Figure 1 illustrates the SOFC-GT-Kalina integrated system proposed, and Figure 2 shows the reference SOFC-GT-ST system flow chart. We can see in the figures, after being compressed by Fuel compressor and reformed in Reformer, the flue gas (3) is fed to anode of SOFC stack. After being compressed by Air compressor and reheated by waste heat from GT exhaust gas (14), air (8) is fed to SOFC cathode. Inside the SOFC cell stack, oxygen is dissociated into oxygen ions at the cathode surface, which then get to the anode through the electrolyte and occurs electrochemical reaction with fuel at anode. Part of the SOFC exhaust gas (5) recycles to the fuel pre-reforming unit to supply water and heat for the endothermic steam reforming. The excess air (11) and unreacted fuel (6) out of SOFC combust completely in Afterburner, then the high temperature and high

pressure gas (13) flow into GT and generate electricity there. The exhaust gas from GT (14) is sequentially used to preheat the air, and then (15) flow into Kalina cycle or Rankine cycle for further heat recovery, in this way to realize the cascade utilization of energy and improve the efficiency of the overall system.

The basic Kalina cycle (KC) is similar with Rankine cycle (RC), mainly consisting of HRSG, turbine and condenser, the main difference is that Kalina cycle uses a distillation subsystem to solve the condensation problem of ammonia-water mixture.

In the proposed system, KC uses ammonia-water mixture as working fluid. The saturated working fluid (NH₃/H₂O) is boosted through high-pressure pump (01), then turns into superheated gas (02) in an ammonia generator which can generate power in AT. Exhaust steam (03) from AT is cooled by regenerator, and mixes with rich aqueous solution (014) from the bottom of the distillation to form the basic solution (05), then condensed completely to saturated liquid (06) through the low-pressure condenser and boosted through low-pressure pump (08). Stream (08) flows into the Sep, a surge (09) after being heated by regenerator (010) flows into the distillation, then separated into rich ammonia solution (011) and rich aqueous solution (012); Another surge mixes with the rich ammonia solution (011) to form working solution (016), then through high-pressure condenser is condensed into saturated working solution (NH₃∙H₂O), in this way to complete the cycle.

In the reference system, RC uses water as working fluid, and produces high pressure (01) and high temperature steam (02) which can generate power in ST.

The parameters and structural size involved in the process simulationis according to the tubular designed by Siemens-Westinghouse, as shown in Table 1 and Table 2 [35] .

We also need to make some assumptions for calculation as follows:

1) Considering the velocity of the fluid flow through the relevant components, heat losses from system to environment are negligible; 2) Temperature and pressure inside the battery are almost uniform, all the battery cells within the stack are in the same state; 3) Due to the high temperature and low pressure, the reaction gas can be regard as ideal compressible gas; 4) Because of good sealing, the mass loss of each component is ignored; 5) The dynamic performance of the system is not considered in this paper, all reactions are in equilibrium state, and SOFC works under steady-state operation; 6) The process is relatively short through the cell stack, the mass and pressure loss in it are negligible. These assumptions may have certain error effect on the absolute values of the calculation results, but do not affect the understanding of the system law.

The current density model of SOFC can be defined as Equation (1):

I = n × F × 4 q CH 4 N c e l l × A c e l l (1)

where: n―Electrons number transferred of each Oxygen atom in the electrochemical reaction, taking 2; F―Faraday constant, 96,485 C/mol; q CH 4 ―me- thane molar flow rate, mol/s; N_cell―number of cells; A_cell―single-cell area, m².

Firstly, select the reference voltage, and then by calculating the influence of pressure, temperature, gas pressure on voltage at other non-reference state to calculate voltage value.

Δ V p ( mV ) = C × 1 log ( p / p r e f ) (2)

where: Δ V p ( m V ) ―The influence of operating pressure on the voltage, mV; C₁ = 76; p―The SOFC operating pressure, bar; P_ref―Reference pressure, 1 bar.

Δ V T ( mV ) = K × ( T − T r e f ) × I (3)

where: V T ―The operating temperature on voltage, mV; K = 8; T―The SOFC operating temperature, ˚C; P_ref― Reference temperature, 1000˚C.

Δ V a n ( mV ) = 172 × log ( p H 2 / p H 2 O ) / ( p H 2 / p H 2 O ) r e f (4)

where: Δ V a n ―The influence of hydrogen and water vapor partial pressure on the voltage, mV; p H 2 / p H 2 O ―Pressure ratio of hydrogen and water vapor;

( p H 2 / p H 2 O ) r e f ―Pressure ratio of hydrogen and water vapor at reference condition, taking 0.15.

Δ V c a t ( mV ) = 92 × log ( p O 2 / ( p O 2 ) r e f ) (5)

where: Δ V c a t ―The influence of the oxygen partial pressure in cathode on voltage, mV; p O 2 ―The average oxygen partial pressure in cathode, bar; ( p O 2 ) r e f ―Oxygen partial pressure at reference condition, taking 0.164.

In summary, the SOFC voltage can be obtained as the Equation (6) below:

V S O F C = ( V r e f + Δ V p + Δ V T + Δ V c a t + Δ V a n ) / 1000 (6)

where: V S O F C ―The SOFC voltage, V.

When using the first law of thermodynamic to evaluate the combined system, we use SOFC power, SOFC electrical efficiency, electrical efficiency of the overall system, total power etc. as the evaluation indexes.

Since the electrochemical reaction occurs in the cell stack, and the whole system is assumed to be adiabatic, therefore the total power generation of the fuel cell can be shown as the Equation (7):

W D C = V S O F C × I (7)

SOFC electrical efficiency can be defined as Equation (8):

η S O F C = W D C × 0.92 m f × L H V f × 100 % (8)

where: 0.92―DC/AC conversion efficiency; LHV_f―Low heat value of fuel, kJ/kg.

The electrical efficiency of proposed and reference system can be defined as Equation (9) and (10):

η p r o − s = ( W S O F C + W G T + W A T − W A C − W F C − W L P − W H P ) / ( m f × L H V f ) × 100 % (9)

η r e f − s = ( W S O F C + W G T + W S T − W A C − W F C − W P U M P ) / ( m f × L H V f ) × 100 % (10)

With doing the second law of thermodynamics analysis, exergy efficiency and exergy loss is always used to evaluate the thermodynamic perfection degree of devices. For the total system, as Equation (11):

∑ k ( E i n ) k = ∑ j ( E o u t ) j + ∑ i W i + I η e x = E x g a i n / E x p a y ≤ 100 % (11)

where: E_in―Input exergy, E_out―Output exergy, W_i―Power, I―System exergy loss.

Exergy efficiency and exergy loss for compressor, turbine, heat exchanger and SOFC are shown as Equations (12)-(15):

η e x , C = E x g a i n / E x p a y = ( E x o u t − E x i n ) / W C E x L , C = E x i n − E x o u t + W C (12)

η e x , T = W n e t / ( E x i n − E x o u t ) E x L , T = E x i n − E x o u t − W n e t (13)

η e x , H E = E x g a i n E x p a y = exergygainedbycoldfluid exergypaiedbyhotfluid E x L , H E = ∑ E x i n − ∑ E x o u t (14)

E x a n , i n + E x c a , i n = E x a n , o u t + E x c a , o u t + W S O F C + E x L , S O F C (15)

In this paper, we use Aspen Plus for simulation, and select more reasonable basic parameters for a specific condition analysis. In this paper, the simulation fuel of the SOFC inlet includes 97% of CH₄ and 3% of N₂. GT exhaust gas temperature is 680.2 K. The ammonia-water mass concentration is 70% and AT pressure ratio is 24 as the specific conditions. By Simulation we can get thermodynamic parameters at each working point of the proposed system in Table 3.

For comparing the two systems, firstly we need to specify the external heat source and cooling water conditions which are exactly the same. When keeping former SOFC-GT under the same operating conditions, make comparison between the performances of the two systems, in order to verify Kalina superiority. Table 4 is performance indexes comparison between proposed system and reference system, it can be seen from the results that using Kalina cycle to recovery waste heat can obvious improve the thermodynamic properties than Rankine cycle. The total electrical efficiency is 2.96% higher and the total exergy efficiency is 2.86% higher, indicating Kalina cycle performance has been significantly improved.

Figure 3 shows the exergy destruction of each components. As can be seen from the figure, the largest exergy destruction occurs in the SOFC being 343.74 kW, accounting for 42.78% of all energy losses. Then follow by the after-burner

for 136.26 kW, accounting for 16.72%. Gas turbine exergy loss is 71.07 kW, accounting for 8.72%. Energy loss of ammonia generator is 45.34 kW, accounting for 5.56%, and its exergy efficiency can get 80.9%. As for the small temperature difference, it can reduce the damage caused by heat transfer irreversible. Exhaust gas temperature is controlled at 70˚C, its energy destruction is 17.71 kW, accounted for a small proportion. We can see from the result that a lot of measures can be taken to increase system utilization, SOFC’s exergy loss can be reduced by improving the interior materials or selecting the appropriate operating temperature and operating pressure; The maximum loss of combustor is mainly combustion irreversible loss, it can be reduced by choosing a suitable air, fuel flow; Energy loss of heat exchanger also have great controllability, selecting an appropriate heat exchanger temperature difference can reduce its exergy loss; To take full advantage of exhaust heat in the exhaust gas, when ensuring the temperature above the dew point, we can use it to a situation temperature as low as possible, thus reducing the exergy taken away by exhaust gas.

By energy analysis we can find out the weaknesses in the system energy use, system performance can be optimized by improving the performance of SOFC, optimizing heat exchanger arrangement, minimizing the temperature difference.

Figure 4(a) and Figure 4(b) respectively shows the effects of compressor pressure ratio on the exergy destruction in each component.

As can be seen from Figure 4(a), when the fuel flow and fuel utilization remains constant, as the compressor pressure ratio increases, the exergy destruction of SOFC decreases, this is due to SOFC operating pressure increases as the pressure ratio increases, it helps the electrochemical reaction react more completely and irreversible loss of reaction reduce. When the compressor pressure ratio increases from 4 to 10, SOFC exergy destruction decreases from 385.95 kW to 350.57 kW; After-burner exergy destruction changes little with the pressure ratio, which is due to its exergy loss is mainly combustion irreversible losses, this is less affected by pressure change. The exergy destruction of AC and GT increases as the pressure rises, but the trend is more and more slowly, because the entropy change increases with the pressure. FC exergy destruction value is quite small, since the fuel flow is relatively small. Exergy destruction of fuel mixer has reduced small amplitude, but not obvious, indicating that the mixing process has little exergy destruction.

We can also see from Figure 4(a) that the largest exergy destruction occurs in SOFC, then after-burner, ammonia gas generator and GT, and the ammonia flow in Kalina cycle is very small, the pump power and pump exergy destruction is small and can be ignored; As the compressor pressure ratio increases, the exergy destruction of ammonia generator decreases, this is due to as the pressure ratio increases, the temperature of GT exhaust gas decreases, temperature difference is smaller; AT exergy destruction decreases as pressure ratio increasing, but more and more slower.

Figure 5(a) shows the effect of pressure ratio on system performance, and Figure 5(b) shows the effect of pressure ratio on exergy efficiency of main components. As can be seen from Figure 5(a), when the pressure ratio changes from 5 to 10, the overall system electrical efficiency and exergy efficiency both increase, the overall system electrical efficiency changes from 70.05% to 71.98%, exergy efficiency changes from 72.46% to 74.46% which is a little higher than

electrical efficiency. Electrical efficiency of SOFC changes from 49.92% to 53.715%; as can be seen from Figure 5(b), the exergy efficiency of GT and AT reduces with pressure ratio increasing, exergy efficiency of compressor increases with pressure ratio increasing.

Figure 6 shows the influence of current density on system performance. As can be seen, with the increase of current density, SOFC voltage and efficiency both reduce, the AC power and power density both increase and reach a peak at 350 mA/cm² and then decrease. SOFC efficiency decreases mainly because of power increasing (AC and FC) and energy input caused by increasing fuel and air flow rate. We generally expect to make SOFC run at the left of peak, at the same time trade-off between power, efficiency, voltage. There exists an optimal current density at 350 mA/cm².

Figure 7 is the influence of air flow on system performance when the air-fuel ratio remains constant. As can be seen from the figure, with the increase of air flow, compressors power consumption increase. SOFC power and SOFC-GT combined cycle power increase slowly at first with air flow, but when the air flow is larger than 180 kmol/h, the power remained almost flat. SOFC efficiency tends to increase within the range of air flow 120 - 200 kmol/h, but the trend is more and more slowly. So the air flow is not the bigger the better when the air-fuel ratio remains constant.

Figure 8(a) and Figure 8(b) show the impact of AT inlet pressure and ammonia concentration on the energy destruction of ammonia steam generator and ammonia steam turbine respectively.

As can be seen from Figure 8(a), when ammonia concentration keeps constant, the exergy destruction of ammonia generator decreases with the turbine inlet pressure increasing, this is due to as a heat exchanger, higher pressure can bring more benefit for its performance; As can be seen from Figure 8(b), when the ammonia concentration keeps constant, the exergy destruction of AT increases with the turbine inlet pressure increasing, but the trend is more and more slow, this is due to the increasing pressure can lead to an increasing of enthalpy drop between import and export of AT; can also see that keeping turbine inlet pressure constant, AT energy destruction increases with the increasing of ammonia concentration, and the larger the turbine inlet pressure is, the influence is more obvious.

In the Kalina cycle when the cooling tower is used as cold source, condensation temperature is greatly affected by ambient temperature. So it’s necessary to study the impact of condensation temperature on system performance.

In order to reveal the internal phenomena of the main processes of the proposed system, EUD method which was proposed by Ishida, was adopted in this study.

When doing EUD analysis for a thermodynamic process, there exists two processes respectively called “energy donor” and “energy acceptor”. The x-coordinate in the EUD diagram is energy change, and the y-coordinate is energy level A, which is a dimensionless criteria, the ratio of the exergy change ΔE and energy change ΔH in the thermal process. The area between Aed and Aea curves represents the exergy destruction in the energy transfer process.