The losses considered in this section are the losses supplied by the PV generator and are expressed as follows : 1. PV series resistance losses (Prs) which equals I*Rs. 2. Motor losses that can be given as (Say, 1980): t .
Armature copper losses (Pcu) = I Ra
Core losses (Pco), eddy (Ped) and hystresis (Phy) where Ped is proportional to w2 ф1 Phy is proportional to w фг
Mechanical and windage losses (Pm) are assumed to be proportional to w. Brush contact losses Pbt, this losses could be included in the copper losses or neglected because it has very small value.
The total system loss supplied by the PV generator is given by :
Ploss = Prs + Pcu + Ped + Phy + Pm (5)
The internal power produced by the PV generator supplies the load power Pld in addition to all the losses (Plosses) mentioned in the preceeding section. If the losses due to the PV generator series resistance Prs and the armature copper loss Pcu are included in the internal power, then the power balance relation is given as
E I = Pld + Ped + Phy + Pm (6)
For a pumping load of a torque (T) , the torque – speed (w)
characteristic is in the form :
T = b w2
Equation 6 is defined in motor operation as
Ka ф w I = b w3 + Ke ф* w* + Kh ф* w + Km w,(7)
For a SE dc motor, the flux ф is kept constant and at any operating point the current is fixed. Consequently, if eq. 7 is simplified and divided by w, a second order eq. in speed will result in the form :
b w2 .+ Ke ф* w + ( Kh ф* + Km – Ka ф I ) = 0 (8)
The analysis followed in the proceeding sections produces two equations in w and I (eqs. 4,8). Equation 4 is a result of the voltage relation and eq. 8 is obtained for the power balance relation. The two equations can be solved using Newton – Raphsonіteration method at each insolation level for a given load and define preceicely the operating point of the system.
A 1400 W maximum output power at 100 4 insolation PV generator is considered in the design to supply a motor of 120 V, 1.2 KW and 1500 rpm. The operating points of each insolation level are illustrated on Fig. 1. Fig. 2 shows the different types of losses of the system at insolation levels 100 4, 80 60 %, 40 4 and 20 %.
Fig. 2 Losses of dc motor – PV generator system.
EFFECTS OF MOTOR PARAMETER CHANGE
Changes in the motor loss terms are due to changes in the motor parameters with temperature, with magnetic flux level-if excitation differs – or in the mechanical conditions.
Any change of one of the loss terms will affect the power balance relation (eg. S) and so the operating point at each insolation level. Effect of the change in motor parameters is applied to three cases:
case I : 50 % increase in the armature resistance,
case II : 50 % increase in the core losses,
case III : doubling the mechanical losses.
In the three cases, the system shows reduction in the net output mechanical power, and the power drop is illustrated in Fig. 3.
Notice that the effect when armature resistance increases (case I)
is high at higher insolation level. While cases II and III account the major part of the power drop at lower insolation level.
Fig. 3 Power drop vs. insolation level.
The utilization efficiency of the system (net mechanical power to the maximum PV generator power percentage) is computed at each insolation level. Table 1 gives the utilization efficiency of the system when no change in the parameter occurs and for cases I, II and III.
To obtain a complete evaluation of the system performance, under change in the motor parameters, the drop in the daily energy is computed, for the three cases using a typical average insolation curve of a clear day in Cairo area, as given in table 2. The results in table 2 show that the increase in iron losses by 50 % (case II) causes the largest drop in daily energy while the increase in the armature reaction leads to the smallest drop, although table I indicates that the drop in the utilization efficiency takes place in cases I, II and III in descending order at 100 % insolation. This means that in the design stage, the daily energy value and how much it changes with the motor parameters should be taken as a primary factor.
TflRI F 2 Drop in Daily Energy
The losses of a dc motor-PV generator system with pumping load are discussed to define accurately the operation of the system. Changes in any of the motor losses due to parameter variation (copper, iron and mechanical) result in change in the system operation. The increase in the motor losses lead to power drop in the net output. The daily energy decreases with any increase in the motor loss component not in the same manner as the output power, but depending also on the daily insolation curve of the area at which the system will be used.
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