Expected Unserved Energy Research Articles

Optimal battery energy storage system deployment from perspectives of private investors and system operators for enhancing power system reliability

Due to their intermittent nature, high penetration of renewable energy resources (RES) can deteriorate power system reliability. A battery energy storage system (BESS) offers an opportunity to reduce the uncertainty associated with RES and hence improve power system reliability. In the last decade, the cost of BESS has declined so its deployment has become increasingly feasible, but the decision ultimately depends on its Net-Benefit to the investor. Depending on the perspective of the investor, the deployment decision involves discovering the most optimal location, capacity, and technology of BESS. A sensitivity analysis based on the Z-bus matrix is used for selecting the optimal location. In this paper, from the narrow perspective of a private investor, the Net-Benefit function is the energy arbitrage value of BESS minus its overall cost. However, the system operator additionally values BESS because it enables more reliable system operation at reduced operating costs. After examining multiple power system reliability indices, the product of Expected Unserved Energy (EUE) and Value of Lost Load (VoLL) is incorporated into the Net-Benefit function of the system operator. MATPOWER Optimal Scheduling Tool (MOST) is used for testing the proposed Net-Benefit functions on a standard reliability test system (RTS) known as RTS-GMLC. Three diverse case studies are examined in three exploration phases; the first phase helps determine search space whereas the second one narrows it down and the third phase finds the optimal BESS solution. Presented research results demonstrate that, over a period of 15 years, optimal BESS deployment can offer as much as $M164.8 and $M33.6 Net-Benefits to the system operator and private investor respectively.

Multi-Objective based Optimal Generation Scheduling Considering Wind and Solar Energy Systems

Abstract This paper presents an optimum day-ahead scheduling of thermal and renewable (wind and solar photovoltaic) power generation as a multi-objective optimization (MOO) problem considering the uncertainty. System operating cost (i.e. cost of thermal, wind, solar PV and battery), reliability and emission cost are considered to be optimized simultaneously. The uncertainties due to the generator outages, wind, solar PV power and load forecast errors are incorporated in the proposed optimization problem using the Loss Of Load Probability (LOLP) and Expected Unserved Energy (EUE) reliability indices. In the proposed approach, the amount of spinning reserves (SRs) required are scheduled based on the desired level of system reliability. The proposed multi-objective optimization problem is solved using NSGA-II algorithm. Different case studies are performed considering different objective functions that may be selected by system operator (SO) based on the preference.

The impact of energy storage modeling in coordination with wind farm and thermal units on security and reliability in a stochastic unit commitment

The environmental concerns and restrictions of fossil fuel resources have led to the deployment of wind power installation. Due to the uncertain nature of wind speed, high penetration of wind power may threaten system reliability and security. Energy storage systems (ESSs) are considered to be a viable solution to this problem. In this study, a stochastic security constrained unit commitment (SCUC) problem is solved in the presence of wind and ESS units. The main concern of this paper is to study the impact of the proposed ESS model on the security and reliability of the system. To assess the reliability of a power system, the expected unserved energy (EUE) for line outage and demand underestimation contingencies is evaluated. The SCUC problem is solved by a scenario-based method incorporated with the Benders decomposition technique to mitigate congestions from power lines and provide feasibility and optimality of the solution in all the scenarios. The performance of the proposed approach has been evaluated using the 6-bus and 39-bus standard power systems. Simulation results demonstrated the economic advantages of the proposed model, while the security constraints are satisfied. Moreover, the impact of energy storage modeling on the EUE in post-contingency circumstances is discussed.

Day-ahead thermal and renewable power generation scheduling considering uncertainty

Abstract This paper proposes a multi-objective optimization (MOO) based optimal day-ahead scheduling of thermal and renewable (wind and solar photovoltaic) power generation problem considering the intermittent/uncertain nature of renewable energy sources, load demands and thermal generators. System operating cost (i.e., cost of thermal, wind, solar PV and battery powers), reliability and emission cost are considered to be optimized simultaneously. The uncertainties due to generator outages, wind, solar PV and load demand forecast errors are incorporated in the proposed optimization problem using Expected Unserved Energy (EUE) and Loss Of Load Probability (LOLP) reliability indices. In the proposed approach, the amount of spinning reserves (SRs) required are scheduled based on the desired level of system reliability. The proposed multi-objective optimization problem is solved using NSGA-II algorithm. Different case studies are performed considering two or three different objective functions that may be selected by the system operator (SO) based on his/her preference. The simulation results obtained on a sample test system validate the benefits of solving the hybrid power system scheduling problem as a transparent and realistic MOO problem considering the uncertainty.

Retracted: Reliability assessment of composite generation expansion planning considering wind turbine

The expansion planning of wind turbine generating (WTG) requires the information of its forced outage rate (FOR) determined by using the continuous-time Markov Chain. In contrast with the conventional power plant, for the case study of WTG, the determination of FOR is utterly unique since it depends on the information of uncertain weather condition. Hence, the loss of load expectation (LOLE) and expected unserved energy (EUE) could be estimated so that it will not infringe its respective predetermined limits indispensable for the expansion planning of WTG using the stochastic approach. The modified IEEE RTS-79 system is used as a case study to verify effectiveness of the proposed method in the determination of WTG expansion planning. The results have shown improvement on the EUE and LOLE in relation with optimal expansion of the WTG units determined by using the proposed method.

Constructing Demand Curves in Forward Capacity Market

This paper presents an economic framework for designing demand curves in Forward Capacity Market (FCM). Capacity demand curves have been recognized as a way to reduce the price volatility inherited from fixed capacity requirements. However, due to the lack of direct demand bidding in FCM, obtaining demand curves that appropriately reflect load's willingness to pay for reliability is challenging. The proposed framework measures the value of reliability by the avoided cost of unserved energy (CUE), i.e., Expected Unserved Energy (EUE) multiplied by Value of Lost Load (VOLL). The total cost of capacity and CUE are then minimized, allowing economic tradeoffs between different reliability levels. EUE, a multivariate function of the total system capacity and its distribution among capacity zones, is decomposed into single-variable functions, which form the base for system and zonal demand curves. VOLL is implied from the Net Cost of New Entry (Net-CONE) based on long-term market equilibrium properties. The proposed framework is applied to a multizone ISO New England system to demonstrate its effectiveness.

Unit Commitment dengan Kekangan Keandalan Menggunakan Algoritme Genetika Mempertimbangkan Ketidakpastian Beban

Unit commitment problem is associated with satisfying load demand and minimizing the total operating cost of the generating unit without violation of unit and system constraints. The solution of unit commitment should be reliable which has adequate spinning reserve in order to anticipate the uncertainty issue. This research proposes a method to handle two uncertainty issues, i.e. unit unavailability and load forecast uncertainty. The unit commitment problem is solved by genetic algorithm with priority list approach. The evaluation of spinning reserve capacity is based on probabilistic criterion by incorporating two reliability indices, i.e. loss of load probability (LOLP) and expected unserved energy (EUE). The effectiveness of the proposed method is tested using IEEE Reliability Test System-1996. The simulation results show that the proposed method is capable for solving unit commitment problem at total operational cost of $ 722186.93 and risk index at 0.347% (while EUE 0.01%, LOLP 1% and standard deviation (SD) 5%). The simulation results also demonstrate that several solution of the method have slightly lower cost up to 0.43% than those obtained in benchmark which the solution based on Simulated Annealing method.

Evolutionary Multi-Objective Day-Ahead Thermal Generation Scheduling in Uncertain Environment

This paper addresses day-ahead thermal generation scheduling as a realistic multi-objective optimization problem in an uncertain environment considering system operation cost, emission cost and reliability as the multiple objectives. The uncertainties occurring due to unit outage and load forecast error are incorporated using loss of load probability (LOLP) and expected unserved energy (EUE) reliability indices. For solving the above-mentioned scheduling problem, a multi-objective generation scheduling algorithm (MOGSA) is proposed in this paper. Three case studies are performed on large scale test systems considering two different bi-objective optimization models and a three-objective optimization model that may be chosen by the system operator according to his/her own preference. The simulation results demonstrate the advantages of solving the thermal generation scheduling problem as a realistic multi-objective optimization problem in an uncertain environment. Finally the authors suggest a systematic procedure for the system operators to choose a single solution for the thermal generation scheduling problem.

Reliability Analysis using Renewable Energy Sources

This paper reviews some of the analytical methods developed in our laboratory for reliability evaluation of large scale power systems including renewable energy sources like photovoltaic units and wind farms. The methods presented here successfully reflect the correlations existing between the hourly load and the fluctuating energy outputs of unconventional generating units. Three different approaches, each an improvement over its predecessor, are presented for computing reliability indices like Loss of Load Expectation (LOLE) and Expected Unserved Energy (EUE). In the first approach, all the generation system models are combined hourly by means of an efficient algorithm for calculating the relevant reliability indices. The second approach uses a clustering algorithm for identifying a set of system states, such that the reliability indices are calculated for each state and then aggregated to yield overall values. The third approach introduces the concept of mean capacity outage tables for efficiently calculating EUE,

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.

Optimal load shedding study of naval-ship power system using the Everett optimization technique

This paper reports an application of the Everett optimization technique for value-based load shedding in naval-ship power system with network constraints and application of reliability constraints. A new congestion analysis index—expected contingency margin (ECM), which considers the probability of disturbance, and reliability indices loss of load probability (LOLP) and expected unserved energy (EUE) are presented to filter the critical outage and congestion cases. The optimal load shedding scheme carried out using the Everett optimization technique uses a utility function, which addresses the cost of allocating pay-off while satisfying the network and reliability constraints and generation capacity limits. The algorithm search for the optimal λ to form a fair pricing mechanism, which produces maximum pay-off and minimum load shedding while, satisfying system constraints. The proposed approach is examined on naval-ship power system and detailed results are shown.

Balancing cost and reliability: a quantitative study at Atlantic Electric

This paper documents a system improvement study conducted by Atlantic Electric (AE) Company using EPRI's reliability analytical tools. With increased emphasis on customer service, reliability and cost control, AE is striving to balance the value of supply reliability to its customers with the costs of system improvement. The paper presents a dollar value quantification of the level of reliability inherent in a given system improvement option. Based on this quantification, the improvement option that best balances the improvement cost and the incremental reliability is selected. Reliability indices including the expected unserved energy (EUE) were computed for each improvement option. Using the EUE, the value of service unreliability to the customers was computed for each option. Dollar value based analysis is then performed to balance cost and reliability quantitatively. A selection process that a utility engineer or system planner may go through to arrive at the option that best balances the cost and reliability of system improvement is covered in the paper.

A new planning model for assessing the effects of transmission capacity constraints on the reliability of generation supply for large nonequivalenced electric networks

This paper presents a new model for calculating the reliability of large electric power networks with transmission constraints. Generation loss of load probability (LOLP) and expected unserved energy (EUE) are calculated with and without transmission constraints and displayed for the system and for each load area over a wide range of load levels. A two step process first finds the cumulative probabilistic the flow distributions from incremental flows resulting from random generator failures and then performs load shedding as a heuristic process to remove line overloads. Convolution of states allows an extremely large number of generator states to be modeled in a reasonable amount of computation time. Test results for a large network and for the IEEE Reliability Test System (RTS) are discussed in the paper.

Application of energy based indices in generating system reliability analysis

The loss of load expectation (LOLE) is the most frequently used reliability index in generating system reliability analysis. Energy based reliability indices, however, are receiving more and more attention, particularly with regard to systems that have energy limitations or with regard to systems that include intermittent sources. In this paper the use of energy based reliability indices, such as the expected unserved energy (EUE) and the energy index of unreliability (EIU), is compared with the use of LOLE in generating system reliability analysis. The comparison is made for two aspects: the minimum required capacity expansion (MRCE) if the load is increased and the load carrying capability (LCC) of intermittent sources. To compare the results of applying LOLE, EUE and EIU in generating system capacity expansion, the IEEE Reliability Test System (RTS) is used as reference. Wind turbines and photovoltaic units are added to the RTS so that the load carrying capability of these intermittent sources can be calculated. The relative differences in the computed MRCE are found to be small: less than about 10% of the expansion of the generating capacity. In the case of intermittent sources, relative differences of similar magnitude are found for the load carrying capability. It is found that the differences in MRCE caused by the use of alternative reliability indices can be related to the slope of the loss of load probability as function of the load. The difference in LCC can be related to the occurrence of hours with high load and low intermittent energy production.

Assessment of the economic penetration levels of photovoltaic panels, wind turbine generators and storage batteries

Assessment of the economic penetration levels of photovoltaic panels (PVPs), wind turbine generators (WTGs) and storage batteries (SBs) into conventional generation systems is the main target of this article. The economic penetration level is that which achieves the maximum permissible reduction in the kWh cost and a certain value of loss-of-load expectation (LOLE) or expected unserved energy (EUE). To carry out this target, the following steps were performed: proposal of an operation strategy for the studied combined (hybrid) system; introduction of the analysis of the LOLE and EUE; and deduction of the mathematical models for estimating the fuel saving, load carrying capability, levelized annual profit and reduction in the kWh cost. The LOLE and EUE of the studied hybrid system were computed for different penetration levels of PVPs, WTGs and SBs. The reductions obtained in the kWh cost were also recorded. The different penetration levels that achieve a specific value of the LOLE or EUE were determined. The economic level was evaluated on the basis of the reduction obtained in the kWh cost.

A concise method for calculating expected unserved energy in generating system reliability analysis

A simple and efficient technique is proposed for the calculation of expected unserved energy (EUE) in generating systems. The technique is new in that it uses a mean capacity outage table, which eliminates the need for construction of a negative margin table. This concept allows both LOLE (loss of load expectation) and EUE to be calculated with little more computational effort than is needed to calculate LOLE alone. The proposed method allows for efficient inclusion of intermittent energy sources and of unit planned outages. The method is applied to the IEEE reliability test system and an EPRI reduced synthetic system. >

Probabilistic Power System Production Cost and Reliability Calculation by the Z-Transform Method

The authors describe a novel method of probabilistic power system production cost and reliability calculation using the Z transform. In the proposed method, the generating unit available capacity probability density functions (PDFs) are represented by probability impulses. These PDFs are convolved using the Z transform to produce equivalent capacity PDFs. By operating the equivalent capacity PDFs on the system demand, the unit energies, loss of load probability (LOLP), and expected unserved energy (EUE) can be calculated for each load level and the total demand. The method is compared with the cumulant method and Calebrese's traditional direct convolution procedure in terms of accuracy and computing time using the IEEE Reliability Test System. The main advantage of the new method is that actual load and generator availability data can be used directly, rather than via a mathematical representation such as cumulants. An efficient recursive algorithm using the Z transform procedure has been formulated to allow fast evaluations of convolution and deconvolution of PDFs. In terms of computing time, the new method is not much slower than the cumulant method. LOLP and EUE are also calculated more accurately. >

Probabilistic power system production cost and reliability calculation by the Z-transform method

The authors describe a novel method of probabilistic power system production cost and reliability calculation using the Z transform. In the proposed method, the generating unit available capacity probability density functions (PDFs) are represented by probability impulses. These PDFs are convolved using the Z transform to produce equivalent capacity PDFs. By operating the equivalent capacity PDFs on the system demand, the unit energies, loss of load probability (LOLP), and expected unserved energy (EUE) can be calculated for each load level and the total demand. The method is compared with the cumulant method and Calebrese's traditional direct convolution procedure in terms of accuracy and computing time using the IEEE Reliability Test System. The main advantage of the new method is that actual load and generator availability data can be used directly, rather than via a mathematical representation such as cumulants. An efficient recursive algorithm using the Z transform procedure has been formulated to allow fast evaluations of convolution and deconvolution of PDFs. In terms of computing time, the new method is not much slower than the cumulant method. LOLP and EUE are also calculated more accurately.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Production costing and reliability evaluation for composite systems with outages and uncertainties

A new method based on Monte Carlo simulation for composite power system production costing and reliability evaluation, considering apparatus outage probabilities and load forecast uncertainties, is presented. Random numbers are generated, according to appropriate laws, to simulate the state of the apparatus and the demand of the bus loads. Through successive application of the minimum cost flow algorithm, it is capable of handling the economic dispatch problem existing in the procedures. In this paper, the reliability of the system is measured in terms of expected demand not served (EDNS) and loss of load probability (LOLP). The EDNS and therefore the expected unserved energy (EUE) associated with an expansion plan can be evaluated further as an equivalent penalty cost due to service interruption. This benefits the application of the proposed method for selection between alternatives in power system planning. Another advantage of this method is that an expected power flow pattern is generated as the byproduct. Application of the method is demonstrated using the IEEE five-bus test system.