Scheduling and control of decentralized energy resources, in practice, is a stochastic mathematical problem, given the intermittency of renewable generation, the uncertainty of users’ consumption patterns, and continuously changing electricity prices, which, in most of the reviewed works, is a key driver. Additionally, the large number and diversity of household appliances and the consideration of user thermal comfort and convenience increase the complexity of optimization, where classical computational techniques such as linear programming (LP), integer linear programming (ILP), and mixed-integer linear programming (MILP) cannot provide feasible solutions within a reasonable timeframe [21]. On the contrary, heuristic optimization techniques, such as PSO, genetic algorithms (GA), ant colony optimization (ACO), and wind-driven optimization (WDO), can support more complex optimization problems with the identification of near-optimal solutions.

In this work, PSO-based resource scheduling models are reviewed given the research “gap” identified in Section 1 but also due to the fact that it presents the following advantages over similar nature-inspired optimization techniques [10,19,20,21,22]:

• It requires fewer parameters for tuning and adjustment;
• Easier implementation and less computational effort are usually needed to reach a near-optimal solution compared to other heuristic algorithms;
• The histories of all particles contribute to the search, while in other methods (e.g., GA), the algorithm’s memory capability is lower due to the replacement of the old population with a new, more efficient one.

In the reviewed research works [21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67, 68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84], different models were designed. They can be classified based on the optimization objectives, the system constraints applied, or the energy system applications. In the latter, the type of energy resources (EVs, distributed generation, energy storage, or appliance type), the number of users (single or multiple), and the type of control (local, decentralized, or centralized) are included.

One of the main considerations of scheduling and control for demand-side management is the formulation of the objective function that needs to be optimized. Additionally, it is very important to define the system constraints and operational limits of key variables that will collectively shape the boundaries of the optimization search space. Optimization objectives can be categorized into the following three groups based on the number of objectives that are investigated.

Single objective:

 In the majority of the reviewed works, the main objective was to optimally schedule different energy resources in order to minimize electricity costs, with or without taking into consideration user comfort, convenience, and peak-to-average (PAR) ratio. Depending on the complexity of the problem, the cost minimization function consists of components such as electricity imports (consumption) and exports back to the main grid [24,30,33,35,42,43,59,66,72,81]. In the case of a microgrid (MG), total cost minimization, investment, operation, and maintenance costs are considered. For instance, in [43,66], the optimization goal was to optimally size microgrid components (DG and ES) by shifting the load to the hours of maximum renewable penetration and therefore minimize total system costs. Some of the reviewed works also present different electricity tariffs based on the customer type (residential, commercial, or industrial).

Single objective with aggregated variables, weights, or penalties: In this case, more than one objective is combined and aggregated as a single function. In some works, weights are assigned to each optimization parameter, leading to a weighted single-objective optimization problem. In most cases, minimization of electricity costs, maximization of user convenience (appliance operational delay), and/or thermal comfort are considered, as in [22,26,41,44,45,46,51,61,67,68]. In a few research publications, such as in [46,68,83], three different objectives are weighted to form a single objective function. In other research works, the authors do not specify a weight factor, as in [38,62,64,65,76], but assign penalties to non-economic constraints in order to combine them into an aggregated single-objective function.

Multiple objectives: 

In [27,29,57,60,63,78], where objectives are conflicting, such as cost minimization and user convenience maximization, the Pareto front, meaning a set of non-dominated solutions, is calculated through the evaluation of different fitness functions that correspond to each objective. The Pareto front consists of compromise solutions. Therefore, a second step, in that case, would be the selection of the best solution from the Pareto set. Additionally, in this review work, bi-level optimization problems are characterized as multi-objective ones. In [48,49,53,69], there is a single “upper level” objective and a single “inner level” objective that need to be optimized hierarchically. The single upper-level objective is initially optimized, and then the output of the upper level is used as an input in the inner-level optimization.

Part of the problem formulation in every work reviewed was to define the system constraints that should be considered in the optimization. The number of constraints differs depending on the system complexity and the type of energy resources considered. The main equality constraint, which can be identified in all works reviewed, is to maintain the energy balance between power supply and demand. The time period and the system boundaries (household, microgrid, or utility level) of such constraints depend on the problem formulation. The constraints that are identified in the reviewed works are the following:

• Power grid thresholds (E_grid): The minimum and/or maximum contracted power of end-users with utility at the connection point. This increases the complexity of the optimization and potentially decreases the amount of energy savings that can be achieved since there is less flexibility to shift more loads to off-peak hours due to constraint violation.
• Storage-related constraints (E_storage): Charging and discharging rates as well as the capacity of storage units are introduced as inequality constraints in works with energy storage, either in the form of batteries or in electric vehicles.
• RES generation capacity (E_RES): The maximum generation capacity of renewable sources is constrained, usually as a share of total household demand (e.g., 30% of net demand is met by RES).
• User convenience: Another important consideration is user convenience in the sense of minimizing the operational delay (waiting time) of different household appliances or prioritizing the operation of appliances over others based on consumer preferences. In some works, such as [38], user convenience is introduced as the minimum amount of appliance switching needed during a DR event.
• Thermal comfort: In many works, not only appliance waiting time but also indoor temperature and water heater temperature is considered when using thermostatically controlled loads. To operate appliances within the preferred temperature range, smart sockets and temperature sensors can be installed, as in [23].
• Voltage level: In [38,40,66,76], bus or node voltage constraints are introduced when optimizing the operation of microgrids connected to the main power network.

 

From the taxonomy of research work, based on optimization objectives and system constraints, it is clear that user convenience and thermal comfort are key considerations when trying to schedule and control residential resources. Operating according to user preferences will inevitably lead to higher electricity costs and vice versa. However, significant energy savings can still be obtained. In [23], using binary PSO (BPSO), 20–25% energy savings were achieved without jeopardizing user convenience. DR services were provided only in a specific timeframe (4–11 p.m.) in a geographical location with a lack of seasonality, so it would be worth testing the system under more challenging conditions. In [22,26,41,44,45,46,51,61,67,68], user convenience and energy savings were combined in the objective function, leading to a weighted single-objective optimization problem. User convenience was modeled with the use of allowed time periods when appliance operation should be completed. More specifically, in [22,26], GA and BPSO were compared, among others, where GA outperformed BPSO in terms of both electricity costs and energy consumption. In [28,32], the tradeoff between user convenience (appliance waiting time) and energy cost was investigated. PSO has the tendency to heavily shift loads from peak to off-peak hours with lower electricity tariffs in order to decrease electricity costs. However, a greater degree of user convenience is sacrificed in that case. Therefore, it can be concluded that the higher the electricity cost, the less the user discomfort, and vice versa in DR residential applications. While in [28], the single objective was to decrease consumer electricity costs, in [32], a single-objective function was formulated with the aim of minimizing energy costs and average-to-peak ratio. The feasible region of solutions was found, and boundaries were set for the objective function. In [30,33,34,55,59,79,80,81], reducing electricity bills while considering user convenience and thermal comfort was analyzed. The authors concluded that overall costs can be decreased without sacrificing user comfort by setting the indoor temperature at a higher level during low-tariff hours.

Each DSM model is characterized by the energy resources that can contribute to demand-side management, the number of users (single or multiple), and the control level (local, microgrid, or utility/aggregator). This review work focuses on residential users. The taxonomy of research works based on the application is illustrated in Figure 1.

Scheduling and control of household appliances is the core focus in the majority of research works. Depending on the flexibility that these appliances can offer for demand-side management, they can be categorized as fixed, shiftable, elastic or interruptible, and power-adjustable. Fixed appliances are characterized by fixed power consumption and a length of operation that cannot be modified. Examples include lights, fans, clothing irons, microwave ovens, toasters, TVs, etc. The operation of shiftable appliances, such as washing machines, dishwashers, and clothes dryers, can be shifted in time but cannot be interrupted while their power consumption is fixed and inelastic. Elastic or interruptible household appliances, such as EVs, can not only be shifted in time but also be interrupted while in operation. This group of appliances can offer flexibility services by shifting their operation in periods of lower electricity tariffs. Last but not least, power-adjustable appliances are interruptible appliances with adjustable power consumption. The majority of these are thermostatically controlled loads (e.g., electric water heaters, ACs, or heat pumps). In research, the above categorization might differ based on the authors’ problem formulation. For instance, EVs can be treated as a shiftable but non-interruptible load in some works, while lights can be considered controllable when using a smart plug. In any case, when using interruptible and power-adjustable appliances for flexibility provision, it is important to ensure that user convenience and thermal comfort are not sacrificed when trying to schedule and control them for demand-side management.

In addition to residential appliances, decentralized energy resources such as EVs, distributed generation (mostly RES), and energy storage can contribute to domestic electricity bill reduction, load balance, and peak shaving. Additionally, a better tradeoff between user comfort and electricity cost reduction can be achieved, given that each household can utilize local or decentralized (microgrid) energy resources instead of consuming from the power grid. For instance, in [28], interruptible loads, including those of an EV and an electric water heater, contributed to achieving a better compromise between user convenience and energy costs. Although EVs are commonly treated as a highly flexible load, their battery-related constraints, such as the charging and discharging rate and maximum energy storage, can set limitations on its storage operation for demand-side management. It can also be observed that renewable power generation is often coupled with local energy storage, which aims at complementing the intermittency of renewable energy resources.

In addition to the objective function formulation and the constraints introduced for load scheduling, an important parameter is the type of DR program/mechanism that consumers are enrolled in. Time-of-use (ToU) retail tariffs have been extensively used in research, with prices usually ranging among high-, medium-, and low-price periods during the day. In some of the works where ToU is selected, it is highlighted that load is heavily shifted to off-peak hours. Therefore, the load tends to become unbalanced, with spikes occurring after these hours, and the peak-to-average ratio (PAR) remains high. A similar phenomenon can also be spotted when using day-ahead, real-time pricing (RTP) tariffs, which typically fluctuate on an hourly basis. For that reason, tariffs with inclined block rates (IBRs) were used in [22,32,39,44,48,51,84]. In this pricing scheme, when the load surpasses a certain level, a monetary penalty is added to the end-user’s electricity bill. In this way, load shifting from peak to off-peak hours is rather limited, PAR decreases, and load spikes are avoided.

In Table 1, the reviewed works are classified based on the optimization objectives for residential load scheduling and control, together with modeling constraints. Table 2 presents the taxonomy of research work based on model applications, including DR programs.