Economical/Environmental Dispatch of Combined Heat and Power Microgrid with Integration of Renewable Energy and Solar Air Heater

With the development of civilization, the demand for energy increases sharply. However, 81% of the energy is supplied by generation sources driven by fossil fuels. These energy resources emit greenhouse gases, which damage the environment and cause global warming. It is important to reach the carbonian neutrality by 2050 in line with the Paris Protocol to limit the emission of greenhouse gases [1]. Buildings are one of the most energy-consuming sectors, as they consume about 40% of the total global energy consumption and contribute about 28% of emissions. Therefore, it is necessary to shift towards the use of renewable energy (RE) sources as an alternative, environmentally friendly energy source to confront climate change and the sustainability of available energy resources [2-7].

In traditional energy grids, the transmission of energy from power plants to the far loads increases energy losses. The wide integration of RE with the power grids increases the complexity of the operation of the grid [5]. Recently, energy sources are installed close to the end user consumer to minimize the losses and energy waste. Microgrid (MG) is the connection of these energy resources close to the end users [8-14]. MG is a low-voltage distribution network that has independent control and can be operated either in separate (island) mode or connected mode with the grid. The MG has many energy sources, including distributed generation (DG), microturbine (MT), and RE, and has energy storage systems (ESSs) in order to achieve optimal use of resources to ensure supplying the load [15]. The MG system is flexible and efficient as it is able to manage energy production according to demand response, unlike conventional systems that may waste half of the energy produced [5]. Exacerbating the problem is the integration of RE sources with the grid due to the stochastic nature of RE and the uncertainty of load demand. Additionally, peak times for energy production from renewable sources occur during periods of low load demand, that affecting the stability of the grid [16]. Currently, the MG supplies both electric and heat loads simultaneously in one entire framework, which is called a combined heat and power microgrid (CHP-MG). contain solar collectors as solar air heaters (SAH) that provide heat to achieve the maximum benefit from the energy coming from the sun [17]. Additionally, the wasted heat which was released when producing electricity can be recovered and reused in utilized benefit heat applications within the system of heating and other applications [18-23].

In order to minimize operation costs and emissions of green gas at produce power while enhancing the reliability and stability of grids, the literature discusses various methods to improve the operation of CHP-MG, multi optimizations approaches used as unit commitment (UC), Heuristic algorithm, genetic algorithm (GA), particle swarm optimization (PSO), and other approaches [24].

Pashaei-Didani et al. [25] modeled an MG system with base CHP, power sources, FC, and storage systems connected to the grid, to minimize cost and emissions by scheduling a demand response program (DRP) with multi-objective Pareto solutions by using the compromising programming approach; then, the optimal solution is chosen by implementing the fuzzy satisfying approach. This approach reduced the set of effective solutions. The use of DRP reduced cost and emissions by 2.8% and 126 kg. In the previous study, distributed energy resources (DERs) and ESSs were used to share the required electricity demand from controllable and uncontrollable loads in short-term scheduling of thermal and electrical grids [26]. As for the authors of study [16], they integrated solar and wind energy sources while prioritizing renewable energy; the Particle Swarm Optimization (PSO) algorithm was used to improve consumption, saving 283.91 MW. According to the demand response with the environmental constraint method, the fuzzy satisfaction approach was used to choose the best compromise solution that was the least cost and the effect of the time DRP on MG in scheduling time demand response, which cost $3652 and emitted 53150.16 tons/day. In the same construction system, previous literature [27] used the multi-objective bacterial colony chemotaxis (MOBCC) algorithm with the Order of Preference by Similarity to the Ideal Solution (TOPSIS) method to choose the final decision solution [28]. Use District Heating Network (DHN) with CHP and buffer tank storage for extra flexibility, as it is able to adjust its electrical power production very quickly, while meeting the heat demand.

In this study, an energy management system of a CHP-MG with integration of renewable sources and SAHs to meet electrical and thermal loads is proposed. The CHP grid contains fuel cells (FCs), MTs, diesel generators (DG), wind turbine (WT), photovoltaic panels (PV), and electrical ESS. Meanwhile, the heat demand is met from the MTs heat recovery (HR) system, gas boiler, the electric heater (EH), and the heat storage system (HSS). Besides, the SAH, which was practically implemented in a previous study [29] and tested, has different designs to determine which design has the lowest operational cost of the system, supplies heat loads. The system was also connected to the public utility grid, where the system can trade heat and electric energy with the utility grid. The proposed problem is formulated as Unit commitment Mixed-Integer Non-Linear Programming (UCMINLP) hourly, employed GAMS software to solve the optimization, also modeling the interaction between the electrical and heat systems, Consider the operational cost of the electrical and heat systems of the network, and the objectives function of multi -objective converted to improving the single objective by considering the costs of the CO₂, SO₂, NO_x and particulate matter (PM) to the monetary concept.

The structure of the proposed Smart MG based on CHP consists of MT, diesel generation DG, WT, photovoltaic panel PV, FC, and ESS, which is charged during off-peak time when the electrical price is lower and discharged to the system during peak hours. The CHP system also has an electrical heater EH, boiler heater, SAH, HSS to store heat, and HR to exploit heat from MT. In addition, the electrical power can be exchanged with the utility grid, and the heat system is connected with the district heating grid to share energy with the grid, to achieve the best performance operation. The proposed system is shown in Figure 3. The system modeling in this study was based on the literature.

3.png

Figure 3. Schematic diagram of combined heat and power microgrid (CHP-MG) and energy flow

3.1 Microturbines model

In this study, the mt is driven by natural gas to generate electricity. The mathematical relationship between electricity power generation and natural gas consumption in MT can be modeled by the linear equation [27, 37, 38]:

$C_{M T}^t=\frac{P_{M T}^t}{L C V * \eta_{M T}} * \lambda_g$              (2)

where, $C_{M T}$ the cost of fuel consumption by used MT in (\$), $L C V$ is the low heating value of natural gas $\left(\mathrm{kWh} / \mathrm{m}^3\right), \lambda_g$ is the price of natural gas $\left(\$ / \mathrm{m}^3\right), P_{M T}^t$ the output electrical power from MT at each time in kWh , and $\eta_{M T}$ it is efficiency of MT can be calculated by used [27]:

$\begin{aligned} \eta_{M T}= & 0.0753\left(\frac{P_{M T}^t}{65}\right)^3-0.3095\left(\frac{P_{M T}^t}{65}\right)^2 +0.1074\left(\frac{P_{M T}^t}{65}\right)+0.1068\end{aligned}$               (3)

The start-up cost $S U C_{M T}$ and shut-down cost $S D C_{M T}$ in $(\$)$ can be determined by:

$S U C_{M T}{ }^t=\mathrm{Sc}_{M T}\left(U_{M T}^t-U_{M T}^t * U_{M T}^{t-1}\right)$                (4)

$S D C_{M T}{ }^t=\mathrm{Sd}_{M T}\left(U_{M T}^{t-1}-U_{M T}^t * U_{M T}^{t-1}\right)$               (5)

The maintenance cost of MT $C_{\text {om.MT}}$ based on the maintenance cost rate coefficient $K_{\text {om.MT}}$ in ($/kWh) is calculated as in [37].

$C_{o m . M T}^t=P_{M T}^t * K_{o m . M T}$              (6)

3.2 Heat recovery model

The heat from the MT can be recovered using HR, where this heat can be expressed by the following equation $H_{M T}^t$ in (kW) by [39]:

$H_{M T}^t=\frac{P_{M T}^t\left(1-\eta_{M T}-\eta_l\right) \eta_{H R}}{\eta_{M T}}$                  (7)

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

3.3 Fuel cell model

The proton membrane FC is used to convert chemical energy stored in the gas into electrical energy. The $C_{F C}$ is the cost of fuel consumption by the used FC in (\$), $P_{F C}^t$ the output electrical power from FC at each time in (kWh), and $\eta_{F C}$ it is the efficiency of FC; the fuel consumption can be modeled by the linear equation [27, 37]:

$C_{F C}{ }^t=\frac{P_{F C}^t}{L C V * \eta_{F C}} * \lambda_g$          (8)

The start-up cost $S U C_{F C}$ and shut-down cost $S D C_{F C}$ in (\$) can be calculated by [35,38].

$S U C_{F C}{ }^t=\mathrm{Sc}_{F C}\left(U_{F C}^t-U_{F C}^t * U_{F C}^{t-1}\right)$             (9)

$S D C_{F C}{ }^t=\mathrm{Sd}_{F C}\left(U_{F C}^{t-1}-U_{F C}^t * U_{F C}^{t-1}\right)$               (10)

The maintenance cost of MT $C_{\text {om.FC}}$ based on the maintenance cost rate coefficient $K_{\text {OM.FC}}$ in ($/kWh) is calculated by the following equation [36]:

$C_{o m . F C}^t=P_{F C}^t * K_{o m . F C}$                (11)

3.4 Diesel generator model

The DG is an internal combustion engine which is driven by diesel fuel. The $C_{\mathrm{DG}}$ the cost of fuel consumption by the used DG in (\$), $P_{\mathrm{DG}}^t$ the output electrical power from FC at each time in (kWh), and $\eta_{\mathrm{DG}}$ it is the efficiency of DG; the fuel consumption can be modeled by the linear equation [37-41]:

$C_{\mathrm{DG}}{ }^t=a P_{\mathrm{DG}}^t{ }^2+b P_{\mathrm{DG}}^t+c$             (12)

where, a,b,c are cost coefficients of DG in ($/kW²h), (\$/kWh), (\$/h), respectively. The start-up cost $S U C_{D G}$ and shut-down $\operatorname{cost} S D C_{D G}$ in $(\$)$ can be determined by [36-40].

$S U C_{D G}{ }^t=\mathrm{Sc}_{D G}\left(U_{D G}^t-U_{D G}^t * U_{D G}^{t-1}\right)$             (13)

$S D U_{D G}^t=\operatorname{Sd}_{D G}\left(U_{D G}^{t-1}-U_{D G}^t * U_{D G}^{t-1}\right)$            (14)

The maintenance cost of DG $C_{\text {om.FC}}$ based on the maintenance cost rate coefficient $K_{o m . D G}$ in ($/kWh) [41].

$C_{o m . D G}^t=P_{D G}^t * K_{o m . D G}$               (15)

3.5 Wind turbine model

The power produced from the WT $P_{W T}^t$ in (kW) depends on the wind speed, and it can be calculated from the following equation [15, 16]:

$P_{W T}^t=\left\{\begin{array}{cc}0, & 0 \leq v_t<v_{\text {in}} \text { ot }>v_{\text {out}} \\ \frac{P_{W T}^R}{v_R^3-v_{\text {in}}^3} v_t^3-\frac{v_{\text {in}}^3}{v_R^3-v_{\text {in}}^3} P_{W T}^R & v_{\text {in}} \leq v_t \leq v_R \\ P_{W T}^R & v_R<v_t \leq v_{\text {out}}\end{array}\right.$             (16)

where, $P_{W T}^R$ is the rated output power from WT in (kW), $v_t$ is the wind speed in $(\mathrm{m} / \mathrm{s}), v_R$ is the rated wind speed of the WT, and $v_{\text {in}}, v_{\text {out}}$ are cut in wind speed and cut out wind speed, respectively.

3.6 Photovoltaic panel model

The PV is utilized to take advantage of solar energy by converting solar radiation into electric power $P_{P V}^t$ in (kW), it depends on solar radiation $I$ in $\mathrm{kW} / \mathrm{m}^2$. The total electrical power produced from PV $P_{P V}^t$ can be expressed by [15-17, 42]:

$P_{P V}^t=I^t *$ Area $P V * \eta_{P V} *$ number of $P V$                (17)

3.7 Solar air heater model

The SAH converts solar energy into useful heat energy. The heat transfer rate for SAH $H_{S A H}^t$ in (kW) can be expressed as Eq. (1).

3.8 Electrical heater model

The EH provides heat to supply heat load demand by converting electrical power to heat energy, where the output heat energy can be expressed $H_{E H}^t$ in (kW) by the following equation [35-37]:

$H_{E H}^t=P_{E H}^t * \eta_{E H}$               (18)

where, $P_{E H}^t$ is the electrical power consumed to produce heat by EH, and $\eta_{E H}$ is the efficiency of EH, and the maintenance cost of $\mathrm{EH} C_{\text {om.EK}}$ based on the maintenance cost rate coefficient $K_{o m . E H}$ in ($/kWh) [36-38].

$C_{o m . E H}^t=H_{E H}^t * K_{o m . E H}$               (19)

3.9 Gas boiler model

The GB generates heat by consuming natural gas. The cost of natural gas consumption in the GB to produce heat $C_{M T}$ in ($) can be determined by the following formula [26].

$C_{G B}{ }^t=\frac{H_{G B}^t}{L C V * \eta_{G B}} * p_g$             (20)

The maintenance cost of MT $C_{\text {om.MT}}$ based on the maintenance cost rate coefficient $K_{o m . M T}$ in ($/kWh) [36].

$C_{o m . G B}^t=H_{G B}^t * K_{o m . G B}$                (21)

3.10 Energy storage system model

ESS or Battery storage is used to store electrical power at times when energy is abundant, available, or cheap and store it for later use when energy is not available. It is useful in shifting energy from peak production times to peak consumption demand times, which increases the reliability and stability of the grid. The state of charge for the battery $S O C_b^t$ in (kWh) can be expressed by [11, 26, 27]:

$S O C_b^t=S O C_b^{t-1}-\frac{P_{b . d i s}^t}{\eta_{b . d i s}}+P_{b . c h}^t \eta_{b . c h}$               (22)

where, $P_{\text {b.ch}}^t, P_{\text {b.dis}}^t$ are the charging and discharging power of the battery in kWh , and $\eta_{c h}, \eta_{d i s}$ are the charging and discharging battery efficiency. The exchanged ESS power in kWh can be expressed by [35]:

$P_b^t=P_{b . d i s}^t-P_{b . c h}^t$              (23)

The $P_b^t$ it (+) at the discharge state where the ESS is purchasing to microgird, and (-) at the charging state where the battery consumes power. The cost of ESS during battery operation $C_b^t$ in \$ depends on the battery charge discharge prince $\lambda_b$ in (\$/kWh) is [38]:

$C_b^t=P_b^t * \lambda_b$               (24)

3.11 Heat storage system model

HSS, or a heat storage tank, stores heat. There are many ways to store heat, including the use of PCM [43, 44]. HSS is used to store heat power at times when it is available and store it for later use when the heat source is not available. It is useful in shifting energy from peak production times to peak consumption demand times, which increases the reliability of the grid. The state of charge for the battery $S O C_h^t$ in (kWh) can be expressed by [19, 25-39]:

$S O C_{h s}^t=S O C_{h s}^{t-1}-\frac{H_{h s . d i s}^t}{\eta_{h s . d i s}}+H_{h s . c h}^t \eta_{h s . c h}$                 (25)

where, $H_{\text {hs.ch}}^t, H_{\text {hs.dis}}^t$ are the charging and discharging power HSS in kWh , and $\eta_{\text {hs.ch}}, \eta_{\text {hs.dis}}$ are the charging and discharging HSS efficiency. The exchanged HSS power in (kWh) can be expressed by [36]:

$H_{h s}^t=H_{h s . d i s}^t-H_{h s . c h}^t$               (26)

The $H_{h s}^t$ it (+) at the discharge state where the HSS purchasing to MG, and (-) at the charging state where HSS consumes power. The cost of HSS in the operation of the battery $C_{h s}^t$ in (\$) depends on the HSS charge discharge prince $\lambda_{h s}$ in (\$/kWh) is [37-39]:

3.12 Interacting power with the utility grid model

The proposed CHP system can exchange power with the utility grid to increase the reliability and stability of the grid as it shares energy with the grid according to the demand. It exports power when there is a surplus in electrical power production due to the availability of RE sources and imports power when electrical prices are low, and it is economical to import from the grid instead of operating production units or when there is a deficit in meeting demand [43]. The trading power $P_{U G}^t$ in (kWh) with the utility grid can be expressed by [37]:

$P_{U G}^t=P_{\text {import}}^t-P_{\text {export}}^t$               (28)

where, $P_{\text {import}}^t$ is import electrical power from grid in $(\mathrm{kWh})$, and $P_{\text {export}}^t$ is export electrical power to grid in $(\mathrm{kWh})$, the $P_{U G}^t$ t (+) at import purchasing state, and (-) at export selling. The power trading cost $C_{\text {e.UG}}^t$ in (\$) depends on the electrical prince $\lambda_{\text {elect} .}^t$ in ($/kWh) is:

$C_{\text {e.UG}}^t=P_{U G}^t * \lambda_{\text {elect}}^t$.                (29)

The constraint capacity of the interacting power it can be expressed by [11, 36]:

$P_{\text {import}}^{m i n} U_{\text {e.import}}^t \leq P_{\text {import}}^t \leq P_{\text {import}}^{m a s} U_{\text {e.import}}^t$                (30)

$P_{\text {export}}^{\min} U_{\text {e.export}}^t \leq P_{\text {export}}^t \leq P_{\text {export}}^{\text {mas}} U_{\text {e.export}}^t$                (31)

$U_{\text {e.import}}^t+U_{\text {e.export}}^t \leq 1$               (32)

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

3.13 Exchanging heat power with the upstream grid model

The CHP system can trade heat energy with the upstream gird or to increase the reliability gird as it shares heat energy with the gird according to the demand response, exports heat power when there is a surplus in heat power and import heat when heat prices are low and it is economical to import from the gird instead of operating production units or when there is a deficit in meeting demand [43]. The trading power $H_{U G}^t$ in (kWh) with the utility grid can be expressed by [36, 37]:

$H_{U G}^t=H_{\text {import}}^t-H_{\text {export}}^t$                 (33)

where, $H_{\text{import}}^t$ is import heat power from the grid in (kWh) and $H_{\text {export}}^t$ is the heat electrical power to grid in (kWh), the $H_{U G}^t$ t (+) at import purchasing state, and (–) at export selling. The power heat trading cost $C_{\text{h,UG}}^t$ in (\$) depends on the electrical prince $\lambda_{\text{heat}}^t$ in (\$/kWh) is [37]:

$C_{\text {h.UG}}^t=H_{U G}^t * \lambda_{\text {heat}}^t$.                  (34)

3.14 Emission cost model

GHG emissions such as CO₂, SO₂, NO_x, and PM are emitted during the energy production process. It is important to reduce these emissions to the minimum possible level. Therefore, the emitted gases are considered as a cost in the cost objective function according to the monetary concept. The total emission cost $C_{E m i .}^t$ in ($) can be expressed by:

$C_{E m i .}^t=\sum_1^i \sum_1^j P_i^t C_j E_{i, j}$                (35)

where, $P_i^t(\mathrm{kWh})$ in is the generated power from DG, MT, and FC. The C_j in (\$/kg) is the expense of the emission price of $j^{\text {th}}$ GHG. The $E_{i, j}$ in (kg/kWh) is the amount of emissions $j^{\text {th}}$ GHGs from $i^{\text {th}}$ generators [25].

The objective function is subject to the constraints that limit the operation of the energy resources. These constraints should be met at each time interval. These constraints are as follows:

5.1 Microturbines constraints

The capacity constraint of the MT can be expressed as follows [35-39]:

$P_{M T}^{\min } U_{M T}^t \leq P_{M T}^t \leq P_{M T}^{\max } U_{M T}^t$               (37)

where, $P_{M T}^{\text {min}}, P_{M T}^{\text {max}}$ is the minimum and maximum power that can be produced by MT in (kW), and the $U_{M T}$ on/off state of MT, and the ramp rate constraint for MT at each time interval should be the ramp-up limit $U R_{M T}$ and ramp-down limit $D R_{M T}$ in (kW) [12, 37 ].

$P_{M T}^t-P_{M T}^{t-1} \leq U R_{M T}$              (38)

$P_{M T}^{t-1}-P_{M T}^t \leq D R_{M T}$                   (39)

5.2 Fuel cell constraints

The capacity constraint of the FC can be expressed as follows:

$P_{F C}^{\min } U_{F C}^t \leq P_{F C}^t \leq P_{F C}^{\max } U_{F C}^t$                (40)

where, $P_{F C}^{\text {min}}, P_{F C}^{\text {max}}$ is the minimum and maximum power that can be produced by FC in (kW), and the $U_{F C}$ on/off state of FC, and the ramp rate constraint for FC at each time interval should be the ramp-up limit $U R_{F C}$ and ramp-down limit $D R_{F C}$ in (kW) [13].

$P_{F C}^t-P_{F C}^{t-1} \leq U R_{F C}$               (41)

$P_{F C}^{t-1}-P_{F C}^t \leq D R_{F C}$               (42)

5.3 Diesel generator constraints

The capacity constraint of DE can be determined using the following equation:

$P_{D G}^{\min } U_{D G}^t \leq P_{b . c h}^t \leq P_{D G}^{\max } U_{D G}^t$                (43)

where, $P_{D G}^{\text {min}}, P_{D G}^{\text {max}}$ is the minimum and maximum power that can be produced by DG in (kW), and the $U_{D G}$ on/off state of DG, and the ramp rate constraint for FC at each time interval should be the ramp-up limit $U R_{D G}$ and ramp-down limit $D R_{D G}$ in (kW) [42, 45].

$P_{D G}^t-P_{D G}^{t-1} \leq U R_{D G}$                (44)

$P_{D G}^{t-1}-P_{D G}^t \leq D R_{D G}$                (45)

5.4 Electrical heater constraints

The constraint of the capacity of the EH can be determined using the following formula:

$H_{E H}^{\min} U_{E H}^t \leq H_{E H}^t \leq H_{E H}^{\max} U_{E H}^t$                 (46)

where, $H_{E H}^{\text {min}}, H_{E H}^{\text {max}}$ is the minimum and maximum power that can be produced by EH in (kW), and the $U_{E H}$ on/off state of EH [38].

5.5 Gas boiler constraints

The constraint of the GB can be expressed by:

$H_{G B}^{\min} U_{G B}^t \leq H_{G B}^t \leq H_{G B}^{\max} U_{G B}^t$             (47)

where, $H_{G B}^{\text {min}}, H_{G B}^{\text {max}}$ is the minimum and maximum power that can be produced by FC in (kW), and the $U_{G B}$ on/off state of GB [35-38].

5.6 Energy storage system constraints

The constraint of the operation of the battery can be expressed as follows:

$P_b^{\min} \leq P_b^t \leq P_b^{\max}$                 (48)

$P_{b . c h}^{\min } U_{b . c h}^t \leq P_{b . c h}^t \leq P_{b . c h}^{\max } U_{b . c h}^t$                 (49)

$P_{\text {b.dis}}^{\min} U_{\text {b.ch}}^t \leq P_{\text {b.dis}}^t \leq P_{\text {b.dis}}^{\max} U_{\text {b.dis}}^t$                 (50)

$U_{b . d i s}^t+U_{b . c h}^t \leq 1$                 (51)

where, the $P_{b . c h}^{\min}, P_{b . d i s}^{\min}$ are the minimum limit charge and discharge power battery in (kW), and $P_b^{\text {max}}, P_b^{\text {min}}$ are limits of battery capacity, and $P_{\text {b.ch}}^{\text {max}}, P_{\text {b.dis }}^{\text {max}}$ are the maximum limit charge and discharge power battery in (kW), and where $U_{\text {b.ch}}^t$, $U_{\text {b.dis}}^t$ are on/ off state of charge and discharge [38-40].

5.7 Heat storage system constraints

The constraint of the operation of the heat storage can be determined using the expression below:

$H_{h s}^{\min} \leq H_{h s}^t \leq H_{h s}^{\max}$                  (52)

$H_{h s . c h}^{\min} U_{h s . c h}^t \leq H_{h s . c h}^t \leq H_{h s . c h}^{\max} U_{h s . c h}^t$               (53)

$H_{h s . d i s}^{\min} U_{h s . c h}^t \leq H_{h s . d i s}^t \leq H_{h s . d i s}^{\max} U_{h s . d i s}^t$                (54)

$U_{h s . d i s}^t+U_{h s . c h}^t \leq 1$                 (55)

where, the $H_{\text {hs.ch }}^{\min}, H_{\text {hs.dis }}^{\min}$ are the minimum limit charge and discharge power battery in (kW), and $H_{h s}^{\text {max}}, H_{h s}^{\text {min}}$ are the limits of HSS capacity, and $H_{\text {hs.ch}}^{m a x}, H_{\text {hs.dis}}^{m a x}$ are the maximum limit charge and discharge power of HSS in (kW), and where $U_{\text {hs.ch}}^t, U_{\text {hs.dis}}^t$ are on/ off state of charge and discharge [36-38].

5.8 Heat power with the upstream grid constraints

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

$H_{\text {import}}^{\text {min}} U_{\text {h.import}}^t \leq H_{\text {import}}^t \leq H_{\text {import}}^{\text {mas}} U_{\text {h.import}}^t$             (56)

$H_{\text {export}}^{\min} U_{\text {h.export}}^t \leq H_{\text {export}}^t \leq H_{\text {export}}^{\operatorname{mas}} U_{\text {h.export}}^t$                  (57)

$U_{\text {h.import}}^t+U_{\text {h.export}}^t \leq 1$                 (58)

where, $H_{\text {import}}^{\min}, H_{\text {import}}^{\operatorname{mas}}$ limit power can be imported and $U_{\text {e.import}}^t$ heat import on/ off state. And where $H_{\text {export}}^{\text {min}}$, $H_{\text {export}}^{\text {mas}}$ limit power can be exported and $U_{\text {h.export}}^t$ heat export on/off state [35-37].

5.9 Power balance constraint model

In order to ensure the production of electrical and heat energies that covers the required electrical and heat demand loads for each period, this constraint should be considered:

$\begin{gathered}P_{M T}^t+P_{F C}^t+P_{D G}^t+P_{P V}^t+P_{W T}^t+P_{\text {b.dis}}^t+P_{\text {import}}^t =P_{\text {export}}^t+P_{\text {b.ch}}^t+P_{E H}^t+L_{\text {elctr}}^t .\end{gathered}$              (59)

where, $L_{\text {elctr} .}^t$ it is the electrical power demand load in (kWh).

$\begin{gathered}H_{M T}^t+H_{G B}^t+P_{\text {SAH}}^t+H_{E H}^t+H_{\text {b.dis}}^t+H_{\text {import}}^t  =H_{\text {export}}^t+H_{\text {b.ch}}^t+L_{\text {heat.}}^t\end{gathered}$               (60)

where, $L_{\text {heat.}}^t$ it is heating power demand load in (kWh).

The formulation of the optimization problem is formulated as UCMOMINL, where the problem includes both continuous and integer variables. The emission level of the GHGs is converted to a monetary concept form and integrated with the objective function in one entire framework, and the problem is converted to a single function that can be solved directly in one step. General Algebraic Modelling System (GAMS) software is employed to formulate and model the proposed optimization problem. Gams is a highly mathematical modelling system for modelling and solving optimization problems. The MINLP solver with interfacing with Microsoft Excel is employed to solve the proposed optimization problem. The flowchart shown in Figure 4 shows the process that has been followed to formulate and solve the proposed approach.

4.png

Figure 4. Flowchart of the formulation of and solution to the proposed optimization problem

This paper presents a new CHP optimization approach to reduce total operational and emission cost by converting the multi-objective optimization function into a single objective by converting the emission into monetary form, and the problem can be solved directly in one step. The problem is formulated as UCMINLP where the UC strategy is considered and developed to accommodate both the electric. In addition, the SAH with novelty designs is implemented and experimentally tested, where the SAH is integrated with an optimization approach as an RE resource to supply the heat load and reduce the cost and emissions of greenhouse gases. The electric and heat systems interact with each other through converting electric and waste heat from the electric grid to heat energy. This interaction between the operation of these systems not only reduces the total cost but also reduces the emission of greenhouse gases and improves the total system efficiency. The results reveal that the integration of the SAHs with the system reduces the total cost significantly. It reduces the total cost by 12.58%, and 62.96$ is saved per day. It can also be concluded that the electric and heat energy storage are planned to reduce the total operating and emission cost. In future work, more RE sources and testing the MG in the island mode will be added, as well as various weather conditions to discover how it will affect the operational cost of the MG.