Loss Of Load Probability Research Articles

Optimal Design of Standalone Photovoltaic System Based on Multi-Objective Particle Swarm Optimization: A Case Study of Malaysia

This paper presents a multi-objective particle swarm optimization (MOPSO) method for optimal sizing of the standalone photovoltaic (SAPV) systems. Loss of load probability (LLP) analysis is considered to determine the technical evaluation of the system. Life cycle cost (LCC) and levelized cost of energy (LCE) are treated as the economic criteria. The two variants of the proposed PSO method, referred to as adaptive weights PSO ( A W P S O c f ) and sigmoid function PSO ( S F P S O c f ) , are implemented using MATLAB software to the optimize the number of PV modules in (series and parallel) and number of the storage battery. The case study of the proposed SAPV system is executed using the hourly meteorological data and typical load demand for one year in a rural area in Malaysia. The performance outcomes of the proposed A W / S F P S O c f methods give various configurations at desired levels of LLP values and the corresponding minimum cost. The performance results showed the superiority of S F P S O c f in terms of accuracy is selecting an optimal configuration at fitness function value 0.031268, LLP value 0.002431, LCC 53167 USD, and LCE 1.6413 USD. The accuracy of A W / S F P S O c f methods is verified by using the iterative method.

Charging Load Prediction and Distribution Network Reliability Evaluation Considering Electric Vehicles’ Spatial-Temporal Transfer Randomness

Integration of large-scale cluster electric vehicles (EVs) and their spatial-temporal transfer randomness are likely to affect the safety and economic operation of the distribution network. This paper investigates the spatial-temporal distribution prediction of EVs’ charging load and then evaluates the reliability of the distribution network penetrated with large-scale cluster EVs. To effectively predict the charging load, trip chain technology, Monte Carlo method and Markov decision process (MDP) theory are employed. Moreover, a spatial-temporal transfer model of EVs is established, and based on which, an EV energy consumption model and a charging load prediction model are constructed with consideration of temperature, traffic condition and EV owner’s subjective willingness in different scenarios. With the application of sequential Monte Carlo method, the paper further evaluates distribution network reliability in various charging scenarios. In the evaluation, indices including per unit value (PUV), fast voltage stability index (FVSI), loss of load probability (LOLP), system average interruption frequency index (SAIFI), system average interruption duration index (SAIDI), and expected energy not supplied (EENS) are incorporated. To validate the proposed prediction model and evaluation method, a series of numerical simulations are conducted on the basis of taking the traffic-distribution system of a typical city as an example. The result demonstrates that the proposed spatial-temporal transfer model is more practical in charging load prediction than the popularly used Dijkstra’s shortest path algorithm. Moreover, high temperature, congestion and the increment of EV penetration rate will further weaken distribution network reliability.

A Chance-Constrained Decentralized Operation of Multi-Area Integrated Electricity–Natural Gas Systems With Variable Wind and Solar Energy

This article presents a decentralized decision-making strategy for the multi-area integrated electricity and natural gas system (IEGS). Independent system operators (ISOs) in the electric power sector and natural gas system operators (NGSOs) in the natural gas sector operate their respective systems independently with the consideration that a limited set of information is shared, and the information privacy and decision-making independence are preserved among operators. In this article, uncertainties associated with the proliferation of variable wind and solar generation as well as load forecast errors are addressed in a chance-constrained programming framework, and the loss of load probability (LOLP) as well as the transmission line overload probability (TLOP) are introduced to ensure a secure and economic operation of IEGS. The proposed multi-area & multi-layer problem is solved by a hierarchical iterative algorithm in which the inner loop deals with the collaboration between ISO and NGSO in each area, and the collaboration among areas is managed by the outer loop. Finally, case studies are carried out on two multi-area IEGSs with different sizes in which numerical results demonstrate the effectiveness of the proposed methods.

Optimum battery depth of discharge for off-grid solar PV/battery system

In this paper, we propose a multi-objective optimization model that considers the loss of load probability (LLP) and the cost of energy (COE) together with the battery life loss cost and the costs of operation, replacement, and maintenance. These factors form the projected operating framework of the off-grid system for which we utilize the non-dominated sorting genetic algorithm (NSGA-II) method. The proposed model includes the depth of discharge (DOD) of the battery, which is determined based on the battery life loss cost. In addition, in the optimal model, the amount of energy flow from the battery bank during the charging and discharging cycles must satisfy the load demand at the lowest cost and with the highest reliability. The results show that the optimal DOD value for a battery in the solar PV system being investigated is 70%, with LLP = 0% and COE = 0.20594 USD/kWh.

How many electric vehicles can the current Australian electricity grid support?

We quantitatively investigate the impact of uncontrolled and controlled charging demand of battery electric vehicles (BEVs) on electricity generation, loss-of-load probability (LOLP), and levelized cost of electricity (LCOE) in Australia. We consider both high- and low-fuel-economy (HE and LE) BEVs, assume BEV penetration rates (EVPR) ranging from 0 to 100%, and three controlled charging participation rates (0%, 53% and 100%). The spatio-temporal distribution of BEV load is estimated by a GIS-based probabilistic model at a high-resolution level for Australia. The BEV charging impact is simulated by an hourly supply-demand model, respecting currently existing installed capacity, operating technologies and LOLP standards, to simulate an electricity dispatch for an entire year. BEV charging is spatially and temporally optimised to achieve minimum levelized cost. We show that the current Australian national grid can support HE and LE BEVs at 5–10% penetration for uncontrolled charging, and around 60–70% for controlled charging. Controlled charging also reduces electricity cost by up to around 4–6%.

Composite Power System Reliability Evaluation Based on Enhanced Sequential Cross-Entropy Monte Carlo Simulation

Due to essential differences in modeling and computation, the traditional sequential cross-entropy method that is greatly effective for generation systems may lose its effectiveness for composite systems. An enhanced sequential cross-entropy method for composite systems is presented to achieve the effectiveness. In the pre-sample stage, a sequential cross-entropy optimization algorithm rather than using a traditional non-sequential optimization algorithm is proposed so that the samples in this stage could also contribute to calculations of reliability indices. In the second stage, an accelerated contingency analysis is presented for further reducing computational burdens, in which a bisection optimization algorithm is used to rapidly identify failure system states. The new likelihood ratios, i.e., frequency likelihood ratio and duration likelihood ratio are developed, resulting in accurate corrections of loss of load frequency (LOLF), loss of load probability (LOLP), and expected energy not supplied (EENS) indices. The performance of the proposed method is demonstrated by comparisons between the proposed and traditional methods using several composite power systems, including the IEEE RTS-79, a modified IEEE RTS-79, and the IEEE RTS-96.

Designing and implementation of energy‐efficient wireless photovoltaic monitoring system

AbstractPhotovoltaic (PV) cell usually shows unpredictable results due to abrupt change in environment. Environmental parameters such as temperature, dust factor, irradiance, and air mass have direct influence on the output of PV cells. Monitoring PV and its related environmental parameters is very important for understanding and analysis of PV in practical conditions. The PV parameters have been found useful in many ways like reliability analysis, life cycle costing, returns on investment calculation, loss of load probability, and optimal designing of PV power supplies. Currently, designed PV monitoring systems (PVMS) are reported to be expensive, complex, and are limited in their applications, out of which only few are wireless. In this article, we design and implement a simple cost‐effective and wireless PV monitoring solution. The design PVMS is based on microcontrollers, light‐dependent resistors, current sensor, analog‐to‐digital converter, solid state relays, ZigBee (XBee) wireless microcontroller, and LabVIEW‐based data logging software. The designed PVMS performs the real‐time analysis and data logging of open circuit voltage (Voc), short circuit current (Jsc), ambient temperature (Ta), cell temperature (Tcell), and maximum power point. In addition, real‐time I‐V and P‐V characterization of PV module is another valuable feature embedded in the designed PVMS.

Optimal sizing of off-grid hybrid energy system based on minimum cost of energy and reliability criteria using firefly algorithm

Solar and wind energy based hybrid energy system (HES) have received considerable global attention for remote applications where extension of grid supply is infeasible. This paper attempts to develop an optimal hybrid energy system model using available solar and wind energy resources with battery storage for fulfilling the electrical needs of three un-electrified remote villages located in Senapati district of Manipur, India. A Firefly algorithm based approach is used to find the optimal hybrid system configuration based on minimum cost of energy (COE) while satisfying a specified reliability criteria identified with loss of load probability (LOLP) reliability index. Further, system investigation has been carried out for optimal system feasibility at various values of LOLP. The optimal hybrid energy system is able to provide feasible solutions for LOLP values lying between 0 and 0.03. For LOLP value above 0.03, the system becomes infeasible as the COE increase with increase in LOLP.

Importance of Reliability Criterion in Power System Expansion Planning

The self-sufficiency of a power system is no longer a relevant issue at the electricity market, since day-to-day optimization and security of supply are realized at the regional or the internal electricity market. Research connected to security of supply, i.e., having reliable power capacities to meet demand, has been conducted by transmission system operators. Some of the common parameters of security of supply are loss of load probability (LOLP) and/or loss of load expectation (LOLE), which are calculated by a special algorithm. These parameters are specific for each power system. This work presents the way of calculating LOLP as well as the optimization algorithm of LOLP, which takes into consideration the particularities of the power system. It also presents a difference in the treatment of LOLP regarding the observed power system and the necessary installed power capacity if applied to the calculated LOLP in relation to the optimized LOLP. As a conclusion, the study analyzed the parameters impact the regional electricity market—where the participants are countries with different development levels and various particularities of power systems—i.e., what it means when the same LOLP criterion is applied to them and the optimized LOLP.

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.

Reliability Evaluation of Stand-Alone Solar PV Energy System for Irrigation

Solar photovoltaic systems convert the energy of light directly into electrical energy. This paper presents Markov model and frequency-duration techniques for calculating the reliability indices of the stand-alone photovoltaic water pumping system. These techniques can be applied to both repairable and non-repairable systems. Markov model and frequency-duration techniques are used for evaluation of reliability indices e.g. failure rate, repair rate, unavailability etc. The results confirmed that failure and repair rate of the system is 0.33 and 41.37 respectively. Loss of load probability and unavailability of the system is 0.00158 /yrs and 13.8 hrs/yrs respectively.

Reliability evaluation of power system incorporating wind farm for generation expansion planning based on ANLSA approach

AbstractReliability evaluation of power‐generating systems gives a mechanism to guarantee proper system operations in the face of different uncertainties including equipment failures. It is regularly not attainable to identify all possible failure states to figure the reliability indices because of the large number of system states engaged with system operations. Therefore, a hybrid optimization technique is required to analyse the reliability of the power system. This paper proposes a hybrid optimization technique to evaluate the reliability of a power system for the generation expansion planning incorporating wind energy source. The proposed hybrid methodology is the joined execution of both ant lion optimization algorithm (ALO) and lightning search algorithm (LSA), and it is named as ANLSA. ALO searching behavior is enhanced by LSA. Through the inherent convergence mechanisms, ANLSA search the meaningful system states. The most probable failure states contribute reliability indices of power generating system including mean down time (MDT), loss of load probability (LOLP), loss of load expectation (LOLE), loss of load frequency (LOLF), and expected demand not supplied (EDNS). Furthermore, ANLSA is utilized to assess the reliability of system under normal condition, integration of wind farm with capacity of 150 MW, and considering spinning reserve requirement (SRR). By then, the proposed work is actualized in MATLAB/Simulink platform and it is demonstrated on IEEE reliability test system (IEEE RTS‐79). Furthermore, the statistical analysis of proposed and existing techniques such as Monte Carlo simulation (MCS) and discrete convolution (DC) is considered. The comparison results demonstrate that proposed approach confirms its ability for evaluating the power system reliability.

Quantifying the Benefits of a Solar Home System-Based DC Microgrid for Rural Electrification

Off-grid solar home systems (SHSs) currently constitute a major source of providing basic electricity needs in un(der)-electrified regions of the world, with around 73 million households having benefited from off-grid solar solutions by 2017. However, in and of itself, state-of-the-art SHSs can only provide electricity access with adequate power supply availability up to tier 2, and to some extent, tier 3 levels of the Multi-tier Framework (MTF) for measuring household electricity access. When considering system metrics of loss of load probability (LLP) and battery size, meeting the electricity needs of tiers 4 and 5 is untenable through SHSs alone. Alternatively, a bottom-up microgrid composed of interconnected SHSs is proposed. Such an approach can enable the so-called climb up the rural electrification ladder. The impact of the microgrid size on the system metrics like LLP and energy deficit is evaluated. Finally, it is found that the interconnected SHS-based microgrid can provide more than 40% and 30% gains in battery sizing for the same LLP level as compared to the standalone SHSs sizes for tiers 4 and 5 of the MTF, respectively, thus quantifying the definite gains of an SHS-based microgrid over standalone SHSs. This study paves the way for visualizing SHS-based rural DC microgrids that can not only enable electricity access to the higher tiers of the MTF with lower battery storage needs but also make use of existing SHS infrastructure, thus enabling a technologically easy climb up the rural electrification ladder.

A novel method for sizing of standalone photovoltaic system using multi-objective differential evolution algorithm and hybrid multi-criteria decision making methods

Abstract Standalone photovoltaic system is promising sustainable energy source. Accurate modeling and sizing of these systems strongly affect the system's feasibility. Thus, in this paper, optimal sizing of standalone photovoltaic system is conducted based on multi-objective differential evolution algorithm integrated with hybrid multi-criteria decision making methods. Multi-objective differential evolution algorithm is used to optimize set of configurations of a system by minimizing technical and cost objective functions simultaneously. After that, an analytical hierarchy process integrated with a technique for order preference by similarity to ideal solution are used to order preference of configurations based on the loss of load probability and life cycle cost of system. The results of the proposed sizing method are validated by a numerical method to explain the superiority of the proposed method. According to results, the proposed sizing method is faster than numerical method by around 27 times. This is because the multi-objective differential evolution algorithm requires roughly 0.23 of simulations that is required by numerical method. Furthermore, the performance of multi-objective differential evolution algorithm is evaluated by various metrics. As a result, for the adapted load demand, the optimal configuration is 63 PV modules and 66 battery unit with maximum capacity of 500 Ah.

A Frequency and Duration Method for Adequacy Assessment of Generation Systems With Wind Farms

This paper proposes a frequency and duration method for the adequacy assessment of generation systems with wind farms (WFs). Based on Markov chains, reliability models for WFs, conventional generators, and load are developed and represented as the corresponding probability-frequency distribution functions (PFDFs). The failures of wind turbines and the uncertainties and correlations of wind speeds are considered and incorporated into the reliability modeling of WFs. With the proposed method, the implementation of the reliability modeling of large WFs becomes simple. Moreover, for a generation system with WFs, not only probability-based reliability indexes, such as the loss of load probability and the expected energy not supplied, but also frequency-based reliability indexes, such as the loss of load frequency and the loss of load duration, can be calculated analytically and efficiently using the PFDFs. An optimal decision-making model for determining the clustering number of random states is proposed to improve the credibility of stochastic process modeling of Markov-chain-based random variables. The tests on two modified IEEE-RTS79 grids with WFs demonstrate the rapidity and validity of the proposed method.

Exploring the boundaries of Solar Home Systems (SHS) for off-grid electrification: Optimal SHS sizing for the multi-tier framework for household electricity access

With almost 1.1 billion people lacking access to electricity, solar-based off-grid products like Solar Home Systems (SHS) have become a promising solution to provide basic electricity needs in un(der)-electrified regions. Therefore, optimal system sizing is a vital task as both oversizing and undersizing a system can be detrimental to system cost and power availability, respectively. This paper presents an optimal SHS sizing methodology that minimizes the loss of load probability (LLP), excess energy dump, and battery size while maximizing the battery lifetime. A genetic algorithm-based multi-objective optimization approach is utilized to evaluate the optimal SHS sizes. The potential for SHS to cater to every tier of the Multi-tier framework (MTF) for measuring household electricity access is examined. The optimal system sizes for standalone SHS are found for different LLP thresholds. Results show that beyond tier 2, the present day SHS sizing needs to be expanded significantly to meet the load demand. Additionally, it is deemed untenable to meet the electricity needs of the higher tiers of MTF purely through standalone SHS without compromising one or more of the system metrics. A way forward is proposed to take the SHS concept all the way up the energy ladder such that load demand can also be satisfied at tier 4 and 5 levels.

Optimizing probabilistic spinning reserve by an umbrella contingencies constrained unit commitment

Spinning reserve (SR) is an important resource to deal with the sudden load change, uncertain renewable energy generation, and component failures in power systems. Surplus SR will cause a higher operating cost while insufficient SR will deteriorate the system reliability level. In this paper, the SR is optimized by solving a loss of load probability constrained unit commitment (LCUC) problem. The loss of load probability (LOLP) is an appealing means to enforce the SR requirement in power systems since it can express reliability visually and explicitly. However, till now, the LCUC has not been addressed well in terms of solution accuracy and computation efficiency, due to the highly nonlinear characteristics of the LOLP. In this context, the characteristics of the LOLP are explicitly analyzed. It is found that the nonlinear LOLP constraint can be theoretically expressed as a series of linear constraints and most of the constraints can be relaxed. Then the original LCUC can be equivalently expressed by a new umbrella contingencies constrained unit commitment (UCCUC) model. An umbrella contingency identification process is proposed and the model is solved by the constraint generation technique. The proposed model possesses high computation efficiency with desirable solution accuracy, and thus it can significantly enhance the practicability of the LCUC based SR optimization method in real power systems. The proposed method was validated by case studies with the IEEE-RTS system and several larger systems.

Short-Term Reliability Assessment for Islanded Microgrid Based on Time-Varying Probability Ordered Tree Screening Algorithm

As the penetration rate of intermittent renewable energy continues to increase in a microgrid, the operational model of interconnected microgrid changes faster and more frequently. To maintain the stability and security of the microgrid, short-term reliability assessment is necessary and must be adapted to the time-varying characteristics of the islanded microgrid. In view of this, this paper proposes a new short-term reliability assessment method based on the time-varying probability ordered tree screening algorithm. First, a screening algorithm based on the time-varying probability ordered tree is proposed, and the number of system states is reduced by screening the system state with high probability at each time. Then, according to the different impact ranges, two event types of load point power supply interruption is defined, and the formulas are given for calculating the time-varying probability. On this basis, the loss of load probability (LOLP) index and the expected demand not supplied (EDNS) index are defined to assess the short-term reliability of the islanded microgrid. Finally, the proposed method is modeled by MATLAB, and a case study is performed on the European low-voltage microgrid system to verify its correctness and effectiveness.

Reliability Varying Characteristics of PV-ESS-Based Standalone Microgrid

Reliability is of critical importance for the microgrid (MG) and deserved more attention. Aiming at photovoltaics (PV) and energy storage system (ESS) based MG, the microturbine (MT), PV, ESS and comprehensive load (CL) which is composed of hourly time-varying component, stochastic component, and controllable component, are chronologically modeled and combined with model of load shedding minimization and sequential Monte Carlo (SMC) simulation algorithm. Then, the reliability assessment framework is developed and employed in the comprehensive case studies. Firstly, varying characteristics of reliability indices, including loss of load probability (LOLP), average service availability index (ASAI), system average interruption duration index (SAIDI), system average interruption frequency index (SAIFI) and customer average interruption duration index (CAIDI), over PV penetration are investigated, and the surge effect of SAIFI (SE-SAIFI) is especially put forward and studied, followed by the principle of PV capacity decision considering SE-SAIFI. Secondly, the clear pictures of reliability profiles over ESS sizes are depicted and analyzed, following with a novel method to reasonably decide ESS sizes based on the definition of expected hourly redundant power (EHRP). At last, reliability indices of multiple scenarios with different percentages of controllable load are calculated and the benefits of load management are analyzed in the viewpoint of reliability of standalone MG. Results of the case studies also confirm the necessities of reliability assessment during the MG planning and size optimization, and the validity of the methodologies developed in this work.

Optimal, Reliable and Cost-Effective Framework of Photovoltaic-Wind-Battery Energy System Design Considering Outage Concept Using Grey Wolf Optimizer Algorithm—Case Study for Iran

In this paper, an optimal, reliable, and cost-effective framework for designing a renewable hybrid photovoltaic-wind-battery system is presented to minimize the total net present cost (TNPC) and to consider reliability constraint as loss of load probability (LPP) for the city of Ahvaz, Iran, considering the components outage rate (COR). The decision variables include the number of photovoltaic panels, wind turbines, batteries, and the angle of the photovoltaic panel optimized by the grey wolf optimizer (GWO) algorithm. The performance of the proposed method is compared with the particle swarm optimization (PSO) method. The results of a system designed in different combinations with and without considering COR are evaluated. The simulation results confirm that the GWO algorithm is superior to the PSO method by yielding lower TNPC (1.199 M$ for GWO and 1.201 M$ for PSO) and better LPP (0.653% for GWO and 0.655% for PSO) for optimal combination (photovoltaic-battery system). The results also showed that a photovoltaic-wind combination is not the most cost-effective and reliable for the Ahvaz region, and the implementation of hybrid systems based on wind power is not cost-effective in this region. In addition, the results showed that considering COR gives the designers of these systems a more accurate view of the cost and reliability. Moreover, considering COR increases the cost of load supply and undermines the load reliability.