The PSO is a stochastic, population-based computer algorithm modelled on swarm intelligence. Swarm intelligence is based on social-psychological principles and provides insights into social behaviour, as well as contributing to engineering applications.
This book presents information on particle swarm optimisation such as using mono-objective and multi-objective particle swarm optimisation for the tuning of process control laws; convergence issues in particle swarm optimisation; study on vehicle routing problems using enhanced particle swarm optimisation and others.
Get BOOK. Particle Swarm Optimization. Author : Andrea E. Particle Swarm Optimization Book Description:. Swarm intelligence is based. Applying Particle Swarm Optimization. Thus, this study emphasizes implementation of various DR strategies that can benefit the utilities and different types of users, such as residential, commercial, and industrial customers with both controllable and uncontrollable loads. The rest of the article is organized as follows: Section 2 elaborates on the dynamic pricing strategies.
Section 3 illustrates the optimization algorithms chosen for solving the dynamic pricing problem followed by the techno-economic analysis of DP strategies in Section 4. Finally, the results obtained are discussed in Section 5. The pricing schemes were used in a combination of optimization algorithms that are addressed in detail in Section 3.
Time-of-Use Pricing The TOU technique is similar to the pricing based on block rates considered for a particular time of day and week when the customers consume electricity. The TOU rates are the fixed electricity prices charged to both residential and small-scale industries. The price of electricity may vary over the day and is updated daily.
Besides, the consumers are allowed to schedule their usage according to their preferences. The proposed scheme has three TOU periods: off-peak, mid-peak, and on-peak periods.
Off-peak is when the energy demand is low, whereas mid-peak occurs when the energy requirement is moderate. In addition, on-peak occurs when there is the maximum energy demand. Consequently, it requires more expensive forms of electricity to be used. In this way, it ensures that the amount paid by the consumers is economically reasonable [21]. The purpose of DR is to schedule the connection time of each shiftable device so that the forecasted load for every user is shifted so that it is as close to the assumed objective consumption curve as possible.
The objective load curve is chosen in such a way that it is inversely proportional to the electricity market prices. The implementation steps of the TOU are depicted in Figure 2. Figure 2. TOU flowchart. Mathematics , 9, 7 of 24 2.
Real-Time Pricing This section focuses on the load scheduling problem, which is framed as an optimal stopping problem. The purpose is to select the most optimal time to start the action to decrease the cost or increase the profit. The RTP is updated periodically, mostly every 30 min.
Each period of one hour in a day is considered as one timeslot. The electricity consumption rate is presumed to be fixed for each timeslot, but it can change across different timeslots, and hence it can be classified as a discrete-time model. Let us assume T to be the duration of the total timeslot in a day, which is typically fixed as one hour. Furthermore, we assume that the duty cycles are less than T.
Thus, when a device starts its operation, during the duty cycle, the price remains fixed. Furthermore, if the timeslot of operation of the device exceeds one hour, the task is broken down into multiple subtasks by the process of task decomposition [34]. Formulation of the RTP Load Scheduling Problem The concept of an optimal stopping rule and its application have been framed as an optimal stopping problem.
The optimal stopping rule OSR depends on whether to maximize the reward or minimize the compensation. In this regard, it is required to select an optimal stopping time t to decrease the generally expected returns. The RTP signals constantly vary in nature, e. The load scheduling problem using RTP [34] is framed in this work by presuming the RTP signal to be an arbitrary variable. This study aimed to reduce the cost of power consumption by considering the timeslot for a day as a variable.
Furthermore, electrical devices are segregated into three segments based on their power consumption, i. The loads that possess low energy consumption and have long duty cycles fall under the category of base loads. These loads encompass lightning, networking devices, and computers.
Regular loads include devices where the power consumption of the particular load is higher than that of base loads. However, their duty cycle is for an extended period as well. For instance, refrigerators, HVAC, and water heaters are included.
The devices whose operation time is constant but add to the peak load form the burst load [35]. For instance, washing machines, dishwashers, and clothes dryers are included. Generally, the peak power period is considered for scheduling; thereby, the scope of this article was also extended to the complete time of device operation. The objective was to reduce the cost of power consumed by the device and the waiting time. The waiting time was modeled as the cost to achieve it.
Thus, the objective function can be estimated using the following formula:! Mathematics , 9, 8 of 24 For practical reasons, the formula considered is simplified as Equation 9. There are two constraints considered in RTP: 3. The device will operate in the timeslot only if the threshold of the device in consideration is lower than the real-time pricing of that hour, i. Power Allocation For each timeslot, it was made sure that enough power was available to operate the device under consideration.
For any appliance, two types of costs were calculated: the cost due to the waiting time and the cost of electricity consumption. This helps in minimizing the mean cost for all the appliances in the long run [36]. The DSA works on the first-come, first-served basis.
Here, each device is made to operate autonomously. The controllable load and the price of electricity at a particular time of operation are the data required for the DSA algorithm. If the timeslot for operating the device is unsatisfactory, the same process must be repeated in the next immediate timeslot until no more devices are scheduled [37].
It can be summarized as follows [38]: 3. Mathematics , 9, 9 of 24 In the CSA, the calculation of the cost equation consists of two segments: the cost of electricity and the postponement cost for each device. Due to the devices getting postponed, additional costs are included as the waiting cost. The cost involved in the delay of each appliance is required for the total time to minimize the total cost.
According to the above algorithm, there is a requirement for the central scheduler to allocate the devices concerning the threshold power setting. Before the central scheduler settles on a choice, all the devices must forward their price limit and power utilization. Peak-to-Average Ratio PAR The ultimate objective of DR is to shift the peak load demand to the non-peak hours and thereby reduce the cost of power consumption without shedding the load.
Optimization Algorithms Optimization algorithms are used in combination with pricing algorithms to obtain cost minimization. PSO and the SBY optimization algorithm were considered based on their effective operation towards getting the global best solution in fewer iterations and ease of handling more controllable loads. The complexity of optimization increases as the controllable loads are increased. Moreover, PSO is employed for ease of implemen- tation, adaptability of control parameters, and as it is widely used for the search for the global best value.
Mathematics , 9, 10 of 24 4. Particle Swarm Optimization PSO PSO is a metaheuristic optimization algorithm that is used to solve a wide range of problems [39—42] with ease of implementation and adaptability of control parameters. It is widely employed in the search for the global best value. To locate the optimal solution of an objective function, PSO generates randomly distributed particles.
These particles travel randomly and reach a convergence point. The inputs given to the optimization problem are swarm size, the total number of iterations, weights, positions, and learning variables. The strawberry plant uses both runners and roots for propagation, search for water resources and minerals. This propagation ideology is used to solve complicated engineering problems.
The algorithm has three differences compared to PSO, namely duplication and elimination of agents at every iteration, all the agents are subjected to both small and large movements from the beginning to the end, and lack of information exchange between agents. The algorithm can very effectively solve even a complicated optimization problem [45]. The SBY optimization algorithm is as follows: 1. Select the number of mother plants e. Set a group for the number of devices. The combination of devices is considered as a variable.
Consider the best pattern after running the permutation for the set of devices in the group; for the best pattern of devices, run the strawberry optimization algorithm. The grouping of controllable devices is considered as the mother plant in this DR problem.
Set the number of mother plants in the search space, as well as the iteration count. Randomly generate two points, the roots and the runners for every mother plant 2N points. The possible allocation of the devices in the group will be obtained as 2N vectors. Evaluate fitness function to be optimized, e. The total of N best solutions from the obtained 2N fitness value is selected. The left-out N values are eliminated. The best N value takes part in the next iteration. Repeat steps 3—5 until the termination condition is satisfied.
System Input Data A sample system with residential, commercial, and industrial loads was considered for the implementation of DR strategies. The devices considered in the system are categorized into controllable and uncontrollable devices.
The list of controllable devices is tabulated in Tables 2—5. The forecasted load areas are shown in Figure 3. Similarly, the total number of devices in the commercial area was , with eight different types of devices. Furthermore, the total number of devices listed in the residential area was , with 14 types of devices. Table 2. Controllable loads present for the industrial area. Hourly pricing and hourly load forecast.
Controllable loads present in the commercial area. Controllable loads present in the residential area. Forecasted industrial, commercial, and residential loads. Figure 4. Mathematics , 9, 13 of 24 5. The optimization problem was executed for 24 h of load data. The combination of devices was considered as the variable for this cost minimization problem.
Thereby, the complexity of this DR problem becomes tangled as the number of variables increases. The hourly costs for the three loads before and after the DR implementation are displayed in Figures 5— According to the cost optimization results for the residential area before and after DSM with TOU-PSO, the cost reduced when the load decreased at the peak periods and was postponed to the off-peak periods.
Figure Figure6. Mathematics , 9, 14 of 24 Figure 6. Figure 6. Figure 7. Figure 8. Figure Figure8. Figure 9. Mathematics , 9, 15 of 24 Figure The cost results for the residential, commercial, and industrial loads were obtained. RTP-DP algorithms proceeded with tentative and power allocation scheduling.
Figures 11—16 display the optimal load curve after the distributed RTP algorithm implementation using PSO and the strawberry optimization technique for the residential, commercial, and industrial areas. Figure Mathematics , 9, 16 of 24 Figure Mathematics , 9, 17 of 24 Figure The optimal load scheduling results for 24 h after implementing the centralized RTP algorithm in the residential, commercial, and industrial areas for the test system deploying PSO optimization are shown in Figures 16— The results indicate that the cost reduction using the centralized RTP algorithm for the residential, commercial, and industrial loads was 2.
Mathematics , 9, 18 of 24 Figure The results of the DSM implemented in the residential, commercial, and industrial areas for the sample system with the SBY optimization algorithm adopting centralized RTP are shown in Figures 20— The results perceived that the cost reduction obtained for the centralized RTP algorithm was 4.
The centralized scheduling algorithm is based on both costs of electricity and postponement costs. Since the cost involved for the delay of each appliance is considered, it minimizes the total cost of energy consumption for a day and gives a better result compared to the distributed algorithm. Thus, the centralized RTP algorithm provides better cost reduction.
The comparison between the centralized and distributed algorithm results is provided in the last section. Mathematics , 9, 19 of 24 Figure Mathematics , 9, 20 of 24 6.
Results and Discussion The comparison of the DSM results with the TOU and RTP pricing using both the centralized and the distributed algorithms for the residential, commercial, and industrial areas are provided in Tables 6—8. The results illustrate that the DR implementation provided a cost reduction of up to This holds for both systems considered. Table 6. Tables 9—11 provide the detailed analysis of the PAR calculation for the residential, com- mercial, and industrial demand.
The PARs of the forecasted residential, commercial, and industrial loads were 1. Table 9. PAR calculation for the residential load.
PAR calculation for the commercial load. PAR calculation for the industrial load. Cost reduction with the implementation of the demand response strategy. Conclusions This work focused on implementing DR strategies that are implemented using two different optimization techniques for the industrial, commercial, and residential loads.
The RTP pricing algorithm was performed using both the distributed and the centralized methodology. Despite complexity of the periodically varying pricing strategy, the results obtained after shifting the load prove that DSM implementation is economical. When the techno-economic analysis was performed to solve the DR problem, the SBY optimization algorithm worked better for all the load scenarios considered.
Moreover, it was found that the SBY optimization technique provided a lower PAR ratio for all the three types of load considered. When the distributed and the centralized RTP algorithms were compared, the centralized algorithm offered better results for the test system. The analysis would motivate the usage of DR in a smart grid environment since these DR algorithms reduce the cost involved in power consumption. Author Contributions: Conceptualization, R.
All authors have read and agreed to the published version of the manuscript. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available upon request from the corresponding author. The data are not publicly available due to their large size. DSR for their technical and financial support. Conflicts of Interest: The authors declare no conflict of interest.
References 1.
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