In this paper, the installation of energy storage systems (EES) and their role in grid peak load shaving in two echelons, their distribution and generation are investigated. First, the optimal placement and capacity of the energy storage is taken into consideration, then, the charge-discharge strategy for this equipment is determined. Here, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are used to calculate the minimum and maximum load in the network with the presence of energy storage systems. The energy storage systems were utilized in a distribution system with the aid of a peak load shaving approach. Ultimately, the battery charge-discharge is managed at any time during the day, considering the load consumption at each hour. The results depict that the load curve reached a constant state by managing charge-discharge with no significant changes. This shows the significance of such matters in terms of economy and technicality.

The Use of a smart grid improves the accessibility to electricity, especially during peak load hours. In other words, using such a grid helps control the amount of load inflicted on the grid and reduces the possibility of power outage in different parts of the grid by preventing customers’ electricity over-use during peak hours. In addition, the quality of supplied electricity to the customers improves [

With the help of information and communication infrastructure, the smart grid can help us achieve our goals. While generating required electricity during peak load hours is one of the most important concerns of electric companies, peak load management is one of the major problems in power generation and distribution. Numerous objectives have been presented and investigated for smart grids; just like any other state-of-the-art technology [

Numerous studies have been conducted in recent years in the field of energy storage systems by the introduction of smart grids and unsteady electric prices during different times of the day and the use of distributed generation resources. In this section, previous literature regarding this field is reviewed. In [

The extensive use of energy storage systems is one of the objectives of electricity smart grids. In [

Reference [

Determining the strategy to optimize the performance of energy storage systems is one of the problems associated with the exploitation of these systems. In [

Flattening the load curve is one of the objectives of use management/control. In this paper, the use of storage is investigated aiming at reducing peak load and flattening the load curve. Considering that gas power plants are utilized in peak load conditions, this paper suggests a substitute solution, namely the energy storage, for these types of power plants. Next, a dynamic programming model is utilized in order to determine the optimal capacity and programming of storage, aiming at reducing the fuel costs of power plants. The unsteady nature of renewable energy resources causes troubles in power grids. Therefore, these types of resources are utilized alongside the energy storage. An economic method for determining the optimal storage capacity is proposed inside the micro-grid. The studies are conducted in two modes, including islanded mode and grid-connected mode. The solver is inspired by integer linear optimization (programming). The results depict that the profit achieved by the micro-grid has increased after installing the storage.

In this paper, the objective is the reduction of peak load by the installation and optimal placement of the energy storage inside the grid and managing the charge-recharge of storage resources. Hence, particle swarm optimization is utilized in order to find the location and capacity of storage resources. Next, a practical and well-rounded program is proposed in order to optimally exploit the storage at different times during the day. In Section 2, an explanation is given concerning objective function and constraints. In Section 3, swarm optimization is explained briefly. In Section 4, the results of simulations are presented and compared with simulation results achieved by previous literature. Ultimately, a summary of results and conclusion are presented in Section 5.

Energy storage systems are among the existing technologies considered in creating and developing electricity smart grids. Hence, energy resources can be utilized as one of the impressive strategies for peak load shaving in the grid. The energy storage is one of leading load management methods in power grids. In this method, power plants always generate energy in an optimal condition of their performance and they are not required to follow the load curve. In the case of surplus energy in the grid, this energy is stored in the storage elements and then, supplied back to the grid during peak hours. In other words, storage is the realization of how the load is transferred in the power grid.

Power consumption varies at different times of the day. Considering the unsteady price of electricity at different times of the day, the storage is supplied energy during off-peak hours (low electricity price). Considering the difference between electricity prices for peak hours and off-peak hours, this matter will increase in the grid profit. Taking the above process into consideration, the ratio of loss reduction during peak hours is more than loss increment during low-peak hours. Moreover, installing storage will bear a number of costs. In this paper, the objective is to maximize profit achieved by storage installation. Cost and profit functions are given as follows for one day:

The investment costs of the storage include two types of costs, namely (1) power electronic equipment costs and (2) storage unit costs.

The annual cost includes annual investment cost, annual replacement cost, and annual maintenance cost. Annual maintenance cost sis calculated as follows [

Balancing cost is as follows:

The annual investment cost can be written as follows:

The number of terms in the above equation equals the number of times the battery is replaced during the life span of the collection. R is period of replacement:

As a result, investment cost per day is as follows [

Storage acquires energy from the grid during off-peak hours. This cost equals:

As mentioned above, storage acquires energy from the grid during off-peak hours. As a result, the loss increased during these hours. As a result, the cost of such event equals:

During peak hours, storage supplies energy to the grid. Hence, the profit gained by energy sales equals [

Particle swarm optimization (PSO), better known as bird swarm algorithm (BSA), is a state-of-the-art heuristic technique that is inspired by the behavior of birds’ flock in nature. PSO is a powerful stochastic optimization algorithm that is inspired by flock movement and intelligence. In

This algorithm utilized social interaction for problem solving and was developed by James Kennedy (social physiologist) and Russell Eberhart (electronic engineer). They used a number of particles forming a group and these particles are moving inside the search space to find the best solution.

A particle is considered a point inside the N-dimensional space that regulates its levitation according to its own and other particles’ levitation experience. Each particle follows its coordinates inside the solution space that is associated with the best solutions achieved by that particle so far. This value is named best person (P_{best}). There is another value for the neighbor particle that is followed by the algorithm. This value is named best global (G_{best}). In other words, it is considered the best global experience.

The main concept of PSO is the acceleration of each particle toward their P_{best} and G_{best} locations that is executed randomly each time with an accelerator, as shown in _{pbest} is the velocity based on Pbest, S^{k+1} is the search or modified point, _{gbest} is the velocity based on G_{best}.

As mentioned earlier, PSO mimics the movement of birds’ flocks. Think about the following scenario:

A group (flock) of birds are searching for food in an area in a random manner and there is only one portion of food inside the searched area. None of the birds knows the location of food but they know the distance from the food at each stage. Therefore, this problem is about finding the best strategy to find food. An effective method is to follow the birds that are closer to the food. By following such a scenario, PSO is utilized to solve the optimization problems. In PSO, each unit is considered to be similar to the one bird in the search space, which is called a particle as mentioned earlier. Two parameters are defined for all particles as follows.

The best response (fitness) is assessed and optimized with the aid of a fitness function.

Velocities in the same direction as particles levitation inside the problem space by following currently optimized particles.

PSO starts with a group of random particles and then, is updated with two optimal quantities. The first one is the best solution (fitness) that is found so far. This quantity is stored and named P_{best}. The other quantity is the best global and is named G_{best}. When a particle considers a part of the population as the location vicinities, the best quantity is transformed to the best location and named P_{best}. After finding the best two quantities, the velocity and location of the particle are updated.

Each particle tries to modify its location with the following data: current position, current velocities, the distance between the current position and P_{best}, and the distance between the current position and G_{best}. They can be modeled with the aid of the following equation mathematically:

rand: generates a random and uniform number that is distributed between 0 and 1.

P_{best} is the best location for agent i, and G_{best} is the best location experienced by the swarm.

c_{1} and c_{2} are personal and collective (swarm) cognitive coefficients and their values vary between 0 and 2. However, these values are usually considered two. An increase in c_{1} and c_{2} values causes the particle to move toward personal best and converge toward the swarm’s best experience. The algorithm process is given as follows:

Creating the initial population (swarm) and assessing it

Determining the best personal memories and collective memories

Updating to new velocities and positions, and evaluating the new responses

Starting from stage 2 if the termination condition is not achieved.

End

Particles’ velocity in each dimension achieves a maximum velocity V_{max}. If the total acceleration causes the velocity to exceed V_{max}, the velocity of that dimension will be limited to V_{max} and the user determines this parameter. In

In this section, the proposed model to determine the capacity and location of storage and the charge-discharge program of these resources within the system are studied. Using particle swarm optimization, the location, capacity, and storage exploitation are investigated. Such an algorithm enjoys high accuracy. PSO parameters are presented in

Population | Iteration | C_{1} = C_{2} |
w | V_{min} |
V_{max} |
---|---|---|---|---|---|

100 | 50 | 2 | 0.7 | 0.4 | 0.9 |

The grid under investigation includes a standard 33-bus distribution system. In

In

In the grid under investigation, three distributed generation resources are taken into consideration. These three resources are considered in bus #6, bus #16, and bus #25 respectively, with the following capacities: 2.4878, 0.3556, and 0.7291 MW [

The amount of power generated from solar panels and wind turbines depends on the radiation and wind speed. As a result, radiation intensity and wind speed in the location under investigation should be determined. Radiation intensity and wind speed during 24 h of investigation are shown in

In

Two different scenarios are utilized in this paper. In the first stage, the location and capacity of the storage are investigated aiming at reducing loss in the grid. In the second stage, this algorithm is utilized for charging and discharging these resources at the selected points, aiming at flattening the load profile.

In this section, the location and capacity of storage resources are investigated. In the simulation, it is assumed that only two areas in the grid can be utilized for storage installation and each of these areas can provide a maximum of 70 collections of installable batteries [

Hence, particle swarm optimization has been utilized aiming at reducing loss in the distribution system. Investigation is conducted at 10 am at the time of peak load occurrence. In the case of non-installing the storage, the amount of loss is reported to be 98.2 kW only in the presence of distributed generation resources in the system. In

The amount of loss is calculated using the following equations for power systems. If the total power injected into the busbar i is known, the total system loss will be equal to the complex power of all machines [

The proposed objective function is defined as

According to the figure, the amount of system loss has decreased to 75.5 kW after installing the storage is in the selected areas. In

A comparison between

The aim of demand response is to reduce peak load in the grid for increasing the capacity of grid spinning reserve and as a result, reduce the need to construct new power plants. Demand response can be utilized in order to reduce the level of electrical power consumption to reach maximum electricity demand efficiency and in this way, many costs can be saved. In a long term, the profit caused by reduced costs can be used to invest in new power plant [

Electricity price varies at different times of the day. This paper provides simulations based on time of use (TOU). This is the most common pricing method and most countries use this method. In this method, hours in a day are divided into several periods, in each of which different prices are considered for energy. The most simple TOU method considers two periods, peak load and low-load (off-peak) hours. In some cases, medium-load hours are also taken into consideration. It is natural that the prices associated with low-load and medium-load hours will be less than peak-load hours. A sample TOU pricing is given in

Price ($) | Hours |
---|---|

0.10074 | Off-load [22 to 6] |

0.28719 | Peak load [6 to 14] |

0.184 | Medium-load [14 to 22] |

As a result, the power needed by the upstream grid can be achieved as

As can be seen in

As expected, storages stored energy at the earlier hours of the day due to low prices of electricity and then were discharged during peak load hours (6 to 24) due to increased electricity price. In the second event, the revenue achieved by electricity sales to the grid can help reduce objective function. The charge and discharge status of these two storages are illustrated in

Next, the genetic algorithm was utilized in order to manage storage resources, charge and discharge in the system under investigation. As a result, the charge and discharge status of the storages are achieved as

The charge and discharge status of all storages are illustrated in

As a result, the power profile needed for the upstream grid was changed as

According to

Minimum load | Peak load | Standard deviation | |
---|---|---|---|

Without storage | 133.33 | 3052.5 | 925.14 |

GA | 606.66 | 2868 | 451.53 |

PSO | 810 | 2568.3 | 478.01 |

GWO | 725 | 2678.2 | 461.21 |

LSA | 802.33 | 2486.4 | 471.21 |

The maximum amount of load in the grid is calculated to be 810 by using the storage and managing energy with the help of PSO. However, this value is reported to be 133.33 for the system without storage. In addition, the maximum load for the system with the storage is calculated to be 2568.3 with particle swarm optimization algorithms. However, this value was calculated to be a maximum of 3052.5. The large difference between the minimum and maximum power demanded by the grid can be seen for the system without storage, compared to the low difference between the minimum and maximum power in the system with the storage. The standard deviation of variation for load demanded by the upstream grid illustrates the minimum changes in the demanded power.

In this paper, placement management, the capacity of storage resources, and energy management of resources are investigated for reducing loss and improving the load profile of the grid under investigation. Optimal installation and placement of the energy storage in the grid and charge-discharge management of storage resources have caused a decrease in peak load. Hence, particle swarm optimization is utilized to find the location and capacity of the storage resources. Simulation results were compared to the genetic algorithm. Ultimately, a well-rounded program is proposed to optimally exploit the storage at different times during the day.

This work was supported in part by an International Research Partnership

The authors declare that they have no conflicts of interest to report regarding the present study.