■ Fan and Pump Operating Characteristics Fan and pump characteristics: H=H0-（H0-1）＊Q2 H－Head Q－Flow rate H0－Head when flow rate is 0 Pipeline resistance: R＝KQ2 R－Pipeline resistance K－Pipeline damping coefficient Q－Flow rate Note: All the above variables are per-unit values, based on the rated value. A value of 1 indicates that the actual value is equal to the rated value. Fan and pump shaft power P: P= KpQH/ηb P－Shaft power Q－Flow rate; H－Pressure; ηb－Fan and pump efficiency; Kp－Calculation constant; Relationship between flow rate, pressure, power and speed: Q1/Q2 = n1/n2; H1/H2 =（n1/n2）2; P1/P2 =（n1/n2）3 ■ Variable Valve Control Variable valve regulation is to adjust the flow rate of pumps and fans by changing the opening of pipeline valves. When adjusting with a variable valve, the power of the pump or fan remains essentially constant, and its performance curve remains unchanged. However, the pipeline resistance characteristic curve changes. The intersection of the pump or fan's performance curve and the new pipeline resistance characteristic curve is the new operating point. ■ Variable Frequency Control (VFD) Variable frequency control changes the operating point by altering the performance curve. Since there is no additional resistance in variable speed control, it is a relatively ideal method. By changing the operating frequency of the power supply through a frequency converter, stepless speed regulation of the AC motor is achieved. When pumps and fans use variable speed control, their efficiency remains almost constant. The flow rate changes with the speed according to a first-order law, while the shaft power changes according to a cubic law. Simultaneously, using variable frequency control can reduce pump and fan noise, reduce wear, and extend service life. ■ Energy Saving Calculation Example Assume the motor efficiency = 98%, the IPER high-voltage frequency converter efficiency = 97% (including transformer), the fan shaft power at rated air volume: 1000kW, fan characteristics: when air volume Q is 0, the head H is 1.4pu (per unit value, based on rated value); assume the curve characteristic is H = 1.4 - 0.4Q², annual operating time: 8000 hours, fan operating modes: 100% air volume, 20% of annual operating time; 70% air volume, 50% of annual operating time; 50% air volume, 30% of annual operating time. When the variable valve regulates and controls the air volume, assume P100 is the power consumption at 100% air volume, P70 is the power consumption at 70% air volume, and P50 is the power consumption at 50% air volume. P100 = 1000/0.98 = 1020kW, P70 = 1000 x 0.7 x (1.4 - 0.4 x 0.72) / 0.98 = 860kW P50 = 1000 x 0.5 x (1.4 - 0.4 x 0.52) / 0.98 = 663kW Annual power consumption: 1020 x 8000 x 0.2 + 860 x 8000 x 0.5 + 663 x 8000 x 0.3 = 6,663,200 kWh Assuming an electricity cost of 0.50 yuan/kWh, the annual electricity cost is: 6,663,200 x 0.5 = 3,331,600 yuan When using frequency converter to control airflow, assuming P100 is the power consumption at 100% airflow, P70 is the power consumption at 70% airflow, and P50 is the power consumption at 50% airflow, P100 = 1000 / 0.98 / 0.97 = 1052kW P70 = 1000 x 0.73 / 0.98 / 0.97 = 360kW P50 = 1000 x 0.53 / 0.98 / 0.97 = 131kW Annual electricity consumption: 1052 x 8000 x 0.2 + 360 x 8000 x 0.5 + 131 x 8000 x 0.3 = 3,437,600 kWh Assuming an electricity price of 0.5 yuan/kWh, the annual electricity cost is 3,437,600 x 0.5 = 1,718,800 yuan. The annual electricity cost savings are 3,331,600 – 1,718,800 = 1,612,800 yuan. The electricity saving rate is 1,612,800/3,331,600. = 48.3%