Energy and exergy analysis-based monthly co-optimization of a poly-generation system for power, heating, cooling, and hydrogen production

Abstract

A novel hybrid system, including photovoltaic, wind turbine, diesel generator, battery, electrolyzer, gas turbine cycle, Rankine cycle, absorption chiller, and hot water line, is introduced in order to supply electricity, cooling, and heating simultaneously for a town in Istanbul. The dynamic method is employed for different parts of the system dependent on meteorological information, and the steady-state situation is considered for the other parts, such as the gas turbine cycle, Rankine cycle, absorption chiller, and hot water line. Therefore, every operational parameter of the proposed system is evaluated monthly based on the meteorological information of 2019 in Istanbul. Also, the combination of the non-dominated sorting algorithm and multi-criteria decision-making of TOPSIS is employed in order to obtain the optimum rates of monthly operational parameters. Accordingly, the maximum rates of energy and exergy efficiencies can be acquired, which belong to September, October, and November, approximately 54–60%. Furthermore, exergy destruction can be achieved at the lowest rate. The highest exergy destruction is dedicated to December, with 1925.7 MW and the combustion chamber in the gas turbine cycle has the highest contribution (48%) in the exergy destruction related to this month. At the end, the COE and NPC of the system based on the optimum operational parameters are obtained 0.05147 $kW h⁻¹ and 579.3 M$, respectively.

Appendix

$${\text{RMSE}}_{{{\text{norm}}}} = \frac{1}{{{\text{avg}}\left( {m_{{\text{i}}}^{^{\prime}} } \right)}}\sqrt {\frac{1}{y}\left( {\mathop \sum \limits_{{{\text{i}} = 1}}^{y} \left( {e_{{\text{i}}} - m_{{\text{i}}}^{^{\prime}} } \right)^{2} } \right)}$$

(37)

$${\mathrm{MAE}}_{\mathrm{norm}}=\frac{1}{y\times \mathrm{avg}\left({m}_{\mathrm{i}}^{^{\prime}}\right)}\sum_{\mathrm{i}=1}^{y}\left|{e}_{\mathrm{i}}-{m}_{\mathrm{i}}^{^{\prime}}\right|$$

(38)

$${\mathrm{MRE}}_{\mathrm{norm}}=\frac{1}{y}\sum_{\mathrm{i}=1}^{y}\left|\frac{{e}_{\mathrm{i}}-{m}_{\mathrm{i}}^{^{\prime}}}{{m}_{\mathrm{i}}^{^{\prime}}}\right|$$

(39)

where e, m$^{^{\prime}}$, and y are the theoretical values, experimental values, and the number of values for comparison.

$${\dot{W}}_{comp}={\dot{m}}_{1}({h}_{2}-{h}_{1})$$

(40)

$$\dot{m}_{{{\text{FUEL\_CO}}}} = \frac{{\dot{m}_{1} \left( {h_{3} - h_{2} } \right)}}{{\left( {{\text{LHV}}_{{{\text{FUEL\_CO}}}} - h_{3} } \right)\eta_{{{\text{comb}}}} }}$$

(41)

where ṁ_{FUEL_CO} and ƞ_comb are the fuel mass flow of the combustion chamber and the efficiency of the combustion chamber, respectively.

$${\dot{Q}}_{\mathrm{comb}}={\dot{m}}_{\mathrm{FUEL}\_\mathrm{CO}}.{\mathrm{LHV}}_{\mathrm{FUEL}\_\mathrm{CO}}$$

(42)

where Q̇_comb is the inlet heat that enters the combustion chamber.

$${\dot{m}}_{3}={\dot{m}}_{\mathrm{FUEL}\_\mathrm{CO}}+{\dot{m}}_{1}$$

(43)

Also, ṁ₃ is the inlet mass flow rate of gas turbine.

$${\dot{W}}_{G-\mathrm{tur}}={\dot{m}}_{3}({h}_{3}-{h}_{4})$$

(44)

$${\dot{W}}_{S-\mathrm{tur}}={\dot{m}}_{5}({h}_{5}-{h}_{6})$$

(45)

$${\dot{W}}_{\mathrm{pump}}={\dot{m}}_{7}({h}_{8}-{h}_{7})$$

(46)

$$\varepsilon =\frac{{T}_{5}-{T}_{8}}{{T}_{4}-{T}_{10}}$$

(47)

$${\dot{W }}_{\mathrm{net},\mathrm{Rank}}= {\dot{W}}_{\mathrm{S}-\mathrm{tur}}-{\dot{W}}_{\mathrm{Pump}}$$

(48)

$${\dot{Q}}_{\mathrm{heating}}={\dot{m}}_{5}({h}_{8}-{h}_{5})$$

(49)

$${\dot{m}}_{19}={\dot{m}}_{\mathrm{SS}}$$

(50)

$${\dot{m}}_{12}={\dot{m}}_{\mathrm{r}}$$

(51)

$${\dot{m}}_{18}={\dot{m}}_{\mathrm{WS}}$$

(52)

$${\dot{Q}}_{\mathrm{eva}}={\dot{m}}_{14}({h}_{15}-{h}_{14})$$

(53)

$${\dot{Q}}_{\mathrm{abs}}={\dot{m}}_{15}{h}_{15}+{\dot{m}}_{21}{h}_{21}-{\dot{m}}_{16}{h}_{16}$$

(54)

$${\dot{W}}_{\mathrm{Pump},\mathrm{abs}}={\dot{m}}_{16}({h}_{17}-{h}_{16})$$

(55)

$${\dot{\mathrm{Ex}}}_{\mathrm{Q}}=\dot{Q}(1-\frac{{T}_{0}}{{T}_{\mathrm{H}}})$$

(56)

$${\dot{\mathrm{Ex}}}_{\mathrm{W}}=\dot{W}$$

(57)

$${\dot{\mathrm{ex}}}_{\mathrm{tot}}={\dot{\mathrm{ex}}}_{\mathrm{ph}}+{\dot{\mathrm{ex}}}_{\mathrm{ch}}$$

(58)

$${\dot{\mathrm{ex}}}_{\mathrm{ph}}=\left(h-{h}_{0}\right)-{T}_{0}(s-{s}_{0})$$

(59)

$$\mathop {{\text{ex}}}\limits^{ \cdot }_{{{\text{ch}}}} = \sum\nolimits_{1}^{n} {x_{{\text{i}}} {\text{ex}}_{{\text{ch,i}}} } + {\text{RT}}_{0} \sum\nolimits_{1}^{n} {x_{{\text{i}}} {\text{ln}}\left( {x_{{\text{i}}} } \right)}$$

(60)

In Eqs. (59, 60), h₀ and s₀ are enthalpy and entropy of the environmental conditions at atmospheric pressure and temperature, x_i is the mole fraction of component in the mixed refrigerant, ex_ch,i is the standard chemical exergy of the ith component in the mixed refrigerant. Also, R is the universal gas constant with the value of 8.314 (JKmol⁻¹). The physical and chemical exergies of every stream are demonstrated in Table 1.

$${X}_{\mathrm{ij}}=\left(\begin{array}{ccc}{X}_{11}& \cdots & {X}_{1\mathrm{n}}\\ \vdots & \ddots & \vdots \\ {X}_{\mathrm{m}1}& \cdots & {X}_{\mathrm{mn}}\end{array}\right)$$

(61)

$${P}_{\mathrm{ig}}=\frac{{X}_{\mathrm{ij}}}{\sum_{i=1}^{m}{X}_{ij}} \mathrm{ j}=1, \dots ,\mathrm{ n}$$

(62)

$${E}_{\mathrm{j}}=-k.\sum_{\mathrm{i}=1}^{m}{P}_{\mathrm{ij}}.\mathrm{ln}({P}_{\mathrm{ij}})$$

(63)

$$k=\frac{1}{\mathrm{ln}(\mathrm{m})}$$

(64)

$${d}_{\mathrm{j}}=1-\mathrm{Ej}$$

(65)

$${W}_{\mathrm{j}}=\frac{{d}_{\mathrm{j}}}{\sum {d}_{\mathrm{j}}}$$

(66)

$${n}_{\mathrm{ij}}=\frac{{X}_{\mathrm{ij}}}{\sqrt{\sum_{\mathrm{i}=1}^{m}{{X}_{\mathrm{ij}}}^{2}}}$$

(67)

$${d}_{\mathrm{i}}^{+}=\sqrt{\sum_{\mathrm{j}=1}^{n}{({v}_{\mathrm{ij}}-{v}_{\mathrm{j}}^{+})}^{2}}$$

(68)

$${d}_{\mathrm{i}}^{-}=\sqrt{\sum_{j=1}^{n}{({v}_{\mathrm{ij}}-{v}_{\mathrm{j}}^{-})}^{2}}$$

(69)

$${\mathrm{Cl}}_{\mathrm{i}}=\frac{{d}_{\mathrm{i}}^{-}}{{d}_{\mathrm{i}}^{-}+{d}_{\mathrm{i}}^{+}}$$

(70)