The fans used for purposes of this research are axial-flow fans with permanent-magnet brushless DC (PMBLDC) motors. Single-phase PMBLDC motors are commonly employed for driving axial fans [4]. In spite of the different limitations of DC motors [4], they are used extensively in PV pumping systems because they can be coupled directly to the PV module giving a simple and inexpensive system. Many researchers have investigated the design and performance of directly coupled PV pumping systems. Most of this research has focused on the matching between DC motors and PV modules for maximising efficiency. Applebaum and Bany [3] studied the performance of separately excited DC motors powered by PV cells. Singer and Applebaum [5] studied the starting characteristics of PV — powered permanent magnet DC motors while Roger [6] examined the direct coupling between DC motors and PV arrays for both pumps and fans. Anis and Metwally [7], and Swamy et al. [8], analysed the dynamic performance of a DC coupled PV pumping system. Koner [9] analysed the PV powered DC series and brushless motors for driving centrifugal pumps by varying the motor constants.

Brushless DC motors, although relatively expensive, are highly efficient when compared to conventional brush motors. Moreover, they require no maintenance and produce less electromagnetic radiation [10]. Permanent magnet motors are generally considered the best motors for direct coupling to PV modules [6] due to their high efficiency and low cost.

A simple circuit of a DC motor is a voltage source (V) in series with the motor’s armature resistance (Ra) and the back emf (E) of the motor generated by the rotating armature. For a PMDC motor the magnetic flux is always constant, resulting in linear speed — voltage and speed-torque curves. The operation of a PMDC motor is governed by the following equations:

where ю is the speed of the fan (r/min), I is the current through the armature, Tm is the motor torque (N. m) and Km is the motor constant (Vs-1). The armature resistance (Q) can be determined from stall conditions (i. e. ю = 0) by taking V-I measurements and by making use of Eqs. 2 and 3. The motor speed constant in Eq. 2 (which has in essence the same

value as the torque constant in Eq. 3) is determined from the no-load conditions using the following equation, which assumes negligible friction [11]:

where ram is the maximum speed attainable by the fan at voltage Vm.

The torque of the fan, Tf, is, in general, a function of its speed according to the relationship,

Tf = Kf ■ a>2 (6)

Where Kf is a constant determined from reference values of speed and torque. At steady state conditions, the fan torque is equal to the motor torque so that

Kf — Ф1 = Km I (7)

Measurements of speed (ю) and current (I) can be used in Eq. 7 to determine Kf.

Figure 1 represents typical H-Q characteristics for axial-flow fans. Axial-flow fans are most appropriate for high flow rate and medium head applications [12]. It is usually desirable to operate in the lower section of the H-Q curve. The flow rate of air from the fan and the total head developed across it are related to the speed of the fan by the affinity laws, which are applicable for both fans and pumps [13]. The H-Q curve of the fan changes as a function of speed. Thus, the head developed across the fan is a function of flow rate and speed (or voltage) of the motor.

In order to simplify the H-Q relationship of an axial flow fan, the curve can be segmented into three straight lines as shown in Fig. 1. The slope and intercept of each of these line segments, as well as the limiting flow rates Q1 and Q2, are functions of speed. The head can be expressed as a function of speed and flow rate by the following equation:

H = qj ■ ®2 + C2>j. a-Q + Сз, j ■ a + C4>j ■ Q (8)

where the C’s are constants and the "j” subscript corresponds to one of the three segments. Thus, for the lower section of the H-Q curve, j = 3 and the constants Ci|3 (for i = 1 to 4) are used only if the flow rate Q is larger than Q2 which is also a function of ю. These constants are fan-specific and can be determined using the affinity laws by generating several curves at different motor speeds from a single manufacturer’s curve.

1.2 Photovoltaic-motor-fan coupling

When the fan is driven by the PV-powered DC motor, the following assumptions can be made:

1. The motor torque is equal to the fan torque as shown by Eq. 7 above.

2. The voltage and current of the motor are equal to those of the PV module.

3. The speed of the fan is equal to the speed of the motor.

The three linear-segment representation of the fans’ H-Q characteristic simplifies the modeling procedure. For a given irradiance and module temperature, the PV I-V characteristic is determined. Making use of the assumptions above, the operational speed of the motor/fan is then evaluated by solving Eqs. (1), (2), (3) and (7) for the given irradiance and PV module temperature. This speed is then used in Eq. 8 to determine the H-Q relationship for each of the three linear sections. The flow rate in the system is determined by solving the system curve with Eq. 8 simultaneously.

The speed of the motor/fan (ю) and the flow rate (Q) in the system can also be determined as a function of the time of day if detailed hourly solar meteorological data is available.