A sufficient stochastic framework for optimal operation of micro-grids considering high penetration of renewable energy sources and electric vehicles

Nomenclature

1 Introduction

In recent years, the increasing concerns over the high amount of pollutions caused by the fossil fuel based devices have motivated the electrical engineers and companies to make use of renewable energy sources (RESs). The use of RESs in the network can provide many benefits including more reliable and secure electrical services, higher power quality, less interruptions, less power losses and lower amount of pollution [1–4]. In the new competitive power market, the use of different types of distributed generations (DGs) such as wind turbine (WT), fuel cell (FC), photovoltaics (PVs) and micro turbine (MT) can help the network to have effective role in the market. Along with these advantages, the high penetration of DGs especially in the form of RESs can create some unforeseen and unwanted challenges for the distribution system. Parts of these challenges are addressed in the issues of Micro-Grid (MG). By definition, MG is a group of interconnected loads and distributed generations (DGs) which can either connect or disconnect to/from the grid to enable its operation in either grid-connected or islanded mode, respectively [5]. In the view of the main grid, MG is either a controllable unit inside the network which can be regarded as a single load to be supplied or as a power source to help supply a portion of the electrical loads [6]. According to the attractiveness of RESs and MGs, wide researches have been implemented in recent years.

In [7], Chedid et al. made use of a linear programming technique to lessen the average power production charges in a solar and wind MG considering the environmental factors. In [8], Niknam et al. proposed a heuristic approach to operate a FC-based MG considering thermal and hydrogen generation ability of FC. In [9], Chakraborty et al. suggested a linear programming method for handling and scheduling the battery charge/discharge rate when minimizing the total cost. In [10], Tsikalakis et al. assessed the bi-directional effect of MG and the up-stream grid on each other while optimizing the total power production. In [11], Hernandez-Aramburo et al. proposed a new formulation for minimizing the total electrical/thermal fuel cost considering minimum reserve power. In [12], Dukpa et al. suggested a price-base participation solution to schedule the WT and storage device for the 24-hour program in the unit commitment problem. A practical three-phase approach based on matrix real-coded genetic evolutionary algorithm was suggested by Chen et al. in [13]. The proposed formulation is constructed based on the prediction, storage and management modules for optimizing the MG costs. While each of these works have considered special aspects of MG, none of them has considered the penetration of electric vehicles (EVs). EV technology is a newly introduced device than has the same purposes as RESs for reducing the air pollutions. Therefore, it has attracted the attention of most of researchers in recent years [14]. According to the statistical reports, EVs would be occupy notable portion of the future transportation system [15, 16]. In this regard, a high number of researches are done on the EVs and their effects on the smart grids [17–20]. In addition, the high amount of uncertainty that is injected to MG should be modeled using an appropriate stochastic method.

According to the above discussion, the main purpose of this paper is to investigate the optimal operation of MGs considering the high penetration of different types of DGs including MT, FC, WT and PV as well as EVs. In this work, plug-in EVs (PEVs) are considered in the MG due to the high popularity and success in the EV market. A PEV is any motor vehicle that can be recharged from an external source of electricity, such as wall sockets [21, 22]. The most significant issue with the appearance of PEVs in the MG is the stochastic behavior of EV owners which can affect all the pre-determined schedules in the MG central control (MGCC). In fact, the high penetration of DGs, RESs and PEVs can inject much uncertainty in the MG which should be handled, appropriately. In this way, a new stochastic framework based on unscented transform (UT) is proposed to model the uncertainties of the problem. UT is a newly introduced superposition approach which has revealed great performance in modeling nonlinear transformations and state estimators [23]. The structure of UT is such that it can model either dependent or correlated uncertainty of parameters. Also, in order to make the existence of PEVs as an opportunity for the MG, the idea of veicle-2-grid (V2G) technology is used to make the control of charge/discharge of energy between the MG and main grid possible. According to the high complexity and nonlinearity of the scheduling RESs and PEVs, a powerful optimization algorithm is required to solve the problem optimally. In this regard, a new optimization method called modified krill herd (MKH) algorithm is proposed too [24]. KH is a novel evolutionary algorithm that mimics the foraging behavior of krill animals in the ocean. Also, a new modification method is proposed for this algorithm to increase its search ability and reduce the possibility of trapping in local optima. The cost function is defined as the total cost of the microgrid including the cost of power generation by DGs and RESs, cost of power supply for PEVs, cost of V2G (battery aging cost), cost of power purchased from the main grid and cost of energy not supplied (ENS) as a reliability index. The optimization problem tries to minimize this cost by optimal scheduling of DGs, RESs and PEVs. This cost is the total microgrid cost which is on the owner of the microgrid. Though the minimization of this cost, the microgrid owner is profited. This is a significant target in the operation of the distribution systems in the electricity market. The feasibility and satisfying performance of the proposed stochastic optimization method is examined on a grid-connected MG.

The rest of this paper is organized as follows: Section 2 describes the PEV technology and the problem formulation. Section 3 describes the proposed UT method. The optimization algorithm based on MKH is explained in Section 4. In Section 5, the application procedure is explained in some steps. The simulation results are discussed in Section 6. Finally, the main conclusions and concepts are given in Section 7.

2 PEV technology and MG problem

This section first describes the PEV technology and then explains the problem formulation including the cost function and the practical limitations of the problem.

As mentioned before, the proposed problem includes a high number of uncertain parameters including the charge/discharge values of PEVs, active and reactive loads, hourly market price, WT/PV output power and number of PEVs in each fleet. In order to model the uncertainty effects of these parameters, UT method is proposed in this section. UT method is one of the most popular and successful methods among the approximate techniques. This method was first introduced for modeling uncertainty in the nonlinear correlated transformations [23]. The existence of some special characteristics such as simplicity, high uncertainty modeling ability, low computational burden and ability of usage in correlated environment make UT method an appropriate choice amongst the other well-known stochastic methods. The main idea of UT is constructed on the fact that it is easier to approximate a probability distribution function (PDF) than an arbitrary nonlinear function [23]. The superiority of UT over some other well-known stochastic methods is demonstrated in the literature [29]. In order to explain this technique, suppose the nonlinear function y = f (X); in which y is the output vector, f is the nonlinear function and X is the input uncertain variables. Considering m uncertain parameters, X would be a vector with length m with the mean value μ and covariance P _x x. In the independent environment, P _x x is a symmetrical matrix. In a correlated environment, P _x x would become non-symmetrical. The UT method converts a stochastic problem with m uncertain parameters to 2m + 1 deterministic problems that each is solved individually. The result is the mean μ _y and covariance matrix P _y y of the output y. Therefore. the below steps are required to solve the problem [29]: x 0 = μ(33) x k = μ + ( n 1 - W 0 P xx ) k ; k = 1 , 2 , … , m(34) x k = μ - ( n 1 - W 0 P xx ) k ; k = 1 , 2 , … , m(35)

where the term (A)  _k in the above equations is the kth row or column of matrix A. Also, W⁰ is the initial weight of the mean value μ.

Step 2: Compute the weighting factor of concentration points as follows: W 0 = W 0(36) W k = 1 - W 0 2 m ; k = 1 , 2 , … , m(37) W k + n = 1 - W 0 2 m ; k + m = m + 1 , … , 2 m(38)

It should be noted that the summation of weighting factors should become one unit: ∑ k = 0 2 m W k = 1(39)

Step 3: Input 2m + 1 sample points to the nonlinear function to find the output samples: y k = f ( X k )(40)

Step 4: Compute μ _y and P _yy for the output variable Y as below [29]: μ y = ∑ k = 0 2 m W k Y k(41) P yy = ∑ k = 0 2 m W k ( Y k - μ y ) ( Y k - μ y ) T(42)

The proposed problem is a kind of nonlinear, complex optimization problem with several equality and inequality constraints. In order to solve the problem optimally, krill herd (KH) algorithm with a new modification method are explained in this section.

The below steps are required to apply the proposed stochastic optimization method on the problem:

Step 1: Collect the input data.

Step 2: Convert the constrained problem into an unconstraint optimization problem using the penalty factors.

Step 3: Generate the initial population of krill. In this problem, each krill contains the optimal output power of the DGs as well as the optimal charging/discharging values of PEVs during the operation time horizon.

Step 4: Run the probabilistic load flow based on UT method.

Step 5: Evaluate the objective function value for the krill population as described in (1–9).

Step 6: Choose the best solution (krill) with lowest cost function value as X ^b .

Step 7: Update the krill population as described in Section 5 part A.

Step 8: Apply the proposed modification method on krill population as described in Section 5 part B.

Step 9: Update the population.

Step 10: Repeat steps 6 to 10 until the termination criterion is satisfied.

6 Simulation results

This section investigates the performance of the proposed method on a standard test system. The test system is a typical MG with 32 buses which is connected to main grid through a circuit breaker [31]. The nominal voltage of the MG is 12.66 kV [31]. The single line diagram of the test system is shown in Fig. 3. As it can be seen from this figure, MG contains two WTs, two MTs, one FC and two PEV fleets. The location of each DG is shown in Fig. 3. It is assumed that there is one circuit breaker in the main feeder and there is a sectionalizer at the beginning of each feeder. The proposed stochastic framework models the uncertainties of charge/discharge pattern in PEVs, active and reactive loads of the MG, hourly market price, WT/PV output power, number of PEVs in each fleet and the arrival or departure time of PEV fleets.

Table 1 shows the number of customers served in each busbar. Also, the complete information of DGs including the capacity, position, start up/shut down costs and cost of energy generation are shown in Table 2. For the sake of simplicity, similar power curves are considered for WTs. The main distinction between the WTs is that the output power of WT-2 is supposed to be 1.2 times of WT-1. The normalized forecast output power of WT and PV sources are depicted in Fig. 4A and B. The hourly total load demand as well as the market price are shown in Fig. 4C and D, respectively.

In terms of PEVs, two fleets with different characteristics are considered in the MG. One of the PEV fleets starts its first trip from inside the MG while the other one comes to MG from the outside area. The number of PEVs in each fleet along with the capacity and parking location are given in Table 4. It is worth noting that in this work lithium-ion battery due to the high popularity is considered for PEVs. The parameters of Wöhler curve for this type of battery are a = 1331 and b = –1.825.

The operation problem is scheduled in 24 hours. It is supposed that all DGs work at unit power factor and thus just produce active power. In addition, the MG can decide to exchange power with the main grid at any hour of the scheduling time based on the benefits. All loads are considered to be electric type and thermal loads are not considered here. According to Table 2, PV and WT have the highest cost of power generation among the DGs. This event roots in the high initial capital cost of these DGs. In order to support the idea of RESs, the MG will buy all the power produced by these DGs at any hour of the day. For better understanding of problem, two different status of operation (SOP) are defined. In SOP1, PEVs are neglected in the MG and it is assumed that all DGs would be ON. In SOP2, the situation is similar to SOP1 just DGs are allowed to turn ON or OFF depending on the benefits in the cost function. Finally in SOP3, DGs can switch between ON/OFF status and PEVs are considered in the MG. All scenarios are solved in both stochastic and deterministic environment. Table 5 shows the optimization of the cost function in SOP1. For better comparison, the simulation results of some other well-known algorithms such as genetic algorithm (GA), particle swarm optimization (PSO) and original krill herd (KH) are given simultaneously. For each algorithm, the problem is solved 20 trails and the results of the best solution, worst solution, average value and standard deviation value are provided. As it can be seen from Table 5, the proposed MKH algorithm could reach more optimal solution than the other algorithms. Moreover, comparing the results of worst solution, average solution and standard deviation of different algorithms, the high robustness of the proposed MKH algorithm is deduced. Table 6 shows the optimal output power of each unit. As it can been from these results, the MG tendency is to keep the output power of dispatchable units at minimum during the hours that the market price is low. In the opposite point, during the mid-day hours that market price is high, most of DGs are forced to work at higher power capacity.

Tables 7 and 8 show the simulation results for SOP2. In this scenario, the power units are allowed to switch between ON and OFF status. In comparison to SOP1, the total cost of the MG is reduced in this scenario. From the optimization point of view, the proposed MKH algorithm shows superior performance in both search and stability. According to Table 8, the lower cost of the MG is SOP2 roots in the authority given to DGs to shut down. As it can be seen from Table 8, FC and MT as dispatchable units are OFF at low cost hours and therefore the required energy is purchased from the main grid. This is an economical policy to reduce the total cost of MG during the day.

Until now, the MG was operated neglecting PEVs effects. In SOP3, the high penetration of PEVs in the form of two fleets is considered. It is assumed that PEV drivers prefer to have their cars fully charged at the beginning of the first trip. Also, it is supposed that the SOC of each PEV battery would be 50% when entering or leaving the MG. According to the simulation results in Table 9, considering PEV fleets has resulted in proper reduction in the total MG costs. In contrast to the first expectation that the high penetration of PEVs in the MG can be supposed as additional load and will increase the MG costs, but the existence of these vehicles has reduced the cost effectively. In fact, the use of V2G technology has made PEVs as movable storages that can be scheduled by the MGCC during the parking hours. As it can be seen from Table 10, PEVs are charged at light load hours (for fleet 1 at early morning) to be able to discharge at heavy load hours.

Finally, Fig. 5 shows the comparative values of the objective function for different SOPs in both deterministic and stochastic frameworks. The stochastic problem considers the uncertainties of charge/discharge pattern in PEVs, active and reactive loads of the MG, hourly market price, WT/PV output power, number of PEVs in each fleet and the arrival or departure time of PEV fleets. According to Fig. 5, considering uncertainty has increased the optimal value of cost function in all SOPs. Nevertheless, it should considered that this amount of additional cost is considered to operate the MG in a more reliable and realistic level.

7 Conclusion

This paper proposed a new stochastic optimization framework based on UT method to solve the optimal operation and management of MGs with high penetration of RESs and PEVs. The proposed method makes use of KH algorithm with a new modification method to search the problem space globally. The simulation results on a standard MG shows that optimal scheduling of power units as well as the charge and discharge of PEVs can reduce the total cost of the MG, effectively. In addition, it is more economical to turn off DGs at light-load hours for avoiding high generation costs. Regarding the PEVs, the use of V2G technology can help to support the idea of PEVs in the MGs. From the optimization point of view, the proposed MKH algorithm showed superior performance than some other famous algorithms such as GA, PSO and original KH algorithm. Last but not least, the high search ability and stability of MKH algorithm were deduced too.