.It has been observed that the reactive power characteristic of fluorescent lights not only varies
from manufacturer to manufacturer, from old to new, from long tube to short tube, but also
varies from capacitive to inductive depending upon applied voltage and frequency. This variation
makes it difficult to obtain a good representation of the reactive power of a composite system and
also makes it difficult to estimate theDQ=DV characteristic of a composite system.
.The relationship between reactive power and voltage is more non-linear than the relationship
between real power and voltage, making Q more difficult to estimate than P.
.For some of the equipment or appliances, the amount of Q required at the nominal operating
voltage is very small; but when the voltage changes, the change in Q with respect to the base Q can
be very large.
.Many distribution systems have switchable capacitor banks either at the substations or along
feeders. The composite Q characteristic of a distribution feeder is affected by the switching
strategy used in these banks.20.5 Static Load Characteristics
The component models appearing inTables 20.1and 20.2 can be combined and synthesized to create
other more convenient models. These convenient models fall into two basic forms: exponential and
polynomial.
20.5.1 Exponential Models
The exponential form for both real and reactive power is expressed in Eqs. (20.1) and (20.2) below as a
function of voltage and frequency, relative to initial conditions or base values. Note that neither
temperature nor torque appear in these forms. Assumptions must be made about temperature and=or
torque values when synthesizing from component models to these exponential model forms.
P¼Po
V
Voav
f
foaf
(20:1)Q¼Qo
V
Vobv
f
fobf
(20:2)TABLE 20.2 Static Models of Typical Load Components—Transformers and Induction Motors
Load Component Static Component Model
Transformer
Core Loss Model P¼
KVA(rating)
KVA(systembase)^0 :00267V
(^2) þ 0 : 73 10 (^9) e 13 :5V 2
Q¼ KVA(rating)
KVA(systembase)
0 :00167V^2 þ 0 : 268 10 ^13 e^22 :76V^2
where V is voltage magnitude in per unit
1-fMotor P¼1.0þ0.5179DVþ0.9122Dtþ3.721DV^2 þ0.350Dt^2 1.326DVDt
Constant Torque Q¼0.9853þ2.7796DVþ0.0859Dtþ7.368DV^2 þ0.218Dt^2 1.799DVDt
3-fMotor (1–10HP) P¼1.0þ0.2250DVþ0.9281Dtþ0.970DV^2 þ0. 086Dt^2 0.329DVDt
Const. Torque Q¼0.7810þ2.3532DVþ0.1023Dt5.951DV^2 þ0.446Dt^2 1.48DVDt
3-fMotor (10HP=Above) P¼1.0þ0.0199DVþ1.0463Dtþ0.341DV^2 þ0.116Dt^2 0.457DVDt
Const. Torque Q¼0.6577þ1.2078DVþ0.3391Dtþ4.097DV^2 þ0.289Dt^2 1.477DVDt
1-fMotor P¼1.0þ0.7101DVþ0.9073Dtþ2.13DV^2 þ0.245Dt^2 0.310DVDt
Variable Torque Q¼0.9727þ2.7621DVþ0.077Dtþ6.432DV^2 þ0.174Dt^2 1.412DVDt
3-fMotor (1–10HP) P¼1.0þ0.3122DVþ0.9286Dtþ0.489DV^2 þ0.081Dt^2 0.079DVDt
Variable Torque Q¼0.7785þ2.3648DVþ0.1025Dtþ5.706DV^2 þ0.13Dt^2 1.00DVDt
3-fMotor (10HP & Above) P¼1.0þ0.1628DVþ1.0514Dtff0.099DV^2 þ0.107Dt^2 þ0.061DVDt
Variable Torque Q¼0.6569þ1.2467DVþ0.3354Dtþ3.685DV^2 þ0.258Dt^2 1.235DV*Dt