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Energy and Power Engineering, 2013, 5, 1474-1477 doi:10.4236/epe.2013.54B279 Published Online July 2013 (http://www.scirp.org/journal/epe) Calculation of the Choked Back Pressure for Steam Turbines with Air Cooled Condensers Haisheng Yang, Shuping Chang, Ruitao Wu Thermal Tec h n ology Depar tment, Hebei E l ectric P ower Research Institute, Shijiazhuang, Hebei PRC. Email: haisheng.yang@gmail.com, hbdyycsp@163.com, hbdyywrt@163.com Received September, 2012 ABSTRACT The choked back pressure characteristic of the steam turbine unit with air cooled condenser is very different with the unit with wet cooling technology, and the understanding of the choked back pressure performance change with opera- tion load is imp ortant to guide the economic operation of the unit. One simplified Variable Operation Cond ition Analy- sis Method was put forward for calculation of the unit output-turbine back pressure characteristics. Based on this method, the choked back pressure for each operation load can be determined. An example was given for a super-critical, regenerative single-shaft, 2-casing with 2-exhaust steam turbine generation unit with air cooled condenser. The calcula- tion result was provided and compared with the result of the unit with wet cooling technology. Keywords: Air Cooled Condenser; Steam Turbine; Chok ed Back Pressure Character istic; Calculation 1. Introduction In the past years, many of the large capacity steam tur- bine generation units with air-cooled condensers (ACCs) have been put into operation. It is shown that the safe operation of the units has been solved based on the op- eration experiences of the built units. On the other hand, very few attentions have been paid to the economic op- eration of the units with ACCs. The major difference between the normal generation units with wet cooling technology and the units with ACCs is the steam turbine cold end design. For steam turbines with ACCs, special designed LP last blading is used, and the resulted characteristic of generator output versus turbine back pressure is completely different with the turbines using wet cooling technology. For choked back pressure the steam turbines with ACCs, few calcu- lation and testing results has been published except some discussions on the theoretical principles of the choked back pressure. Analysis of the change of turbine choked back pres- sure with the operation load can provide direct guidance on the economic operation of the generation units. This paper will analyze this issue theoretically, and provide a simplified method for calculation. 2. Calculation Model of Choked Back Pressure for Steam Turbine with Air-cooled Condensers The turbine choked back pressure refers to the back pressure under which the steam flow speed at the exit of the turbine last blade is close to the local sound speed (Mach number around 0.95). The choked back pressure is related to the turbine inlet steam flow, that is, with the change of the inlet steam flow, the choked back pressure also varies. Under normal operation condition, to keep the unit generator output stable and constant, the turbine inlet steam flow decreases with the lowering down of the tur- bine back pressure. But if the decreasing of back pressure exceeds a limit or the turbine choked back pressure, the steam inlet flow increases to maintain the same g enerator output. For the units with ACCs, it is possible that the actual operation turbine back pressure is controlled below the choked back pressure limit, thus the unit performance will deteriorate. This could be avoid ed by lowering down of speed the ACC fans. 2.1. The Calculation of the Steam Turbines Choked Back Pressure It can be deduced from the definition of the turbine choked back p ressure that under the constant turbin e inlet flow, the generator output will increase with the de- creasing of the turbine back pressure until a critical back pressure value is reached. If the back pressure is con- tinuously decreased than this critical back pressure, the unit power output will not increase but decrease. This critical back pressure can be regarded as the turbine choked back pressure. Copyright © 2013 SciRes. EPE H. S. YANG ET AL. 1475 Therefore, the solution of the turbine choked back pressure can be change into a problem of how to deter- mine the turbine power output change as a function of the turbi ne b ack pressu r e change . When the impact of the turbine back pressure on unit output is considered, the commonly used calculation method adopted is described in [1], using the detailed variable operation analysis for th e LP turbine last blading . Yet many of the difficulties need to be solved for this method, including: Many of the parameters related to the detailed variable operation analysis can’t be collected. Many of the turbine last stages are curved and twisted. But many o f the equation s in the v ariable operation analysis for the last stage are still de- duced from one dimension condition. This can’t guarantee the accuracy of the calculated results. 2.2. The Application of the Simplified Variable Operation Condition Analysis Method When the turbine steam inlet control valves are set to a position and kept unchanged (such as under the boiler follow operation mode), the flow passage area of the control stages and thus the steam inlet flow is constant when the turbine back pressure has some variations. The control stage efficiency can be regarded as constant, and the efficiency of the following turbine pressure stages is unchanged under turbine operation change conditions. The only exceptio n is the LP turbine last stage, where the operation condition of the LP last stage will be influ- enced by the turbine back pressure change and the stage efficiency will be affected. In summary, the LP turbine is the only part where the turbine back pressure change has impact on turbine work. The LP turbine expansion process is shown on Figure 1. Where the lpi is the LP turbine inlet enthalpy under baseline condition, c is the LP turbine back pressure under baseline condition, elep is the LP turbine expan- sion line end point enthalpy under baseline condition, el is the LP turbine last stage exhaust loss under base- line condition, id is the LP turbine ideal enthalpy drop under baseline condition. The symbols with “’” represent the operation condition with changed turbine back pressure. h p h h h It can be shown on Figure 1 that during normal o pera- tion, when the LP turbine inlet steam condition is stable, the LP turbine exhaust volumetric flow will decrease with the rising of the turbine back pressure, which will lead to a smaller exhaust loss and thus a higher LP tur- bine efficiency UEEP (indicated by the slope of the dashed line on Figure 1). For the LP turbine, it can be reasonably assumed that the LP turbine expansion line shape and expansion process is unchanged except for the expansion line end point. Thus the new LP turbine ex- pansion line end point enthalpy can be calculated by: '' elepjqjr elep hhh (1) The steam parameters of the LP turbine extractions can be determined by similar method. First calculate the extraction steam flow for the LP heaters, and calculate the new corrected extraction pressure. The new extrac- tion parameters can be found using the corrected extrac- tion pressure and the same LP turbine expansion line. This iteration process continues until the parameter dif- ference of the two iterations is lower than certain error. Based on the LP turb ine exhaust flow calculated in the above Simplified Variable Operation Condition Analysis, and the last stage exhaust loss curve provided by the tur- bine manufacture, the LP turbine last stage exhaust loss and the LP turbine used en ergy end point enth alpy UEEP can be calculated, and the final generator output change can be calculated using the heat balance method. h This Simplified Variable Operation Condition Analy- sis Method considers both the LP turbine last stage ex- haust loss change and the extraction steam flow change of the LP heaters for turbine back pressure change condi- tions. This Simplified Variable Operation Condition Analy- sis Method is used in [2] for analyzing the generator output change with the turbine back pressure. The calcu- lation result matches the real situation for one 600MW sub-critical generation unit. 3. Calculation Example of Turbine Choked Back Pressure for Steam Turbine with ACCs For one example generation unit, the 660MW steam tur- bine is a critical, single-shaft, two-casing two-exhaust Figure 1. LP turbine expansion line under different LP tur- bine back pressure operation conditions. condensing steam turbine with ACCs. There are totally Copyright © 2013 SciRes. EPE H. S. YANG ET AL. Copyright © 2013 SciRes. EPE 1476 The turbine choked back pressure result is shown in Ta- ble 2 and Figure 3. 28 stages in the turbine, including 1 control stage and 9 pressure stages for the HP turbine, 6 pressure stages for the IP turbine, and 2×6 pressure stages for the LP turbine. The LP turbine last blade has a height of 939.8 mm. The steam turbine is controlled by nozzles. The steam flow into the four nozzle groups on the HP turbine is con- trolled by the four mail control valves. The ACC system is the mechanically drafted direct air-cooled system pro- duced by the domestic manufacture. Table 1. Main design data of the steam turbine. Item Unit THA TRL Unit Output kW 660.01660.00 Unit Heat Rate kJ/kWh 7778.318225.81 Main Steam Pressure MPa(a) 24.20 24.20 Hot Reheat Steam Pressur e MPa(a) 3.71 3.94 HP Turbine Exhaust Pr e ssure MPa(a) 4.12 4.38 Main Steam Temperature ℃ 566.00 566.00 Hot Reheat Steam Temperature ℃ 566.00 566.00 HP Turbine Exhaust Temperature ℃ 305.07 312.13 Main Steam Flow t/h 1878.422013.35 Reheat Steam Flow t/h 1600.901701.48 Turbine Back Pressure kPa 16 33 LP Turbine Exhaust Entha l py kJ/kg 2454.672550.0 LP Turbine Exhaust F l ow t/h 1254.781349.40 Makeup Water % 0 3 Final Feedwater Temperature ℃ 273 277.2 The main design data of the steam turbine is summa- rized in Table 1. 3.1. The Calculation Result of the Steam Turbines Choked Back Pressure Based on the turbine last stage exhaust loss curve, the turbine exhaust steam used energy end point enthalpy and the exhaust loss and the final generator output are calculated for various turbine back pressure operation conditions. For each load condition, the turbine back pressure corresponding to the maximum generator output can be regarded as the turbine choked back pressure. Using this method, the turbine choked back pressures under different operation load conditions are calculated. On Figure 2, the generator output change with the back pressure is shown for various operation load conditions. -10 -8 -6 -4 -2 0 2 4 6 8 051015 20 25 3035 40 Turbine Back P re s sure (kP a ) Unit Output Relative Change ( % THA 90%THA 75%THA 50%THA Figure 2. Performance curves of the unit output with turbine back pressure. H. S. YANG ET AL. 1477 0 2 4 6 8 10 12 40 5060 70 8090100110120 Unit L oad Rate (%) T urbine Choked Back Pr essur e (kP a ) Sub-Critica l 600MW Unit with Wet Cooling Techno logy Super-Critical 600MW Unit with ACC 线性 (Sb C iil 600MWUiih WCliThl) Figure 3. Performance curves of the turbine choked back pressure with unit load. Table 2. Calculation results of choked back pressure under various operation loads. Operation Load (%) Turbine Choked Back Pressure (kPa) 100 9.0 90 8.2 75 7.0 50 5.0 For comparison purpose, the choked back pressure for 600 MW four-casing four-exhaust sub-critical generation unit with wet cooling technolog y is illustrated on Figure 3. It can be shown from the Table 2 and Figure 3 that the turbine choked back pressure is in nearly linear rela- tionship with the operation loads. For the choked back pressure curves, there is a significant increasing of the chocked pressure values for the units with ACCs com- pared with the similar curve of the units with wet cooling technology. 4. Conclusions Based on the clear definition of the turbine choked back pressure, the solution of the choked back pressure is changed into a problem of how to determine the turbine power output change as a function of the turbine back pressure change. The proposed simplified variable operation condition analysis method is adopted for one sub-critical genera- tion unit with ACCs. The performance curve of the power output versus the turbine back pressure under various operation loads is given, and curve of the turbine choked back pressure under different loads is provided. These curves provide valuable guidance for the economic operatio n of t he power plant u ni t s . REFERENCES [1] H. Lin, “Calculation and Correction of the Impact of Tur- bine Back Pressure on Turbine Output,” Turbine Tech- nology, Harbin China, Vol. 46 No. 1, 2004, pp. 18-21. [2] H. S. Yang, “Simplified Calculation Method of Turbine Back Pressure Correction Curves,” Turbine Technology. Harbin China, Vol. 49, No. 1, 2007, pp. 32-34. Copyright © 2013 SciRes. EPE |