Voltage stability constrained multi-objective optimal reactive power dispatch under load and wind power uncertainties: A stochastic approach

Optimal reactive power dispatch (ORPD) problem is an important problem in the operation of power systems. It is a nonlinear and mixed integer programming problem, which determines optimal values for control parameters of reactive power producers to optimize specific objective functions while satisfying several technical constraints. In this paper, stochastic multi-objective ORPD (SMO-ORPD) problem is studied in a wind integrated power system considering the loads and wind power generation uncertainties. The proposed multi objective optimization problem is solved using ε-constraint method, and fuzzy satisfying approach is employed to select the best compromise solution. Two different objective functions are considered as follow: 1) minimization of the active power losses and 2) minimization of the voltage stability index (named L-index). In this paper VAR compensation devices are modeled as discrete variables. Moreover, to evaluate the performance of the proposed method for solution of multi-objective problem, the obtained results for deterministic case (DMO-ORPD), are compared with the available methods in literature. The proposed method is examined on the IEEE-57 bus system. The proposed models are implemented in GAMS environment. The numerical results substantiate the capability of the proposed SMO-ORPD problem to deal with uncertainties and to determine the best settings of control variables.     

An efficient algorithm for multi-objective optimal operation management of distribution network considering fuel cell power plants

This paper presents an interactive fuzzy satisfying method based on Hybrid Modified Honey Bee Mating Optimization (HMHBMO). Its purpose is to solve the Multi-objective Optimal Operation Management (MOOM) problem which can be affected by Fuel cell power plants (FCPPs). Minimizing total electrical energy losses, total electrical energy cost, total pollutant emission produced by sources and deviation of bus voltages are the objective functions in this method. A new interactive fuzzy satisfying method is presented to solve the multi-objective problem by assuming that the decision-maker (DM) has fuzzy targets for each of the objective functions. Through the interaction with the DM, the fuzzy goals are quantified by eliciting the corresponding membership functions. Considering the current solution, the DM updates the reference membership values until the best solution can be obtain. The MOOM problem is modeled as a mixed integer nonlinear programming problem. Therefore, evolutionary methods can be used to solve this problem since they are independence of objective function’s type and constraints. Recently researchers have presented a new evolutionary method called Honey Bee Mating Optimizations (HBMO) algorithm. Original HBMO often converges to local optima and this is a disadvantage of this method. In order to avoid this shortcoming we propose a new method. This method improves the mating process and also combines the modified HBMO with a Chaotic Local Search (CLS). Numerical results on a distribution test system have been presented to illustrate the performance and applicability of the proposed method.     

Probabilistic approach to multi-objective Volt/Var control of distribution system considering hybrid fuel cell and wind energy sources using Improved Shuffled Frog Leaping Algorithm

Deregulation and restructuring in power systems, the ever-increasing demand for electricity, and concerns about the environment are the major driving forces for using Renewable Energy Sources (RES). Recently, Wind Farms (WFs) and Fuel Cell Power Plants (FCPPs) have gained great interest by Distribution Companies (DisCos) as the most common RES. In fact, the connection of enormous RES to existing distribution networks has changed the operation of distribution systems. It also affects the Volt/Var control problem, which is one of the most important schemes in distribution networks. Due to the intermittent characteristics of WFs, distribution systems should be analyzed using probabilistic approaches rather than deterministic ones. Therefore, this paper presents a new algorithm for the multi-objective probabilistic Volt/Var control problem in distribution systems including RES. In this regard, a probabilistic load flow based on Point Estimate Method (PEM) is used to consider the effect of uncertainty in electrical power production of WFs as well as load demands. The objective functions, which are investigated here, are the total cost of power generated by WFs, FCPPs and the grid; the total electrical energy losses and the total emission produced by WFs, FCPPs and DisCos. Moreover, a new optimization algorithm based on Improved Shuffled Frog Leaping Algorithm (ISFLA) is proposed to determine the best operating point for the active and reactive power generated by WFs and FCPPs, reactive power values of capacitors, and transformers’ tap positions for the next day. Using the fuzzy optimization method and max-min operator, DisCos can find solutions for different objective functions, which are optimal from economical, operational and environmental perspectives. Finally, a practical 85-bus distribution test system is used to investigate the feasibility and effectiveness of the proposed method.     

Stochastic-heuristic methodology for the optimisation of components and control variables of PV-wind-diesel-battery stand-alone systems

In this paper a new stochastic-heuristic methodology for the optimisation of the electrical supply of stand-alone (off-grid) hybrid systems (photovoltaic-wind-diesel with battery storage) is shown. The objective is to minimise the net present cost of the system. The stochastic optimisation is developed by means of Monte Carlo simulation, which takes into account the uncertainties of irradiation, temperature, wind speed and load (correlated Gaussian random variables), using their probability density functions and the variance-covariance matrix. Also the uncertainty of diesel fuel price inflation rate was considered. The heuristic approach uses genetic algorithms to obtain the optimal system (or a solution near the optimal) in a reasonable computation time. This methodology includes an accurate weighted Ah-throughput battery model with several control variables, which can be set in the modern battery controllers or inverter/chargers with State of Charge control. A case study is analysed as an example of the application of this methodology, obtaining the stochastic optimisation an optimal system similar to the one obtained by the deterministic optimisation. It is recommended to perform first the deterministic optimisation (with low computation time), then the search space should be reduced and finally the stochastic optimisation can be obtained in a reasonable computation time.     

Impact of heat,power and hydrogen generation on optimal placement and operation of fuel cell power plants

In this paper, a stochastic model is proposed for planning the location and operation of Fuel Cell Power Plants (FCPPs) as Combined Heat, power, and Hydrogen (CHPH) units. Total cost, emissions of FCPPs and substation, and voltage deviation are the objective functions to be minimized. Location and operation of FCPPs as CHPH are considered in this paper while their investment cost is not taken into account. In the proposed model, indeterminacy refers to electrical and thermal loads forecasting, pressure of oxygen and hydrogen, and the nominal temperature of FCPPs. In this method, scenarios are produced using roulette wheel mechanism and probability distribution function of input random variables. Using this method, the probabilistic problem is considered to be distributed as some scenarios and consequently probabilistic problem is considered as combination of some deterministic problems. Considering the nature of objective functions, the problem of locating and operating FCPPs as CHPH is considered as a mixed integer nonlinear problem. A Self Adaptive Charged System Search (SACSS) algorithm is employed for determining the best Pareto optimal set. Furthermore, a set of non-dominated solutions is saved in repository during simulation procedure. A 69-bus distributed system is used for verifying the beneficiary proposed method.     

Optimal operation management of fuel cell/wind/photovoltaic power sources connected to distribution networks

In this paper a new multiobjective modified honey bee mating optimization (MHBMO) algorithm is presented to investigate the distribution feeder reconfiguration (DFR) problem considering renewable energy sources (RESs) (photovoltaics, fuel cell and wind energy) connected to the distribution network. The objective functions of the problem to be minimized are the electrical active power losses, the voltage deviations, the total electrical energy costs and the total emissions of RESs and substations. During the optimization process, the proposed algorithm finds a set of non-dominated (Pareto) optimal solutions which are stored in an external memory called repository. Since the objective functions investigated are not the same, a fuzzy clustering algorithm is utilized to handle the size of the repository in the specified limits. Moreover, a fuzzy-based decision maker is adopted to select the ‘best’ compromised solution among the non-dominated optimal solutions of multiobjective optimization problem. In order to see the feasibility and effectiveness of the proposed algorithm, two standard distribution test systems are used as case studies.     

Assessing wind uncertainty impact on short term operation scheduling of coordinated energy storage systems and thermal units

Renewable resources, especially wind power, are widely integrated into the power systems nowadays. Managing uncertainty of the large scale wind power is often known as one of the most challenging issues in the power system operation scheduling. Additionally, energy storage systems (ESSs) have been widely investigated in the power systems owing to their valuable applications, especially renewable energy smoothing and time shift. In this paper, a stochastic unit commitment (UC) model is proposed to assess the impact of the wind uncertainty impact on ESSs and thermal units schedule in UC problem. Wind uncertainty is modeled based on the two measures. First, the wind penetration level is changed with respect to the basic level. Second, the wind forecasting error is modeled through a normal probability distribution function with different variances. The ESSs are modeled based on several technical characteristics and optimally scheduled considering different levels of the wind penetration and forecasting accuracies. The proposed formulation is a stochastic mixed integer linear programming (SMILP) and solved using GAMS software. Simulation results demonstrate that the wind uncertainty have a considerable impact on operation cost and ESSs schedule while proposed optimum storage scheduling through the stochastic programming will reduce the daily operational cost considerably.     

A method for remaining discharge time prediction of lithium‐ion batteries under dynamic uncertainty

Remaining discharge time of the battery system in electric vehicles relates strongly to the decision‐making of driving. Subjected to the various uncertainties, such as modeling uncertainty, state estimation uncertainty, and future load uncertainty, the accuracy and reliability of the remaining discharge time prediction reduce, which will lead to range anxiety. A stochastic framework based on the state‐of‐charge estimation and prediction strategy is proposed to predict remaining discharge time against the uncertainty. Firstly, the equivalent circuit model is established to model the dynamic behavior of the battery. Through the analysis of different fitting functions of open circuit voltage and state‐of‐charge, the Akaike information criterion is introduced to select the best function. Secondly, the coestimator is employed to bound the influence of the model parameter uncertainty and noise uncertainty. Finally, the uncertainties are quantified by a probabilistic method, and a Monte Carlo–based stochastic prediction strategy is proposed to predict the probability distribution of remaining discharge time under dynamic uncertainty. Experimental results demonstrate that the proposed prediction framework is of great effectiveness as it can provide an accurate remaining discharge time interval under dynamic uncertainty, which helps to promote the energy‐saving driving and overcome the range anxiety.     

Efficient climate policies under technology and climate uncertainty

This article explores efficient climate policies in terms of investment streams into fossil and renewable energy technologies. The investment decisions maximise social welfare while observing a probabilistic guardrail for global mean temperature rise under uncertain technology and climate parameters. Such a guardrail constitutes a chance constraint, and the resulting optimisation problem is an instance of chance constrained programming, not stochastic programming as often employed. Our analysis of a model of economic growth and endogenous technological change, MIND, suggests that stringent mitigation strategies cannot guarantee a very high probability of limiting warming to 2 °C since preindustrial time under current uncertainty about climate sensitivity and climate response time scale. Achieving the 2 °C temperature target with a probability P? of 75% requires drastic carbon dioxide emission cuts. This holds true even though we have assumed an aggressive mitigation policy on other greenhouse gases from, e.g., the agricultural sector. The emission cuts are deeper than estimated from a deterministic calculation with climate sensitivity fixed at the P? quantile of its marginal probability distribution (3.6 °C). We show that earlier and cumulatively larger investments into the renewable sector are triggered by including uncertainty in the technology and climate response time scale parameters. This comes at an additional GWP loss of 0.3%, resulting in a total loss of 0.8% GWP for observing the chance constraint. We obtained those results with a new numerical scheme to implement constrained welfare optimisation under uncertainty as a chance constrained programming problem in standard optimisation software such as GAMS. The scheme is able to incorporate multivariate non-factorial probability measures such as given by the joint distribution of climate sensitivity and response time. We demonstrate the scheme for the case of a four-dimensional parameter space capturing uncertainty about climate and technology.     

An improved particle swarm optimisation for unit commitment in microgrids with battery energy storage systems considering battery degradation and uncertainties

Using electric storage systems (ESSs) is known as a viable strategy to mitigate the volatility and intermittency of renewable distributed generators (DGs) in microgrids (MGs). Among different electric storage technologies, battery energy storage (BES) is considered as the best option. In unit commitment (UC) module, the set of committed dispatchable DGs along with their power, power exported to/imported from macrogrid and status and power of ESS units are determined. In this paper, BES degradation is considered in UC formulation and an efficient particle swarm optimisation with quadratic transfer function is proposed for solving UC in BES‐integrated MGs, while the uncertainties of demand, renewable generation and market price are considered and dealt with robust optimisation. UC is formulated as a multi‐objective optimisation problem whose objectives are MG operation cost and BES degradation. The resultant multi‐objective optimisation problem is converted into a single‐objective optimisation problem and the effect of weight factors on MG operation cost and BES lifecycle are investigated. The results show that by consideration of BES degradation in objective function, BES lifecycle increases from 350 to 500 and the minimum depth of charge increases from 5.5% to 34%; however, MG operation cost increases from $8717 to $8910.2. The results also show that by consideration of uncertainties, MG's operation cost increases by 8.22%.     

Ancillary services and optimal household energy management with photovoltaic production

This article presents a project designed to increase the monetary value of photovoltaic (PV) solar production for residential applications. To contribute to developing new functionalities for this type of PV system and an efficient control system for optimising its operation, this article explains how the proposed system could contract to provide ancillary services, particularly the supply of active power services. This provision of service by a PV-based system for domestic applications, not currently available, has prompted a market design proposal related to the distribution system. The mathematical model for calculating the system's optimal operation (sources, load and exchanges of power with the grid) results in a linear mix integer optimisation problem in which the objective is to maximise the profits achieved by taking part in the electricity market. Our approach is illustrated in a case study. PV producers could gain by taking part in the markets for balancing power or ancillary services despite the negative impact on profit of several types of uncertainty, notably the intermittent nature of the PV source.     

Robust optimization of hydrogen network

Process integration is an effective way to reduce hydrogen utility consumption in refineries. A number of graphical and mathematical programming approaches have been proposed to synthesis the optimal network. However, as the operation of refineries encounters uncertainty with the rapidly changing market and deteriorating crude oil, existing approaches are inadequate to achieve robust hydrogen network distribution due to the uncertain factors. In this paper, robust optimization is introduced as a framework to optimize hydrogen network of refineries under uncertainty. In this framework, a number of scenarios representing possible future environments are considered. Both model robust and solution robust are explicitly incorporated into the objective function. A possible optimal network distribution which is less sensitive to the change of scenarios and has the minimum total annual cost is achieved by the tradeoff between the total annual cost and the expected error. Case studies indicate that this method is effective in dealing with hydrogen network design and planning under uncertainty in comparison to the deterministic approach and the stochastic programming method.     

基于机会约束规划的风电源与充电站的优化配置

为了改善分布式电源与电动汽车的接入对电网安全性、经济性和电能质量的不良影响。考虑风力资源的随机波动性、电动汽车充电需求、分时电价等,以配电系统投资运行成本、有功损耗和电压质量为规划目标,建立了基于机会约束规划的优化配置模型,采用改进遗传算法进行求解。以IEEE33节点配电系统为例,验证了所提模型和算法的有效性。仿真分析表明,将电压质量纳入规划目标,能够以较小的经济成本保证较好的电能质量,考虑输出功率不确定性等因素,得到的规划方案具有较好的经济性。     

含风电场的电力系统经济——排放多目标调度

从火电机组燃料成本和污染物排放两方面入手,构建了含风电场的电力系统发电调度运营管理多目标优化模型。引入了一种新的概率分布模型——截断多用途分布模型(TVD)来表征风电场,并简化风电的不确定性,同时引入基于TVD的可调节置信区间(ACI)风电场成本函数模型及一种基于列维飞行及解决非凸问题的改进型闪电算法(ILFA),可在随机多目标框架中有效地解决经济—排放调度(EED)问题。最后,通过算例与其他经典分布模型进行对比分析,结果表明所提模型可更准确地反映风电情况,该算法在平衡经济成本和污染物排放方面有效。     

Genetic single objective optimisation for sizing and allocation of renewable DG systems

The optimal design of renewable-based distributed generations (DGs) is a challenging issue in order to maximise their benefits and to overcome power quality problems. Therefore, this paper proposes a methodology for optimal allocation and sizing of renewable DG units to minimise total power losses over radial distribution systems. The planning problem is formulated as a single objective nonlinear mixed integer-constrained optimisation problem and is solved by using the augmented Lagrangian genetic algorithm (ALGA) by combining the objective function and the nonlinear constraints. In that case, the ALGA solves a sequence of sub-problems where the objective function penalises the constraints violation in order to obtain the best solution. The proposed technique is applied to IEEE radial test systems including 33-bus, 69-bus and 119-bus and is implemented with different scenarios including all possible combinations and various types of renewable DG units to prove the effectiveness of the proposed methodology.     

Economic performance optimization of an absorption cooling system under uncertainty

Many of the strategies devised so far to address the optimization of energy systems are deterministic approaches that rely on estimated data. However, in real world applications there are many sources of uncertainty that introduce variability into the decision-making problem. Within this general context, we propose a novel approach to address the design of absorption cooling systems under uncertainty in the energy cost. As opposed to other approaches that optimize the expected performance of the system as a single objective, in our method the design task is formulated as a stochastic bi-criteria non-linear optimization problem that simultaneously accounts for the minimization of the expected total cost and the financial risk associated with the investment. The latter criterion is measured by the downside risk, which avoids the need to define binary variables thus improving the computational performance of the model. The capabilities of the proposed modeling framework and solution strategy are illustrated in a case study problem that addresses the design of a typical absorption cooling system. Numerical results demonstrate that the method presented allows to manage the risk level effectively by varying the area of the heat exchangers of the absorption cycle. Specifically, our strategy allows identifying the optimal values of the operating and design variables of the cycle that make it less sensitive to fluctuations in the energy price, thus improving its robustness in the face of uncertainty.     

Joint market clearing in a stochastic framework considering power system security

This paper presents a new stochastic framework for provision of reserve requirements (spinning and non-spinning reserves) as well as energy in day-ahead simultaneous auctions by pool-based aggregated market scheme. The uncertainty of generating units in the form of system contingencies are considered in the market clearing procedure by the stochastic model. The solution methodology consists of two stages, which firstly, employs Monte–Carlo Simulation (MCS) for random scenario generation. Then, the stochastic market clearing procedure is implemented as a series of deterministic optimization problems (scenarios) including non-contingent scenario and different post-contingency states. The objective function of each of these deterministic optimization problems consists of offered cost function (including both energy and reserves offer costs), Lost Opportunity Cost (LOC) and Expected Interruption Cost (EIC). Each optimization problem is solved considering AC power flow and security constraints of the power system. The model is applied to the IEEE 24-bus Reliability Test System (IEEE 24-bus RTS) and simulation studies are carried out to examine the effectiveness of the proposed method.     

Recent trends in power management strategies for optimal operation of distributed energy resources in microgrids: A comprehensive review

The current era in sustainable development is focused on the rapid integration of renewable energy sources driven by a wide range of socio-economic objectives. Due to the inherent property of time-varying weather conditions, the intermittent sources, that is, Solar PV and Wind Energy, are considered as variable energy resources. The uncertainty and variability problem of these sources has brought many complications to distributed network operators to operate and control the complex or multi-microgrids with limited fast-ramping resources in order to maintain the power system flexibility. It led many researchers to find an alternative strategy since the conventional approaches are no longer adequate to handle the economic implications of operational decision making. At first, the brief review of various deterministic and probabilistic approaches, stochastic programming and robust optimisation strategies to address the uncertainty of variable energy resources are discussed. Furthermore, in the energy management point of view, the optimal scheduling problem of distributed sources of the microgrid is considered, and a brief review of optimisation models, advanced control strategies and demand response strategies to maximise economic benefits of microgrids are also elaborately presented. Finally, the multiagent-based distributed and decentralised control strategies for seamless integration of distributed generator units are reviewed under various configurations of the power grid along with communication network topologies.     

Aerodynamic design optimization of wind turbine rotors under geometric uncertainty

Presented is a robust optimization strategy for the aerodynamic design of horizontal axis wind turbine rotors including the variability of the annual energy production because of the uncertainty of the blade geometry caused by manufacturing and assembly errors. The energy production of a rotor designed with the proposed robust optimization approach features lower sensitivity to stochastic geometry errors with respect to that of a rotor designed with the conventional deterministic optimization approach that ignores these errors. The geometry uncertainty is represented by normal distributions of the blade pitch angle, and the twist angle and chord of the airfoils. The aerodynamic module is a blade‐element momentum theory code. Both Monte Carlo sampling and the univariate reduced quadrature technique, a novel deterministic uncertainty analysis method, are used for uncertainty propagation. The performance of the two approaches is assessed in terms of accuracy and computational speed. A two‐stage multi‐objective evolution‐based optimization strategy is used. Results highlight that, for the considered turbine type, the sensitivity of the annual energy production to rotor geometry errors can be reduced by reducing the rotational speed and increasing the blade loading. The primary objective of the paper is to highlight how to incorporate an efficient and accurate uncertainty propagation strategy in wind turbine design. The formulation of the considered design problem does not include all the engineering constraints adopted in real turbine design, but the proposed probabilistic design strategy is fairly independent of the problem definition and can be easily extended to turbine design systems of any complexity. Copyright © 2014 John Wiley & Sons, Ltd.     

Solving the economic dispatch problem with a modified quantum-behaved particle swarm optimization method

In this paper, a modified quantum-behaved particle swarm optimization (QPSO) method is proposed to solve the economic dispatch (ED) problem in power systems, whose objective is to simultaneously minimize the generation cost rate while satisfying various equality and inequality constraints. The proposed method, denoted as QPSO-DM, combines the QPSO algorithm with differential mutation operation to enhance the global search ability of the algorithm. Many nonlinear characteristics of the generator, such as ramp rate limits, prohibited operating zones, and nonsmooth cost functions are considered when the proposed method is used in practical generator operation. The feasibility of the QPSO–DM method is demonstrated by three different power systems. It is compared with the QPSO, the differential evolution (DE), the particle swarm optimization (PSO), and the genetic algorithm (GA) in terms of the solution quality, robustness and convergence property. The simulation results show that the proposed QPSO–DM method is able to obtain higher quality solutions stably and efficiently in the ED problem than any other tested optimization algorithm.