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An analytical approach and a control strategy are proposed in Part I of this two-part paper for leveraging the aggregate demand of a population of thermostatically-controlled loads (TCLs) to deliver contingency-type reserve capacity. Further, a metric is introduced to quantify the TCL users' comfort satisfaction in response to a control signal. In Part II, we address the validation of the concepts put forth in the first part of the paper. To do so, we develop an extensive set of case studies based upon a population of 10\thinspace000 electric water heaters (EWH). Here, a physically-based model is first derived for the calculation of EWHs on-time statistics. The model is then extended to calculate the probability of EWH users' comfort satisfaction. The analytical approach and control strategy presented in Part I are validated using the EWH model against Monte Carlo simulations. Further, the trade-off between demand response capacity and EWH users' comfort satisfaction is investigated. [ABSTRACT FROM AUTHOR]

This paper presents a methodology and set of validation criteria for the systematic creation of synthetic power system test cases. The synthesized grids do not correspond to any real grid and are, thus, free from confidentiality requirements. The cases are built to match statistical characteristics found in actual power grids. First, substations are geographically placed on a selected territory, synthesized from public information about the underlying population and generation plants. A clustering technique is employed, which ensures the synthetic substations meet realistic proportions of load and generation, among other constraints. Next, a network of transmission lines is added. This paper describes several structural statistics to be used in characterizing real power system networks, including connectivity, Delaunay triangulation overlap, dc power flow analysis, and line intersection rate. The paper presents a methodology to generate synthetic line topologies with realistic parameters that satisfy these criteria. Then, the test cases can be augmented with additional complexities to build large, realistic cases. The methodology is illustrated in building a 2000 bus public test case that meets the criteria specified. [ABSTRACT FROM AUTHOR]

In order to provide the ancillary service for smart grid, this paper proposes a modelling and control protocol design approach for the aggregation of heterogeneous thermostatically controlled loads (TCLs). A 2-D state bin is proposed to model the second-order TCL dynamics in a population model. Detailed procedure of calculating the transition probability in the system matrix is provided. In the controller design, a model predictive control (MPC) scheme is proposed to obtain the optimal control actions along the prediction horizon. In addition, implementation of the control signal for adjusting TCLs' statuses are also investigated with practical situations considered. Simulation results reveal the feasibility and efficacy of the proposed modelling and control approach when applied on a large population of TCLs. Some factors that may affect the service performance are also discussed in this paper. [ABSTRACT FROM AUTHOR]

To respond to volatility and congestion in the power grid, demand response (DR) mechanisms allow for shaping the load compared to a base load profile. When tapping on a large population of heterogeneous appliances as a DR resource, the challenge is in modeling the dimensions available for control. Such models need to strike the right balance between accuracy of the model and tractability. The goal of this paper is to provide a medium-grained stochastic hybrid model to represent a population of appliances that belong to two classes: deferrable or thermostatically controlled loads. We preserve quantized information regarding individual load constraints, while discarding information about the identity of appliance owners. The advantages of our proposed population model are 1) it allows us to model and control load in a scalable fashion, useful for ex-ante planning by an aggregator or for real-time load control; 2) it allows for the preservation of the privacy of end-use customers that own submetered or directly controlled appliances. [ABSTRACT FROM PUBLISHER]

Under the deregulated environment, electric utility companies have been encouraged to ensure maximum system reliability through the employment of cost-effective long-term asset management strategies. Previously, the age based Weibull distribution has been used vastly for modeling and forecasting aging failures. However, this model is only based on asset age and does not consider additional information such as asset infant mortality period and equipment energization delay. Some works on modifying Weibull distribution functions to model bathtub-shaped failure rate function can be practically difficult due to model complexity and inexplicit parameters. To improve the existing methods, this paper proposes four modified Weibull distribution models with straightforward physical meanings specific to power system applications. Furthermore, this paper proposes a novel method to effectively evaluate different Weibull distribution models and select the suitable model(s). More importantly, if more than one suitable model exists, these models can be mathematically combined as a joint forecast model, which could provide better accuracy to forecast future asset reliability. Finally, the proposed approach was applied to a Canadian utility company for the reliability forecast of electromechanical relays and distribution poles to demonstrate its practicality and usefulness. [ABSTRACT FROM AUTHOR]

In order to optimize hydro power plants generator scheduling according to 24-h system demand, a parallel self-adaptive differential evolution algorithm has been applied. The proposed algorithm presents a novel approach to considering the multi-population and utilization of the preselection step for the improvements of the algorithm's global search capabilities. A preselection step with the best, middle, and worst populations' individuals establishes the new trial vectors. This algorithm has been verified on two different models. The first one consists of eight power plants with real parameters, and the second one consists of four power plants, mostly used as a test model in scientific papers. The main goal of the optimization process is to satisfy system demand for 24 h with a decreased usage of water quantity per electrical energy unit. The initial and final states of the reservoirs must also be satisfied. [ABSTRACT FROM PUBLISHER]

Under transactive (market-based) coordination, a population of distributed energy resources (DERs), such as thermostatically controlled loads (TCLs) and storage devices, bid into an energy market. Consequently, a certain level of demand will be cleared based on the operating conditions of the grid. This paper analyzes the influence of various factors, such as price signals, feeder limits, and user-defined bid functions and preferences, on the aggregate energy usage of DERs. We identify cases that can lead to load synchronization, undesirable power oscillations and highly volatile prices. To address these issues, the paper develops an aggregate model of DERs under transactive coordination. A set of Markov transition equations have been developed over discrete ranges (referred to as “bins”) of price levels and their associated DER operating states. A detailed investigation of the performance of this aggregate model is presented. With reformulation of the transition equations, the bin model has been incorporated into a model predictive control setting using both mixed integer programming and quadratic programming. A case study shows that a population of TCLs can be managed economically while avoiding congestion in a distribution grid. Simulations also demonstrate that power oscillations arising from synchronization of TCLs can be effectively avoided. [ABSTRACT FROM AUTHOR]

There are few systematic methodologies capable of predicting and leveraging the reserve capacity potential of large populations of thermostatically-controlled loads (TCLs). For such reserves to have economic and technical value, it is essential that demand-side flexibility aggregators and system operators be able to do so quickly and robustly. In addition, aggregators need to ensure TCL users' comfort and end use satisfaction. Part I of this two-part paper introduces an analytical approach to characterize and control the statistical bounds on the potential aggregated response of a population of TCLs, while ensuring users' comfort satisfaction. First, the uncertainty associated with the instantaneous power consumption of a typical TCL is described by a set of random variables and their statistics. TCL statistics are then employed to characterize the exploitable flexibility from a large population of similar devices. From this, a control strategy and parameters are introduced for sporadic (i.e., contingency-type) reserve provision by the population. In Part II, the proposed analytical approach and control strategy are validated for the special case of electric water heaters (EWHs). Further, the trade-off between demand response capacity and EWH users' comfort satisfaction is investigated through several case studies. [ABSTRACT FROM AUTHOR]

Existing population-based Stochastic Search Algorithms (SSAs) are too time-consuming to solve dynamic optimal power flow (OPF). The solution proposed in this paper is to accelerate SSAs with memory. Two memory schemes, the similarity retrieval scheme and the mean-based immigrants scheme, are proposed and applied together to the Differential Evolution and Particle Swarm Optimizer, which are two representatives of SSAs. Experiments are conducted on modified IEEE 30-bus and IEEE 118-bus systems with changing load buses and the objective of minimizing real power transmission loss. The results show that the proposed schemes significantly improve the performance of the two existing algorithms, and that SSAs could be practical for tracking optima of dynamic OPF. [ABSTRACT FROM AUTHOR]

Energy storage systems play a significant role in both distributed power systems and utility power systems. Among the many benefits of an energy storage system, the improvement of power system cost and voltage profile can be the salient specifications of storage systems. Studies show that improper size and placement of energy storage units leads to undesired power system cost as well as the risk of voltage stability, especially in the case of high renewable energy penetration. To solve the problem, a hybrid multi-objective particle swarm optimization (HMOPSO) approach is proposed in the paper to minimize the power system cost and improve the system voltage profiles by searching sitting and sizing of storage units under consideration of uncertainties in wind power production. Furthermore, the probability cost analysis is first put forward in this paper. The proposed HMOPSO combines multi-objective particle swarm optimization (MOPSO) algorithm with elitist nondominated sorting genetic algorithm (NSGA-II) and probabilistic load flow technique. It also incorporates a five-point estimation method (5PEM) for discretizing wind power distribution. The IEEE 30-bus system is adopted to perform case studies. The simulation results for each case clearly demonstrate the necessity for optimal storage allocation, and the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

Quantifying the impact of new technologies on a single distribution feeder is a tractable analysis problem. But the analysis of a single distribution feeder does not provide insight into the complexities and variations of a system-wide deployment. The inability to extrapolate system-wide impacts hinders the deployment of many promising new technologies. This paper presents a three-stage method of extrapolating technological impacts, either simulated or from a field demonstration, from a limited number of distribution feeders to the entire system. The size of the system can vary from the service territory of a single utility, to a region, or to an entire country. The paper will include an example analysis using the United States Department of Energy funded Smart Grid Investment Grant projects, extrapolating their benefits to a national level, and an example of a regionalized deployment of Volt-VAR optimization for peak demand reduction. Both of the example analyses utilize the presented three-stage extrapolation method. [ABSTRACT FROM PUBLISHER]

The impact of the electric vehicle (EV) charging on node voltages and feeder currents of an electric grid can be reduced by upgrading its feeder capacity or deploying onsite photovoltaic (PV) and battery energy storage (BES), or their appropriate combination. It, in turn, enhances the quality of service (QoS) of the charging. This paper proposes an approach, which can enable a distribution network operator/business owner in finding the appropriate combination of the solutions above for providing the best QoS at a minimum cost while reducing the grid impact. The developed approach takes into account the previously scarcely incorporated characterization aspects (whether it is a constant power, constant current, or constant impedance load) of the EV charging. It has been applied to an IEEE 37-bus system in conjunction with the parking lots of the University of Queensland for a case study. The numerical results show that the proposed approach can effectively find the appropriate combination of the solutions above and the corresponding optimal sizes of PV and BES for a given EV penetration level or a given QoS. [ABSTRACT FROM AUTHOR]

Utilizing battery storage systems (BSSs) can reduce the intermittent output of PV generation systems (PVGSs) and make them dispatchable. The aim of this paper is to design an optimal charging/discharging scheduling for BSSs such that the line loss of distribution systems interconnected with sizeable PVGSs can be minimized. A mathematical model for BSSs which can be used to simulate the charging procedures such as the commonly-used constant current to constant voltage (CC-CV) charging method, the discharging procedures and the state of charge (SOC) is proposed first. The minimum line loss problem considering the intermittent output of PVGSs and the scheduling of BSSs is then formulated based on the BSS mathematical model. The optimal charging/discharging scheduling of BSSs can then be obtained by a genetic algorithm (GA) based method. Test results demonstrate the validity of the proposed mathematical model and optimal charging/discharging scheduling for BSSs. [ABSTRACT FROM PUBLISHER]

This paper addresses the challenge of scheduling a large population of electric water heaters (EWHs) by incorporating a physically-based aggregate model of the population into the day-ahead unit commitment (UC). This goal has been accomplished via several innovations: (i) consideration of a large controllable temperature range over which random distributions of heaters can take many different shapes; (ii) modeling the random nature of the heater population and its dynamics via histograms and their transition equations; (iii) for varying levels of energy stored in the EWH population, finding the specific shapes of stationary EWH histograms that have minimum overlaps with the uncontrollable temperature zones; (iv) from such histograms, computing the bounds on the number of heaters that can be turned on/off in terms of the energy stored in the population; (v) incorporating the aggregate EWH power consumed and energy stored and their constraints into a modified UC; (vi) developing a scheme whereby individual EWHs self-dispatch to meet the scheduled histograms along with their aggregate energy and power levels. Numerical simulations illustrate the applicability and benefits of the approach, which, with minor extensions, can be extended to other forms of electric loads with energy storage such as space heating and cooling systems and electric vehicles. [ABSTRACT FROM PUBLISHER]

The dynamic economic dispatch problem is a high-dimensional complex constrained optimization problem that determines the optimal generation from a number of generating units by minimizing the fuel cost. Over the last few decades, a number of solution approaches, including evolutionary algorithms, have been developed to solve this problem. However, the performance of evolutionary algorithms is highly dependent on a number of factors, such as the control parameters, diversity of the population, and constraint-handling procedure used. In this paper, a self-adaptive differential evolution and a real-coded genetic algorithm are proposed to solve the dynamic dispatch problem. In the algorithm design, a new heuristic technique is introduced to guide infeasible solutions towards the feasible space. Moreover, a constraint-handling mechanism, a dynamic relaxation for equality constraints, and a diversity mechanism are applied to improve the performance of the algorithms. The effectiveness of the proposed approaches is demonstrated on a number of dynamic economic dispatch problems for a cycle of 24 h. Their simulation results are compared with each other and state-of-the-art algorithms, which reveals that the proposed method has merit in terms of solution quality and reliability. [ABSTRACT FROM AUTHOR]

Electric vehicles (EVs) have been well recognized as a deferrable load with the flexibility to shift their energy demands over time. Although this one-dimensional flexibility has been extensively investigated both by research and industrial implementations, the expanding energy demand and the associated uncertainties still make the integration of a large population of EVs into power system reliably and economically greatly challenging. In this paper, we design an auction scheme via mechanism design to elicit two additional flexibilities from EVs, namely energy flexibility and deadline flexibility. An offline mechanism is firstly designed as a benchmark based on the famous Vickrey–Clark–Groves mechanism. Then based on the primal-dual approach, we propose an online auction, in which all bids are truthful, the loss of social welfare is bounded by competitive ratio, and the mechanism can be implemented in polynomial time. By the numerical results, we quantitatively show that both the power system operators and individual EVs can benefit from the integration of the multi-dimensional flexibilities through our proposed mechanisms. [ABSTRACT FROM AUTHOR]

Stability is an important constraint in power system operation and the transient stability constrained optimal power flow (OPF) has always received considerable attention in recent years. In this paper, the defects of the existing models and algorithms around this topic are firstly analyzed, on the basis of which, a multi-objective optimization method is proposed. The basic idea of the proposed method is to model transient stability as an objective function rather than an inequality constraint and consider classic transient stability constrained OPF (TSCOPF) as a tradeoff procedure using Pareto ideology. Second, a master-slave parallel elitist non-dominated sorting genetic algorithm II is used to solve the proposed multi-objective optimization problem, the parallel algorithm shows an excellent acceleration effect and provides a set of Pareto optimal solutions for decision makers to select. An innovative weight assigning technique based on fuzzy membership variance is also introduced for a more scientific and objective optimal solution decision. Case study results demonstrate the proposed multi-objective method has many advantages, compared with traditional TSCOPF methods. [ABSTRACT FROM PUBLISHER]

Distribution system reconfiguration (DSR) is a multi-objective, nonlinear problem. This paper introduces a new, fast, nondominated sorting genetic algorithm (FNSGA) for the purpose of solving the DSR problem in normal operation by satisfying all objectives simultaneously with a relatively small number of generations and relatively short computation time. The objectives of the problem are to minimize real power losses and improve the voltage profile and load balancing index with minimum switching operations. Instead of generating several ranks from the nondominated set of solutions, this algorithm deals with only one rank; then the most suitable solution is chosen according to the operator's wishes. If there is no preference and all objectives have the same degree of importance, the best solution is determined by simply considering the sum of the normalized objective values. Also, a guided mutation operation is applied instead of a random one to speed up convergence. Radial system topology is satisfied using graph theory by formulating the branch-bus incidence matrix (BBIM) and checking the rank of each topology. To test the algorithm, it was applied to two widely studied test systems and a real one. The results show the efficiency of this algorithm as compared to other methods in terms of achieving all the goals simultaneously with reasonable population and generation sizes and without using a mutation rate, which is usually problem-dependent. [ABSTRACT FROM PUBLISHER]

In order to optimize their assets, electrical power distribution companies seek out various techniques to improve system operation and its different variables, like voltage levels, active power losses and so on. A few of the tools applied to meet these objectives include reactive power compensation, use of voltage regulators, and network reconfiguration. One target most companies aim at is power loss minimization; one available tool to do this is distribution system reconfiguration. To reconfigure a network in radial power distribution systems means to alter the topology changing the state of a set of switches normally closed (NC) and normally opened (NO). In restructured electrical power business, a company must also consider obtaining a topology as reliable as possible. In most cases, reducing the power losses is no guarantee of improved reliability. This paper presents a multiobjective algorithm to reduce power losses while improving the reliability index using the artificial immune systems technique applying graph theory considerations to improve computational performance and Pareto dominance rules. The proposed algorithm is tested on a sample system, 14-bus test system, and on Administración Nacional de Electricidad (ANDE) real feeder (CBO-01 23-kV feeder). [ABSTRACT FROM PUBLISHER]

Reliability analysis of power systems has been attracting increasing attention. Regulatory agencies establish reliability standards that, if infringed, result in costly fines for the utility suppliers. A special concern pertains to the distribution networks on which most failures occur. The allocation of switches is a possible strategy to improve reliability, by allowing network reconfiguration to isolate contingencies and restore power to dark areas. This paper proposes an optimization methodology to allocate switches on radially operated distribution networks. The solution framework considers sectionalizing and tie switches of different capacities, with manual or automatic operation schemes. The approach minimizes the costs of allocation and energy not supplied, under reliability and flow capacity constraints. The solution framework is based on memetic algorithm concepts with a structured population. Case studies with a large network and real-world scenarios were used to evaluate the methodology. The results indicate that significant cost reductions can be achieved using the proposed solutions. [ABSTRACT FROM PUBLISHER]

This paper proposes a new optimization tool based on the cross-entropy (CE) method to assess security-constrained optimal power flow (SCOPF) solutions. First, the corresponding SCOPF stochastic problem is defined so that the optimum solution is interpreted as a rare event to be reached by a random search. Second, the CE method solves this new problem efficiently by making adaptive changes to the probability density function according to the Kullback–Leibler distance, creating a sequence of density functions that guides the search in the direction of the theoretically degenerate density at the optimal point. Different types of density functions are tested in order to cope with discrete variables present in the SCOPF problem. Two test systems, namely the IEEE 57 bus and the IEEE 300 bus, are used to evaluate the effectiveness of the proposed method in terms of solution quality and computational effort. Comparisons carried out with reference algorithms in the literature demonstrate that the CE method is capable of finding better solutions for the SCOPF problem with fewer evaluations. [ABSTRACT FROM AUTHOR]

This paper describes a probabilistic method based on a total risk index (probability times consequences) for assessing the number of spare breakers required for a group of similar high voltage breakers used in switching and transformer stations. The proposed method uses a Markov model for assessing the probability of failures and a bulk power system reliability program for evaluating failure consequences. The method considers a number of factors such as the group size, unit failure rate, unit repair time, transmission station layout, and other power system parameters that may impact the number of spare breakers. A cost/benefit analysis approach is used in determining the required number of spare breakers. The number of spare units is determined when the total cost (sum of spare unit costs, system operating costs and system outage costs due to breaker failures) is minimum. An example is given to illustrate the proposed method of assessment. [ABSTRACT FROM PUBLISHER]

Aggregate thermostatically controlled loads (TCLs) are good candidates for providing load following services in power systems. This paper is concerned with the modeling, evaluation, and control problems of a population of heterogeneous TCLs. Specifically, the heterogeneous population is divided into multiple homogeneous clusters and each cluster, i.e., TCL aggregator, is modeled by an approximated three-input single-output state space model. Here, the aggregators serve as a bridge connecting the load utility and the terminal TCLs, which have their own decision makers and are responsible for aggregate estimation and command issuing. And aggregate evaluation is carried out for the aggregator so as to provide the aggregate regulation capacities and ramping rates, which is useful for setting of the reference power trajectory. Based on the established control model, we furthermore propose a hierarchical centralized control algorithm for a bus load utility to regulate all TCLs inside it so as to provide load following service, while not affecting the customers’ comfort levels. Finally, simulation results with respect to a common bus load are provided to demonstrate the effectiveness of the proposed aggregate modeling and the centralized load following strategy. [ABSTRACT FROM AUTHOR]

It is widely accepted that thermostatically controlled loads (TCLs) can be used to provide regulation reserve to the grid. We first argue that the aggregate flexibility offered by a collection of TCLs can be succinctly modeled as a stochastic battery with dissipation. We next characterize the power limits and energy capacity of this battery model in terms of TCL parameters and random exogenous variables such as ambient temperature and user-specified set-points. We then describe a direct load control architecture for regulation service provision. Here, we use a priority-stack-based control framework to select which TCLs to control at any time. The control objective is for the aggregate power deviation from baseline to track an automatic generation control signal supplied by the system operator. Simulation studies suggest the practical promise of our methods. [ABSTRACT FROM PUBLISHER]

An increasing number of municipalities are striving for energy autonomy. This study determines in which municipalities and at what additional cost energy autonomy is feasible for a case study of Germany. An existing municipal energy system optimization model is extended to include the industrial, commercial and personal transport sectors. Multiple regression methods are benchmarked in order to identify the model best suited for the transfer of individual optimization results to a large proportion of German municipalities. The resulting levelized cost of energy (LCOE) from the optimization of representative case study municipalities are transferred using energy-relevant indicators. The study demonstrates that energy autonomy is technically feasible in 6,314 (56%) municipalities. Thereby, the LCOEs increase in the autonomous case on average by 0.41 €/kWh compared to the minimum cost scenario. Apart from energy demand, base-load-capable bioenergy and deep geothermal energy have the greatest influence on the LCOEs. Overall, it appears that municipal energy autonomy is not economically viable under current framework conditions. This study represents a starting point for defining possible scenarios in studies of future national energy system or transmission grid expansion planning, which for the first time consider completely energy autonomous municipalities. [ABSTRACT FROM AUTHOR]

Using distributed energy resources (DERs), such as thermostatically controlled loads (TCLs), electric vehicles (EVs), and energy storage systems (ESSs) as a way to manage demand has been known for decades. A demand management scheme that explicitly considers the individual DER's local quality of service (QoS) is known as demand dispatch. Packetized energy management (PEM) is a demand dispatch paradigm that borrows packet-based concepts from wireless communications to dynamically manage fleets of DER at-scale and in realtime via small, discrete fixed-duration/fixed-power energy packets. PEM addresses QoS in a bottom-up fashion by having a coordinator authorize/deny incoming requests from DERs to consume energy packets. This manuscript extends prior work on modeling a large-scale population (i.e., macro-model) of homogeneous TCLs and ESSs operating under the PEM paradigm. In particular, we extend the macro-model methodology to include deferrable loads (DLs), such as EVs, together with analysis of QoS guarantees. Comparisons between an agent-based (micro-model) simulation and the proposed macro-model are presented to validate modeling accuracy and QoS guarantees. [ABSTRACT FROM AUTHOR]

The optimal scheduling of hydrothermal systems requires the representation of uncertainties in future streamflows to devise a cost-effective operations policy. Stochastic optimization has been widely used as a powerful tool to solve this problem but results will necessarily depend on the stochastic model used to generate future scenarios for streamflows. Periodic autoregressive (PAR) models have been widely used in this task. However, its parameters are typically unknown and must be estimated from historical data, incorporating a natural estimation error. Furthermore, the model is just a linear approximation of the real stochastic process. The consequence is that the operator will be uncertain about the correct linear model that should be used at each period. The objective of this work is to assess the impacts of incorporating the uncertainty of the parameters of the PAR models into a stochastic hydrothermal scheduling model. The proposed methodology is tested with case studies based on data from the Brazilian hydroelectric system. It is shown that when the uncertainty of the parameters is ignored, the policies given by the stochastic optimization tend to be too optimistic. [ABSTRACT FROM AUTHOR]

The IEEE Standard 1366-2003-2.5 Beta Methodology was developed to provide a methodology to define a Major Event Day (MED) with respect to distribution reliability performance. The method applies to utilities experiencing interruptions every day or just some days of the year. [ABSTRACT FROM PUBLISHER]

A multi-objective power unit commitment problem is framed to consider simultaneously the objectives of minimizing the operation cost and minimizing the emissions from the generation units. To find the solution of the optimal schedule of the generation units, a memetic evolutionary algorithm is proposed, which combines the non-dominated sorting genetic algorithm-II (NSGA-II) and a local search algorithm. The power dispatch sub-problem is solved by the weighed-sum lambda-iteration approach. The proposed method has been tested on systems composed by 10 and 100 generation units for a 24-hour demand horizon. The Pareto-optimal front obtained contains solutions of different trade off with respect to the two objectives of cost and emission, which are superior to those contained in the Pareto-front obtained by the pure NSGA-II. The solutions of minimum cost are shown to compare well with recent published results obtained by single-objective cost optimization algorithms. [ABSTRACT FROM PUBLISHER]