**2.2. Variable speed fans and pumps**

Variable speed fans and pumps are the fans and pumps equipped with VFDs. Since their speeds vary as the frequency of supply power changes, these pumps and fans are also called variable frequency fans and pumps. The operating characteristic of centrifugal fans and pumps makes them the excellent candidates for VFD applications. According to the fan and pump affinity laws, the fan or pump power has a cubic relationship with the motor speed. Therefore, significant power savings could be achieved by reducing the motor speeds with the proper controls.

The variables related to the fan or pump performance are impeller diameter *D*, rotation speed *N*, gas/water density *ρ*, volume flow rate *Q*, pressure *P*, power *W*, and mechanical efficiency *η*. In a typical application, the fan or pump diameter is constant. The airflow or water flow, fan or pump head, and power solely relies on the speed. These relations are presented by the following equations [3] (where equations (1) and (2) denote two working conditions):

$$\frac{\mathbf{Q}\_1}{\mathbf{Q}\_2} = \frac{N\_1}{N\_2} \tag{1}$$

$$\frac{P\_1}{P\_2} = \left(\frac{N\_1}{N\_2}\right)^2\tag{2}$$

$$\frac{\mathcal{W}\_1}{\mathcal{W}\_2} = \left(\frac{\mathcal{N}\_1}{\mathcal{N}\_2}\right)^3 \tag{3}$$

Equation (3) clearly indicates how the speed change affects the power change. For example, 50% speed reduction results in 87.5% power reduction theoretically. There are several types of air and water systems including the single-duct variable air volume (SDVAV) system, dualduct variable air volume (DDVAV) system, single-zone system, multi-zone system, primary and/or secondary chilled water system, and the hot water system. Each type of system requires specific control strategy rather than a fixed low-speed operation without modulation.

### **2.3. Variable speed compressors**

Variable speed compressors or variable frequency compressors are compressors equipped with VFDs. In the HVAC industry, there are several types of compressors associated with the refrigeration systems: reciprocating, screw, scroll, and centrifugal. All of them are viable components for a VFD application. The commonly used working media includes air and refrigerant. Air compressors are frequently used in industrial processes as a power source for pneumatic control systems. Refrigerant compressors are typically used in air conditioners, unitary air-handling units (AHU), or chillers in residential and commercial buildings. Signif‐ icant progresses on the theoretical study and applications on variable speed compressors were made during the past thirty years. As early as 1982, Itami et al. [5] conducted an experimental study on the performance and reliability of a rotary compressor and reciprocating compressor combined with frequency inverters. In 1996, Qureshi and Tassou [6] presented a review of application of variable speed capacity control on refrigeration systems. It pointed out that VFD applications on compressors were largely restricted to small-capacity air-conditioning units thus far, with only a small amount of applications to medium-range capacity units. More research work was still required. Since then, dramatic studies were conducted on applications of variable speed drives in HVAC systems [7–9].

Unlike other types of compressors, centrifugal compressors have similar energy performance as centrifugal fans and pumps. A scroll compressor is especially suitable for a VFD due to its intrinsic structural design. Scroll compressors and reciprocating compressors are the most commonly used types on rooftop units (RTUs) and heat pumps (HPs) units. For the majority

of existing constant speed compressors, installing a VFD on the compressor is the most feasible way. In recent years, some original equipment manufacturers (OEMs) of compressors, such as Emerson and Danfoss, have already manufactured variable speed compressors. Several large HVAC manufacturers, such as Trane, Carrier, McQuay, Lennox, AAON, York, and Emerson, started equipping variable speed compressors in their new products, such as RTUs, HPs, computer room air-conditioning (CRAC) units, or chillers. compressors, such as Emerson and Danfoss, have already manufactured variable speed compressors. Several large HVAC manufacturers, such as Trane, Carrier, McQuay, Lennox, AAON, York, and Emerson, started equipping variable speed compressors in their new products, such as RTUs, HPs, computer room air‐conditioning (CRAC) units, or chillers.

the most feasible way. In recent years, some original equipment manufacturers (OEMs) of

[6] presented a review of application of variable speed capacity control on refrigeration systems. It pointed out that VFD applications on compressors were largely restricted to small‐capacity air‐conditioning units thus far, with only a small amount of applications to medium‐range capacity units. More research work was still required. Since then, dramatic studies were conducted on applications of variable speed drives in HVAC systems [7–9].

Unlike other types of compressors, centrifugal compressors have similar energy performance as centrifugal fans and pumps. A scroll compressor is especially suitable for a VFD due to its intrinsic structural design. Scroll compressors and reciprocating compressors are the most commonly used types on rooftop units (RTUs) and heat pumps (HPs) units. For

Unlike fans and pumps, the scroll and reciprocating compressors usually do not have a cubic relationship between power and frequency. Figure 3 shows an approximate linear relationship between power and frequency for a 5-ton RTU with a scroll compressor, based on the exper‐ imental study [10]. This relationship clearly demonstrates how the compressor power changes with frequency. The linear correlation is also helpful to develop a new, simpler compressor model [11]. Unlike fans and pumps, the scroll and reciprocating compressors usually do not have a cubic relationship between power and frequency. Figure 3 shows an approximate linear relationship between power and frequency for a 5‐ton RTU with a scroll compressor, based on the experimental study [10]. This relationship clearly demonstrates how the compressor power changes with frequency. The linear correlation is also helpful to develop a new, simpler compressor model [11].

Figure 3 Relationship between compressor power and frequency for a 5‐ton RTU **Figure 3.** Relationship between compressor power and frequency for a 5-ton RTU
