## STEAM TURBOGENERATOR EFFICIENCY AND STEAM RATE CALCULATION TUTORIALS

A 20,000-kW turbogenerator is supplied with steam at 300 lb / in2 (abs) (2067.0
kPa) and a temperature of 650-F (343.3-C). The backpressure is 1 in (2.54 cm) Hg
absolute. At best efficiency, the steam rate is 10 lb (25.4 kg) per kWh. (a) What is
the combined thermal efficiency (CTE) of this unit? (b) What is the combined
engine efficiency (CEE)? (c) What is the ideal steam rate?

Calculation Procedure:
1. Determine the combined thermal efficiency
(a) Combined thermal efficiency, CTE = (3413/wr)(1/[h1 - h2]), where wr = combined steam rate, lb/kWh (kg/kWh); h1 = enthalpy of steam at throttle pressure and temperature, Btu/ lb (kJ / kg); h2 = enthalpy of steam at the turbine backpressure, Btu/ lb (kJ / kg). Using the steam tables and Mollier chart and substituting in this equation, CTE = (3413/10)(1/[1340.6 - 47.06]) = 0.2638, or 26.38 percent.

2. Find the combined engine efficiency
(b) Combined engine efficiency, CEE = (wi)/(we ) = (weight of steam used by ideal engine, lb /kWh (weight of steam used by actual engine, lb /kWh). The weights of steam used may also be expressed as Btu/ lb (kJ / kg). Thus, for the ideal engine, the value is 3413 Btu/ lb (7952.3 kJ/ kg). For the actual turbine, h1 – h2x is used, h2x is the enthalpy of the wet steam at exhaust conditions; h1 is as before.

Since the steam expands isentropically into the wet region below the dome of the T-S diagram, we must first determine the quality of the steam at point 2 either from a T-S diagram or Mollier chart or by calculation.

By calculation using the method of mixtures and the entropy at each point: S1 = S2 = 0.0914 – (x2 (1.9451). Then x2 = (1.6508 - 0.0914)/1.9451 = 0.80, or 80 percent quality. Substituting and summing, using steam-table values, h2x = 47.06 - 0.8(1047.8) = 885.3 Btu/ lb (2062.7 kJ/ kg).

(c) To find the CEE we first must obtain the ideal steam rate, wi = 3413/ (h1 - h2x ) = 3413/(1340.6 - 885.3) = 7.496 lb /kWh (3.4 kg/kWh).

Now, CEE = (7.496/10)(100) = 74.96 percent. This value is excellent for such a plant and is in a range being achieved today. Related Calculations. Use this approach to analyze the efficiency of any turbogenerator used in central-station, industrial, marine, and other plants.