Capacity Outage Probability Table Research Articles

A Reliability Model for Integrated Energy System Considering Multi-energy Correlation

An integrated energy system (IES) is a regional energy system incorporating distributed multi-energy systems to serve various energy demands such as electricity, heating, cooling, and gas. The reliability analysis plays a key role in guaranteeing the safety and adequacy of an IES. This paper aims to build a capacity reliability model of an IES. The multi-energy correlation in the IES can generate the dependent capacity outage states, which is the distinguished reliability feature of an IES from a generation system. To address this issue, this paper presents a novel analytical method to model the dependent multi-energy capacity outage states and their joint outage probabilities of an IES for its reliability assessment. To model the dependent multi-energy capacity outage states, a new multi-dimen-sional matrix method is presented in the capacity outage probability table (COPT) model of the generation system. Furthermore., a customized multi-dimensional discrete convolution algorithm is proposed to compute the reliability model, and the adequacy indices are calculated in an accurate and efficient way. Case studies demonstrate the correctness and efficiency of the proposed method. The capacity value of multi-energy conversion facilities is also quantified by the proposed method.

Reliability assessments of an islanded hybrid PV-diesel-battery system for a typical rural community in Nigeria

This paper presents the use of a novel approach in assessing the generation reliability of a hybrid mini-grid system (HMS) based on the optimal design result obtained from the HOMER software. A typical Nigerian rural community – Lade II in Kwara State was used as a case study where the energy demand for the residential and commercial loads was 2.5MWh/day and 171kWh/day respectively. The optimized HMS results from HOMER comprising of a solar photovoltaic (PV) array (1.5MW), diesel generators (350kW) and battery storage (1200 units) has a combined least net present cost of $4,909,206 and a levelized electricity tariff of $0.396 per kWh. Contrasting the HMS with a diesel-only system for the community, an approximate 97% reduction in all pollutant emissions was observed. Furthermore, fluctuations in diesel fuel prices, variations in average solar insolation, and variations in the solar PV's capital/replacement costs were utilized in conducting a sensitivity analysis for the HMS. The capacity outage probability table (COPT) was utilized in validating the reliability of the simulation results obtained from HOMER. The HMS was observed to experience a load loss of 0.769MW, 0.594MW & 0.419MW when zero, one and two diesel generator(s) respectively were operational for all of the Solar PV's and Batteries being off-line. The loss of load probability (LOLP), loss of load expectation (LOLE), and total expected load loss (ELL) obtained from the COPT were 5.76 × 10−8, 5.0457 × 10−4 hr/yr and 0.025344Watt respectively. The results show the reliability of the HMS and also depicts a highly economical and feasible hybrid energy system.

Stochastic multi-objective dynamic dispatch of renewable and CHP-based islanded microgrids

Micro-grids (MGs) are practical solutions for integrating distributed energy resources (DERs) in order to supply electrical and heat demands. In this study, a stochastic model for optimal management of combined heat and power (CHP)-based MGs considering economic, environmental and reliability aspects have been proposed. Two sources of uncertainty including forecast errors of electrical load demand and wind power are considered in scenario generation process using roulette wheel mechanism. Availabilities of units are taken into account to model reliability using capacity outage probability table (COPT). For solving such non-linear, non-convex and complicated stochastic problem, exchange market algorithm (EMA) and the weighted sum method are employed for combining three conflicting objectives and solving multi-objective problem as a single objective problem. Fuzzy satisfying method is applied to choose best compromise solution. The main goal of the stochastic dynamic reliable economic emission dispatch (SDREED) problem is to determine output of each generating unit so that fuel cost and amount of emission are minimized while the electrical demand is provided by more reliable units and operational constraints are met. The output of stochastic problem gives better sight for generation scheduling of MGs. The obtained results show the effectiveness and ability of the proposed method in solving SDREED.

Multi-state system reliability analysis of HVDC transmission systems using matrix-based system reliability method

This paper presents a new reliability analysis method for High Voltage Direct Current (HVDC) transmission systems based on the Matrix-Based System Reliability method. The proposed method can compute the failure probability of HVDC transmission systems by use of efficient matrix-based procedures. Unlike conventional system reliability methods whose practicability strongly depends on the system size and the complexity of its multiple states, the proposed method can describe any general system event in a simple matrix form and therefore provides a straightforward way of handling the system events and estimating their probabilities. The main qualities of the proposed method are demonstrated by the reliability assessment of two multi-terminal HVDC (MTDC) transmission systems with multiple derated states. The performance of the proposed method and the results obtained were compared with two traditional assessment methods: Capacity Outage Probability Table (COPT) and Monte Carlo simulation. In this comparative analysis it is shown that the proposed method is a competitive alternative for reliability analysis of MTDC systems in terms of simplicity and efficiency.

ARIMA Based Wind Speed Modeling for Wind Farm Reliability Analysis and Cost Estimation

Necessity has compelled man to improve upon the art of tapping wind energy for power generation; an apt reliever of strain exerted on the non-renewable fossil fuel. The power generation in a Wind Farm (WF) depends on site and wind velocity which varies with time and season which in turn determine wind power modeling. It implies, the development of an accurate wind speed model to predict wind power fluctuations at a particular site is significant. In this paper, Box-Jenkins ARIMA (Auto Regressive Integrated Moving Average) time series model for wind speed is developed for a 99MW wind farm in the southern region of India. Because of the uncertainty in wind power developed, the economic viability and reliability of power generation is significant. Life Cycle Costing (LCC) method is used to determine the economic viability of WF generated power. Reliability models of WF are developed with the help of load curve of the utility grid and Capacity Outage Probability Table (COPT). ARIMA wind speed model is used for developing COPT. The values of annual reliability indices and variations of risk index of the WF with system peak load are calculated. Such reliability models of large WF can be used in generation system planning.

Modelling the operation strategies of storages and hydro resources in adequacy analysis of power systems in presence of wind farms

This study addresses the adequacy of a generating system considering the impact of operation strategies of storages and hydro energy resources. It is assumed that the installed storage capacity of a system can be assigned for two purposes: first, economical operation which adopts storage to shift electric energy and smooth the load curve; and the second, reliability-based operation, which deploys storage to avoid load curtailments. The economical operation strategy is represented by starting from time domain data and using the load curve modification method to synthesise the overall impact of storage. The reliability-based operation is modelled with a new method based on Markov chain model that considers the dynamic behaviour of storage during time. Moreover, a novel state reduction method is presented for decreasing the number of Markov states in applications to large systems. The effectiveness of the presented methods is evaluated by running several simulation scenarios with results presented on three test systems. The results demonstrate that evaluating the system reliability in the presence of energy storage by considering the frequency and duration of system states is more effective than using methods based on the Capacity Outage Probability Table (COPT).

A new analytical technique for incorporating base loaded energy limited hydro units in reliability evaluation

Energy limited hydro generation is one of the important sources for electricity. Hydro units, however, behave differently as compared to conventional fossil fueled units. The output of these facilities is largely dependent on the availability of the primary resource of water while the effect of unit forced unavailability is usually not significant in comparison. Energy limited hydro resource can, however, significantly affect electric power system reliability. It is therefore very important to accurately incorporate energy limited nature of hydro units in reliability assessment. This paper presents a new capacity modification technique to model energy limited characteristics of hydro generation serving as base load units. In this method the effect of unit's energy limitation is reflected by modifying the capacity and treating the energy limitation as reduced capacity. The method is illustrated using simple examples and applied to model hydro units in two reliability test systems. The results are compared with those obtained using the load modification approach proposed in other published work. The two methods produce exactly the same results. One of the salient advantages of the proposed method is that reliability indices can be calculated by convolving appropriate load model with system capacity outage probability table. It is, therefore, easier to incorporate energy limited hydro units in commercially available reliability evaluation softwares. The proposed technique also has the advantage of easily incorporating large number of hydro units in reliability evaluation as compared to other methods.

A novel method for reliability and risk evaluation of wind energy conversion systems considering wind speed correlation

This paper investigates an analytical approach for the reliability modeling of doubly fed induction generator (DFIG) wind turbines. At present, to the best of the authors’ knowledge, wind speed and wind turbine generator outage have not been addressed simultaneously. In this paper, a novel methodology based on the Weibull- Markov method is proposed for evaluating the probabilistic reliability of the bulk electric power systems, including DFIG wind turbines, considering wind speed and wind turbine generator outage. The proposed model is presented in terms of appropriate wind speed modeling as well as capacity outage probability table (COPT), considering component failures of the wind turbine generators. Based on the proposed method, the COPT of the wind farm has been developed and utilized on the IEEE RBTS to estimate the well-known reliability and sensitive indices. The simulation results reveal the importance of inclusion of wind turbine generator outage as well as wind speed in the reliability assessment of the wind farms. Moreover, the proposed method reduces the complexity of using analytical methods and provides an accurate reliability model for the wind turbines. Furthermore, several case studies are considered to demonstrate the effectiveness of the proposed method in practical applications.

Probabilistic Spinning Reserve Model of Power System Containing Wind

In order to reflect the influences of the stochastic uncertain of wind power on the optimal decision-making of the power system spinning reserve, a probabilistic optimization model of the spinning reserve is proposed. Considering uncertain factors such as predicted-deviation of wind, predicted-deviation of load and fault outage of generator, the capacity outage probability table is combined with predicted-deviation of wind and predicted-deviation of load. By introducing the analytic expressed probability reserve constraints into the unit commitment model considering the wind power, the spinning reserve of power system can be optimized to the expectable contingency level. Using a calculation example, the effectiveness of the model is proved, providing a new model for uncertainty analysis and optimal scheduling decisions of power system containing wind.

Particle swarm optimization based generation maintenance scheduling using probabilistic approach

This paper presents maintenance scheduling (MS) of generating units using particle swarm optimization (PSO) based probabilistic levelized risk method. The PSO for the generator maintenance scheduling generates optimal and feasible solution and overcome the limitations of the conventional methods. The maintenance of generators are directly associated with the overall reliability of the power system. The objective function of this paper is to reduce the loss of load probability (LOLP) for a power system. The capacity outage probability table (COPT) is the initial step in creating the maintenance schedule using the probabilistic levelized risk method. Probabilistic techniques are widely used in power system reliability evaluation of long-term planning. Moreover, this paper proposes the PSO to construct the generation model COPT without utilizing the analytical model. A case study for the roy billinton test system (RBTS) and real power system model, Thailand power system shows that the developed algorithm can achieve a substantial levelization in the reliability indices over the planning horizon and demonstrates the effectiveness of the proposed approach.

Optimising probabilistic spinning reserve using an analytical expected-energy-not-supplied formulation

Spinning reserve (SR) is an important resource, which can protect power systems without involuntary load shedding. The SR requirement needs to be assigned appropriately. In this study, a probabilistic method is used to optimise the SR requirement. The SR amount is determined by simultaneously optimising the operating cost, reserve cost and the expected interruption cost. Tremendous computational requirements introduced by the expected-energy-not-supplied (EENS) calculation make the major impediment to the optimisation solutions. In this study, a multi-step method is proposed to overcome the computation intractability of the EENS problem. The EENS of each optimisation period is analytically formulated as a piecewise linear function of system spinning reserve of that period. The parameters of the piecewise linear function are derived from the capacity outage probability table, which is established based on the exogenous unit schedule. The efficiency and validity of the proposed method is verified using the IEEE-RTS system.

Reliability/cost evaluation of a wind power delivery system

When the geographical locations with good wind resources are not close to the main load centers, it becomes extremely important to assess adequate transmission facility to deliver wind power to the power grid. A probabilistic method is presented to evaluate the contribution of a wind power delivery system to the overall system reliability. The basic model incorporates transmission line connecting a remotely located large wind farm to a conventional grid system. The classical generation system adequacy evaluation model is extended to incorporate limited transmission system. The mean Capacity Outage Probability Table (mean-COPT) concept is used to increase the computational efficiency as it allows determination of EUE (expected unserved energy) and LOLE (loss of load expectation) simultaneously in calculation of reliability indices of the generating system. The wind farm generation model is obtained by superimposing simulated wind speed, obtained from developed ARMA time series model, on power curve of WTG. An apportioning method has been used to reduce the number of states in the resulting model, obtaining an equivalent reduced 5-state model. Applying transmission line constraints result in wind generation model ranging from 2- to 5-state models. The study recognizes benefits from fuel offset by wind power, reliability worth and environmental improvement and determines appropriate transmission line capacity based on its contribution to the overall system risk and associated transmission system cost. The paper illustrates results using a real wind farm. The presented methods and discussions should be useful to power system planners and policy makers.

Probabilistic Electrical Power Generation Modeling Using Genetic Algorithm

system reliability assessment is an important task which can be performed using deterministic or probabilistic techniques. The probabilistic approaches have significant advantages over the deterministic methods. However, more complicated modeling is required by the probabilistic approaches. Power generation model is a basic requirement for this assessment. One form of the generation models is the well known capacity outage probability table (COPT). Different analytical techniques have been used to construct the COPT. These approaches require considerable mathematical modeling of the generating units. The models are combined to build the COPT which will add more burdens on the process of creating the COPT. This paper proposes the utilization of the Genetic Algorithm (GA) to sample the states of the COPT without engaging in analytical units modeling. The simple binary representation, 0 and 1 is used to model the states of generating units. The effect of the GA parameters is examined. The proposed technique is proven to be an effective approach to build the generation model. The proposed technique is applied to the RBTS.

An interactive package for risk evaluation and maintenance scheduling

The calculation of the Loss of Load Probability (LOLP) is an important element in generation planning studies. LOLP is calculated either independently to evaluate the risk of a certain generation system or in conjunction with several planning application programs such as, generator maintenance scheduling, probabilistic production costing, hydrothermal scheduling, generation expansion, etc. Exact calculation of the LOLP requires the calculation of the Capacity Outage Probability Table (COPT). This table takes into consideration the capacity rating the the forced outage rates of the generating units of the system and it provides the probability values associated with various amounts of system capacity on outage. The capacity outage table is calculated by utilizing the well known recursive convolution formula. Usually the table is simplified by rounding the capacity outage table to selected discrete capacity levels. The size of the round off increment depends on the desired accuracy. The classic approach is time consuming and requires a considerable amount of computer memory. In order to reduce the computational time and computer storage several methods have been proposed, in which the capacity outage probabilities are approximated with analytic continuous probability distributions. Most of these methods utilize the Central Limit Theorem, Fourier techniques and the Gram Charlier's expansion. Closely related to the LOLP is the maintenance scheduling problem. Preventive maintenance is required for all generating units in order to reduce the probability of capacity shortage and improve the overall reliability of the power system.

Adjusting Maintenance Schedules to Levelize Risk

When scheduling generating units for maintenance one of the goals is to level the risks of capacity shortages throughout the year. Level reserves have been used as an indication of level risk. This paper illustrates that better schedules can be found by a method that uses effective capability in place of reserve. The five step method of incorporating risk considerations into existing maintenance scheduling procedures is described and illustrated. The same capacity outage probability table as used in the loss-of-load probability method is used to determine the effective load-carrying capability of each unit to be scheduled. These effective capabilities take the place of the unit ratings in the reserve leveling portion of existing procedures. The loads forecast for each maintenance period are also converted into an equivalent load which reflects the variability of peak loads during the period.