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2. Demand and supply analysis and minimum penstock pipe diameter selection Daily electrical energy demand profile 9 Enter last digit of student number (A) Enter second last digit of student number (B) Time Electrical demand 12 00 00 AM 1:00:00 AM 2:00:00 AM 300 00 AM 4:00:00 AM 5:00:00 AM 6 00 00 AM 7:00:00 AM 8:00:00 AM 9 00 00 AM 10.00:00 AM 11:00:00 AM 12 00 00 PM 1:00:00 PM 2:00:00 PM 300 00 PM 4:00:00 PM 5:00:00 PM 600 00 PM 7:00:00 PM 8:00:00 PM 900.00 PM 10:00:00 PM 11:00:00 PM 12:00:00 AM KW 25.4 30.5 36.6 44 0 528 28.7 374 71.4 87.4 824 45.9 55.1 761 40.7 38.6 829 B5.5 98.8 109.5 120.0 95.0 93.7 95.7 74.0 25.4 Solar Energy available on the inclined surface to the local latitude. This is the angle at which the solar PV panels will be installed. W/m2 0 0 0 0 0 1 50 171 308 453 603 723 810 B35 794 690 562 402 235 80 4 0 0 0 0 Efficiency = 15 % for each solar panel PVC pipe length = 6 m Velocity of the water in the hydro turbine penstock line = limited to 1.5 m/s Velocity of the water in the pump penstock line = limited to 7 m/s Consider, A = 9,B=1 Gross available head = 170 +0.4*A + 0.1*B) = (70+0.4*9 +0.1*1) = 73.7 m Length of hydro turbine penstock line (pipeline) = (80 +0.24*A) = (80 +0.24*9) = 82.16 m Length of pumping line penstock = 2 +82.16 = 84.16 m Number of 90Deg Elbows = 2+0.5*8 = 2 +0.5*1 = 2.523 (K = 0.3 for each 90 des elbow) Number of 45 Deg Elbows = 3 +0.5* A=3+0.5*9=752B (K = 0.17 for each 45 deg elbow) Number of 20Deg Elbows = 4 +0.5* A = 4+0.5*9=8.5 29 (K = 0.15 for each 20 de elbow) K=1.5 (One strainer at the inlet) K=10 completely open condition of one globe valve) Nozzle, Kfactor = 0.2 (full load condition) Nozzle, K factor = 0.2 + (1 -jet diameter ratio) (at part load condition) Sum of factors, pump penstock fittings = [8.1 +0.0Z*A-0.01*8) = (8.1 +0.02*9 -0.01*1] = 8.27| 1.6 CLASSIFICATION Pipe and fittings shall be classified by nominal pressure as follows: PN 4.5for a nominal working pressure of 0.45 MPa at 20C. PN 6for a nominal working pressure of 0.6 MPa at 20C. PN 9for a nominal working pressure of 0.9 MPa at 20C. PN 12for a nominal working pressure of 1.2 MPa at 20C. PN 15for a nominal working pressure of 1.5 MPa at 20C. PN 16for a nominal working pressure of 1.6 MPa at 20C. PN 18for a nominal working pressure of 1.8 MPa at 20C. PN 20for a nominal working pressure of 2.0 MPa at 20C. NOTE: Selection of class should be based on consideration of all factors that may affect the operation of the pipe, e.g. temperature of operation, fluctuating pressure, and external loading. Reference should be made to AS/NZS 2032 for the design and installation of PVC systems. TABLE 4.1 DIMENSIONS OF PVC PRESSURE PIPES-SERIES 1: METRIC PIPE SERIES millimetres Wall thickness Nominal size DN PN 4.5 PN 6 PN9 PN 12 PN 15 PN 18 Tolerance on end squareness Outside diameter Mean outside Maximum diameter out-of Danis) Damas roundness 17.0 17.3 0.5 21.2 21.5 0.5 26.6 26.9 0.5 Tinin Tas Tain T Tinin TI This Tax Tin TO Tin Tas 10 15 20 1.4 1.7 1.7 2.1 1.4 1.6 2.0 1.7 2.0 2.4 1 1 1.4 1.7 III 11 0.5 1.7 ||||| 1.7 25 32 40 2.5 33.7 42.4 1.4 1.7 1.9 2.1 2.7 2.1 2.6 3.0 2.5 3.2 0.5 3.0 3.7 2.1 3.2 1 1 2 48.4 0.3 1.4 1.7 2.3 2.3 3.1 3.6 3.6 33.4 42.1 48.1 60.2 75.2 88.7 50 65 80 60.5 75.5 89.1 0.6 0.7 0.9 1.5 1.8 1.9 2.2 1.6 2.0 2.4 2.0 2.4 2.8 3.0 3.5 2.8 3.5 4.1 3.1 3.9 4.6 3.6 4.5 5.3 3.8 4.8 5.7 4.4 5.5 6.5 4.6 5.7 6.7 5.3 6.5 7.6 2 3 3 3.0 4.5 5.9 100 125 150 114.1 140.0 160.0 1.2 1.4 1.6 2.8 3.3 3.7 3.7 4.2 3.5 4.3 4.8 3.5 6.3 5.2 6.3 7.1 7.2 8.3 6.7 8.1 9.3 7.3 8.9 10.2 8.2 10.0 11.4 8.6 10.6 12.1 9.7 11.9 13.5 4 5 6 3.2 114.5 140.4 160.5 200.5 225.6 250.7 2.0 175 200 225 200.0 225.0 250.0 3.6 4.0 4.5 4.2 4.6 5.1 4.8 5.4 6.0 5.4 6.1 6.7 7.1 7.9 8.8 8.0 8.9 9.9 10.5 11.6 10.4 11.7 13.0 11.5 12.9 14.4 12.8 14.4 16.0 13.6 15.3 17.0 15.2 17.1 19.0 7 8 9 2.5 250 300 350 280.0 315.0 355.0 280.8 315.9 356.0 2.8 3.1 3.6 5.0 5.7 6.4 5.7 6.4 7.2 6.7 7.5 8.5 7.5 8.5 9.5 9.9 11.1 12.5 11.1 12.4 14.0 13.0 14.7 16.5 14.5 16.3 18.4 16.1 18.1 20.4 17.9 20.1 22.6 19.1 21.5 21.2 23.8 26.8 10 11 12 375 400 450 400.0 450.0 500.0 401.0 451.0 501.0 561.0 631.0 4.0 4.5 5.0 7.2 8.1 9.0 8.1 9.1 10.1 9.5 10.7 11.9 10.7 12.0 13.3 14.1 15.9 17.6 15.7 17.7 19.6 18.6 20.9 23.3 20.7 23.2 25.8 23.0 25.9 28.7 25.5 28.6 31.8 27.3 30.7 34.1 30.2 34.0 37.7 14 16 17 14.9 35.6 500 575 560.0 630.0 5.6 6.3 10.1 11.3 11.3 12.6 13.3 15.0 19.8 22.2 21.9 24.7 26.0 29.3 28.9 32.4 32.2 36.2 38.2 43.0 42.2 47.5 19 22 40.0 16.2 Using the above information and the turbine and pump performance parameters provide in section 3 and 4 estimate the minimum diameter of the penstock pipe for both charging pipeline (pump penstock) and discharging pipeline (hydro turbine penstock). And select a suitable standard pipe size (in metric) for the penstocks from series 1 PVC pressure pipes as per AS/NZ-1477. Also assume that PVC pipe is smooth, so the roughness is zero. 3. Hydro power system design It is advised to use Pelton turbine coupled with electric generator (turbo-generator unit) to convert energy from fluid to electrical energy. You are expected to design the hydro power system with a power output capacity to supply for the peak (maximum) power demand for your own demand profile You are expected to design the Pelton turbine for the best efficiency point, which is at bucket velocity to jet velocity ratio of 0.5 Design the Pelton turbine/ nozzle assembly that is capable of producing enough mechanical power to support the peak electrical power under supply For the Pelton turbine, assume the inlet to outlet relative velocity ratio of 0.85. Mechanical efficiency of this turbine is expected to be minimum (90 - 0.3*A) % (where A is the last digit of your student number). Further assume that the generator efficiency is (90 +0.2*A) % and this remains constant for the entire range of the power output. For the purpose of this design exercise, assume that the turbine rotates at 1500 rpm and is directly coupled with the electrical generator with 2-pole pairs to achieve 50Hz frequency of the output electrical power. For the Pelton turbine buckets use the angle of deflection as 160 Develop and present velocity triangles for the best efficiency design, this includes estimating the values of all the velocity components and angles and draw velocity triangle diagrams. Estimate the dimensions of the turbine and nozzle such as mean turbine diameter (wheel diameter) and full load jet diameter (this is the maximum nozzle exit diameter). Design of any dynamic system requires iterative approach to find a converged solution. Now use the turbine and nozzle geometry to estimate the performance of the system under part load conditions (i.e. for every hour when turbine needs to generate power). This will help to estimate the total volume of water that needs to be stored in the upper reservoir. For first iteration assume the jet velocity at part load operation is same as the full load condition, where you have used nozzle K-factor= 0.2 (as the jet diameter ratio for full load is equal to 1). For every hour estimate hydraulic efficiency, flow rate (m/s and m/hr), jet diameter and jet diameter ratio. Also estimate total volume of water to be stored in the upper reservoir (m). Now use the jet diameter ratio to estimate the modified nozzle K-factor for every hour using the equation provided in section 2. Now use the modified nozzle K-factor to estimate modified jet velocity for every hour and use this modified jet velocity to recalculate the hydraulic efficiency, flow rates, and so on for every hour. Repeat this step till the value of the total storage volume converges to within 5m? Present all the hourly values (Part load) in a tabular format. And at least one sample calculation for every parameter that you determine. Note: For part load operation assume that the mechanical and electrical generator efficiency remains constant for the entire range of operation. The turbine geometry cannot be changed during the operation, but the nozzle spear position can be adjusted to achieve the part load flow rate and jet diameter. The part load jet diameter information will be assist the control systems engineering design team to develop spear valve control system and strategies. The turbine rotational speed will be maintained at 1500rpm even during the part load operation, so the electrical power generated is always at 50Hz. Hint For part load performance estimation you will have to do multiple iterations, so it will help to use excel. In the first iteration assume the jet velocity is same as what you used for designing the nozzle and the turbine, this will help you get the part load flow rates, total volume of water, part load jet diameters, part load jet diameter ratios, part load nozzle K-factors and rest of the parameters, while keeping turbine geometry and rotational speed constant at 1500 rpm. In the following iterations use the part load nozzle K-factor to modify the part load jet velocity and use this to determine the rest of the parameter. Continue the iteration, until the value of total volume of water to be stored in the upper reservoir (in m) converges to within 5m? (This total volume of storage may change following the pump impeller design and reassessment of the solar PV panel size) 2. Demand and supply analysis and minimum penstock pipe diameter selection Daily electrical energy demand profile 9 Enter last digit of student number (A) Enter second last digit of student number (B) Time Electrical demand 12 00 00 AM 1:00:00 AM 2:00:00 AM 300 00 AM 4:00:00 AM 5:00:00 AM 6 00 00 AM 7:00:00 AM 8:00:00 AM 9 00 00 AM 10.00:00 AM 11:00:00 AM 12 00 00 PM 1:00:00 PM 2:00:00 PM 300 00 PM 4:00:00 PM 5:00:00 PM 600 00 PM 7:00:00 PM 8:00:00 PM 900.00 PM 10:00:00 PM 11:00:00 PM 12:00:00 AM KW 25.4 30.5 36.6 44 0 528 28.7 374 71.4 87.4 824 45.9 55.1 761 40.7 38.6 829 B5.5 98.8 109.5 120.0 95.0 93.7 95.7 74.0 25.4 Solar Energy available on the inclined surface to the local latitude. This is the angle at which the solar PV panels will be installed. W/m2 0 0 0 0 0 1 50 171 308 453 603 723 810 B35 794 690 562 402 235 80 4 0 0 0 0 Efficiency = 15 % for each solar panel PVC pipe length = 6 m Velocity of the water in the hydro turbine penstock line = limited to 1.5 m/s Velocity of the water in the pump penstock line = limited to 7 m/s Consider, A = 9,B=1 Gross available head = 170 +0.4*A + 0.1*B) = (70+0.4*9 +0.1*1) = 73.7 m Length of hydro turbine penstock line (pipeline) = (80 +0.24*A) = (80 +0.24*9) = 82.16 m Length of pumping line penstock = 2 +82.16 = 84.16 m Number of 90Deg Elbows = 2+0.5*8 = 2 +0.5*1 = 2.523 (K = 0.3 for each 90 des elbow) Number of 45 Deg Elbows = 3 +0.5* A=3+0.5*9=752B (K = 0.17 for each 45 deg elbow) Number of 20Deg Elbows = 4 +0.5* A = 4+0.5*9=8.5 29 (K = 0.15 for each 20 de elbow) K=1.5 (One strainer at the inlet) K=10 completely open condition of one globe valve) Nozzle, Kfactor = 0.2 (full load condition) Nozzle, K factor = 0.2 + (1 -jet diameter ratio) (at part load condition) Sum of factors, pump penstock fittings = [8.1 +0.0Z*A-0.01*8) = (8.1 +0.02*9 -0.01*1] = 8.27| 1.6 CLASSIFICATION Pipe and fittings shall be classified by nominal pressure as follows: PN 4.5for a nominal working pressure of 0.45 MPa at 20C. PN 6for a nominal working pressure of 0.6 MPa at 20C. PN 9for a nominal working pressure of 0.9 MPa at 20C. PN 12for a nominal working pressure of 1.2 MPa at 20C. PN 15for a nominal working pressure of 1.5 MPa at 20C. PN 16for a nominal working pressure of 1.6 MPa at 20C. PN 18for a nominal working pressure of 1.8 MPa at 20C. PN 20for a nominal working pressure of 2.0 MPa at 20C. NOTE: Selection of class should be based on consideration of all factors that may affect the operation of the pipe, e.g. temperature of operation, fluctuating pressure, and external loading. Reference should be made to AS/NZS 2032 for the design and installation of PVC systems. TABLE 4.1 DIMENSIONS OF PVC PRESSURE PIPES-SERIES 1: METRIC PIPE SERIES millimetres Wall thickness Nominal size DN PN 4.5 PN 6 PN9 PN 12 PN 15 PN 18 Tolerance on end squareness Outside diameter Mean outside Maximum diameter out-of Danis) Damas roundness 17.0 17.3 0.5 21.2 21.5 0.5 26.6 26.9 0.5 Tinin Tas Tain T Tinin TI This Tax Tin TO Tin Tas 10 15 20 1.4 1.7 1.7 2.1 1.4 1.6 2.0 1.7 2.0 2.4 1 1 1.4 1.7 III 11 0.5 1.7 ||||| 1.7 25 32 40 2.5 33.7 42.4 1.4 1.7 1.9 2.1 2.7 2.1 2.6 3.0 2.5 3.2 0.5 3.0 3.7 2.1 3.2 1 1 2 48.4 0.3 1.4 1.7 2.3 2.3 3.1 3.6 3.6 33.4 42.1 48.1 60.2 75.2 88.7 50 65 80 60.5 75.5 89.1 0.6 0.7 0.9 1.5 1.8 1.9 2.2 1.6 2.0 2.4 2.0 2.4 2.8 3.0 3.5 2.8 3.5 4.1 3.1 3.9 4.6 3.6 4.5 5.3 3.8 4.8 5.7 4.4 5.5 6.5 4.6 5.7 6.7 5.3 6.5 7.6 2 3 3 3.0 4.5 5.9 100 125 150 114.1 140.0 160.0 1.2 1.4 1.6 2.8 3.3 3.7 3.7 4.2 3.5 4.3 4.8 3.5 6.3 5.2 6.3 7.1 7.2 8.3 6.7 8.1 9.3 7.3 8.9 10.2 8.2 10.0 11.4 8.6 10.6 12.1 9.7 11.9 13.5 4 5 6 3.2 114.5 140.4 160.5 200.5 225.6 250.7 2.0 175 200 225 200.0 225.0 250.0 3.6 4.0 4.5 4.2 4.6 5.1 4.8 5.4 6.0 5.4 6.1 6.7 7.1 7.9 8.8 8.0 8.9 9.9 10.5 11.6 10.4 11.7 13.0 11.5 12.9 14.4 12.8 14.4 16.0 13.6 15.3 17.0 15.2 17.1 19.0 7 8 9 2.5 250 300 350 280.0 315.0 355.0 280.8 315.9 356.0 2.8 3.1 3.6 5.0 5.7 6.4 5.7 6.4 7.2 6.7 7.5 8.5 7.5 8.5 9.5 9.9 11.1 12.5 11.1 12.4 14.0 13.0 14.7 16.5 14.5 16.3 18.4 16.1 18.1 20.4 17.9 20.1 22.6 19.1 21.5 21.2 23.8 26.8 10 11 12 375 400 450 400.0 450.0 500.0 401.0 451.0 501.0 561.0 631.0 4.0 4.5 5.0 7.2 8.1 9.0 8.1 9.1 10.1 9.5 10.7 11.9 10.7 12.0 13.3 14.1 15.9 17.6 15.7 17.7 19.6 18.6 20.9 23.3 20.7 23.2 25.8 23.0 25.9 28.7 25.5 28.6 31.8 27.3 30.7 34.1 30.2 34.0 37.7 14 16 17 14.9 35.6 500 575 560.0 630.0 5.6 6.3 10.1 11.3 11.3 12.6 13.3 15.0 19.8 22.2 21.9 24.7 26.0 29.3 28.9 32.4 32.2 36.2 38.2 43.0 42.2 47.5 19 22 40.0 16.2 Using the above information and the turbine and pump performance parameters provide in section 3 and 4 estimate the minimum diameter of the penstock pipe for both charging pipeline (pump penstock) and discharging pipeline (hydro turbine penstock). And select a suitable standard pipe size (in metric) for the penstocks from series 1 PVC pressure pipes as per AS/NZ-1477. Also assume that PVC pipe is smooth, so the roughness is zero. 3. Hydro power system design It is advised to use Pelton turbine coupled with electric generator (turbo-generator unit) to convert energy from fluid to electrical energy. You are expected to design the hydro power system with a power output capacity to supply for the peak (maximum) power demand for your own demand profile You are expected to design the Pelton turbine for the best efficiency point, which is at bucket velocity to jet velocity ratio of 0.5 Design the Pelton turbine/ nozzle assembly that is capable of producing enough mechanical power to support the peak electrical power under supply For the Pelton turbine, assume the inlet to outlet relative velocity ratio of 0.85. Mechanical efficiency of this turbine is expected to be minimum (90 - 0.3*A) % (where A is the last digit of your student number). Further assume that the generator efficiency is (90 +0.2*A) % and this remains constant for the entire range of the power output. For the purpose of this design exercise, assume that the turbine rotates at 1500 rpm and is directly coupled with the electrical generator with 2-pole pairs to achieve 50Hz frequency of the output electrical power. For the Pelton turbine buckets use the angle of deflection as 160 Develop and present velocity triangles for the best efficiency design, this includes estimating the values of all the velocity components and angles and draw velocity triangle diagrams. Estimate the dimensions of the turbine and nozzle such as mean turbine diameter (wheel diameter) and full load jet diameter (this is the maximum nozzle exit diameter). Design of any dynamic system requires iterative approach to find a converged solution. Now use the turbine and nozzle geometry to estimate the performance of the system under part load conditions (i.e. for every hour when turbine needs to generate power). This will help to estimate the total volume of water that needs to be stored in the upper reservoir. For first iteration assume the jet velocity at part load operation is same as the full load condition, where you have used nozzle K-factor= 0.2 (as the jet diameter ratio for full load is equal to 1). For every hour estimate hydraulic efficiency, flow rate (m/s and m/hr), jet diameter and jet diameter ratio. Also estimate total volume of water to be stored in the upper reservoir (m). Now use the jet diameter ratio to estimate the modified nozzle K-factor for every hour using the equation provided in section 2. Now use the modified nozzle K-factor to estimate modified jet velocity for every hour and use this modified jet velocity to recalculate the hydraulic efficiency, flow rates, and so on for every hour. Repeat this step till the value of the total storage volume converges to within 5m? Present all the hourly values (Part load) in a tabular format. And at least one sample calculation for every parameter that you determine. Note: For part load operation assume that the mechanical and electrical generator efficiency remains constant for the entire range of operation. The turbine geometry cannot be changed during the operation, but the nozzle spear position can be adjusted to achieve the part load flow rate and jet diameter. The part load jet diameter information will be assist the control systems engineering design team to develop spear valve control system and strategies. The turbine rotational speed will be maintained at 1500rpm even during the part load operation, so the electrical power generated is always at 50Hz. Hint For part load performance estimation you will have to do multiple iterations, so it will help to use excel. In the first iteration assume the jet velocity is same as what you used for designing the nozzle and the turbine, this will help you get the part load flow rates, total volume of water, part load jet diameters, part load jet diameter ratios, part load nozzle K-factors and rest of the parameters, while keeping turbine geometry and rotational speed constant at 1500 rpm. In the following iterations use the part load nozzle K-factor to modify the part load jet velocity and use this to determine the rest of the parameter. Continue the iteration, until the value of total volume of water to be stored in the upper reservoir (in m) converges to within 5m? (This total volume of storage may change following the pump impeller design and reassessment of the solar PV panel size)
