Particle Swarm Optimization in Residential Demand-Side Management: A Review on Scheduling and Control Algorithms for Demand Response Provision
Abstract
:1. Introduction
- Economic benefits:
- ◦
- DR can lead to dispatching fewer hours of uneconomical generation units when the power system becomes tight, i.e., when generation cannot meet demand or when the security of supply margins decreases;
- ◦
- End-users profit by either consuming in low-tariff hours, selling power back to the grid with the use of local storage, or other incentives (e.g., bill discount);
- ◦
- DR can decrease distribution network stress and therefore reduce the need for network investments.
- Power system operation:
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- System reliability increases when providing frequency response, contingency reserves, and flexibility services;
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- Renewable energy source (RES) curtailment is reduced by modifying demand to match green power generation.
- Reduction in greenhouse gas emissions:
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- Utilization of distributed resources (EVs, PVs, and local storage) is higher;
- ◦
- Energy efficiency is higher, and thus, energy consumption decreases.
- AI group:Some review papers classify demand response applications and investigate only a single group of AI methods. Other papers analyze more than one group of AI methods and thus provide a more holistic review of the state-of-the-art from a computational intelligence (CI) perspective.
- Energy sub-systems:This set of attributes refers to the different energy sub-systems reviewed in the literature for scheduling and control in DR applications. Distributed generation, heating/cooling devices, EVs, local energy storage, and residential appliances are the different areas considered in this category.
- Energy management system (EMS) scheduling and control:Load modeling, scheduling, and control methods in response to signals for DR are reviewed. Additionally, the classification of methods based on demand-side strategies is considered.
- Optimization objectives:AI algorithms in demand response can be used for various optimization objectives, such as the minimization of energy consumption with or without considering user comfort, the minimization of energy cost, and the provision of load balancing.
- Text found in title, abstract, or keyword: “demand AND response” OR “demand AND side AND management”;
- Text found in title, abstract, or keyword: “particle AND swarm”;
- Text found in title, abstract, or keyword: “residential OR household OR home”;
- Text found in title, abstract, or keyword: “controller OR scheduling OR control”.
- This is the only review paper that classifies PSO methods used specifically for scheduling and control based on the type of the residential energy sub-system (EVs, heating/cooling devices, local storage, residential appliances, and DG);
- It identifies different optimization objectives when using PSO methods, taking into consideration user convenience (in the form of appliances’ operational time delay) but also user thermal comfort (indoor ambient and hot water temperature);
- It discusses the limitations and challenges of PSO methods and models in residential demand response management systems and suggests potential future research areas for investigation.
2. Basic Principles of PSO
- Record the individual best location found so far with the help of a fitness function that evaluates how close each particle is to the optimal solution;
- Record their current direction and intensity of movement (velocity);
- Be informed about which location is the global best, defined as the optimal location among all particles.
- The inertia component w Vi(t): this term tends to maintain the current movement direction (velocity) of each particle;
- The cognitive/individual component : this component describes the distance between each particle’s current position and the individual best location found;
- The social component : this component calculates the distance between the particle’s current position and the best position found by the entire swarm.
- Simple and easy to use;
- Fast convergence and robustness, even in complex and highly constrained multi-dimensional search spaces;
- High applicability since it can be used in various optimization problems;
- High adjustability since it can be easily hybridized and modified to fit the purpose of each problem and improve its performance.
- Risk of suboptimal solutions (local optima) due to either the problem formulation characteristics or a lack of diversity in particle movement that leads to premature convergence;
- No guarantee that PSO will reach the global optimum solution since there is a risk of premature convergence to local optima;
- Lack of interpretability/explainability given that the algorithm is not based on a strong mathematical theoretical basis (lack of mathematical proof of convergence).
3. Models for Residential Load Scheduling and Control Using PSO
- 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.
3.1. Optimization Objectives
- 1.
- Single objective:
- 2.
- Single objective with aggregated variables, weights, or penalties:
- 3.
- Multiple objectives:
3.2. Constraints
3.2.1. System Constraints
- Power grid thresholds (Egrid):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 (Estorage):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 (ERES):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:
3.2.2. Electricity Costs and User Convenience/Comfort
3.3. Applications
3.3.1. Energy Systems
3.3.2. DR Programs—Electricity Tariffs
3.4. Taxonomies
4. PSO Methods
- Hybrid methods:
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- ◦
- PSO–ANN [37];
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- BPSO–integer linear programming [55];
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- PSO–evolutionary algorithm [58];
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- PSO–sequential quadratic programming optimizer (SQP) [59];
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- PSO–local vortex search [62];
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- PSO–bacterial foraging (BF) [63];
- ◦
- PSO–fuzzy logic [71];
- ◦
- PSO–sinusoidal and cosine acceleration (SCAC) [75];
- ◦
- BSPO–chaos optimization [76];
- ◦
- PSO–harmony search (HS) [77];
- ◦
- BPSO–gradient-based NLP solver [79];
- ◦
- BPSO–fuzzy Mamdani and fuzzy Sugeno [80].
- Quadratic BPSO [41];
- Cooperative PSO:
5. Evaluation
5.1. Problem Design
- System architecture—HEMS design. As the first step, it is important to define the energy system resources and the way that they are connected with other users and the main power grid. It is also useful to describe the flow of data information and the point of control where scheduling will take place: local control, decentralized control of grid-connected or standalone microgrids, or centralized control on a utility/aggregator level.
- Appliance classification and user categorization. Residential household appliances can be characterized as fixed, flexible, interruptible, and power-adjustable. In a microgrid, users can be passive (unidirectional power flow without self-consumption), semi-active (unidirectional power flow with self-consumption and storage), or active (bidirectional power flow with self-consumption and storage).
- Energy consumption. Equality constraints that ensure load balance at each time interval are introduced. In some works, a maximum and/or minimum grid consumption constraint is defined so that load shift to off-peak hours will not lead to demand spikes. Additionally, grid exchange capabilities (selling back to the grid) might increase the problem complexity even further but provide a more realistic modeling approach.
- Local RES generation and energy storage. In some works, local RES generation with coupled energy storage is considered. A set of constraints (charge/discharge rates and maximum energy stored) is essential to properly model local energy storage. Depending on the problem design, either RES production follows a predefined profile or a RES forecasting model is utilized.
- DR program and electricity tariffs. The DR program that each user follows is a crucial feature of the problem design, since in the majority of problems, cost minimization is the main objective. In research, inclined block rates (IBRs) can ensure a smoother load shift from peak to off-peak hours.
- Other considerations. PAR can be introduced as a minimization objective or can be investigated when modeling results are obtained. In other works, a set of constraints is introduced to ensure that model results respect users’ thermal comfort and convenience preferences (appliance operational delay).
- Objectives. The most common objective, as shown in Section 3, is electricity cost minimization. User convenience, thermal comfort, PAR, and emission reduction can also be considered as optimization objectives.
5.2. Complexity
- High complexity. The problems in [22,28,29,32,46,49,51,57,61,62,66,68,74,78,79,80,81] can be characterized as highly complex, since they have a complex energy system architecture (high number of users); they consider many energy resources, including interruptible and power-adjustable household appliances; they are heavily constrained; and in most cases, the optimization functions involve multiple objectives.
- Moderate complexity. The problems in [21,24,26,27,30,31,33,34,37,38,39,40,41,42,44,45,48,53,54,55,56,59,60,63,64,69,72,75,76,77,82,83,84] show moderate complexity either due to a single objective combined with a large number of constraints and energy resources or due to a combination of more objectives with fewer resources and constraints applied.
- Lower complexity. The problems in [23,25,35,36,43,47,50,52,58,65,67,70,71,73] present lower complexity compared to the research works mentioned above. The smaller number of system constraints, the simpler energy system architecture (small number of users), the lack of power-adjustable and/or interruptible appliances, and the single-objective optimization are the main reasons for this categorization.
5.3. Accuracy
6. Future Research
6.1. Advanced and Explainable Methods
6.2. Consideration of Uncertainties
6.3. End-Users as Price Makers
6.4. Fully Utilize EV Potential
6.5. Energy Model Scalability
6.6. Comprehensive Metrics for DSM Evaluation
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
AC | Air conditioning |
ACO | Ant colony optimization |
AI | Artificial intelligence |
ANN | Artificial neural network |
BBSA | Binary backtracking search algorithm |
BFOA | Bacterial foraging optimization algorithm |
BPSO | Binary particle swarm optimization |
CI | Computational intelligence |
CBPSO | Chaotic binary particle swarm optimization |
CLPSO | Comprehensive learning particle swarm optimization |
CPSO-R | Cooperative particle swarm optimization with stochastic repulsion |
CPSO-SARD | Cooperative particle swarm optimization with stochastic attraction–repulsion of diversity |
DG | Distributed generation |
DLC | Direct load control |
DNO | Distribution network operator |
DR | Demand response |
DSM | Demand-side management |
EV | Electric vehicle |
ES | Energy storage |
GA | Genetic algorithm |
HVAC | Heating, ventilation, and air conditioning |
IBR | Inclined block rates |
ILP | Integer linear programming |
LP | Linear programming |
LS | Local search |
MG | Microgrid |
ML | Machine learning |
MILP | Mixed-integer linear programming |
PAR | Peak-to-average ratio |
PSO | Particle swarm optimization |
PV | Photovoltaic |
RES | Renewable energy resources |
RL | Reinforcement learning |
RTP | Real-time pricing |
SRPSO | Self-regulated particle swarm optimization |
ToU | Time of use |
UPSO | Unified particle swarm optimization |
V2G | Vehicle-to-grid |
WDO | Wind-driven optimization |
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Ref. | AI Group | Energy Sub-Systems | Scheduling and Control | Optimization Objectives | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
PSO | Other Single | Multiple | Heating/Cooling Devices | EVs | DG | Local Energy Storage | Residential Appliances | Energy Consumption and User Comfort | Load Balancing | Energy Cost | ||
[7] | √ | √ | √ | √ | √ | |||||||
[8] | √ | √ | √ | √ | √ | √ | √ | |||||
[10] | √ | √ | √ | √ | √ | √ | √ | √ | √ | |||
[11] | √ | √ | √ | √ | √ | √ | √ | √ | ||||
[12] | √ | √ | √ | √ | √ | √ | √ | |||||
[13] | √ | √ | √ | √ | √ | |||||||
[14] | √ | √ | √ | √ | √ | √ | ||||||
[15] | √ | √ | √ | √ | √ | √ | √ | |||||
This paper | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ |
Refs | Type of Constraints | Objective Type | Objectives |
---|---|---|---|
[21] | Egrid + Estorage + User Convenience | Single | Electricity cost minimization |
[22] | Egrid + Estorage + ERES + User Convenience | Single with weights | Electricity cost minimization + user convenience maximization |
[23] | Thermal Comfort | Single | Energy consumption minimization |
[24] | Estorage | Single | Electricity cost minimization |
[25,56] | Estorage + User Convenience | Single | Electricity cost minimization |
[26,44,67] | User Convenience | Single with weights | Electricity cost minimization + user convenience maximization |
[27] | ERES | Multiple (Pareto) | Electricity cost minimization, distributing load across two energy sources (wind + solar) with different fitness functions |
[28] | ERES + User Convenience | Single | Electricity cost minimization |
[29] | Egrid + Estorage + ERES | Multiple (Pareto) | Electricity cost minimization + Environmental cost (emissions) minimization |
[30,33] | Egrid + Estorage + Thermal Comfort + User Convenience | Single | Electricity cost minimization |
[31] | Egrid + ERES | Single | Electricity cost minimization |
[32] | Egrid + Estorage + User Convenience | Single (aggregated objectives) | Electricity cost minimization + PAR minimization |
[34] | Egrid + Estorage + ERES + Thermal Comfort + User Convenience | Single | Electricity cost minimization |
[35] | Egrid + Estorage | Single | Electricity cost minimization |
[36] | Egrid + ERES | Single | Consumer profit maximization |
[37] | Thermal Comfort + User Convenience | Single | Energy consumption minimization |
[38] | Voltage levels + User Convenience | Single with penalties | Electricity cost minimization + power loss cost minimization + constraints (penalties) |
[39] | Estorage + User Convenience | Single (aggregated objectives) | Electricity cost minimization + PAR minimization |
[40] | Egrid + Estorage + ERES + Voltage levels | Single | Distribution power loss minimization |
[41] | User Convenience | Single with weights | Electricity cost minimization + discomfort index minimization |
[42] | Egrid + Estorage | Single | Utility electricity cost minimization (DA, imbalance costs, and battery cycling cost) |
[43] | Estorage | Single | Total system cost minimization (incl. investments) to optimize minigrid components |
[45] | Egrid + User Convenience | Single with weights | Electricity cost minimization + user convenience maximization |
[46] | Egrid + Estorage + Thermal Comfort + User Convenience | Single with weights | Electricity cost minimization + user convenience maximization + grid load variance minimization (peak caused by DR actions) |
[47] | Estorage + Thermal Comfort | Single | Consumer profit maximization |
[48] | User Convenience | Multiple (bi-level) | Consumer profit maximization, after scheduling manually operated appliances with the worst impact on electricity payments |
[49] | Egrid + User Convenience | Multiple (bi-level) | Retailer profit maximization, after consumer electricity cost minimization |
[50,82] | - | Single | Electricity cost minimization |
[51] | Estorage + User Convenience | Single with weights | Electricity cost minimization + user convenience maximization |
[52] | Egrid + User Convenience | Single | Electricity cost minimization |
[53] | Estorage | Multiple (bi-level) | System cost minimization (NPC) + power shortage minimization |
[54] | Egrid + User Convenience | Single (aggregated objectives) | Electricity cost minimization + PAR minimization + user convenience maximization |
[55] | Egrid + Thermal Comfort + User Convenience | Single | Electricity cost minimization |
[57] | Estorage + ERES | Multiple (Pareto) | Electricity cost minimization + environmental cost/emission minimization |
[58] | Estorage + Thermal Comfort | Single | Flexibility potential estimation |
[59,81] | Estorage + Thermal Comfort + User Convenience | Single | Electricity cost minimization |
[60] | User Convenience | Multiple (Pareto) | Electricity cost minimization + load deviation minimization + user convenience maximization |
[61] | Estorage + Thermal Comfort + User Convenience | Single with weights | Electricity cost minimization (incl. battery degradation costs) + user comfort (incl. thermal and convenience) |
[62] | Egrid + Estorage | Single with penalties | Electricity cost minimization + DR curtailment minimization + Pmax violation (penalty) |
[63] | Egrid + User Convenience | Multiple (Pareto) | Electricity cost minimization + PAR minimization + CO2 minimization |
[64] | Estorage + Thermal Comfort | Single with penalties | Electricity cost minimization + User comfort (penalties) |
[65] | User Convenience | Single with penalties | Utility electricity cost minimization for DR + consumer load interruptions (penalties) |
[66] | Egrid + Voltage levels + Estorage + User Convenience | Single | Total system cost minimization |
[68] | Estorage + User Convenience | Single with weights | Electricity cost minimization + user convenience maximization + CO2 minimization |
[69] | Egrid | Multiple (bi-level) | DNO operational cost minimization after MG operational cost minimization |
[70,73] | User Convenience | Single | Electricity cost minimization |
[71] | Thermal Comfort | Single | Electricity cost minimization |
[72] | Estorage + Thermal Comfort + User Convenience | Single | User comfort maximization |
[74] | Egrid + Estorage + ERES + Thermal Comfort + User Convenience | Single (aggregated objectives) | Electricity cost minimization + PAR minimization + user convenience maximization + CO2 minimization |
[75] | Egrid + User Convenience | Single with weights | Load deviation minimization + MG profit maximization |
[76] | Egrid + Voltage levels + Estorage | Single with penalties | Total system cost minimization + network loss minimization + constraints (penalty) |
[77] | Egrid + Estorage + Thermal Comfort | Single | Electricity cost minimization |
[78] | Egrid + Estorage + Thermal Comfort | Multiple (Pareto) | System cost minimization + Environmental cost minimization |
[79] | Egrid + Estorage + Thermal Comfort + User Convenience | Single | Energy bill (electricity and gas) minimization |
[80] | Thermal Comfort + User Convenience | Single | Electricity cost minimization |
[83] | Estorage + ERES | Single with weights | Total system cost minimization + CO2 minimization + curtailed RES minimization |
[84] | User Convenience | Single | Electricity cost minimization (per appliance cluster) |
Ref. | No. Users | Control Level | Electricity Tariffs | Energy Resources |
---|---|---|---|---|
[21,25,35] | Single | Local—Household | ToU | DG + energy storage + household appliances (excl. heating/cooling) |
[22] | Multiple | Local—Household | ToU + IBR | Heating/cooling + DG + energy storage + Household appliances (excl. heating/cooling) |
[23] | Single | Local—Household | DLC | Heating/cooling + household appliances (excl. heating/cooling) |
[24] | Multiple | Decentralized—Microgrid | RTP | DG + energy storage |
[26] | Multiple | Local—Household | RTP | Heating/cooling + household appliances (excl. heating/cooling) |
[27] | Single | Local—Household | - | Heating/cooling + DG + household appliances (excl. heating/cooling) |
[28] | Single | Local—Household | ToU | Heating/cooling + EV + DG + energy storage + Household appliances (excl. heating/cooling) |
[29,57] | Multiple | Decentralized—Microgrid | Price-offer packages (incentive-based) | DG + energy storage |
[30,72] | Single | Local—Household | RTP | Heating/cooling + DG + energy storage + household appliances (excl. heating/cooling) |
[31] | Single | Local—Household | ToU | EV + DG + energy storage + household appliances (excl. heating/cooling) |
[32] | Multiple | Local—Household + Decentralized—Microgrid | RTP + IBR | Heating/cooling + DG + energy storage + household appliances (excl. heating/cooling) |
[33] | Single | Local—Household | ToU | Heating/cooling + EV + DG + Household appliances (excl. Heating/cooling) |
[34,59,79] | Single | Local—Household | RTP | Heating/cooling + energy storage + household appliances (excl. heating/cooling) |
[36] | Multiple | Decentralized—Microgrid | Dynamic pricing based on RES generation | DG |
[37] | Single | Local—Household | - | Heating/cooling + household appliances (excl. heating/cooling) |
[38] | Multiple | Centralized— Utility or Aggregator | Consumer bidding prices | Power transformers + EV + household appliances (excl. heating/cooling) |
[39,51] | Single | Local—Household | RTP + IBR | Heating/cooling + DG + energy storage + Household appliances (excl. heating/cooling) |
[40] | Multiple | Centralized— Utility or Aggregator | - | Power transformers + DG + energy storage |
[41,54,60,71] | Single | Local—Household | ToU | Heating/cooling + household appliances (excl. heating/cooling) |
[41,54,55,60,73] | Single | Local—Household | RTP | Heating/cooling + household appliances (excl. heating/cooling) |
[42] | Multiple | Decentralized—Microgrid | - | Heating/cooling + DG + energy storage |
[43] | Multiple | Decentralized— Standalone Microgrid | - | EV + DG + energy storage + Household appliances (excl. heating/cooling) |
[44] | Single | Local—Household | RTP + IBR | Heating/cooling + DG + household appliances (excl. heating/cooling) |
[45] | Multiple | Local—Household | CPP, RTP | Household appliances (excl. heating/cooling) |
[46] | Multiple | Decentralized—Microgrid | RTP | Heating/cooling + household appliances (excl. heating/cooling) |
[47] | Single | Local—Household | ToU, CPP | Heating/cooling + EV + DG |
[48] | Single | Local—Household | RTP + IBR | heating/cooling + household appliances (excl. heating/cooling) |
[49] | Multiple | Decentralized—Microgrid | RTP | Heating/cooling + EV + household appliances (excl. heating/cooling) |
[50,63,82] | Multiple | Centralized— Utility or Aggregator | RTP | Household appliances (excl. heating/cooling) |
[51] | Single | Local—Household | ToU, CPP, RTP + IBR | Heating/cooling + DG + energy storage + household appliances (excl. heating/cooling) |
[52] | Single | Local—Household | RTP | Household appliances (excl. heating/cooling) |
[53] | Multiple | Decentralized— Standalone Microgrid | - | heating/cooling + DG + energy storage + household appliances (excl. heating/cooling) |
[56,61,74] | Single | Local—Household | RTP | Heating/cooling + EV + DG + energy storage + household appliances (excl. heating/cooling) |
[58] | Single | Local—Household | - | Heating/cooling + DG + energy storage |
[62] | Multiple | Centralized— Utility or Aggregator | ToU | Heating/cooling + DG + energy storage + household appliances (excl. heating/cooling) |
[63] | Multiple | Centralized— Utility or Aggregator | ToU, CPP, RTP | Household appliances (excl. heating/cooling) |
[64] | Multiple | Local—Household | RTP | Heating/cooling + EV + energy storage |
[65] | Multiple | Centralized— Utility or Aggregator | Load curtailment (incentive-based) | Household appliances (excl. heating/cooling) |
[66] | Multiple | Centralized— Utility or Aggregator | Trip-reducing and trip-shifting schemes (incentive-based) | Power transformers + EV + DG |
[67] | Single | Local—Household | RTP, ToU, load curtailment (incentive-based) | Heating/cooling + EV + household appliances (excl. heating/cooling) |
[68] | Single | Local—Household | RTP | Heating/cooling + EV + DG + household appliances (excl. heating/cooling) |
[69] | Multiple | Decentralized-—Microgrid | RTP | DG |
[70] | Single | Local—Household | ToU | Household appliances (excl. heating/cooling) |
[75] | Multiple | Decentralized—Microgrid | - | DG + Household appliances (excl. heating/cooling) |
[76] | Multiple | Decentralized—Microgrid | - | DG + energy storage + household appliances (excl. heating/cooling) |
[67,77] | Single | Local—Household | ToU | Heating/cooling + EV + household appliances (excl. heating/cooling) |
[78] | Single | Decentralized—Microgrid | RTP | Heating/cooling + DG + energy storage + household appliances (excl. heating/cooling) |
[80] | Multiple | Local—Household | RTP | Heating/cooling + DG + household appliances (excl. heating/cooling) |
[81] | Multiple | Decentralized—Microgrid | RTP | Heating/cooling + EV + DG + energy storage + household appliances (excl. heating/cooling) |
[82] | Multiple | Centralized— Utility or Aggregator | RTP | Household appliances (excl. heating/cooling) |
[83] | Multiple | Decentralized— Standalone Microgrid | - | DG + energy storage + household appliances (excl. heating/cooling) |
[84] | Multiple | Decentralized—Microgrid | RTP + IBR | Household appliances (excl. heating/cooling) |
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Menos-Aikateriniadis, C.; Lamprinos, I.; Georgilakis, P.S. Particle Swarm Optimization in Residential Demand-Side Management: A Review on Scheduling and Control Algorithms for Demand Response Provision. Energies 2022, 15, 2211. https://doi.org/10.3390/en15062211
Menos-Aikateriniadis C, Lamprinos I, Georgilakis PS. Particle Swarm Optimization in Residential Demand-Side Management: A Review on Scheduling and Control Algorithms for Demand Response Provision. Energies. 2022; 15(6):2211. https://doi.org/10.3390/en15062211
Chicago/Turabian StyleMenos-Aikateriniadis, Christoforos, Ilias Lamprinos, and Pavlos S. Georgilakis. 2022. "Particle Swarm Optimization in Residential Demand-Side Management: A Review on Scheduling and Control Algorithms for Demand Response Provision" Energies 15, no. 6: 2211. https://doi.org/10.3390/en15062211