Question 5.3: A combined-cycle power plant with a power output PCC of 520 ......

I. Combined-cycle power plant without supplementary firing
1. Overall efficiency of the combined-cycle power plant

\eta_{C C}=\eta_{GT}+\eta_{ST}\left({1-\eta_{GT}}\right)=0.4+0.35(1-0.4)=0.61

2. Heat rate of the power plant

\mathrm{HR}=3600/\eta_{\mathrm{CC}}=3600/0.61=5901.6\ \mathrm{kJ/kW}\,\mathrm{h}

3. Rate of heat addition in the gas turbine combustor

Q_{GT}=P_{C C}/\eta_{C C}=520/0.61=852.5\;\mathrm{MJ/s}

4. Fuel rate of the power plant

m_{f}=Q_{GT}/\mathrm{HV}=852.5~\mathrm{MJ}/s/42.5~\mathrm{MJ}/\mathrm{Kg}=20.06~\mathrm{kg/s}

5. Power output of gas turbine and steam turbine, respectively, and their shares in P_{CC}

P_{\mathrm{GT}}=Q_{\mathrm{GT}}\;\eta_{\mathrm{GT}}=852.5\times0.4=341\;\mathrm{MW},\;that is, 65.6{\mathrm{\%}}\ {\mathrm{of}}\ P_{\mathrm{CC}}

P_{\mathrm{ST}}=P_{\mathrm{CC}}-P_{\mathrm{GT}}=520-341=179\mathrm{~MW}, that is, 34.4{\mathrm{\%}}\ {\mathrm{of}\,}P_{\mathrm{CC}}

II. Combined-cycle power plant with an supplementary firing
1. Overall efficiency of the combined-cycle power plant

\mathbf{h}_{\mathrm{CC}}=[\mathbf{h}_{\mathrm{GT}}+\mathbf{h}_{\mathrm{ST}}(1-\mathbf{h}_{\mathrm{GT}}+f_{\mathrm{SF}})]/(1+f_{\mathrm{SF}})

\mathbf{h}_{\mathrm{{CC}}}=[0.4+0.35\times(1-0.4+0.28)]/(1+0.28)=0.553

2. Heat rate of the combined-cycle power plant

\mathrm{H R}=3600/\eta_{\mathrm{C C}}=3600/0.553=6510\,\mathrm{kJ/kW\,h}

3. Total rate of heat addition in gas turbine combustor and supplementary firing

Q_{\mathrm{in}}=Q_{\mathrm{GT}}+Q_{\mathrm{SF}}=P_{\mathrm{CC}}/\eta_{\mathrm{CC}}=520/0.553=940.3\ \mathrm{MJ/s}

4. Plant fuel rate (total)

5. Rate of heat addition in gas turbine combustor

6. Power output of gas turbine and steam turbine, respectively, and their shares in P_{CC}

Thus, in comparison with the combined-cycle without supplementary firing, the combined-cycle power plant with supplementary firing has a lower efficiency and thus a higher heat rate.