Optimization of Combined Cooling, Heating, and Power Systems with Integrated Solar Collectors for Enhanced Thermal and Energy Performance

Figure 1 depicts the CCHP's suggested structure. A power MG, micro-gas system, micro-heat system, and micro-cool system make up the CCHP. The CCHP uses MT, FC, GB, EH, EC, AC, and P2G technology to facilitate communication between these systems. Natural gas powers the CHP-based MT, which concurrently produces power and heat. The FC converts the natural gas to power, the GB turns it into heat, and the EH uses the energy to produce heat. Additionally, AC turns heat into cool, whereas EC turns electricity into cooling the P2G system. The MG provides the power after CO₂ is extracted from CHP and combined with H2 to create synthetic natural gas (SNG). By lowering CO₂ emissions into the atmosphere, this procedure lessens environmental harm [1, 31-33].

Figure 1. Schematic diagram of combined cooling, heating, and power (CCHP) microgrid

2.1 Heat recovery model

Heat recovery (HR), also known as CHP, is utilized in this study to recover lost heat when electrical power is produced from a microturbine. HR or microturbine heat: $H_{M T}^t$ in KW may be written as follows:

$H_{M T}^t=\frac{P_{M T}^t\left(1-\eta_{M T}-\eta_l\right) \eta_{H R}}{\eta_{M T}}$                    (1)

where, $\eta_l$ is the heat loss factor, $\eta_{H R}$ is the efficiency of HR.

2.2 Diesel generator model

Diesel generator (DG) is an internal combustion diesel fuel generator used in this study to generate power during peak hours. The fuel consumption may be represented by the following linear equation: $P_{D G}^t$ is the output electrical power from FC at each time in (KWh), $\eta_{D G}$ is the efficiency of DG, and C_DG is the cost of fuel consumption by using DG in $ [34].

$C_{D G}{ }^t=a P_{D G}^t{ }^2+b P_{D G}^t+c$                      (2)

The cost coefficient of DG is represented by a, b, and c in $\left(\frac{\$}{K W^2 h}\right),\left(\frac{\$}{K W h}\right),\left(\frac{\$}{h}\right)$ correspondingly. One may calculate the start-up cost $S U C_{D G}$ and shut-down cost $S D C_{D G}$ in \$ by:

$S U C_{D G}{ }^t=S c_{D G}\left(U_{D G}^t-U_{D G}^t * U_{D G}^{t-1}\right)$                      (3)

$S D U_{D G}^t=S d_{D G}\left(U_{D G}^{t-1}-U_{D G}^t * U_{D G}^{t-1}\right)$                      (4)

The battery's limitation capacity can be stated as follows:

$P_{D G}^{min } U_{D G}^t \leq P_{b . c h}^t \leq P_{D G}^{max } \,\, U_{D G}^t$                     (5)

where, $P_{D G}^{min }, P_{D G}^{max }$ and the $U_{D G}$ on/off state of DG are the lowest and greatest power that DG may produce in KW. and Ramp up limit $U R_{D G}$ and ramp down limit $D R_{D G}$ in KW should be the ramp rate limitation for FC at each time interval.

$P_{D G}^t-P_{D G}^{t-1} \leq U R_{D G}$                  (6)

$P_{D G}^{t-1}-P_{D G}^t \leq D R_{D G}$                   (7)

Based on the maintenance cost rate coefficient $K_{o m . D G}$ in ($\frac{\$}{K W h}$), the maintenance cost of DG $C_{om . F C}$.

$C_{{om.DG }}^t=P_{D G}^t * K_{ {om.DG }}$                    (8)

2.3 Microturbines model

The users receive heat and power from the MT-based CCHP unit. The micro-turbine is used as a CHP device. It is powered by natural gas, where using the nanoparticles with fuel lowers greenhouse gas emissions. The following formula is used to determine the gas usage. can be represented by the linear formula [35]:

$C_{M T}^t=\frac{P_{M T}^t}{L C V * \eta_{M T}} * \beta_g$                       (9)

where, LCV was the low heating value of natural gas $\left(\frac{K W h}{m^3}\right)$, βg is the price of natural gas $\left(\frac{\$}{m^3}\right), P_{M T}^t$ is the output electrical power from MT at each time in KWh, and $C_{M T}$ is the cost of fuel consumption by the utilized microturbine in $.

It is possible to tune, the start-up cost $S U C_{M T}$ and shut-down cost $S D C_{M T}$ in (\$) by:

$S U C_{M T}{ }^t=S c_{M T}\left(U_{M T}^t-U_{M T}^t * U_{M T}^{t-1}\right)$                    (10)

$S D C_{M T}{ }^t=S d_{M T}\left(U_{M T}^{t-1}-U_{M T}^t * U_{M T}^{t-1}\right)$                     (11)

The maintenance cost of MT $C_{o m . M T}$ base on maintenance cost rate coefficient $K_{o m . M T}$ in $\left(\frac{\$}{K W h}\right)$.

$C_{o m . M T}^t=P_{M T}^t * K_{o m . M T}$                   (12)

The microturbine's constraint capacity can be stated as follows:

$P_{M T}^{min } U_{M T}^t \leq P_{M T}^t \leq P_{M T}^{max } U_{M T}^t$                      (13)

where, $P_{M T}^{min }, P_{M T}^{max }$, and the $U_{M T}$ on/off state of $M T$ represent the lowest and greatest power that $M T$ can produce in KW. Ramp up limit $U R_{M T}$ and Ramp down limit $D R_{M T}$ in KW should be the ramp rate constraints for $M T$ at each time interval.

$P_{M T}^t-P_{M T}^{t-1} \leq U R_{M T}$                 (14)

$P_{M T}^{t-1}-P_{M T}^t \leq D R_{M T}$                 (15)

2.4 Fuel cell model

In this work, chemical energy held in the gas was transformed into electrical energy using a proton membrane FC, which was then employed as a source to generate power. The fuel consumption may be represented using the following linear equation: $P_{F C}^t$ is the output electrical power from FC at each time in KWh, $\eta_{F C}$ is the efficiency of FC, and $C_{F C}$ is the cost of fuel consumption by using FC in \$ [35].

$C_{F C}{ }^t=\frac{P_{F C}^t}{L C V * \eta_{F C}} * \beta_g$                  (16)

Both the start-up cost $S U C_{F C}$ and shut-down cost $S D C_{F C}$ in \$ can be decided by:

$S U C_{F C}{ }^t=S c_{F C}\left(U_{F C}^t-U_{F C}^t * U_{F C}^{t-1}\right)$                (17)

$S D C_{F C}{ }^t=S d_{F C}\left(U_{F C}^{t-1}-U_{F C}^t * U_{F C}^{t-1}\right)$                (18)

Based on the maintenance cost rate coefficient $K_{{om.FC }}$ in \$⁄KWh, the maintenance cost of MT $C_{ {om.FC }}$:

$C_{o m . F C}^t=P_{F C}^t * K_{o m . F C}$              (19)

The constraint capacity of a microturbine can be expressed by:

$P_{F C}^{min } U_{F C}^t \leq P_{F C}^t \leq P_{F C}^{max } U_{F C}^t$                  (20)

where, $P_{F C}^{min }, P_{F C}^{max }$, and the $U_{F C}$ on/off state of FC represent the lowest and greatest power that FC can produce in KW. and each time interval's ramp rate restriction for FC should be Limits of ramp up $U R_{F C}$ and ramp down $D R_{F C}$ in \$.

$P_{F C}^t-P_{F C}^{t-1} \leq U R_{F C}$                  (21)

$P_{F C}^{t-1}-P_{F C}^t \leq D R_{F C}$               (22)

2.5 Electric chiller model

By using cooling electricity, the EC supplies the cooling demand. The following formula represents the EC's output cooling power [31]:

${Cec}(t)={Pec}(t) . {COP}_{e c}$                  (23)

When the electric power provided to EC is represented by ${Pec}(t)$ and the coefficient of performance is represented by $\left(C O P_{e c}\right)$.

2.6 Absorber chiller model

By using cooling electricity, the AC supplies the cooling load. The following formula determines the AC's output cooling power:

${Cac}(t)={Hac}(t) \cdot {COP}_{a c}$                  (24)

where, $C O P_{a c}$ is the coefficient of performance and ${Hac}(t)$ is the heat that is given to AC.

2.7 Wind turbine model

Wind turbine power output, expressed $P_{W T}^t$ in KW, is correlated with wind speed. In Table 1, the wind power value was taken from the study [35].

Table 1. Hourly loads, prices, and renewable generation

2.8 Photo voltage panel model

Utilizing PV panels, PV in this study converts solar radiation into electric power $P_{P V}^t$ in KW, which is dependent on solar radiation $S$ in $\mathrm{KW} / \mathrm{m}^2$, which was measured in Baghdad in January as shown in Table 1. The $P_{P V}^t$ total electrical power product can be written as follows:

$P_{P V}^t=s^t * {Area} \, P V * \eta_{P V} * n o . P V$                   (25)

2.9 Solar air heater model

A SAH was utilized in this study to transform solar energy into usable thermal energy. Cans of aluminum were set up to examine how they affected performance. The temperature in various sections of the SAH was also measured using a K-type thermocouple, which was connected to an Arduino to provide data to a laptop. As illustrated in Figures 2 and 3. Four research cases and dimensions of AL cans were used that were placed into SAH [36]:

• Case 1: A smooth absorbent plate is used to compare the results.
• Case 2: Longitudinal arrangement of aluminum cans.
• Case 3: Transversely arranged aluminum cans.
• Case 4: A diagonal arrangement of aluminum cans. Case.

The rate of heat transfer for SAH $H_{S A H}^t$ in KW can be expressed by [38-40]:

$H_{S A H}^t=m^{\circ} * C_p *\left(T_o-T_i\right)$            (26)

whereas, $T_o, T_i$ are the average air outlet and inlet temperatures in $C^{\circ}, C_p$ is the air specific heat in $\mathrm{KJ} / \mathrm{Kg}^* \mathrm{~K}$, and $m^{\circ}$ is the mass flow rate in the SAH duct in $\mathrm{kg} / \mathrm{s}$, the value of $H_{S A H}^t$ was measured experimentally for this work in Table 1.

2.10 Electrical heater model

The thermal loads receive heat from the EH, and the output heat $H_{E H}^t$ in KW is represented as follows:

$H_{E H}^t=P_{E H}^t * \eta_{E H}$                  (27)

The constraint capacity of EH can be defined as follows, where $\eta_{E H}$ is the efficiency of EH and $P_{E H}^t$ is the electrical power used to produce heat by EH :

$H_{E H}^{min } U_{E H}^t \leq H_{E H}^t \leq H_{E H}^{max } U_{E H}^t$                (28)

where, $U_{E H}$ is the EH 's on/off state and $H_{E H}^{min }, H_{E H}^{max }$ are the lowest and highest power that EH can produce in KW, and EH $C_{ {om.EK }}$ maintenance cost based on the $K_{om . E H}$ maintenance cost rate coefficient in $\$ /\mathrm{KWh}$.

$C_{o m . E H}^t=H_{E H}^t * K_{o m . E H}$               (29)

2.11 Gas boiler model

Natural gas consumption in the GB produced heat. The cost of natural gas consumption in the GB to produce heat $C_{M T}$ in \$ can be stated as follows [40]:

$C_{G B}^t=\frac{H_{G B}^t}{L C V * \eta_{G B}} * p_g$                   (30)

Based on the maintenance cost rate coefficient $K_{om . MT}$ in \$/$\mathrm{KWh}$, the maintenance cost of MT $C_{{om.MT }}$

$C_{o m . G B}^t=H_{G B}^t * K_{o m . G B}$                  (31)

The constraint capacity of GB it can be expressed by:

$H_{G B}^{min }\,\, U_{G B}^t \leq H_{G B}^t \leq H_{G B}^{max } \,\,U_{G B}^t$                 (32)

where, the $U_{G B}$ on/off state of GB and $H_{G B}^{min }, H_{G B}^{max }$ are the lowest and highest power that FC can produce in KW.

2.12 Energy Storage System model

When energy is plentiful, affordable, or readily available, electrical power is stored for later use using the Energy Storage System (ESS), often known as battery storage. It helps move energy from periods of peak production to periods of high demand for consumption, improving grid stability and dependability. Battery state of charge ${SOC}_b^t$ in KWh can be written as follows:

${SOC}_b^t={SOC}_b^{t-1}-\frac{P_{b . d i s}^t}{\eta_{b . d i s}}+P_{b . c h}^t \eta_{b . c h}$                   (33)

where, $\eta_{c h}, \eta_{d i s}$ are the charging and discharging battery efficiency and $P_{b . c h}^t, P_{b . d i s}^t$ are the charging and discharging power battery in KWh. The battery's constraint capacity can be stated as follows:

$P_b^{min } \leq P_b^t \leq P_b^{max }$                      (34)

$P_{b . c h}^{min } U_{b . c h}^t \leq P_{b . c h}^t \leq P_{b . c h}^{max } U_{b . c h}^t$                    (35)

$P_{\text {b.dis }}^{min } U_{ {b.ch }}^t \leq P_{ {b.dis }}^t \leq P_{ {b.dis }}^{max } U_{ {b.dis }}^t$                     (36)

$U_{b . d i s}^t+U_{b . c h}^t \leq 1$                     (37)

The battery's maximum limit charge and discharge power in KW is denoted by $P_{b . c h}^{min }, P_{b . d i s}^{min }$, and the minimum limit charge and discharge power in KW by $P_{b . c h}^{min }, P_{b . d i s}^{min }$, and the maximum limit charge and discharge power in KW by $P_b^{max }, P_b^{min }$, and $U_{ {b.ch }}^t, U_{ {b.dis }}^t$. The following is anexchange ofn for the exchanging ESS power in KWh:

$P_b^t=P_{b . d i s}^t-P_{b . c h}^t$                (38)

When the ESS is purchasing a micro grid, the $P_b^t$ is $(+)$; when the battery is charging, it is (-). Depended on battery charge discharge principle $\omega_b$ in \$$/ \mathrm{KWh}$, the cost of ESS at operating battery $C_b^t$ in $S$ is:

$C_b^t=P_b^t * \omega_b$                    (39)

2.13 Heat storage system model

When heat power is available, it is stored in heat storage system (HSS) for later use in the event that a heat source is unavailable. The state of charge for battery $S O C_h^t$ in KWh can be expressed by [40]:

${SOC}_{h s}^t=\operatorname{SOC}_{h s}^{t-1}-\frac{H_{h s . d i s}^t}{\eta_{h s . d i s}}+H_{h s . c h}^t \,\,\eta_{h s . c h}$                      (40)

The charging and discharging power HSS in KWh is represented by $H_{h s . c h}^t, H_{h s . d i s}^t$, while the charging and discharging efficiency is represented by $\eta_{h s . c h}, \eta_{h s . d i s}$. The HSS's constraint capacity may be stated as follows:

$H_{h s}^{min } \leq H_{h s}^t \leq H_{h s}^{max }$                 (41)

$H_{h s . c h}^{min } U_{h s . c h}^t \leq H_{h s . c h}^t \leq H_{h s . c h}^{max } U_{h s . c h}^t$                    (42)

$H_{h { s.dis }}^{min } U_{h { s.ch }}^t \leq H_{h { s.dis }}^t \leq H_{h { s.dis }}^{max } \,\, U_{h { s.dis }}^t$                (43)

$U_{h s . d i s}^t+U_{h s . c h}^t \leq 1$                (44)

The minimum limit charge and discharge power of the battery is represented by $H_{h s . c h}^{ {min }}, H_{h s . d i s}^{ {min }}$ in KW, the maximum limit charge and discharge power of the HSS in KW is represented by $H_{h s . c h}^{max }, H_{h s . d i s}^{max }$, and the on/off states of charge and discharge are represented by $U_{h s . c h}^t, U_{h s . d i s}^t$. The following is an expression for the exchange HSS power in KWh:

$H_{h s}^t=H_{h s . d i s}^t-H_{h s . c h}^t$                    (45)

In a discharge condition, when the HSS purchases power from the microgrid, the $H_{h s}^t$ is (+); in a charging state, when the HSS consumption is (–). Depended on HSS charge discharge prince $\omega_{h s}$ in \$/ $\mathrm{KWh}$, the cost of HSS at operation battery $C_{h s}^t$ in \$ is:

$C_{h s}^t=H_{h s}^t * \omega_{h s}$               (46)

2.14 Power and utility grid interaction

Because it shares energy with the gird based on demand response, exports power when there is an excess of electrical power production due to the availability of RE sources, and imports power when electrical prices are low and it is cost-effective to import from the gird rather than operating production units or when there is a deficit in meeting demand, the CCHP-MG was connected to the gird to increase its reliability and stability [41]. With the utility grid, the trading power $P_{U G}^t$ in KWh may be written as follows:

$P_{U G}^t=P_{ {import }}^t-P_{ {export }}^t$              (47)

where, $P_{ {import }}^t$ is importing electricity from the grid in $(\mathrm{KWh})$ and $P_{ {export }}^t$ is export electricity to grid in KWh, the $P_{U G}^t \mathrm{t}(+)$ at import purchasing state, and (–) at export selling. The power trading cost $C_{ {e.UG }}^t$ in \$ deponed on electrical prince $\omega_{ {elect. }}^t$ in $\left(\frac{\$}{K W h}\right)$ is:

$C_{ {e.UG }}^t=P_{U G}^t * \omega_{ {elect. }}^t$                 (48)

The constraint capacity of the interacting power it can be expressed by:

$P_{ {import }}^{min } U_{ {e.import }}^t \leq P_{ {import }}^t \leq P_{ {import }}^{ {mas }} U_{ {e.import }}^t$               (49)

$P_{ {export }}^{min } U_{ {e.export }}^t \leq P_{ {export }}^t \leq P_{ {export }}^{ {mas }} U_{ {e.export }}^t$               (50)

$U_{ {e.import }}^t+U_{ {e.export }}^t \leq 1$                  (51)

where, $U_{ {e.import }}^t$ electrical import on/off state and $P_{ {import }}^{ {min }}$, $P_{ {import }}^{max }$ limit power can be imported. Additionally, $U_{ {e.export }}^t$ electrical export on/off state and $P_{ {export }}^{ {min }}, P_{ {export }}^{ {max }}$ limit power can be exported.

2.15 Heat power with upstream grid model

Because it shares heat energy with the gird based on demand response, exports heat power when there is a surplus, and imports heat when heat prices are low and it is cost-effective to import from the gird rather than operating production units or when there is a deficit in meeting demand, the CCHP-MG was connected to the District Heating Network (DHN) or the heat upstream gird in order to increase the reliability of the gird [31]. With the utility grid, the trading power $H_{U G}^t$ in KWh may be written as:

$H_{U G}^t=H_{ {import }}^t-H_{ {export }}^t$               (52)

where, $H_{{import }}^t$ is using grid-imported thermal power in KWh and $H_{ {export }}^t$ is the grid's source of thermal electrical power in KWh, the $H_{U G}^t \mathrm{t}(+)$ at import purchasing state, and (–) at export selling. The power heat trading cost $C_{h . U G}^t$ in \$ deponed on electrical prince $\omega_{ {heat. }}^t$ in $\left(\frac{\$}{K W h}\right)$ is:

$C_{h . U G}^t=H_{U G}^t * \omega_{h e a t.}^t$                (53)

The constraint capacity of the interacting heat power can be expressed by:

$H_{ {import }}^{ {min }} U_{ {h.import }}^t \leq H_{ {import }}^t \leq H_{ {import }}^{ {mas }} U_{ {h.import }}^t$                     (54)

$H_{ {export }}^{min } U_{ {h.export }}^t \leq H_{ {export }}^t \leq H_{ {export }}^{ {mas }} U_{ {h.export }}^t$                  (55)

$U_{ {h.import }}^t+U_{ {h.export }}^t \leq 1$                    (56)

where, $H_{{import }}^{ {min }}, H_{ {import }}^{ {mas }}$ limit power can be imported and $U_{ {e.import }}^t$ heat import on/off state. And where $H_{ {export }}^{ {min }}, H_{ {export }}^{ {mas }}$ limit power can be exported and $U_{ {h.export }}^t$ heat export on/off state.

2.16 Model of emission costs

Greenhouse gases (GHGs) such as carbon dioxide (CO₂), sulfur dioxide (SO₂), nitrogen oxides (Nox), and particulate matter (PM) are released during the energy production process, with the exception of RE sources. It is crucial to minimize these emissions. According to the monetary notion of cost constraint, the released gases are therefore seen as a cost in the cost objective function. The expression for the total emission cost $C_{E m i.}^t$ in \$ is as follows [42]:

$C_{E m i .}^t=\sum_1^i \sum_1^j P_i^t C_j E_{i, j}$                   (57)

where, $P_i^t(K W h)$ is the power product can emotion GHGs of $i^{ {th }}$ in this research DG, MT, and FC. The $C_j$ in $\left(\frac{\$}{K g}\right)$ this is expense of emission prince of $j^{ {th }}$ GHG in this research is $\mathrm{CO}_2$, $\mathrm{So}_{2,} \mathrm{No}_{\mathrm{x}}$, and PM . The $E_{i, j}$ in $\left(\frac{K g}{K W h}\right)$ this is the amount of can emission $j^{ {th }}$ where product power for each $i^{ {th }}$.

2.17 Power balance constraint model

This limitation must be met in order to guarantee that electrical power production meets the necessary electrical demand loads for each time:

$P_{M T}^t+P_{F C}^t+P_{D G}^t+P_{P V}^t+P_{W T}^t+P_{b . d i s}^t+P_{i m p o r t}^t=P_{\text {export }}^t+P_{b . c h}^t+P_{c e}^t+P_{E H}^t+L_{{elctr. }}^t$                 (58)

where, $L_{ {elctr }}^t$ is a load that requires electrical power in KWh.

To ensure that heat power is supplied that satisfies the required heat demand loads for each period, this restriction must be fulfilled:

$H_{M T}^t+H_{G B}^t+P_{S A H}^t+H_{E H}^t+H_{b . d i s}^t+H_{ {import }}^t=H_{ {export }}^t+H_{b . c h}^t+H_{c a}^t+L_{ {heat. }}^t$                   (59)

where, $L_{{heat }}^t$ is heat power demand load in KWh.

To ensure that cool electricity is supplied that satisfies the required cool demand loads for each period, this restriction must be observed:

$P_{c e}^t+H_{c a}^t=P_c^t+L_{c o o l.}^t$                     (60)

where, $L_{ {cool. }}^t$ is cool power demand load in KWh.

2.18 Objective function cost model

In order to obtain the minimal cost function CF in \$, this study changed its multi-objective goal to a single aim by considering emission cost as a monetary notion [43].

$\begin{aligned} C F=\sum_{t=1}^{24}\left[C_{M T}^t+\right. & S U C_{M T}{ }^t+S D C_{M T}{ }^t+C_{o m . M T}^t+C_{F C}{ }^t+S U C_{F C}{ }^t+S D C_{F C}{ }^t+C_{o m . F C}^t+C_{D G}{ }^t+S U C_{D G}{ }^t \\ & \left.+S D U_{D G}^t+C_{o m . D G}^t+C_{G B}{ }^t+C_{o m . G B}^t+C_b^t+C_{h s}^t+C_{e . U G}^t+C_{h . U G}^t+C_{E m i .}^t\right]\end{aligned}$                 (61)

A combined-objective UCIMIQP is the formulation of the suggested EMS. A single function that can be solved directly in a single step develops from this integrated objective optimization function [44]. Software called the General Algebraic Modeling System (GAMS) is used to construct and describe the suggested optimization problem [45]. Gams is an extremely mathematical modeling system used to solve optimization challenges. To solve the suggested CCHP optimization issue, the NLP solver is employed. The procedure used to define and resolve the suggested optimization issue is illustrated in the flowchart, as shown in Figure 4.

Figure 4. Flow chat of model and solution the proposed system

First, the economic operation function serves as the foundation for the formulation of each CCHP component. Furthermore, the operation-related constraints are developed and modeled in the way described in the preceding section. Additionally, the combined goal function is designed to reduce the cost of operation and emissions. At last, the entire issue is resolved, and the results are shown. Absent optimization, the system in the suggested CCHP doesn't work. This is due to the interaction between the heating, cooling, and electric systems, where energy is transformed into different forms to ensure optimal system performance. Furthermore, the pricing structure governs energy trading with the main grid, and it is challenging to predict the timing and volume of energy exchanges with the utility grid.

The suggested CCHP system operates in a cheap and environmentally friendly approach because of the interaction between the electric, heating, and cooling systems. As a result, the objective function's formulation takes these systems' interactions into account.