A Survey on Home Energy Management <s> C. RESIDENTIAL LOAD UNCERTAINTIES <s> This paper evaluates the real-time price-based demand response (DR) management for residential appliances via stochastic optimization and robust optimization approaches. The proposed real-time price-based DR management application can be imbedded into smart meters and automatically executed on-line for determining the optimal operation of residential appliances within 5-minute time slots while considering uncertainties in real-time electricity prices. Operation tasks of residential appliances are categorized into deferrable/non-deferrable and interruptible/non-interruptible ones based on appliances' DR preferences as well as their distinct spatial and temporal operation characteristics. The stochastic optimization adopts the scenario-based approach via Monte Carlo (MC) simulation for minimizing the expected electricity payment for the entire day, while controlling the financial risks associated with real-time electricity price uncertainties via the expected downside risks formulation. Price uncertainty intervals are considered in the robust optimization for minimizing the worst-case electricity payment while flexibly adjusting the solution robustness. Both approaches are formulated as mixed-integer linear programming (MILP) problems and solved by state-of-the-art MILP solvers. The numerical results show attributes of the two approaches for solving the real-time optimal DR management problem for residential appliances. <s> BIB001 </s> A Survey on Home Energy Management <s> C. RESIDENTIAL LOAD UNCERTAINTIES <s> High quality demand side management has become indispensable in the smart grid infrastructure for enhanced energy reduction and system control. In this paper, a new demand side management technique, namely, a new energy efficient scheduling algorithm, is proposed to arrange the household appliances for operation such that the monetary expense of a customer is minimized based on the time-varying pricing model. The proposed algorithm takes into account the uncertainties in household appliance operation time and intermittent renewable generation. Moreover, it considers the variable frequency drive and capacity-limited energy storage. Our technique first uses the linear programming to efficiently compute a deterministic scheduling solution without considering uncertainties. To handle the uncertainties in household appliance operation time and energy consumption, a stochastic scheduling technique, which involves an energy consumption adaptation variable , is used to model the stochastic energy consumption patterns for various household appliances. To handle the intermittent behavior of the energy generated from the renewable resources, the offline static operation schedule is adapted to the runtime dynamic scheduling considering variations in renewable energy. The simulation results demonstrate the effectiveness of our approach. Compared to a traditional scheduling scheme which models typical household appliance operations in the traditional home scenario, the proposed deterministic linear programming based scheduling scheme achieves up to 45% monetary expense reduction, and the proposed stochastic design scheme achieves up to 41% monetary expense reduction. Compared to a worst case design where an appliance is assumed to consume the maximum amount of energy, the proposed stochastic design which considers the stochastic energy consumption patterns achieves up to 24% monetary expense reduction without violating the target trip rate of 0.5%. Furthermore, the proposed energy consumption scheduling algorithm can always generate the scheduling solution within 10 seconds, which is fast enough for household appliance applications. <s> BIB002 </s> A Survey on Home Energy Management <s> C. RESIDENTIAL LOAD UNCERTAINTIES <s> Innovations in the residential sector are required to reduce environmental impacts, as the sector is a contributor to greenhouse gas emissions. The increasing demand for electricity and the emergence of smart grids have presented new opportunities for home energy management systems (HEMS) in demand response markets. HEMS are demand response tools that shift and curtail demand to improve the energy consumption and production profile of a dwelling on behalf of a consumer. HEMS usually create optimal consumption and productions schedules by considering multiple objectives such as energy costs, environmental concerns, load profiles and consumer comfort. The existing literature has presented several methods, such as mathematical optimization, model predictive control and heuristic control, for creating efficient operation schedules and for making good consumption and production decisions. However, the effectiveness of the methods in the existing literature can be difficult to compare due to diversity in modelling parameters, such as appliance models, timing parameters and objectives. The present chapter provides a comparative analysis of the literature on HEMS, with a focus on modelling approaches and their impact on HEMS operations and outcomes. In particular, we discuss a set of HEMS challenges such as forecast uncertainty, modelling device heterogeneity, multi-objective scheduling, computational limitations, timing considerations and modelling consumer well-being. The presented work is organized to allow a reader to understand and compare the important considerations, approaches, nomenclature and results in prominent and new literary works without delving deeply into each one. <s> BIB003 </s> A Survey on Home Energy Management <s> C. RESIDENTIAL LOAD UNCERTAINTIES <s> Robust-index method is proposed to tackle the challenges of uncertainties caused by customer behavior in order to minimize comfort violation in household load scheduling. Robust indexes for different kinds of loads are developed and integrated into the load scheduling optimization problems in the form of additional constraints, and thus the obtained load schedules are able to reach the expected robust level. The robust-index method is simple in modeling, independent of historical data, and with low additional computational burden. Simulation results verified the validity of the proposed method and demonstrated their application in load scheduling. <s> BIB004 </s> A Survey on Home Energy Management <s> C. RESIDENTIAL LOAD UNCERTAINTIES <s> Abstract Home energy management (HEM) is one of the crucial requirements for future smart grid environment. Usually, utility companies motivate residential consumers to participate in household demand side management (DSM) techniques. The residential consumers’ main intention is to reduce their electricity bills whereas utilities’ primary goal is to reduce their system peak load demand. The benefits of DSM can be enhanced with smart energy storage systems. In this paper, an intelligent multi-objective household DSM with battery storage systems is proposed to minimize both the objectives simultaneously. Generally, the residential DSM deals with various controllable appliances that normally have different operating time priorities according to the consumers’ preferences. Because of this, the DSM problem is modelled as a mixed integer optimization problem. In this paper, the multi-objective mixed integer linear programming technique (MOMILP) is used to solve the proposed residential DSM problem. The proposed model is tested on a system having four different residential consumers. The benefits of the battery energy storage systems are analysed by taking six different scenarios. An economic analysis of each residential consumer's battery storage system with load uncertainty modelling is also done in this paper. Simulation results of various scenarios with different objectives demonstrate the effectiveness of the proposed model. <s> BIB005
In household environments, accurate predictions of electricity demand and local micro generation are difficult. If tariffs are fixed, utility grid prices can be determined, otherwise they can only be estimated, with a certain degree of confidence. These uncertainties have an impact on computed load schedules, which ultimately compromise energy bill and may lead to breaches of contracted power limits or even impacting residents' comfort level. The main sources of uncertainty in HEMSs are: (i) appliance operation needs, (ii) appliance consumption, (iii) local micro energy production, and (iv) utility grid prices. A way to address uncertainties on forecasts is to remove predicted data from the decision-making process, and solely relying on past and present data. In such cases, it is suggested to consider heuristics and game-theory-based approaches, or when uncertainty is explicitly included, stochastic, robust, chance-constrained, (stochastic) dynamic programming and (stochastic) fuzzy optimisation approaches are recommended BIB003 . (a) Stochastic optimisation -uncertainties are modelled as random variables and explicitly included in both the objective function and constraints BIB002 - BIB005 , being the optimisation carried out for the expected value of the objective function. If statistic distributions and corresponding parameters are known, a simple approach consists in replacing each random variable with the underlying expected value. In the case of finite uncertainty realisations, the expected value can be determined by computing the objective function value for all possible realisations and taking its expectation. For other cases, an approximation of the set of possible realisations can be computed via Monte Carlo sampling, assuming a stochastic model, or based on field observations BIB002 , BIB001 -  . Finally, in some particular problems, decisions need to be obtained based on a sequential methodology, commonly via two-stage or multi-stage-based stochastic optimisation approaches BIB003 ,  . (b) Robust optimisation -no assumptions regarding the underlying uncertain variables are made, being them modelled them based on intervals of values BIB001 , BIB004 . These methods address uncertainties by considering realisations with stronger (worse) impact on problem solutions. For instance, minimisation of household electricity bill under uncertain non-schedulable demands considers non-controllable demands to be as high as possible. A generic formulation for a robust optimisation problem is as follows  : where is the uncertainty set and χ is the space of decision variables. (c) Chance-constrained optimisation -not as strict as robust alternatives, since optimisation is conducted for the worst-case scenario with a predetermined confidence interval, which is represented by a parameter α: In short, this method ensures that the probability of matching one or more constraints is above a given threshold. Therefore, it restricts the feasible region in order to guarantee a high confidence level on computed solutions. Unlike robust optimisation methods, chance-constraints can use unbounded distributions of uncertainty BIB003 . (d) Stochastic dynamic programming -relies on the estimation of a state-space model, such that for each state a finite set of actions can be taken with a given probability, thus resulting in transitions to other states. This method is applied recursively from the end nodes to the initial node. As a finite set of states must be defined, a rather simplistic and often incorrect model may be obtained. Since a significant number of states may emerge when modelling complex systems, stochastic dynamic programming-based problems can become NP-hard. Nevertheless, some approximations can allow solutions to be achieved in polynomial time BIB003 . (e) Stochastic fuzzy optimisation -consider fuzzy logic theory, such that truth values are in the interval [0, 1]. When dealing with forecasts, uncertainties can be replaced with non-crisp values, which enable HEMSs to make quick decisions that lead to approximate optimal schedules, within a certain level of confidence BIB003 .