Energy Management of Cooperative Combined Cooling, Heating, and Power Microgrids Considering User Comfort

The imbalance due to increasing energy demand and the depletion of energy resources leads to an unstable power system. In conventional microgrids, the surplus heat of micro-turbines is wasted as electrical energy is used for various loads. Demand-side management scheduling the shiftable appliances based on cost-per-unit, overlooking consumer preferences and comfort. To address these challenges, a unified framework for managing and trading energy within renewable integrated combined cooling heating and power microgrids is proposed. Within this framework, each combined cooling heating and power microgrid initially employs demand-side management to fulfill its energy requirements while adhering to different constraints. If the load demands of any combined cooling heating and power microgrid are not fulfilled by its local renewable energy generation, then energy can be procured from nearby connected combined cooling heating and power microgrids or from the utility. Conversely, excess energy can be sold out to nearby combined cooling heating and power microgrids or to the utility. Additionally, in emergency situations, diesel generators can supplement the energy needs of any microgrids. Simulation results demonstrate 34.01% and 32.98% reductions in system costs and peak power demand while considering user preferences and comfort. Reducing the peak power demand will improve the system’s performance and efficiency.

SECTION I. Introduction

Increasing the use of renewable energy has become the focus of research due to the depletion of fossil resources. The combined cooling, heating, and power (CCHP) microgrid is important for increasing energy efficiency since it can supply the energy needed for electrical, heating, and cooling loads [1]. The integrated management of multi-carrier energy systems has gained considerable attention for its ability to improve efficiency, enhance flexibility, and reduce environmental impact. Notably, precise and optimal system design is essential for ensuring their effective operation [2]. The widespread adoption of distributed generation and the development of multi-carrier energy systems further highlight the need for energy hub systems. As an innovative concept within these systems, an energy hub facilitates the transfer, reception, and storage of various energy forms [3].

Many industrial processes require heat at different stages of production, with electricity and heat being the primary energy sources. Energy savings can be achieved through heat recovery within an energy hub. Since a significant portion of electricity is converted into heat to meet heating demands, recovering refining-generated heat for heating purposes is essential [4]. The energy hub plays a crucial role in smart power systems due to its high efficiency. Its advanced and cost-effective operation is analyzed by integrating thermo-economic analysis, reliability and availability assessment, and load profile prediction [5].

The CCHP microgrid has emerged as a vital component of energy hubs, contributing to increased energy efficiency and reduced greenhouse gas (GHG) emissions in response to growing energy demands. To achieve efficient energy utilization, the CCHP microgrid integrates power generation, auxiliary boilers, heat recovery systems, energy storage devices, refrigeration equipment, and renewable energy sources (RES) [6]. The primary components of the CCHP unit include the gas turbine (GT), absorption chiller, and heat recovery unit. The GT operates by burning natural gas to generate electricity while simultaneously recycling waste heat to produce thermal energy for heating or cooling applications [7].

Over the past few decades, there has been a sharp increase in energy demand as a result of population growth and industrial expansion [8]. Presently, the two primary concerns that greatly trouble people are the energy crisis and the environment [9]. With the escalating impact of climate change and energy-related calamities, the utmost priorities for the entire energy sector now revolve around minimizing emissions due to flue gas and enhancing energy consumption efficiency [10]. Compared to normal microgrids, CCHP can dramatically boost fuel efficiency up to (60-80)% [11].

Due to the simultaneous production of heat and power, the role of the CHP system in the current power system is constantly increasing [12]. However, in various locations where harsh weather exists in both the winter and summer, the CCHP system having integrated RES may increase the efficiency of the power system [13]. A predecessor to CCHP, CHP provided only heating and electrical loads. CCHP systems come in a range of capacities, from 20 kW to 20 MW. CCHP microgrids operate using diverse energy sources, including wind energy, solar thermal, solar PV, natural gas, geothermal, biogas, and biomass. Unlike solar thermal, which generates heat energy, wind turbines and solar PV systems produce electrical power [14]. In addition to commercial applications, CCHP systems are increasingly often employed in residential areas as a result of the development of small generating units [15].

Khan et al. considered various necessary factors such as human interaction and consumer preference for the operation of shiftable appliances [16]. Electrical and thermal energy are both generated using geothermal energy where natural gas is utilized to produce heat and electricity by using a boiler and engine respectively [17]. A crucial part of a CCHP microgrid is the prime mover, which can be powered by a variety of technologies, including internal combustion engines, fuel cells, micro-turbines, Stirling engines, gas turbines, steam turbines, and PV collectors [18]. The prime movers can be distinguished based on a number of variables, including capacity, overall efficiency, capital cost, maintenance and operation cost, and $CO_{2}$ emission rate [19].

Mitsos and co-authors introduced McCormick envelopes as a means of convex relaxation for bi-linear functions [20]. Deng and his co-authors presented the nonlinear operation of the CHP system, which posed a challenge due to the presence of non-linear terms in the model of heat flow. McCormick relaxation has been used to address the issue of non-linearity and enhance the quality of solution and computational performance [21]. Castro et al. applied piece-wise McCormick relaxation for the linearization of bi-linear problems and noted that partition-specific upper and lower bounds improved the quality of the relaxation [22].

Scott et al. established a generalized form of McCormick envelopes to linearize the problems of global optimization, which have become popular due to their computational efficiency and simple implementation [23]. Jing and his co-authors developed a model for energy trading for residential and commercial prosumers, with the objective to reduce the costs of heat and electricity trading use. Nevertheless, the multi-energy trading environment gave rise to a non-linear system. In order to address this issue, they opted to utilize McCormick envelopes as a means to linearize the system [24].

Due to the increased emphasis on air pollution and energy efficiency in the world, CCHP microgrids are now much more common. A CCHP microgrid is a viable method for generating domestic power in a number of locations, including hospitals, supermarkets, and educational institutions [25].

A. Related Literature

In order to mitigate peak demand, Li et al. conducted a study on energy management (EM) techniques for CCHP microgrids [1]. Qazi et al. introduced an EM approach for CCHP microgrids that utilized distributed proximal policy optimization, aiming to minimize overall system costs [26]. Particle swarm optimization was used by Luo et al. to determine operational strategies for unit commitment in the initial phase of their evaluation of a two-phase EM approach for CCHP microgrids, and heuristic algorithms were used to control the variation in power that occurs between the microgrid and the main grid in the second stage [27].

To optimize the overall costs considering diverse distributed energy sources, Shabani et al. conducted EM in a microgrid system [28]. In the context of a CCHP microgrid, Keskin et al. developed an hourly energy interaction model that incorporates variables such as energy price, temperature, and seasonal conditions. Their approach effectively reduced the system’s total cost, power loss, peak energy demand, and emissions of greenhouse gas [15].

Xiaoting et al. focused on PAPR reduction, user comfort, and total cost minimization in their EM approach for CCHP microgrids. Genetic algorithms were employed to solve the problem [29]. In the pursuit of lowering electricity prices and enhancing energy efficiency, EM is conducted for CCHP microgrids by Cheng et al. [30]. For the operation of a multi-energy microgrid, Yang et al. developed a model and utilized MILP to solve it [31]. Xu et al. successfully decreased the operational expenses of CCHP microgrids through a three-stage optimization strategy and an EM framework. The three stages involved day-ahead economic scheduling, intraday rolling optimization, and real-time modification [32].

Ma et al. conducted multi-objective optimization for the CCHP microgrid, aiming to reduce cost, waste power, and emissions of greenhouse gas [33]. A mathematical model developed by Anatone et al. for the optimal scheduling and management of CCHP systems, with a focus on reducing the system’s cost and emissions of GHG [34]. To decrease operational costs and computational complexity of the CHP system, Zhang et al. implemented EM techniques [35], [36]. Luo et al. performed EM in two stages to encompass economic dispatch and real-time adjustment, in order to achieve cost reduction [13]. Arcuri et al. utilized mixed integer linear programming (MILP) for EM of the trigeneration system, with the goal of achieving benefits in terms of the economy, environment, and energy utilization [37]. Cao et al. investigated the optimal operation of renewable integrated CCHP microgrids, achieving a 4% reduction in system costs alongside a decrease in peak power demand [38].

Ahsan et al. suggested a scenario where a building equipped with batteries and solar panels could enhance its financial and environmental performance by engaging in energy trading with neighboring buildings, thus reducing its dependence on the main grid [39]. To lower system costs, buildings participate in energy trading (ET) activities [40]. The introduction of multiple CCHP microgrids into energy systems aims to decrease expenses of monthly operation and reduce reliance on the primary grid [41].

Liu et al. demonstrated an energy trading technique aimed at reducing the overall cost of the system. As per their proposal, a CCHP microgrid has the option to purchase electricity from microgrids or from utility when its own energy generation is not enough to meet its demands. Additionally, the microgrid can sell excess energy to utility or other CCHP microgrids [42]. Riaz et al. utilized a branch and bound algorithm for the energy management and trading of a CCHP microgrid, with the objective of minimizing total costs [43]. To decrease the operating expenses of the system, Guo et al. introduced a multi-energy trading system for independently working CCHP microgrids [44]. Yunshou et al. investigated cooperative operation strategies for the CCHP system, aiming to enhance the effectiveness and profitability system [45].

Numerous studies in the literature suggest that employing the model for energy management in combination with the model for energy trading can help to address the supply-demand imbalance. The model for energy management involves shifting flexible loads to off-peak times, but this approach often results in user discomfort. On the other hand, energy cooperation among interconnected CCHP microgrids is promoted by applying the model for energy trading. However, to the best of our knowledge, no previous attempts have considered the simultaneous integration of various parameters such as energy management, energy trading, and user comfort. To fill these gaps, combined energy management and energy exchange framework are proposed for interconnected CCHP microgrids, aiming to minimize overall costs but not compromise of user comfort. User comfort has been ensured by considering the factors like human interaction and consumer preferences while optimizing the system performance. The summary of relevant literature is available in Table 2.

TABLE 1 Nomenclature

TABLE 2 Comparison With the Available Literature, Energy Management (EM), Energy Trading (ET), Peak-To-Average Power Ratio (PAPR), Cost Minimization (CM), Power Loss Minimization (PLM), Energy Efficiency (EE), Renewable Energy Generation (REG)

B. Motivation for the Research

Increased energy consumption is putting a strain on various segments of the conventional power system, including the generating portion, power transmission line, and distribution network. This overwork leads to problems like blackouts and line power losses, resulting in decreased system performance and efficiency. Additionally, conventional energy production heavily depends upon fossil fuels like natural gas, oil, and coal, which contribute to environmental pollution through the release of harmful gases. To tackle these issues and reduce line losses, distributed energy generation systems are required like CCHP microgrids. CCHP microgrids utilize the excess turbine heat for thermal and cooling loads, which helps in the reduction of production costs. Instead of relying on fossil fuels, these microgrids make use of RES such as solar PV and wind turbines for electricity generation, as well as solar thermal collectors for heat generation. By utilizing RES for producing electrical, heating, and cooling energy, CCHP microgrids contribute to minimizing environmental pollution.

C. Various Contributions

Various contributions of this research article are as follows:

1. The research article presents a framework that optimizes both energy management and cooperation for interconnected CCHP microgrids. This model can be applied to both islanded as well as grid-connected CCHP microgrids that have integrated RES.

2. The proposed framework considers multiple factors that affect the power system’s performance. These factors are load shedding, consumer load profile, consumer preferences, valley filling, peak clipping, human interaction factor, and appliance priority.

3. The mathematical model of the proposed framework contains bi-linear constraints, making it an MINLP. However, due to these bi-linear constraints, the structure of optimization in the proposed framework is non-convex. To address this issue, the article employs McCormick envelopes to transform the MINLP optimization problem into a MILP.

4. The proposed model achieves several objectives, including minimizing the system’s total cost, reducing the PAPR, and ensuring user comfort.

5. The proposed model maximizes the utilization of distributed renewable energy generation.

D. Organization of the Paper

The remaining sections of the paper are arranged as follows: Section II provides an explanation of the structure of the grid-connected CCHP microgrid. Section III presents a mathematical analysis of the proposed system model, while Section IV provides the results and discussion. Lastly, Section V concludes the article.

SECTION II. Structure of Grid Connected CCHP Microgrid

The architecture of a grid-connected CCHP microgrid is presented in Fig. 1. CCHP microgrid consists of generation, storage devices, energy conversion components, and various types of load. The generation part has various sources such as solar photovoltaic (PV), wind turbine (WT), solar thermal collector (STC), prime mover (PM), steam turbine (ST), etc. The conversion components include a heat recovery unit (HRU), electric boiler (EB), absorption chiller (AC), electric chiller (EC), etc. Electrical and thermal loads are also part of the CCHP microgrid.

FIGURE 1.

Structure of grid-connected CCHP microgrid.

A. Electrical Energy Generated

The total electrical energy generated is the sum of electrical energy generated by renewable energy sources ($E_{res}$ ) and prime mover ($E_{pm}$ ) which is graphically shown in Fig. 1 and expressed mathematically in Eq. (1)

$$\begin{equation*} E_{t,g}^{m}=E_{res}+E_{pm} \tag {1}\end{equation*}$$ Various sources that contribute to renewable energy generation ($E_{res}$ ) are the energy produced by the steam turbine $(E_{st})$ , wind turbine $(E_{wt})$ , and solar PV $(E_{pv})$ . It can be written formally as in Eq. (2). $$\begin{equation*} E_{res}=E_{st}+E_{wt}+E_{pv} \tag {2}\end{equation*}$$ The electrical energy generated by prime mover $(E_{pm})$ depends upon the efficiency of the prime mover and fuel supplied to the prime mover ($F_{pm}$ ) as shown in Eq. (3) [46]. $$\begin{equation*} E_{pm}=F_{pm}\eta _{pm} \tag {3}\end{equation*}$$

B. Heat Energy Generated

Heat energy available in the system comes from the electric boiler ($H_{eb}$ ) and heat recovery unit $(H_{ru})$ as shown in Eq. (4).

$$\begin{equation*} H_{n}^{t,g}=H_{eb}+H_{ru} \tag {4}\end{equation*}$$ where $H_{eb}$ depends upon electrical energy provided to the electric boiler ($E_{eb}$ ) and the boiler’s efficiency ($\eta _{eb}$ ). It is expressed mathematically in Eq. (5) [47]. $$\begin{equation*} H_{eb}=E_{eb}\eta _{eb} \tag {5}\end{equation*}$$ The heat energy supplied by the heat recovery unit ($H_{ru}$ ) is the sum of heat recovered from the steam turbine ($H_{rst}$ ) and prime mover ($H_{rpm}$ ) as shown in Eq. (6). $$\begin{equation*} H_{ru}=H_{rst}+H_{rpm} \tag {6}\end{equation*}$$ Heat recovered from prime mover $(H_{rpm})$ depends upon the excess heat available from prime mover ($F_{pm}(1-\eta _{pm})$ ) and the efficiency of heat recovery unit for prime mover $(\eta _{rpm})$ as expressed mathematically in Eq. (7) [48].

$$\begin{equation*} H_{rpm}=F_{pm}(1-\eta _{pm})\eta _{rpm} \tag {7}\end{equation*}$$ Heat recovered from stream turbine $(H_{rst})$ depends upon the excess heat available from stream turbine ($H_{st}$ ) and conversion efficiency of heat recovery unit for steam turbine ($\eta _{rst}$ ). It can mathematically be denoted as in Eq. (8) [48]. $$\begin{equation*} H_{rst}=H_{st}\eta _{rst} \tag {8}\end{equation*}$$

C. Cooling Energy Generated

Cooling energy is generated by the absorption chiller ($Q_{ac}$ ) and electric chiller ($Q_{ec}$ ). The conversion of energy depends upon the efficiency of the electric chiller ($\eta _{ec}$ ) and the absorption chiller ($\eta _{ac}$ ). Cooling energy generated is mathematically shown in Eq. (9).

$$\begin{equation*} Q_{n}^{t,g}=Q_{ac}+Q_{ec} \tag {9}\end{equation*}$$

D. Various Types of Loads and Storage Components

The energy provided to the grid-connected CCHP microgrid by the utility, as illustrated in Fig. 1, can be used for various types of loads such as electric ($E_{l}$ ), heating ($H_{l}$ ), and cooling load ($Q_{l}$ ). To supply heating and cooling loads electric boiler and chiller are used respectively. If the electrical energy produced by the RES of the CCHP microgrid exceeds its demand, it will be sold to the utility. Thermal storage units and batteries are used to store excess thermal energy and electric energy respectively.

SECTION III. Mathematical Analysis of the Proposed System Model

A graphical representation of the proposed system model is depicted in Fig. 2, where CCHP microgrids $(1,2\ldots .. M)$ are interconnected with each other and with the utility through a two-way communication network. Every CCHP microgrid is supposed to have various local REG sources. The local REG sources include solar PV, wind turbines, and solar thermal generators. Every CCHP microgrid can obtain energy from the utility if required. Every CCHP microgrid has a diesel generator inside its premises for backup power. On the consumption side, a total number of B consumers is connected with the energy management controller (EMC) of the CCHP microgrid. Each consumer has three types of loads such as electric, thermal, and cooling load. The step-by-step process is comprehended below for a complete understanding of the overall framework.

• Step 1: Every CCHP microgrid in the network will use its local REG to fulfill its energy demands while taking various constraints like human interaction factor (HIF), load-shedding (LS), and consumer preferences (CP) into account. the model for energy management will reshuffle the shiftable electrical appliances if the local REG of the CCHP microgrid is insufficient to fulfill electrical, heating, or cooling load demand.

• Step 2: If, after applying the EMC in the initial step, the capacity of the local REG of each CCHP microgrid is still insufficient to fulfill the demand of its loads, then the model for energy trading will be applied to procure energy from other connected CCHP microgrids.

• Step 3: The ETC will procure energy from the utility if the CCHP microgrids in Step 2 do not have any additional energy that the needy CCHP microgrid can purchase.

• Step 4: The CCHP microgrid will use a diesel generator in the case of emergency to meet its energy needs if, in Step 3, the necessary energy from the utility is also not available.

In the proposed framework the model for energy management is followed by the model for energy trading. At the CCHP microgrid level, the shiftable appliances are rescheduled using the demand side management (DSM). If the local REG of the CCHP microgrid is not sufficient to satisfy its energy demands, then it will procure the energy required from nearby connected CCHP microgrids or from a utility through an ETC. Below is the explanation of these two models.

FIGURE 2.

System model.

A. Model for Energy Management

As described in the step-by-step process of the framework implementation before applying the model for energy management every CCHP will try to meet its electrical, cooling, and heating demand by its self-generation without considering any constraints. The self-generation capacity of electrical, cooling, and heating energy is denoted by $E_{m,g}^{t}$ , $H_{m,g}^{t}$ , and $Q_{m,g}^{t}$ respectively. If load demands are not satisfied with its own generation then DSM will be used to reshuffle the shiftable appliances. The ON/OFF status of shiftable appliances are maintained by the decision variable $Z_{a,b}^{t,m}$ in Eq. (10).

$$\begin{align*} Z^{t,m}_{a,b} = \begin{cases} \displaystyle 1 & \text {ON status of}~ {a^{th}} ~\text{appliance of the}~ b^{th} ~\text{consumer} \\ \displaystyle & \text {in the}~ m^{th} ~\text{CCHP microgrid at time} ~{t} \\ \displaystyle 0 & \text {otherwise} \end{cases} \tag {10}\end{align*}$$ Various constraints are taken into account while applying DSM to reshuffle the shiftable appliances. These constraints are appliance priority, LS, HIF, CP, and peak clipping. On the basis of appliance priority, the shiftable appliances are categorized into two groups such as $\sigma _{1}$ and $\sigma _{2}$ . The decision variable in Eq. (11) determines the selection of an appliance either from a group $\sigma _{1}$ or $\sigma _{2}$ at any given time. $$\begin{equation*} \sum _{a\in {\sigma _{1}}} Z^{t_{1},m}_{a,b}+\sum _{a\in {\sigma _{2}}} Z^{t_{2},m}_{a,b} \leq {1}, \forall (t_{1}\lt {t_{2}}),\ \ a,m,b \tag {11}\end{equation*}$$ The condition $(t_{1}\lt t_{2})$ in Eq. (11) denotes that the priority of appliances from group $\sigma _{1}$ is higher than the appliances of group $\sigma _{2}$ , where the time slot $(t_{1},t_{2})\in \{1,2,3,4,5\ldots ..T\}$ . If the appliance either from a group $\sigma _{1}$ or $\sigma _{2}$ is ON, then the right side of Eq. (11) will be “1”, otherwise, it will be “0”. The schedule of shiftable appliances must ensure its uninterrupted operation and this condition is mathematically expressed in Eq. (12). $$\begin{equation*} \sum _{t=t_{s,b}^{a}}^{t_{s,b}^{a}+{t_{a}^{b}}}Z^{t,m}_{a,b} =t_{a}^{b}\;\;\;\;\;\; \forall a,m,b \tag {12}\end{equation*}$$ The starting time slot for the $a^{th}$ appliance of the $b^{th}$ consumer is $t_{s,b}^{a}$ and the number of required time slots for its complete operation is $t_{a}^{b}$ . To provide clarity, let’s consider an example where the total operation time for a dishwasher is 45 minutes, and each time slot has a duration of 15 minutes. In order to ensure the uninterrupted operation of the dishwasher, the value of $t_{a}^{b}$ would be 3, indicating that the dishwasher will be active for three consecutive time slots. As a result, the decision variable $Z^{t,m}_{a,b}$ will have a value of “1” from the starting time slot $t_{s,b}^{a}$ to $t_{a}^{b}$ . Consequently, the total value of Eq. (12) would be 3, indicating that the dishwasher requires three-time slots for its complete operation.

The schedule of the shiftable appliances is affected by the availability of electricity which is considered an LS factor. The value of the LS factor is “1” if electricity is available otherwise its value will be “0”. LS factor is mathematically represented in Eq. (13)

$$\begin{align*} L^{t}_{m} = \begin{cases} \displaystyle 1 & \text {if the electricity is available in}~ m ~{{\mathrm {CCHP}}} \\ \displaystyle & \text {microgrid at time} ~{t} \\ \displaystyle 0 & \text {otherwise} \end{cases} \tag {13}\end{align*}$$ With the consideration of the LS factor in the scheduling of shiftable appliances the Eq. (12) will become as. $$\begin{equation*} \sum _{t=t_{s,b}^{a}}^{t_{s,b}^{a}+{t_{a}^{b}}}Z^{t,m}_{a,b}L^{t}_{m} =t_{a}^{b}\;\;\;\;\;\; \forall a,m,b \tag {14}\end{equation*}$$ Many household items, such as washing machines and electric iron, depend on the availability of humans. The HIF needs to be taken into account to ensure that consumers are available for the appliance’s operation. The value of HIF is either “1” or “0” depending on the appliance. HIF is mathematically represented in Eq. (15). $$\begin{align*} H^{t,m}_{a,b} = \begin{cases} \displaystyle 1 & \text {if the}~ b^{th} ~\text{consumer of the}~ m^{th} ~\text{CCHP} \\ \displaystyle & \text {microgrid is available for the operation} \\ \displaystyle & \text {of the}~ {a^{th}} ~\text{appliance at the}~ t^{th} ~\text{time slot}~ \\ \displaystyle 0 & \text {otherwise} \end{cases} \tag {15}\end{align*}$$ With the consideration of HIF the Eq. (14) becomes as. $$\begin{equation*} \sum _{t=t_{s,b}^{a}}^{t_{s,b}^{a}+{t_{a}^{b}}}Z^{t,m}_{a,b}L^{t}_{m}H^{t,m}_{a,b} =t_{a}^{b}\;\;\;\;\;\; \forall a,m,b \tag {16}\end{equation*}$$ Another constraint that affects the schedule of shiftable appliances is CP. CP is related to consumer satisfaction and comfort which means that consumer is sometimes not comfortable operating the appliance even if DSM have shifted it to a time slot where the cost is minimum. The CP factor is mathematically represented as in Eq. (17). $$\begin{align*} \omega ^{t,m}_{a,b} = \begin{cases} \displaystyle 1 & \text {if the}~ b^{th} ~\text{consumer of the}~ m^{th} ~\text{CCHP} \\ \displaystyle & \text {microgrid wants to operate the}~{a^{th}}~ \\ \displaystyle & \text {appliance at the}~ t^{th} ~\text{time slot}~ \\ \displaystyle 0 & \text {otherwise} \end{cases} \tag {17}\end{align*}$$ Including the impact of CP, the Eq. (16) becomes as. $$\begin{equation*} \sum _{t=t_{s,b}^{a}}^{t_{s,b}^{a}+{t_{a}^{b}}}Z^{t,m}_{a,b}L^{t}_{m}H^{t,m}_{a,b}\omega ^{t,m}_{a,b} =t_{a}^{b}\;\;\;\;\;\; \forall a,m,b \tag {18}\end{equation*}$$

Another constraint that affects the schedule of shiftable appliances is the peak clipping limit. Peak clipping constraint will ensure that the maximum demand of any CCHP microgrid at any time slot will not exceed a certain limit. The energy management controller (EMC) sets the peak clipping limit to ensure the stability of the power system and a consistent power supply. Peak clipping constraint is mathematically expressed in Eq. (19).

$$\begin{align*} & \sum _{t=t_{a}^{s,b}}^{t_{a}^{s,b}+{t_{a}^{b}}}Z^{t,m}_{a,b}L^{t}_{m}H^{t,m}_{a,b} \omega ^{t,m}_{a,b}{EL}^{t,m}_{a,b}+{EL}_{m}^{t} \\ & \quad + {HL}_{m}^{t}+{QL}_{m}^{t}\leq {\gamma _{m}^{t}}, \;\forall \; m,t,b \tag {19}\end{align*}$$ In Eq. (19), the shiftable electrical load is denoted by ${EL}^{t,m}_{a,b}$ , and the base heating, electrical, and cooling loads are represented by ${HL}_{m}^{t}$ , ${EL}_{m}^{t}$ , and ${QL}_{m}^{t}$ respectively. The peak clipping limit is denoted by $\gamma _{m}^{t}$ and this limit must not be violated to reduce PAPR. PAPR can be expressed mathematically as in Eq. (20). $$\begin{equation*} PAPR=\frac {Peak\;power\;demand} {Average\;power\;demand} \tag {20}\end{equation*}$$ Reducing the peak power demand in Eq. (20) will decrease the PAPR. Reduction in PAPR will reduce the line power losses and ultimately the efficiency of the system will be enhanced. The model for energy trading will follow the model for energy management if the REG of the microgrid itself is insufficient to meet its energy demands.

B. Model for Energy Trading

A bi-directional communication network is used to link each CCHP microgrid with utility and neighboring CCHP microgrids, as illustrated in Fig. 2. The fundamental idea behind energy trading is that any CCHP microgrid within the interconnected system can procure additional energy when its own REG falls short of meeting its energy demands. Initially, the microgrid will attempt to purchase energy from nearby connected CCHP microgrids, as they offer lower tariffs compared to the utility. Only if energy from the nearby microgrids is unavailable will it resort to purchasing energy from the utility. Conversely, any CCHP microgrid is able to sell its surplus energy either to nearby microgrids or to the utility. In emergency situations, diesel generators will be employed as a backup power source. Table 1 provides an overview of the various notations used in the mathematical modeling of energy trading.

Electrical energy balance constraint for the $m^{th}$ CCHP microgrid as illustrated in Eq. (21). The left side of this constraint is the sum of energy produced by its own REG $(E_{m,g}^{t})$ , energy procured from utility $(E_{u,m}^{t})$ and nearby the $k^{th}$ CCHP microgrids $(E_{k,m}^{t})$ . The right side of this constraint is the sum of energy sold to utility $(E_{m,u}^{t})$ and nearby connected CCHP microgrids $(E_{m,k}^{t})$ plus the energy required for shiftable $({EL}^{t,m}_{a,b})$ and non-shiftable $({EL}_{m}^{t})$ electrical loads.

$$\begin{align*} & E_{m,g}^{t}+E_{u,m}^{t}+\sum _{k=1,k\neq m}^{M} E_{k,m}^{t}=E_{m,u}^{t} \\ & \quad +\sum _{k=1,k\neq m}^{M} E_{m,k}^{t}+{EL}_{m}^{t} \\ & \quad +\sum _{t=t_{a}^{s,b}}^{t_{a}^{s,b}+{t_{a}^{b}}}Z^{t,m}_{a,b}L^{t}_{m}H^{t,m}_{a,b}\omega ^{t,m}_{a,b}{EL}^{t,m}_{a,b}, \;\;\;\forall \;\;\;\ m,t,b \tag {21}\end{align*}$$ The heat energy balance constraint for the $m^{th}$ CCHP microgrid is illustrated in Eq. (22). The left side of this constraint is the sum of heat energy produced by its own REG $(H_{m,g}^{t})$ and heat energy procured from nearby the $k^{th}$ CCHP microgrids $(H_{k,m}^{t})$ . The right side of this constraint is the summation of heat energy sold to other CCHP microgrids $(H_{m,k}^{t})$ plus the base heating load $({HL}_{m}^{t})$ . $$\begin{align*} H_{m,g}^{t}+\sum _{k=1,k\neq m}^{M} H_{k,m}^{t}\;=\;\sum _{k=1,k\neq m}^{M} H_{m,k}^{t}+{HL}_{m}^{t},\ \forall \ \ m,t \tag {22}\end{align*}$$ The balancing constraint for cooling energy of the $m^{th}$ CCHP microgrid is expressed in Eq. (23). The left side of this constraint is the sum of self-production of cooling energy $(Q_{m,g}^{t})$ and cooling energy procured from nearby the $k^{th}$ CCHP microgrids $(Q_{k,m}^{t})$ . The right side of this constraint is the sum of cooling energy sold to nearby connected CCHP microgrids $(H_{m,k}^{t})$ plus the cooling energy required for base cooling load $({QL}_{m}^{t})$ . $$\begin{align*} Q_{m,g}^{t}+\sum _{k=1,k\neq m}^{M} Q_{k,m}^{t}\;=\;\sum _{k=1,k\neq m}^{M} Q_{m,k}^{t}+{QL}_{m}^{t},\;\forall \; m,t \tag {23}\end{align*}$$

A CCHP microgrid can generate electricity from a variety of sources, such as wind turbines, solar PV, solar thermal generators, etc. The maximum generating capacity of electrical energy by each CCHP microgrid can be written mathematically as in Eq. (24). Each CCHP microgrid has access to a variety of heat-generating sources, such as solar thermal collectors and heat from micro-turbines. Every CCHP microgrid’s capacity to generate heat is constrained by a certain maximum limit, as demonstrated in Eq. (25). Similar to this, every CCHP microgrid has a certain limit for its cooling energy generation, which is depicted in Eq. (26).

$$\begin{align*} 0 & \leq {E_{m,g}^{t}}\leq {E_{m,g,max}^{t}},\;\;\; \forall \; m,t \tag {24}\\ 0 & \leq {H_{m,g}^{t}}\leq {H_{m,g,max}^{t}},\;\;\; \forall \; m,t \tag {25}\\ 0 & \leq {Q_{m,g}^{t}}\leq {Q_{m,g,max}^{t}},\;\;\; \forall \; m,t \tag {26}\end{align*}$$

When the cooling, heating, and electric energy demands of the $m^{th}$ CCHP microgrid cannot be satisfied with its own REG then it will procure energy from nearby connected $k^{th}$ CCHP microgrids. The procurement of energy from nearby the $k^{th}$ CCHP microgrid is bounded by a maximum value and it is expressed mathematically in Eqs. (27), (28), and (29) for electrical, heating and cooling energy respectively.

$$\begin{align*} 0 & \leq E_{k,m}^{t}\leq {E}_{k,m}^{t,max} \;\;\;\forall \; m,k,t \tag {27}\\ 0 & \leq H_{k,m}^{t}\leq {H}_{k,m}^{t,max} \;\;\;\forall \;m,k,t \tag {28}\\ 0 & \leq Q_{k,m}^{t}\leq {Q}_{k,m}^{t,max} \;\;\;\forall \; m,k,t \tag {29}\end{align*}$$ If the obtained energy from the $k^{th}$ CCHP microgrid is still insufficient to satisfy the energy requirements of the $m^{th}$ CCHP microgrid, the $m^{th}$ microgrid will seek to purchase energy from the utility. However, there is a limit on the maximum amount of energy that can be purchased from the utility, denoted by a bound specified in Eq. (30). $$\begin{equation*} 0 \leq {E_{u,m}^{t}}\leq {E_{u,m,max}^{t}},\;\;\; \forall \;m,t \tag {30}\end{equation*}$$ Exchange of energy with itself is not permitted and this condition is illustrated mathematically in Eqs. (31), (32), and (33), for electrical, cooling and heating energy respectively. $$\begin{align*} E_{m,m}^{t}& =0,\;\;\;\forall \; m,t \tag {31}\\ Q_{m,m}^{t}& =0,\;\;\;\forall \; m,t \tag {32}\\ H_{m,m}^{t}& =0,\;\;\;\forall \; m,t \tag {33}\end{align*}$$

The simultaneous sale and purchase of energy are not allowed for any CCHP microgrid, and this restriction is outlined in Eqs. (34), (35) and (36) for electrical, cooling, and heating energy respectively between the $m^{th}$ and $k^{th}$ CCHP microgrids.

$$\begin{align*} E_{k,m}^{t} E_{m,k}^{t}& \leq 0,\;\;\;\forall \; m,k,t \tag {34}\\ Q_{k,m}^{t} Q_{m,k}^{t}& \leq 0,\;\;\;\forall \; m,k,t \tag {35}\\ H_{k,m}^{t }H_{m,k}^{t}& \leq 0,\;\;\;\forall \; m,k,t \tag {36}\end{align*}$$ The mathematical model of this research work is non-convex bi-linear due to the non-linear constraints in Eqs. (34), (35) and (36). Therefore, by using McCormick envelopes, these constraints can be relaxed. Eq. (34), which demonstrates the non-linear constraint for electrical energy, is relaxed by the use of McCormick envelopes as in Eq. (37). $$\begin{align*} & f(E_{k,m}^{t},E_{m,k}^{t}) \\ & =E_{k,m}^{t}E_{m,k}^{t} \\ & h(E_{k,m}^{t},E_{m,k}^{t}) \\ & = \max \{E_{k,m}^{min}E_{m,k}^{t}+E_{m,k}^{min}E_{k,m}^{t} \\ & \quad -E_{k,m}^{min}E_{v}^{min},E_{k,m}^{max}E_{m,k}^{t} +E_{m,k}^{max}E_{k,m}^{t}-E_{k,m}^{max}E_{m,k}^{max}\} \\ & \quad \times E_{k,m}^{min}E_{m,k}^{t}+ E_{m,k}^{min}E_{k,m}^{t}-E_{k,m}^{min}E_{m,k}^{min}\leq {C}_{E} \\ & \quad \times E_{k,m}^{max}E_{m,k}^{t}+E_{m,k}^{max}E_{k,m}^{t}-E_{k,m}^{max}E_{m,k}^{max}\leq {C}_{E} \tag {37}\end{align*}$$

The upper and lower limits for electrical energy are represented in Eq. (37) by the terms $E_{m,k}^{max}$ , $E_{k,m}^{max}$ and $E_{k,m}^{min}$ , $E_{m,k}^{min}$ . Electrical energy’s convex envelope coefficient is denoted by ${C}_{E}$ . The non-linear constraints for cooling energy are illustrated in Eq. (35). The McCormick envelopes for Eq. (35) are written in Eq. (38), in which the upper and lower boundaries for cooling energy are represented by $Q_{m,k}^{max}$ , $Q_{k,m}^{max}$ and $Q_{k,m}^{min}$ , $Q_{m,k}^{min}$ respectively. ${C}_{Q}$ is the coefficient for the convex envelope of cooling energy.

$$\begin{align*} & f(Q_{k,m}^{t},Q_{m,k}^{t}) \\ & =Q_{k,m}^{t}Q_{m,k}^{t} \\ & h(Q_{k,m}^{t},Q_{m,k}^{t}) \\ & = \max \{Q_{k,m}^{min}Q_{m,k}^{t}+Q_{m,k}^{min}Q_{k,m}^{t} \\ & \quad {-} Q_{k,m}^{min}Q_{m,k}^{min}, Q_{k,m}^{max}Q_{m,k}^{t}+ Q_{m,k}^{max}Q_{k,m}^{t}-Q_{k,m}^{max}Q_{m,k}^{max}\} \\ & \quad \times Q_{k,m}^{min}Q_{m,k}^{t}+ Q_{m,k}^{min}Q_{k,m}^{t}-Q_{k,m}^{min}Q_{m,k}^{min}\leq {C}_{Q} \\ & \quad \times Q_{k,m}^{max}Q_{m,k}^{t}+Q_{m,k}^{max}Q_{k,m}^{t}-Q_{k,m}^{max}Q_{m,k}^{max}\leq {C}_{Q} \tag {38}\end{align*}$$ A non-linear constraint for thermal energy is written in Eq. (36), for which the McCormick envelopes are presented in Eq. (39). $$\begin{align*} & f(H_{k,m}^{t},H_{m,k}^{t}) \\ & =H_{k,m}^{t}H_{m,k}^{t} \\ & h(H_{k,m}^{t},H_{m,k}^{t}) \\ & = \max \{H_{k,m}^{min}H_{m,k}^{t}+H_{m,k}^{min}H_{k,m}^{t} \\ & \quad -H_{k,m}^{min}H_{m,k}^{min}, H_{k,m}^{max}H_{m,k}^{t}+ H_{m,k}^{max}H_{k,m}^{t}-H_{k,m}^{max}H_{m,k}^{max}\} \\ & \quad \times H_{k,m}^{min}H_{m,k}^{t}+ H_{m,k}^{min}H_{k,m}^{t}-H_{k,m}^{min}H_{m,k}^{min}\leq {C}_{H} \\ & \quad \times H_{k,m}^{max}H_{m,k}^{t}+H_{m,k}^{max}H_{k,m}^{t}-H_{k,m}^{max}H_{m,k}^{max}\leq {C}_{H} \tag {39}\end{align*}$$

The upper and lower bounds of the heating energy are denoted by $H_{k,m}^{max}$ , $H_{m,k}^{max}$ and $H_{k,m}^{min}$ , $H_{m,k}^{min}$ respectively in Eq. (39), where ${C}_{H}$ is the coefficient for the convex envelope of heating energy.

The overall cost of the system is the sum of expenses and revenues, which is mathematically modeled in Eq. (40). Various expenses include the cost of generating electricity, heating, and cooling energy; the cost of purchasing electrical, heating, and cooling energy from $(M-1)$ CCHP microgrids; and the cost of purchasing electrical energy from the utility. Various revenues come from selling electrical, heating, and cooling energy to $(M-1)$ CCHP microgrids as well as from selling electrical energy to the utility.

$$\begin{align*} & \sum _{t=1}^{T}\Bigg [\sum _{m=1}^{M}\bigg (C(E_{m,g}^{t})+C(H_{m,g}^{t})+C(Q_{m,g}^{t}) \\ & \quad +C(E_{u,m}^{t})-C(E_{m,u}^{t})\bigg )+\sum _{k=1, k\neq m}^{M}\bigg (C(E_{k,m}^{t}) \\ & \quad +C(Q_{k,m}^{t})+C(H_{k,m}^{t})-C(E_{m,k}^{t}) \\ & \quad -C(Q_{m,k}^{t})-C(H_{m,k}^{t})\bigg )\Bigg ] \tag {40}\end{align*}$$ Our proposed architecture aims to reduce the system’s overall cost while satisfying all the constraints. The complete mathematical model of the proposed system is shown in Eq. (41). $$\begin{align*} & \min _{\substack {E_{m,g}^{t},E_{u,m}^{t},E_{m,u}^{t},E_{m,k}^{t},E_{k,m}^{t} \\ H_{m,g}^{t},H_{m,k}^{t},H_{k,m}^{t},Q_{m,g}^{t},Q_{k,m}^{t} \\ Q _{m,k}^{t},Z_{a,b}^{t,m},\;\forall \;t,b,k,m,a}} \sum _{t=1}^{T}\sum _{m=1}^{M}\Bigg [\bigg (C(E_{m,g}^{t}) \\ & \hphantom {\qquad \text {subject to}~}+C(H_{m,g}^{t})+C(Q_{m,g}^{t})+C(E_{u,m}^{t}) \\ & \hphantom {\qquad \text {subject to}~}-C(E_{m,u}^{t})\bigg ) \\ & \hphantom {\qquad \text {subject to}~}+\sum _{k=1, k\neq m}^{M}\bigg (C(E_{k,m}^{t})+C(Q_{k,m}^{t})+C(H_{k,m}^{t}) \\ & \hphantom {\qquad \text {subject to}~}-C(E_{m,k}^{t})- \\ & \hphantom {\qquad \text {subject to}~}C(Q_{m,k}^{t})-C(H_{m,k}^{t})\bigg )\Bigg ] \\ & \qquad \text {subject to}~ C_{1}: E_{m,g}^{t}+E_{u,m}^{t}+\sum _{k=1,k\neq m}^{M} \\ & \hphantom {\qquad \text {subject to}~}E_{k,m}^{t}=E_{m,u}^{t}+\sum _{k=1,k\neq m}^{M} E_{m,k}^{t}+ \\ & \hphantom {\qquad \text {subject to}~}{EL}_{m}^{t}+\sum _{t=t_{a}^{s,b}}^{t_{a}^{s,b}+{t_{a}^{b}}}Z^{t,m}_{a,b}L^{t}_{m}H^{t,m}_{a,b} \omega ^{t,m}_{a,b}{EL}^{t,m}_{a,b}, \\ & \hphantom {\qquad \text {subject to}~}\forall m,t,b \\ & \hphantom {\qquad \text {subject to}~} C_{2}: H_{m,g}^{t}+\sum _{k=1,k\neq m}^{M} H_{k,m}^{t}\; \\ & \hphantom {\qquad \text {subject to}~}=\;\sum _{k=1,k\neq m}^{M} H_{m,k}^{t}+{HL}_{m}^{t},\;\forall \; m,t \\ & \hphantom {\qquad \text {subject to}~} C_{3}: Q_{m,g}^{t}+\sum _{k=1,k\neq m}^{M} Q_{k,m}^{t}\; \\ & \hphantom {\qquad \text {subject to}~}=\;\sum _{k=1,k\neq m}^{M} Q_{m,k}^{t}+{QL}_{m}^{t},\;\forall \; m,t \\ & \hphantom {\qquad \text {subject to}~} C_{4}: \sum _{a\in {\sigma _{1}}} Z^{t_{1},m}_{a,b}+\sum _{a\in {\sigma _{2}}} Z^{t_{2},m}_{a,b} \leq {1} \\ & \hphantom {\qquad \text {subject to}~}\forall (t_{1}\lt {t_{2}}) a,m,b \\ & \hphantom {\qquad \text {subject to}~} C_{5}: \sum _{t=t_{s,b}^{a}}^{t_{s,b}^{a}+{t_{a}^{b}}}Z^{t,m}_{a,b}L^{t}_{m}H^{t,m}_{a,b}\omega ^{t,m}_{a,b} =t_{a}^{b}\;\;\;\;\;\; \forall a,m,b \\ & \hphantom {\qquad \text {subject to}~} C_{6}: \sum _{t=t_{a}^{s,b}}^{t_{a}^{s,b}+{t_{a}^{b}}}Z^{t,m}_{a,b}L^{t}_{m}H^{t,m}_{a,b}\omega ^{t,m}_{a,b}{EL}^{t,m}_{a,b}+{EL}_{m}^{t}+ \\ & \hphantom {\qquad \text {subject to}~}{HL}_{m}^{t}+{QL}_{m}^{t}\leq {\gamma _{m}^{t}}, \;\forall \; m,t,b \\ & \hphantom {\qquad \text {subject to}~} C_{7}: 0 \leq {E_{m,g}^{t}}\leq {E_{m,g,max}^{t}},\;\;\; \forall \; m,t \\ & \hphantom {\qquad \text {subject to}~} C_{8}: 0 \leq {H_{m,g}^{t}}\leq {H_{m,g,max}^{t}},\;\;\; \forall \; m,t \\ & \hphantom {\qquad \text {subject to}~} C_{9}: 0 \leq {Q_{m,g}^{t}}\leq {Q_{m,g,max}^{t}},\;\;\; \forall \; m,t \\ & \hphantom {\qquad \text {subject to}~} C_{10}: 0 \leq E_{k,m}^{t}\leq E_{k,m}^{t,max},\;\;\;\forall \; m,k,t \\ & \hphantom {\qquad \text {subject to}~} C_{11}: 0 \leq H_{k,m}^{t}\leq {H}_{k,m}^{t,max},\;\;\;\forall \;m,k,t \\ & \hphantom {\qquad \text {subject to}~} C_{12}: 0 \leq Q_{k,m}^{t}\leq {Q}_{k,m}^{t,max},\;\;\;\forall \; m,k,t \\ & \hphantom {\qquad \text {subject to}~} C_{13}: 0 \leq {E_{u,m}^{t}}\leq {E_{u,m,max}^{t}},\;\;\; \forall \;m,t \\ & \hphantom {\qquad \text {subject to}~} C_{14}: E_{m,m}^{t}=0,\;\forall \; m,t \\ & \hphantom {\qquad \text {subject to}~} C_{15}: H_{m,m}^{t}= 0,\;\forall \; m,t\; \\ & \hphantom {\qquad \text {subject to}~} C_{16}: Q_{m,m}^{t}= 0,\;\forall \; m,t \\ & \hphantom {\qquad \text {subject to}~} C_{17}: E_{k,m}^{min}E_{m,k}^{t}+ E_{m,k}^{min}E_{k,m}^{t} \\ & \hphantom {\qquad \text {subject to}~}-E_{k,m}^{min}E_{m,k}^{min}\leq {C}_{E}, \\ & \hphantom {\qquad \text {subject to}~} \forall \; m,k,t \\ & \hphantom {\qquad \text {subject to}~} C_{18}:E_{k,m}^{max}E_{m,k}^{t}+E_{m,k}^{max}E_{k,m}^{t} \\ & \hphantom {\qquad \text {subject to}~}-E_{k,m}^{max}E_{m,k}^{max}\leq {C}_{E}, \\ & \hphantom {\qquad \text {subject to}~}\forall \; m,k,t \\ & \hphantom {\qquad \text {subject to}~} C_{19}: H_{k,m}^{min}H_{m,k}^{t}+ H_{m,k}^{min}H_{k,m}^{t} \\ & \hphantom {\qquad \text {subject to}~}-H_{k,m}^{min}H_{m,k}^{min}\leq {C}_{H}, \\ & \hphantom {\qquad \text {subject to}~}\forall \; m,k,t \\ & \hphantom {\qquad \text {subject to}~} C_{20}:H_{k,m}^{max}H_{m,k}^{t}+H_{m,k}^{max}H_{k,m}^{t} \\ & \hphantom {\qquad \text {subject to}~}-H_{k,m}^{max}H_{m,k}^{max}\leq {C}_{H}, \\ & \hphantom {\qquad \text {subject to}~}\forall \; m,k,t \\ & \hphantom {\qquad \text {subject to}~} C_{21}: Q_{k,m}^{min}Q_{m,k}^{t}+ Q_{m,k}^{min}Q_{k,m}^{t} \\ & \hphantom {\qquad \text {subject to}~}-Q_{k,m}^{min}Q_{m,k}^{min}\leq {C}_{Q}, \\ & \hphantom {\qquad \text {subject to}~}\forall \; m,k,t \\ & \hphantom {\qquad \text {subject to}~} C_{22}:Q_{k,m}^{max}Q_{m,k}^{t}+Q_{m,k}^{max}Q_{k,m}^{t} \\ & \hphantom {\qquad \text {subject to}~}-Q_{k,m}^{max}Q_{m,k}^{max}\leq {C}_{Q}, \\ & \hphantom {\qquad \text {subject to}~}\forall \; m,k,t \tag {41}\end{align*}$$

SECTION IV. Results and Discussion

The proposed model’s effectiveness has been demonstrated through simulations conducted in Matlab. To ensure simplicity and clarity for readers, the simulations involve four connected CCHP microgrids while the proposed model can be applied to any numbers of CCHP microgrids. These microgrids are also connected to the utility through a bi-directional communication network. Each CCHP microgrid is equipped with distributed energy resources, including wind turbines, solar PV systems, solar thermal collectors, and diesel generators. The generation capacity of various sources are limited by upper bounds. Additionally, various components are assumed to be installed within each microgrid to convert energy from one form to another. On the consumption side, each CCHP microgrid accommodates a set of B consumers. These consumers have both shiftable loads and fixed loads. Initially, the microgrids attempt to meet the energy demands of the shiftable and fixed loads using their own REG. However, if the energy demand cannot be fulfilled by the microgrid’s own REG, the model for energy management is applied to address the deficit.

Every CCHP microgrid is equipped with an EMC to implement the model for energy management. The process of implementing the model for energy management is outlined in Algorithm 1. The algorithm describes the various input parameters necessary for the implementation. The EMS plays a crucial role in organizing the scheduling of shiftable appliances within each microgrid. It aims to achieve multiple objectives such as reducing the system’s cost and peak power demand while ensuring that constraints such as HIF, CP, LS, and appliance priority are not violated. If the energy demands of the microgrid cannot be met even after rearranging the shiftable appliances, the model for energy trading is applied.

SECTION Algorithm 1 Pseudo-Code for the Model of Energy Management

1:

Initialize the M, T, B, and total iterations (I)

2:

Initialize the self generation of each CCHP microgrid $E_{m,g}^{t}$ , $Q_{m,g}^{t}$ , $H_{m,g}^{t}$ for all time slots

3:

Initialize the energy from the utility $E_{u,m}^{t}$ .

4:

Initialize the pattern of LS, HIF, and CP for shiftable appliances

5:

Initialize the peak clipping limit

6:

$C_{u,m}^{t} \gets$ Get utility tariff for each CCHP microgrid to schedule the load profile of each appliance in a set $B^{m}$ .

7:

$Z_{a,b}^{t,m} \gets$ Get load profile of shiftable appliances in a set $B^{m}$

8:

Perform energy management using branch and bound algorithm and calculate the demand curve for each CCHP microgrid.

9:

Share the demand curve of each CCHP microgrid with the energy trading center (ETC).

10:

if Self-Generation is greater than or equal to load demand for all time slots then

11:

Run all the appliances as per their schedule/recommended by the energy management module

12:

else

13:

Perform energy management using branch and bound algorithm.

14:

end if

Each CCHP microgrid incorporates an ETC that facilitates the implementation of the model for energy trading. Algorithm 2 outlines the step-by-step procedure for implementing the model for energy trading, including the necessary input parameters. During the model for energy management, a comparison is made between the energy demands and self-generation of each microgrid, and this information is shared with the ETC. Based on this comparison, the ETC determines whether the $m^{th}$ CCHP microgrid needs to purchase or sell energy. To comprehensively explore the solution, several scenarios are considered. These scenarios encompass various aspects and factors, allowing for a holistic understanding of the system. The overall solution of the proposed model is shown in Fig. 3.

FIGURE 3.

Flowchart of the proposed solution.

SECTION Algorithm 2 Pseudo-Code for the Model of Energy Trading

1:

Get Tariff utility and CCHP microgrid to sell energy, load profile, and self-REG capacity

2:

Procure energy from connected CCHP microgrids or from utility grid during the time when self-REG is less than loads demand

3:

Compute the system’s total cost

4:

Plot the Results

5:

if Termination Criteria Met then

6:

Stop the simulation process

7:

else

8:

Go to step 7 of Algorithm 1

9:

end if

A. Case 1

In the first step same time of use (ToU) tariff is offered to all CCHP microgrids by the utility, as depicted in Fig. 4. Every CCHP microgrid contains shiftable as well as non-shiftable appliances. Demand-side management basically deals with shiftable appliances. Various shiftable appliances that are considered in these simulations are washing machines (WM), dryers (Dy), electric vehicles (EVs), and dishwasher (DW). The schedule of shiftable appliances in Fig. 4 is (0-380) minutes where the cost per kWh is the lowest. Various constraints like peak clipping limit, LS, HIF, CP, etc. have not been taken into account in this case. The status of HIF, CP, and LS constraints for WM, Dy, DW, and EV is shown in Fig. 5. These constraints are set to 1 in Fig 5, clearly indicating that the impact of these constraints is neglected while making a schedule for shiftable appliances in Case 1.

FIGURE 4.

Shiftable appliances schedule and an initial ToU tariff.

FIGURE 5.

Pattern of HIF, LS, CP constraints.

After scheduling of shiftable appliances as shown in Fig. 4, the renewable energy generation (REG) of each CCHP microgrid is compared to the energy consumed by electrical, heating, and cooling loads, as depicted in Fig. 6. To get the minimum value of overall cost the schedule of shiftable appliances is set during those time slots that have the lowest cost per unit. The overall cost is decreased by 35.31% but in this scenario, certain energy management constraints such as peak clipping, LS, HIF, and CP are neglected. As a result, maximum demand will occur which increases the line losses and hence reduces the efficiency of the system. Neglecting HIF and CP may cause user discomfort.

FIGURE 6.

Comparison of load demands with REG without applying EM and ET.

Based on the comparison presented in Fig. 6, energy trading is performed among several CCHP microgrids which are shown in Fig. 7. Any CCHP microgrid will apply the model for energy trading if it lacks the necessary energy or has excess energy. In the case of energy deficiency from its own REG, the CCHP microgrid will buy the required energy from nearby connected CCHP microgrids or from the utility. Conversely, if the energy generated by REG is more than its demand then it will sell out the surplus energy to nearby CCHP microgrid or utility. Multiple CCHP microgrids such as 2, 3, and 4 can be noted in Fig. 7 that they are using diesel generators to meet their energy demands. Diesel generators are operated during emergencies when a CCHP microgrid’s energy demands cannot be satisfied by other sources such as self-REG, energy acquired from nearby connected CCHP microgrids, or from the utility.

FIGURE 7.

Energy trading before applying EM.

B. Case 2

The ToU tariff will be updated for every CCHP microgrid on the basis of the comparison shown in Fig. 6, between energy consumption and REG. Fig. 8 illustrates the schedule of shiftable appliances on the basis of the new ToU price for every CCHP microgrid. Each CCHP microgrid shares the most updated ToU tariff with a nearby connected CCHP microgrid through an ETC. In this case, the shiftable appliances are arranged in a way that will reduce the peak demand along with the reduction in the overall cost of the CCHP system. Various other constraints that are taken into account are LS, HIF, and CF. Patterns of HIF for various shiftable appliances such as WM, DW, Dy, and EV as well as CP and load shedding patterns are shown in Fig. 9. Cumulative constraint 1 (CC1) combines the pattern of HIF, LS, and CP for WM, Dy, and DW while cumulative constraint 2 (CC2) combines the impact of HIF, CP, and LS for electric vehicles. The pattern of CC1 and CC2 are shown in Fig. 9.

FIGURE 8.

Updated ToU tariff and shiftable loads profile.

FIGURE 9.

Updated pattern of HIF, LS, CP constraints.

After scheduling the shiftable appliances, the consumption of energy by each CCHP microgrid is compared with the REG as shown in Fig. 10. It can be noted in Fig. 10, that peak demand is reduced by 37.02% whereas the system’s cost is reduced by 31.32%. Reduced line losses as a result of decreased peak demand will increase the system’s efficiency.

FIGURE 10.

Comparison of load demands with REG after applying EM and ET.

Based on the comparison between energy consumption and REG after the recent ToU tariff, energy trading is carried out as shown in Fig. 11. It is clear in Fig. 11, that every CCHP microgrid has a variety of options for meeting its energy needs, including self-energy generation, energy purchases from nearby connected CCHP microgrids, or utility. When a CCHP microgrid’s REG falls short of meeting its energy requirements, it will obtain energy from nearby interconnected CCHP microgrids. In the event that the local microgrids do not possess the required energy, the CCHP microgrid will purchase it from the utility, ensuring an adequate energy supply. A diesel generator will be used in case of emergency when energy from other sources is not available. Alternatively, when a CCHP microgrid’s renewable energy generation surpasses its energy demands, it has the option to sell the surplus energy to other connected CCHP microgrids or to a utility.

FIGURE 11.

Energy trading after applying EM.

C. Case 3

In Case 2 of energy trading, every CCHP microgrid will update its ToU pricing, as depicted in Fig. 12. The revised ToU tariffs are then shared with the ETC, which subsequently distributes them to the other CCHP microgrids involved in the trading process. Consequently, every CCHP microgrid will reconfigure the arrangement of its shiftable appliances based on the updated ToU pricing, as illustrated in Fig. 12. The reorganization of shiftable appliances aims to fulfill multiple criteria, including peak clipping, HIF, LS, CP, and appliance priority. Additionally, the objective is to minimize the system’s cost. Various shiftable appliances such as DW, WM, Dy, and EV are planned for a specific time duration ranging from 250 to 820 minutes, as indicated in Fig. 12.

FIGURE 12.

Updated ToU tariff and shiftable loads profile.

Energy consumed by various loads such as heating, cooling, and electrical is compared with the REG of every CCHP microgrid as illustrated in Fig. 13. Reduction in peak power demand by 32.72% is presented in Fig. 13, due to which the line losses decrease and hence enhancement takes place in the performance of the system. Improvement in the system’s economic performance is due to the reduction in the overall cost by 33.13%. Fig. 13 also demonstrates that the rescheduling of shiftable appliances will reduce the differences between REG and energy consumption. Energy trading among various CCHP microgrids and utility is based on the comparison made in Fig. 13. Energy exchange in Fig. 14 is based on a deficiency of REG to meet its own energy demands. During energy trading, every CCHP microgrid buys energy when its own REG is not enough to meet its demands. Similarly, it sells the excess energy to earn profit from nearby CCHP microgrids or from utility. Furthermore, if the necessary energy cannot be obtained from the utility or other CCHP microgrids, a diesel generator will be employed, as can be seen in Fig. 14.

FIGURE 13.

Updated comparison of load demands with REG after applying EM and ET.

FIGURE 14.

Updated energy trading after applying EM.

D. Case 4

On the basis of the comparison made in Case 3, the ToU pricing is updated again for every CCHP microgrid which is illustrated in Fig. 15. The updated ToU tariff of each CCHP microgrid is shared with other CCHP microgrids in the network through the ETC. Based on the updated ToU pricing every CCHP microgrid will rearrange its shiftable appliances in such a way that will not only further reduce system cost but also satisfy all the associated constraints.

FIGURE 15.

Pattern of shiftable appliances after updated ToU tariff.

After rescheduling the shiftable appliances in accordance with the updated ToU tariff, The energy consumption of each CCHP microgrid is evaluated by comparing it with the self-REG, as shown in Fig. 16. Optimal satisfaction of energy demand can be observed in Fig. 16 by its own REG. It will ultimately reduce the overall cost by 34.01% and will improve the reliability and efficiency of the system. In this case peak energy demand of CCHP microgrids is decreased by 32.98%.

FIGURE 16.

Updated comparison of load demands with REG after applying EM and ET.

The comparison of energy generation and consumption, as shown in Fig. 16, serves as the foundation for energy trading among different CCHP microgrids, as illustrated in Fig. 17. Every CCHP microgrid buys electricity from nearby connected CCHP microgrids or from a utility when its demands are not covered by its own sources, as shown in Fig. 17. Surplus energy if any can be sold to utility or nearby CCHP microgrids.

FIGURE 17.

Updated energy trading after updatedToU tariff and EM.

Reduction in peak demand plays a critical role in the enhancement of system performance and efficiency. Line losses are directly related to peak demand and hence will be reduced. Secondly, a reduction in peak demand will also make it possible to fulfill the energy requirements of any CCHP microgrid with its local REG. It will reduce the overall cost and dependency of the CCHP microgrid on utility and diesel generators. Reduction in peak demand for different iterations is depicted in Fig. 18. The results of various iterations have been summarized in Table 3.

TABLE 3 Summary of Results

FIGURE 18.

Reduction in peak demand for various iterations after applying EM and ET.

E. Comparative Analysis With Literature

The summary of the literature review is presented in Table 2, highlighting cost reduction as the most significant factor. The reported cost reductions in various studies are 16.51% [13], 17.75% [26], 19.10% [28], 8.7% [30], 12.46% [31], 16.77% [32], and 4% [38]. Additionally, Table 2 summarizes various other factors not considered in the cited articles such as human interaction factor, consumer preferences, user comfort and peak power reduction. In our study, we achieved a 31.13% reduction in overall system cost, surpassing the reductions reported in the cited articles, thereby validating our findings against the available literature.

F. Limitations of the Proposed Approach

In the proposed approach, it is assumed that CCHP microgrids are located in close proximity, enabling the exclusion of thermal transmission losses. However, neglecting these losses may impact the system’s performance and efficiency. Additionally, the influence of uncertainties in factors such as renewable energy resources and load has not been considered, which could also affect overall system operation and efficiency.

SECTION V. Conclusion

A model for energy management has been developed for cooperative CCHP microgrids having various renewable energy sources. Initially, the utility provides ToU tariffs for all CCHP microgrids, which typically have higher costs per kilowatt-hour. The EMC schedules the shiftable appliances to reduce system costs and peak energy demand while taking into account various factors to avoid user discomfort. These factors are human interaction factor, load shedding, consumer preference, and appliance priority. The profiles of energy consumption and REG are set by the EMC of the respective CCHP microgrid which is then shared with the ETC. On the basis of profiles shared by the EMC, the ETC updates the ToU tariff for every CCHP microgrid. On the basis of the new ToU tariff, every CCHP microgrid will reshuffle its shiftable appliances with the aim to reduce the system’s peak energy demand and cost without sacrificing user comfort. During energy cooperation, every CCHP microgrid can exchange energy with the nearby connected CCHP microgrids as well as with utility. Purchasing energy from other CCHP microgrids is estimated to be less expensive per kilowatt-hour than purchasing from a utility due to REG. It can be observed from simulations that the maximum energy demands of every CCHP microgrid are satisfied by its local REG. Purchase from neighboring CCHP and utility is also minimized which will ultimately reduce the system’s cost. The operation of diesel generators is only for emergencies to avoid environmental pollution. The results further indicate that the reduction in the system’s total cost is 31.13% which will ultimately reduce the financial burden of the end users. Peak power demand is reduced by 23.35% due to which line losses will decrease and hence the system performance and efficiency will be enhanced without compromising the user comfort. In the future, this work can be further improved by incorporating uncertainties in various factors, such as load demand and power generation. Additionally, thermal transmission losses can also be taken into account for a more comprehensive analysis.

ACKNOWLEDGMENT

(Muhammad Riaz and Amad Zafar contributed equally to this work.)