1. Introduction
The global demand for energy has been increasing in recent years, and a rapid escalation in fossil fuel prices has also been seen. An old-fashioned way of fulfilling multiple demands was to establish a new central generating plant, but that results in high capital costs and pollution. Today, microgrid (MG) as a savior solution which not only solves the old distribution network problems, but also deals with technical and nontechnical problems such as power quality, local reliability, power management, total network efficiency, and interconnections between networks [
1].
In fact, MG as a small part of a power system, is a low voltage distribution network comprised of controllable/non-controllable loads and distributed energy resources (DERs) with clearly defined electrical and thermal boundaries; it acts as a single controllable entity with respect to the main grid [
2]. MG can be in either grid-connected modes to operate cooperatively or in islanded modes. A key characteristic of an MG is its ability to disconnect and isolate itself from the utility with little or no outage to loads within the MG during a utility grid disturbance [
3].
Studies have shown that connecting multiple MGs can improve the operation and reliability of the system [
4,
5]. The economic scheduling of generating units and storage elements to fulfill multi-carrier demands in each MG is a crucial task which can be handled by the distribution management system (DMS). This management is carried out using the microgrid central controller (MGCC) by receiving or sending signals to local controllers [
6]. In multi-microgrids (MMGs), each MG is managed by its own MGCC, while these controllers are controlled by one main called the multi-microgrid central controller (MMGCC). This procedure simplifies energy management and manages the overall stability of MMGs by monitoring and analyzing the power quality of each MG to decide which one operates autonomously in island mode or interconnected to a distribution grid [
7]. Moreover, MGs can operate as a backup system [
8].
Today, optimal operation and planning problems are the main topics of research in MGs and, albeit rarely, MMGs [
5,
9,
10]. Arefifar et al. have discussed the large-scale power distribution system as a number of MGs in order to facilitate the control strategy and operation infrastructure in future distribution systems based on IEEE Std 1547.4. [
11]. Furthermore, the economic advantages of MMGs and its energy scheduling considering the uncertainty of electrical load has been studied [
12]. The work in [
13] studied optimal types, sizes, and locations of distributed generations (DGs) in an MG using the genetic algorithm method. One of the most important problems in MG is the management of available sources to satisfy demands [
14]. Moreover, the capability to energy share between MGs, exclusively thermally demand sharing, is an important issue that has rarely been discussed in previous studies [
15,
16].
In the literature, different methods were used to solve the power dispatch problem [
15,
17]. For instance, [
15] used an optimization model based on the mixed integer linear programming (MILP) in grid-connected mode of a thermally-networked microgrid (TNMG) whereas multi-objective optimization problem without taking into account sold and purchased energy has been considered for an economic dispatch (ED) problem [
17]. The particle swarm optimization (PSO) method [
18], Tabu search (TS), genetic algorithm (GA) [
19], ant colony [
20], game theory, new recurrent neural network [
21], mesh adaptive direct search algorithm [
22], and optimally-condition-decomposition (OCD) technique are commonly used methods in solving optimal dispatching problems. The optimal economic short-term management problem along with elastic and inelastic loads is studied in an MG [
23]. The objective function is the minimization of the operation energy costs (include energy purchase costs and energy sales revenues) and sensitivity analysis is carried out by varying the maximum amount of power exchanged with the main grid.
However, some DERs have intermittent behavior due to their nature, and under this assumption, deterministic energy scheduling may be unrealistic and not useful [
24,
25]. Moreover, higher penetration of small scale energy resources (SSERs) such as wind and photovoltaic (PV) sources may fulfill demands, but it causes intermittencies in the grid. These uncertainties can cause challenges in operational and long- and medium-term system planning [
12]. Hence, the probabilistic analysis is impossible to ignore due to the uncertain behavior of some SSERs and the energy consumers. The probabilistic tools for power system analysis have been studied and used in the literature [
26,
27,
28].
Energy scheduling under the intermittent behaviors of renewable energy resources is studied in [
28]. The uncertainty of renewable sources, e.g., wind speed and solar irradiance, was investigated in [
29]. Furthermore, in [
12], load uncertainty was modeled and studied. A new technique, based on the Beta probability distribution, for the generation of the aggregate demand patterns through the modelling of the energy consumption behavior of a group of residential consumers is presented [
30]. Goodness of fit tests such as the Kolmogorov–Smirnov test and the average mean absolute percentage error are used for the evaluation of the proposed scenario generation. A simplified optimization problem formulated as a mixed integer linear programming (MILP) is modeled to enhance the management of the distributed energy sources in a real site islanded microgrid [
31]. The results reveals that the optimization is robust enough against variations in the time step interval, timeframes and changes in system parameters. The assessment of power system uncertainties can be represented either probabilistically or possibilistically. Probabilistic methods are applicable when sufficient historical data about uncertain variables or their probability distribution function (PDF) is available. In [
32], an analytical probabilistic-possibilistic tool for power flow uncertainty assessment was proposed to solve the system modeling problem with different variables (mixed of probabilistic and possibilistic). The probabilistic techniques have been used to assess the impact of a power system since the early seventies [
33].
The probabilistic methods are divided into three categories: numerical, approximate, and analytical. Mount Carlo simulation (MCS), Latin hypercube sampling (LHS), PSO, and the imperialist competitive algorithm (ICA) are widely used as numerical methods to model uncertainties [
34,
35]. Approximate methods such as the point estimate method (PEM) and two-point estimate method (2PEM) were used in [
36,
37]. To burden the computational effort, analytical methods such as the combined Cumulants and Gram-Charlier expansion theory and the Cumulant-based method are widely used [
38,
39]. Mathematical models for the statistical behavior of load and renewable sources have been used in many studies. The Normal, Weibull, and Beta distribution functions have been used to model load, wind speed, and solar radiation behavior, respectively [
6,
12].
A novel standard classification of uncertainty handling methods along with the promising lines of future researches for decision making process is proposed [
40]. According to the paper clarification, the uncertain parameters in power system studies are generally classified as technical and economical. In addition, the uncertainty modeling methods comprise probabilistic, possibilistic and hybrid possibilistic-probabilistic approaches, information gap decision theory, robust optimization (RO), and interval analysis. Based on the comprehensive classification, each method is suitable for a specific type of uncertainty and the possibility of using a new class of uncertain numbers called “Z-numbers” is investigated for the first time. An RO-based algorithm is proposed for day-ahead scheduling of multi-microgrids in grid-connected mode [
41]. A deterministic uncertainty set (upper and lower bounds) is used in this formulation instead of using probability distribution of the uncertain data. The result reveals that the model is capable of providing guaranteed immunity against the worst-case scenario and remains tractable even for large systems.
Considering the aforementioned researches, the probabilistic energy scheduling of multiple energies within multi-microgrids has not been studied extensively in previous studies. As a consequence, this paper solves the optimal power dispatch problem considering uncertainties in loads for electrical and thermal types, electricity price, and the probabilistic modeling of generated power by renewable sources. One prominent solution to tackle the oscillations of renewable sources is utilization of energy storage elements and demand side management as the renewable sources complements. Hence, responsive and non-responsive loads are covered and a novel time-based demand side management model based on the final energy price (FEP) is proposed. The proposed model correlates the final energy price of responsive loads for multiple carriers with energy market price, energy purchase, and on-site generations. For each of the input variables, a specific PDF is considered and different scenarios are generated in MATLAB (R2011b, 7.13.0.0561) environment. Then, probabilistic energy scheduling problem as an MINLP model is solved for each of the generated scenarios in a 24-h interval, using GAMS (24.1.2) software. Input data such as load and energy price of each multi-carrier microgrid (MCMG) as well as generated power by renewable units are described in the form of PDF, and the results are shown in PDF or cumulative distribution function (CDF) forms in a specific interval. In the proposed structure, the energy generation at each MCMG, the purchased and sold energies by each MCMG, and the energy transactions between MCMGs and the main grid are analyzed based on operation and maintenance costs. Moreover, the network of heat between MCMGs is considered. Briefly, the main contributions and innovations of this paper are summarized as follows:
A network of MCMGs structure is taken into account for studying MCMG optimal scheduling to resolve prevalent disadvantage of conventional structures of MGs. The centralized energy scheduling of the MCNMG is managed by the MMGCC which aggregates signals from each MGCC to economically distribute the energies to the consumers.
Proposing a novel time-based demand side management model which correlates the final energy price of responsive loads for multiple carriers with energy market price, energy purchase, and on-site generations.
The proposed network is studied under uncertainties of electrical and thermal loads, electricity price, and RERs generations.
5. Simulation Results and Discussion
In this paper, a smart distribution network with multiple MCMGs to fulfill multiple energy demands in a 24-h interval was modeled as shown in
Figure 1. In the figure, the MCMGs are in interconnected mode to balance the supply-demand of the district heat network, and each MCMG is linked to the electric and natural gas main grid. So, MCMG can buy electric and natural gas energies from the main grid when the MCMG is unable to provide its own multiple demands from its sources. An MCMG with surplus electricity can sell its electricity to the main grid. The characteristics of MCNMG’s elements are stated in
Table 1.
Owing to the intermittent behavior of some RESs, electricity prices, and load variations, this study was conducted based on uncertainty in input data. For every hour, to simulate the uncertainty behavior of the mentioned variables, 500 samples were considered, but the results are shown for only one hour of the day in PDF and CDF forms. The PDF function was applied for loads, electricity prices, wind speeds, and solar radiation; these input variables are defined as probabilistic variables. Based on the correlation between input and output variables, the output variables demonstrate probabilistic behavior. The electrical and thermal loads of each MCMG are illustrated in
Figure 3. It should be mentioned that electricity purchasing and selling prices are considered equally in three steps, and the density for a specific hour is shown in
Figure 4, whereas the natural gas purchasing price is permanently fixed at 0.07 dollars per hour.
To model the uncertainty of wind speed and solar irradiation, historically measured data for a given 24 h of the day in Kashan city, Iran, was used as practical data. The probabilistic modeling of both wind speed and solar irradiation and, consequently, the probabilistic modeling for WT and PV units are illustrated in
Figure 5. In
Table 2, the values of the parameters of the WT and PV units that were used in simulation are given.
The statistical analysis of generated power by units and energy storage elements of the MCNMG are described based on mean values for a specific hour in
Table 3.
According to the results in
Table 3, a big share of electricity demand in MCMG1 is supplied by PV and CHP and the extra electricity generation by PV is sold to the main grid. But the electricity demand in MCMG2 is mostly supplied by the main grid owing to no-cost energy generation of WT at this specific hour while boiler supplied the most share of the heat demand in the MCMG2. As the network is managed by the MMGCC to reduce the total cost of MCNMG, so the MCMG2 and more efficiently MCMG3 supply a big share of heat demand in MCMG1. It is evident in
Table 3 that the boiler of MCMG2 and MCMG3 produced more heat to transfer heat to MCMG1.
Since the MCNMG is connected to the main grid and can trade energies, the PDFs of total purchased electricity and natural gas energies are displayed in
Figure 6. The heat balance in each MCMG must be met according to the cooperative operation of the MCNMG. To be more specific, if the heat demand in one MCMG cannot be supplied by its sources, the adjacent MCMGs must meet the needy MCMG’s demand. The PDFs of received and transferred heat by each MCMG are depicted in
Figure 7 and
Figure 8, respectively. Comparing the following two figures shows that MCMG1 received the most heat energy from MCMG2 and MCMG3 due to the renewable generation in MCMG1 and the higher efficiencies of the other two MCMG’s boilers. A comparison of total thermal energy wastage after and before thermal energy exchange between MCMGs is shown in
Table 4. It can be observed that the thermal energy wastage and, consequently, total costs are lower in case of interconnected MCNMG operation. It should be mentioned that the result may not seem remarkable, but it will surely be significant in a wide network.
Electrical and thermal controllable loads form 10% of total loads as observed in
Figure 9 and
Figure 10 in PDF forms, respectively. These responsive loads are encouraged or forced to shift their demands in peak intervals to off-peak intervals. The peak period for electrical load is considered from interval 15–22, whereas that of the thermal load is in intervals 1–7 and 23–24. As shown in
Figure 9 and
Figure 10, electrical and thermal responsive loads shift their demand to off-peak intervals, and customers participate as active loads.
The FEPs of electrical and thermal controllable loads were acquired and are depicted in
Figure 11 and
Figure 12, respectively. The base energy price of electrical controllable load was considered equal to 0.05
$/KWh for all given intervals, whereas that of the thermal controllable load was considered equal to 0.07 for intervals 1–7 and 23–24, 0.06 for intervals 8–18, and 0.05 for intervals 19–22. It can be seen that the final energy prices of electrical and thermal controllable loads are higher than their base prices. Therefore, customers are encouraged to shift their demand to less costly hours.
In
Figure 13 the load factor (LF) of MCNMG is shown in PDF form. Moreover, responsive load participation as 10% and 30% of total load is simulated, and LF and total MCNMG cost are compared in
Table 5. It is clear that LF is optimally increased, while the total cost of the network is lower in the case of higher participation of responsive load.
Finally, the PDF and CDF of total cost of the MCNMG are shown in
Figure 14. The results show that the operation cost of the network is totally dependent on the probable behavior of the relevant variables and so taking into more uncertain variable would realize the results more effectively. In conclusion, probabilistic analysis of ED increases the complexity of the optimization process severely, but it gives a better insight to the dispatcher for evaluating the risk of change in a system’s total costs. Such results are more trustworthy from the energy operation management point of view.