between component failures and the value of flexible transmission assets when power systems are exposed to natural hazards. We consider a network that is hypothetically located in northern Chile, a region that is prone to earthquakes. Using a simulation model, we compute the probabilities of spatially-correlated outages of transmission and substations based on information about historical earthquakes in the area. We determine optimal network designs using a deterministic reliability criterion and probabilistic models that either consider or disregard correlations among component failures. Our results show that the probability of a simultaneous failure of two transmission elements exposed to an earthquake can be up to 15 times higher than the probability simultaneous failure of the same two elements when we only consider independent component failures. Disregarding correlations of component failures changes the optimal network design significantly and increases the expected levels of curtailed demand in scenarios with spatially-correlated failures. We also find that, in some cases, it becomes optimal to invest in HVDC instead of AC transmission lines because the former gives the system operator the flexibility to control power flows in meshed transmission networks. This feature is particularly valuable to systems exposed to natural hazards, where network topologies in post-contingency operating conditions might differ significantly from pre-contingency ones.

... A broad overview of the literature covering the subject of both power systems adequacy and security, under the influence of probabilistic uncertainties, may be observed in [2], [3], indicating that considerable maturity in this field has already been attained. Adequacy analysis considering the treatment of power system uncertainties under the realm of fuzzy variables has also been introduced [4]- [6], but the probabilistic approach still remains clearly dominant, even in more recent publications [7], [8]. Probabilistic security analysis, despite recent advances [9], still lags behind adequacy analysis in useful applications for actual large scale power systems [10]. ...

This paper presents a simplified but effective procedure to represent power system uncertainties that allow the development of a computational tool to tackle the power system probabilistic security problem from both the small signal stability (SSS) perspective, and the transient stability (TRS) analysis perspective. A set of examples using the New England test-system is presented and discussed. Among the advantages of the suggested method, the following points are evident: (i) the ability to discriminate between the three types of uncertainties (scenarios, fault events, and noise types) that permeate power systems and that are relevant to the system security; (ii) the capacity to use existing traditional tools from both small signal dynamic analysis and transient stability analysis to adapt them easily to the well-established concept of probabilistic adequacy assessment, without resorting to abstruse and hard-to-implement theoretical techniques; (iii) the enormous advantage of usual availability for the required statistical data (no hard-to-collect data are required); and (iv) proposal of a conceptual procedure that renders a highly combinatorial problem amenable to current state-of-the-art hardware resources, within acceptable limits of computational burden. Important practical results that one may wish to highlight are related to the effective representation of noise uncertainties through a straightforward combination of weighted histograms, and the successful performance of the new Apparent Stability Index-ASI.

... If the PF diverges, it impacts the solvability of the unsolvable power flow. A minimum load shedding model [28,29] can help obtain a highly critical state with solution of power flow. It is pertinent to note that Y LL is called bus admittance sub-matrix relevant to non-generator buses. ...

Avoltagestabilityindexisproposedusinganewsingle-portequivalentdependingoncomponentpeculiarityrepresentationandsensitivitypersistencetolocateanddeterminelong�termvoltageinstabilityintransmissionanddistributionpowernetworks.Thesuggestedsingle�portequivalenteffectivelyrepresentstheequivalenceofvariouscomponenttypesandassurestheconsistencyofsensitivityinformationbeforeandaftertheequivalencewhichiscompulsoryfortheequivalentaccuracyinestimatingthevoltagestabilityanalysis.Thestabilityindexisderivedfromthenewsingle-portequivalenttodeterminethesystemvoltageinstability.TheproposedstabilityindexiscomparedwithindicesbasedonvirtualimpedanceandTheveninimpedancemodels.ThisnewstabilityindexshowsmoreaccuracyandeffectivenessascomparedtotheindicesbasedonvirtualandTheveninequivalentmodels.Theindexalsodeterminestheweakbuses,whereanimprovementorfunctionalmeasurecanbeusedtoreducethesystemvoltageinstability.Thevalidityoftheproposedequivalentapproachandstabilityindexispresentedbyutilizingtworadialsystems,fourIEEEsystemsandanactualsystemhavingbussizefromfiveto1010buses.

... In this case, only the short term horizon planning is considered; whereby, probabilistic models of the power system random variables are built. Topology changes must be also considered in order to reflect the system behavior as close as possible to the actual system condition [44]. Initial information to construct the database using the MC simulation method [40] corresponds to: i) probabilistic model of the nodal demand; ii) economic dispatch, and iii) probabilistic N-1 contingencies model. ...

The ever increasing active and reactive power demands, along with limited sources of generation and delays in transmission expansion projects, have led many power systems to operate near their voltage stability limits. In this context, voltage stability monitoring methodologies have become an important topic in power systems research. This paper presents a novel methodology for long-term voltage stability monitoring in power systems that exploits the feasibility of phasor-type information in order to estimate the long-term voltage stability status. The information regarding the current system condition is acquired through synchronized phasor measurements and the power system is divided in sub-areas for improving its supervision; then, an artificial intelligence approach based on kernel extreme learning machine is used for long-term voltage stability assessment. The proposed scheme allows foreseeing the voltage instability caused by limitations in reactive power transmission, and it also permits alerting when a system area experiences a deficit of reactive power from supply sources. The validation of the proposed method is performed on the 39-bus test system, obtaining feasible results. The tests confirmed that the proposed method works properly under different scenarios and system conditions, always ensuring proper voltage stability status results independently of its cause. Ó 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

... There is a rich body of literature on fundamental concepts in composite power system probabilistic reliability evaluation [2] - [14]. General concepts of power system planning under uncertainty are presented in [4], [15] - [16]. The probabilistic reliability assessment methodologies are based on one of two approaches: contingency enumeration and Monte Carlo simulations. ...

This paper presents a probabilistic reliability planning (PRP) approach for selecting Treasure Valley (TV) 75-year buildout transmission strategies at Idaho Power Company (IPC). Paper illustrates IPC’s experience in applying a probabilistic reliability-based approach to develop long-term transmission system planning strategies. The PRP approach is based on analytical enumeration technique. A Computer Program Transmission Reliability Evaluation of Large Scale Systems (TRELSS) developed by Electric Power Research Institute (EPRI) has been used for evaluating composite system reliability. Three concurrent long-term 75-year transmission planning strategies named ISLD, LOOP and HYBR have been evaluated and compared. The results obtained showed merits and demerits of analyzed TV buildout strategies.

Distributed energy resources (DER) have the potential to significantly contribute to network security and hence release latent capacity of existing transmission assets. In this context, we propose a distributionally robust approach to network security in order to recognize the limited data and knowledge associated with the underlying process behind the realization of system contingencies within the transmission expansion planning (TEP) problem, and thus determine the optimal portfolio of DER services necessary to displace, in a secure fashion, inefficient network investments. To do so, we propose a two stage optimization model where the first stage determines the transmission expansion plan and the scheduling of DER post-contingency services in coordination with further corrective control measures such as generation reserves. The second stage minimizes the expected cost of corrective actions under various contingencies. Through various case studies, we demonstrate the benefits of security services provided by DER and the advantages of our proposed distributionally robust approach (where outage rates are assumed ambiguous) against alternative n − K security and stochastic approaches, where outage rates are either ignored or assumed fully known, respectively.

The data is not always shared among sub‐networks due to concerns about information privacy or difficulties in synchronous information exchange. It is difficult or even impossible to obtain the probabilistic power flow (PPF) by the centralized analysis. In this paper, an equivalent model considering static power‐frequency characteristics (SPFCs) and renewable uncertainties is proposed. In this model, SPFCs of equivalent loads and generators are derived to retain SPFCs of original external loads and generators, respectively. In addition, probabilistic characteristics and correlations of equivalent loads are formulated based on Cholesky decomposition to preserve original external renewable uncertainties. The proposed model is further applied to PPF and then PPF can be solved via Monte Carlo simulation method, which makes that the PPF results can be obtained when the detailed data of the original external network cannot be shared. Due to efficiently preserving the external SPFCs and renewable uncertainties in the proposed equivalent model, the accuracy of PPF results can be guaranteed. Simulation results of IEEE 14‐bus and IEEE‐118 bus systems demonstrate the effectiveness
and superiority of the proposed equivalent model and its applications to PPF, compared with existing well‐known equivalent models and their applications to PPF.

The paper deals with the problem of the accounting of renewable energy sources and energy storage systems in assessment of power system adequacy. Development of renewable energy sources and energy storage systems in the present day power systems is one of the main focuses. In power systems of some countries the share of electric energy generated by renewable energy sources is above 50 % in the energy balance. Therefore, the plans on development of the present day power systems must be elaborated with the proper accounting of operation of renewable energy sources and energy storage systems and the sound capacity reserves in terms of these facilities. The paper presents the algorithms for the accounting of renewable energy sources and energy storage systems. The experimental studies performed illustrate feasibility of the suggested algorithms.

Increasing calculation speed of the electric power system (EPS) reliability of is one of the key issues in their operational management and long-term development planning. Analytical methods to assess the EPS reliability seem to be impossible due to large size of the problem and, as a consequence, essentially the only option for assessing is to use the Monte Carlo method. When it is used both the speed and the accuracy of calculation directly depend on the number of randomly generated system states and the complexity of their calculation in the model. Methods aimed at increasing computational efficiency can relate to two directions - reducing the states under consideration and simplifying the computational model for each state. Both options are performed provided that calculation accuracy is retained.
The article presents research on using the machine learning methods and, in particular, the multi-output regression method to modernize the reliability assessment technique via the Monte Carlo method. Machine learning methods are used to determine the power deficit (realization of a random variable) for each random EPS state.
The use of multi-output regression enables comprehensive determining of values of all the required variables. The experimental studies are based on the two test circuits of electric power systems: three-zone and IEEE RTS-96 with 24 zones of reliability.

In this paper, we propose a data-driven load fluctuation model, based on high resolution historical demand data from multi-regional systems, that can be used for research such as power system generation control studies and probabilistic load flow studies. As in previous studies, the random load fluctuations are modeled as independent Gaussian random variables; however, unlike in previous studies, we do not assume the relationship between the standard deviation and the base demand in each region is known a priori. Instead, we propose a framework for determining the relationship between the base demand level and short-term demand uncertainty. The developed framework has been tested using actual 5-minute demand data from the New York and New Zealand power systems. The results demonstrate that the proposed models outperform those used in previous work. Coefficients of the example cases are included, the parameters of which can be applied to similar multi-region systems.

Energy and water management systems are closely interrelated through the operating regimes of Hydro Power Plants (HPP) or HPP cascades. This is first of all, characteristic of energy systems with a large share of HPP. One of such systems is the energy system of Siberia, which includes the Angara-Yenisei cascade of HPP, the largest in Russia and one of the largest in the world. The studies were carried out on the example of this energy system and the water management system of the Angara and Yenisei basins. A specific feature of the energy and water management systems of Siberia is a significant impact of stochastic factors on their operation. These factors include natural (water inflow in the reservoirs in the spring-summer period and outdoor temperature in the autumn-winter period), and also economic (demand for electric and thermal energy, electricity and heat prices) factors. The paper presents mathematical models for the joint study of energy and water systems. These models factor in the specifics of the systems during planning for a period of up to 1 year. Modeling of the interconnected operation of energy and water systems makes it possible to solve important problems. These are the improvement in the reliability and stability of the considered systems, increase in their economic efficiency (minimization of electricity prices for consumers), assessment and minimization of various risks, prevention from or reduction in possible damages, rational planning of repairs, the formation of fuel reserves at thermal power plants, and others.

This paper describes a reliability study that has been performed at Hydro One to compare the reliability of two deterministic criteria used in the planning of high voltage auto-transformer stations. One criterion calls for designing the station to withstand the loss of one unit transformer (single contingency criterion) while the other calls for designing it to withstand the loss of two units (double contingency criterion). Two system reliability measures are used in the comparison namely the system availability index and the loss of energy index. The study proposed a number of Markov models to evaluate the probability of system failures under each criterion. Examples are provided to illustrate these models and see how the two deterministic planning criteria are compared from the reliability point of view.

A steady trend towards the development of electric power systems leads to their continuous enlargement and sophistication. As a result, new ways of their control appear. In this regard, the existing models and complexes for adequacy assessment may work inadequately and ineffectively in terms of the obtained results adequacy. To assess the current state of the existing models and complexes, we reviewed and analyzed the domestic and foreign software and computer systems. In particular, we considered mathematical models of minimizing the power shortage. This work is based on the problem of modifying mathematical models of minimizing the power shortage used in adequacy assessment of the electric power systems of one of the complexes under consideration. As a modification of mathematical models, it is proposed to exclude the existing method of using the line capacities and start use correct accounting for the maximum permissible active power flow in controlled sections. The experimental part reflected in the paper concerns the testing of options for models to minimize the power shortage, as well as the proposed modifications on various systems, including those consisting of three and seven reliability zones with a variable number of controlled sections and power lines included in them. The results of the study have shown that the proposed modifications are efficient and can be used in the future. The authors also obtained the most adequate results in terms of the physical laws of electric power system operation due to the model of minimizing the power shortage with quadratic losses which takes into account the limitations of power transmission over controlled sections.

The article is devoted to improving the methods of planning the development of an electric power system (hereinafter - EPS) for the long term. The list of tasks to be solved when planning the development of EPS, the formulation of the task of substantiating the development of EPS, and the features of its solution are considered. Within the framework of the study of the multicriteria formulation of the problem of substantiating the development of EPS, possible criteria for planning an EPS are proposed. Calculations were performed for two and four criteria. Based on the results obtained, conclusions were drawn about the prospects of a multicriteria approach to planning the development of EPS.

Para planejar e operar adequadamente uma Rede Elétrica Inteligente (REI), muitas novas considerações técnicas, no âmbito de sistemas de distribuição, devem ser apreciadas, por exemplo: a estabilidade – devido a instalação de Geração Distribuída (GD), o despacho de carga e geração, o gerenciamento de dispositivos de armazenamento de energia e a avaliação do impacto da conexão de veículos elétricos na rede de distribuição. O principal pré-requisito para muitas destas novas funções do centro de controle do sistema de distribuição é a determinação do estado da rede elétrica (módulo e a fase das tensões nodais) em tempo real a partir de dispositivos de medição nela instalados. Em centros de controle de sistemas de transmissão esta tarefa é realizada por ferramentas de estimação de estado. Desta forma, a Estimação de Estado em Redes de Distribuição (EERD) é um dos alicerces para a implantação de uma REI. A presença de um número reduzido de medições pode tornar a rede elétrica não-observável no âmbito da EERD. Isto é, as variáveis de estado (módulo e fase das tensões nodais em todas as barras) não podem ser determinadas a partir de um conjunto de medições por um estimador de estado. Devido a isto, geralmente adiciona-se um grande número de pseudo-medições ao plano de medição existente para assegurar a observabilidade e viabilizar a EERD. Um problema com esta estratégia é que a precisão do estado estimado é comprometida devido ao fato de que os erros associados com as pseudo-medições são consideravelmente maiores do que aqueles referentes às medições reais. Consequentemente é necessário alocar medidores (magnitude das tensões, fluxos de potência ativa e reativa, magnitude das correntes, etc.) para garantir a precisão do EERD. O problema de alocação de medidores para a estimação de estado em redes de transmissão é, geralmente, realizado com o objetivo de assegurar a observabilidade. Por outro lado, a alocação de medidores para EERD é realizada visando minimizar índices probabilísticos associados com os erros entre os vetores de estado estimado e verdadeiro. Um componente importante do método usado para resolver o problema de alocação de medidores é a técnica probabilística usada para estimar a função objetivo. Devido à natureza não-linear do problema de EERD, a melhor opção tem sido utilizar a Simulação Monte Carlo (SMC). Uma desvantagem da SMC para estimar a função objetivo do problema de alocação é o seu alto custo computacional devido a necessidade de resolver um problema de estimação de estado não-linear para cada elemento da amostra. O principal objetivo desta dissertação é propor técnicas probabilísticas para melhorar o desempenho computacional de metodologias existentes para alocação de medidores sem sacrificar a precisão do estado estimado. Este compromisso foi estabelecido usando-se duas estratégias. Na primeira, um modelo linearizado é usado para estimar o estado e a SMC para determinar os riscos da função objetivo. Na segunda, uma fórmula analítica fechada é usada para determinar os riscos com base no modelo linearizado. Além disso, as versões melhoradas dos algoritmos de alocação propostos nesta dissertação consideram o efeito da correlação entre as medições. As metodologias de alocação propostas foram testadas no sistema de distribuição britânico de 95 barras. Os resultados dos testes demonstraram que a introdução das estratégias propostas em um algoritmo de alocação de medidores reduziu significativamente o seu custo computacional. Além disso, pode-se observar que ocorreram melhorias na precisão em alguns casos, pois as estimativas dos riscos fornecidas pela SMC não são precisas com pequenas amostras.

In the previous chapters, reliability models of individual components and small systems were discussed. It was already mentioned that it easily becomes too complicated to combine these models to create a reliability model of a large system. Therefore, for large systems, special reliability analysis approaches have been developed. This chapter discusses three of these approaches. The first, state enumeration, is an analytical analysis of possible system failure states. State enumeration will be discussed in detail in Sect. 5.1. The second approach, generation adequacy, focuses on the reliability of generation systems and is discussed in Sect. 5.2. The third, Monte Carlo simulation, is a (computer) simulation approach of the system behavior. This will be discussed in Sect. 5.3.

To realize design automation of mechatronic systems, there are two major issues to be dealt with: opentopology generation of mechatronic systems and simulation or analysis of those models. For the first issue, we exploit the strong topology exploration capability of genetic programming to create and evolve structures representing mechatronic systems. With the use of ERCs (ephemeral random constants) in genetic programming, we can evolve the sizing of mechatronic system components together with the system structures simultaneously. The second issue, simulation and analysis of those system models, is made more complex when the systems are mixed-energy-domain systems. We take advantage of bond graphs as a tool for multi- or mixed-domain modeling and simulation of mechatronic systems. Because there are many considerations in mechatronic system design that are not completely captured by a bond graph, it is beneficial to generate multiple solutions, allowing the designer more latitude in choosing a model to implement. The approach in this paper is capable of providing a variety of design choices to the designer for further analysis, comparison and trade-off study. The approach is shown to be efficient and effective and is demonstrated in an example of open-ended real-world mechatronic system design application, a typewriter re-design problem.

This article discussed the issues around power system equipment aging, including concepts of equipment lifetime, approaches to estimating the mean life and age, Weibull and normal-distribution-based models to assess the end-of-life failure probability. The relationship between aging and maintenance activities, limitations of maintenance in extending equipment life, and determination of timing of retirement were also discussed. A few examples showing actual data of transformers, cables, and reactors at BCTC have been presented. Maintenance activities can extend the life of equipment but could be very costly for equipment at their end-of-life stage. A compromise between maintenance and replacement must be carefully considered. RCM and probabilistic analysis approaches are available for utilities to guide maintenance activities and manage aged assets in a more efficient and economic manner

This paper presents the basic framework of probabilistic transient stability assessment using Monte Carlo methods. The assessment requires two simulation processes: probability simulation and transient stability simulation of system states associated with fault events. The focus is placed on probability models and Monte Carlo simulation methods. The procedures for two types of studies are provided. The first one is evaluation of average system risk index due to system instability and the second one is determination of a relationship between probability of system instability and a system operation condition for a given fault. The presented method can provide useful information in secure system operation for control centers of utilities. The example given in the paper demonstrates an application of the presented method in an actual power system in Canada.

Considerating operating conditions of controllable equipment and corrective controls for voltage stability, a quadratic optimal model of minimizing the total load curtailment was proposed to identify power flow solvability. This model is combined with the modal analysis method to recognize system voltage instability. Based on the proposed method, a risk assessment technique for static voltage stability was presented using Monet Carlo simulation for selecting system states. The technique evaluates the probability of system voltage instability, expected load curtailments required to avoid system collapse and relationship between load curtailment and probability of voltage instability. The simulation results of the IEEE14 bus system demonstrate the effectiveness of the proposed method and technique.

This paper presents a method to develop and incorporate a reliability component in transmission pricing. The method includes the following three tasks: (1) developing a technique to establish a unit reliability value; (2) quantifying impacts of customer on system reliability; (3) incorporating the reliability component in the rate design. The proposed method calculates the charge or credit to a native, wheeling, or generation customer in terms of its impact on system reliability. Incorporation of the reliability component will force all players in the system (the utility and customers) to share their responsibility in system reliability through a price signal and provide an incentive message to encourage the right setting of new generations. The method also reflects the long run incremental investment requirement of a transmission company. The procedure of the proposed method has been explained using the BCTC system in Canada as an example.

Presents a Monte Carlo method for reliability evaluation of large-scale composite generation-transmission systems. The method is based on combining the basic random sampling technique with a direct analytical approach for system analysis, and the utilization of a minimization model for load curtailment. The technique is particularly suited to simulating large-scale systems and multiple states of generating units. Many utilities are now using multi-state models to assess capacity adequacy. The utilization of multi-state models in a composite generation and transmission study can create considerable computational difficulties when a conventional contingency enumeration approach is used. The Monte Carlo method can be used to assess the effects of multi-state modelling in composite system adequacy assessment. The technique is illustrated by application to two test systems in order to demonstrate the effectiveness of the method.

Fuzzy models for weather-related outages of overhead lines and a combined probabilistic and fuzzy technique for transmission system reliability assessment are presented. The region-divided weather states are modelled using a probability approach. This approach and the fuzzy models of weather-related outages are combined and incorporated into a Monte Carlo simulation procedure of transmission system reliability assessment to evaluate membership functions and mean values of reliability indices. The reliability test system is used to demonstrate an application of the proposed models and method. The membership functions of reliability indices provide a wider insight into the fuzziness of weather effects, which cannot be modelled by traditional probability concepts.

An algorithm is presented to evaluate substation reliability. This algorithm takes into account breaker failures, blocked breakers, and breaker backup protection to isolate faults in a substation. Passive and active outages are considered. Two evaluation criteria are used: substation fails if one point of load fails, and substation fails if all points of load fail. The cost of energy not supplied is used to evaluate and economically compare the substation reliability.

The paper presents an approach to incorporating the aging failure mode and multiple capacity states of a HVDC system in power system reliability assessment. Subcomponents in HVDC converter stations have a much shorter mean life compared to an ac line or cable. When their age approaches the mean life, the failure rate due to aging increases greatly and it is necessary to include their aging failure mode in the assessment. The modeling method presented for multiple capacity states includes three reliability block networks. Probabilities of a HVDC system being at the full, derated and zero capacities can be easily calculated using the three reliability networks. Once the state probabilities are obtained, the HVDC system can be represented using a three-state model in overall power system reliability evaluation. An actual example in a utility is given to demonstrate the application of the presented approach in a power supply system with an aged HVDC link.

The paper presents a network state enumeration technique combined with a labeling bus set approach for reliability evaluation of substation configuration in power systems. The presented method is easy to handle dependent failures, multiple failure modes and multiple states of components. Another merit is that network failure states enumerated are mutually exclusive and therefore avoid complex calculations associated with union and intersections which have to be conducted in the minimum cut set method. The basic procedure of the labeling bus set approach for identifying a network failure state is explained using a substation configuration with protection action and operational switching. An example of a substation layout is given to demonstrate effectiveness of the proposed method.

Summary form only given. The paper presents a risk evaluation based approach to the replacement strategy of aged HVDC components. It includes estimation of unavailability of individual HVDC components due to aging failures, calculation of capacity state probabilities of the HVDC system, quantified risk evaluation of the power system containing the HVDC link and benefit/cost analysis for different replacement strategies. The presented approach can be also applied to other system components. The replacement strategy for an aged submarine cable of the HVDC link in a power supply system at British Columbia Transmission Corporation has been analyzed as an example to demonstrate the actual application. The procedure of the analysis has been explained in detail in the example.

Determining the retirement time of aged equipment in power systems has been a challenge in the utility industry for many years. The paper presents a probabilistic analysis approach to making decision on retirement of aged equipment in transmission systems. The basic idea is to quantify and compare the expected damage cost and capital saving due to delaying the retirement of aged equipment. An actual example of an aged underground cable in a regional transmission system of a utility is used to demonstrate the application of the presented approach step by step.

Continuation power flow is a powerful tool to simulate power system steady-state stationary behaviours with respect to a given power injection variation scenario. Although continuation power flow methods have been implemented in several commercial packages, they may be still too slow for online applications. The authors aim to improve the continuation power flow methods, mainly their speed and, to a less extent, their reliability. Nonlinear predictors are developed based on the polynomial interpolations. The authors' numerical studies show that continuation power flow with the proposed nonlinear predictors can be much faster than that with traditional linear predictors such as tangent or secant predictors. Of the nonlinear predictors, second-order polynomial approximation-based and third-order-based nonlinear predictors show their superior performance in speed. Continuation power flow with second-order nonlinear predictors is generally slightly faster than that with third-order nonlinear predictors. In addition, a hybrid corrector is developed and incorporated into continuation power flow. It is numerically shown on several test systems ranging from 118-bus to 1648-bus that continuation power flow with the proposed hybrid corrector can be much faster than that with traditional correctors such as the Newton method and the fast decoupled method. Finally, an improved continuation power flow with the developed nonlinear predictor and hybrid corrector is presented and evaluated.

A hybrid approach using Monte-Carlo simulation and an enumeration
technique for the reliability evaluation of large scale composite
generation-transmission systems is presented. The method is suited to
the analysis of large systems and can be used to include multi-state
representation of generating units. Studies presented illustrate that
derating-adjusted two-state models for generating units can lead to
pessimistic appraisals of composite system adequacy. Variability in
system load can be incorporated by using a chronological load
representation or by an aggregated load model. The accuracy of the load
representation and the required computation time increases with the
utilisation of more steps in the annual load duration curve

This paper presents a method to calculate probability distribution of HVDC capacity considering both repairable and aging failures of HVDC components. With integration of the aging failure mode, the capacity probability distribution is varied with years. It can be used as a multiple state model of HVDC links in transmission reliability evaluation. The expected capacity obtained from the capacity probability distribution is an index to quantify and prioritise importance of HVDC components in reliability centred maintenance.

This letter presents a method to build weather-related fuzzy models of outage rate, repair time, and unavailability of overhead power lines.

This letter presents a method to incorporate a combined fuzzy and probabilistic load model in power system reliability assessment.

This letter presents a statistic-fuzzy technique for clustering load curves. Historical statistical records of load curves are used to create membership functions of the compatible fuzzy relation matrix and the self-multiplication rule of the fuzzy matrix is used to obtain the transferable nearness coefficients which can be utilized to systematically perform clustering of load curves. An example is given to demonstrate the application

This letter addresses two weaknesses of traditional common cause outage models, presents a simpler and conceptually more accurate modeling approach, and discusses differences between the traditional and the proposed models.

This paper presents a basic method of probabilistic transmission
planning used in BC Hydro. The method is based on transmission system
reliability evaluation and an overall economic analysis including damage
cost due to system unreliability. Four alternatives for the Vancouver
South Metro system of BC Hydro have been evaluated using the method: the
first one is addition of a 230 kV line; the second one local
configuration changes (“cuts and ties”) in the 69 kV
subsystem; the third one operational manipulation; and the fourth one
curtailable industrial load management. The third and the fourth
alternatives can be considered as noninvestment reinforcements. The
results indicate that the cut-and-tie alternative in the 69 kV subsystem
can provide the same reliability level as the 230 kV line addition but
with much lower investment and therefore the initial 230 kV line
addition could be deferred by 10 years. This deferral allows a major
capital expenditure of $26.4 million (1997$) to be avoided. The studies
show that the application of quantitative transmission reliability
assessment in power system planning can provide utilities with
significant economic benefits

This paper describes a method for static security analysis based
on a coordinated combination of PI methods, subnetwork solutions,
compensation methods and sparse vector methods. The method is hybrid
utilizing PI methods and contingency screening/analysis methods. This
paper focuses on the contingency screening/analysis method. It is
capable of efficiently handling PV/PQ bus type conversions and islanding
conditions caused by contingencies. It also features an
“optimal” combination of computational procedures which
yields the least execution time for a specified level of accuracy. The
performance of the method is statistically evaluated on large power
systems. The results clearly illustrate the superior performance of the
method

Both the very dishonest Newton (VDHN) and the successive over
relaxed (SOR) Newton algorithms have been implemented on the iPSC/2 and
Alliant FX/8 computers for power system dynamic simulation using complex
generator and nonlinear load models. The main thrust is to explore the
match between the algorithms, their implementation, and the machine
architectures. For example, the less parallel but sequentially faster
VDHN runs faster on the hypercube (iPSC/2) whereas the more parallel
SOR-Newton requires data sharing more often because of the extra
iterations and does better on the Alliant. The implementation on the
hypercube requires significant manual programming to schedule the
processors and their communication whereas the compiler in the Alliant
recognizes parallel steps but only if the software is properly coded.
The authors present these various considerations together with the
results