where aoþa 1 þa 2 ¼ 1
boþb 1 þb 2 ¼ 1
Dpreal power frequency damping coefficient, per unit
Dqreactive power frequency damping coefficient, per unit
Dffrequency deviation from scheduled value, per unit
The per-unit form of Eqs. (20.6) and (20.7) is the following.
Pu¼
P
Po¼ aoþa 1
V
Vo
þa 2
V
Vo"# 2
[1þDpDf] (20:8)Qu¼
Q
Po¼
Qo
Poboþb 1
V
Vo
þb 2
V
Vo"# 2
[1þDqDf] (20:9)20.5.3 Combined Exponential and Polynomial Models
The two previous kinds of models may be combined to form a synthesized static model that offers
greater flexibility in representing various load characteristics (EPRI, 1987; Price et al., 1988). The
mathematical expressions for these per-unit models are the following.
Pu¼PpolyþPexp1þPexp2
Po(20:10)Qu¼QpolyþQexp1þQexp2
Po
(20:11)TABLE 20.3 Parameters for Voltage and Frequency Dependencies of Static Loads
Component=Parameters pf av af bv bf Nm pfnm avnm afnm bvnm bfnm
Resistance Space Heater 1.0 2.0 0.0 0.0 0.0 0.0 — ————
Heat Pump Space Heater 0.84 0.2 0.9 2.5 1.3 0.9 1.0 2.0 0.0 0.0 0.0
Heat Pump=Central A=C 0.81 0.2 0.9 2.5 2.71.0— ————
Room Air Conditioner 0.75 0.5 0.6 2.5 2.81.0— ————
Water Heater & Range 1.0 2.0 0.0 0.0 0.0 0.0 — ————
Refrigerator & Freezer 0.84 0.8 0.5 2.5 1.4 0.8 1.0 2.0 0.0 0.0 0.0
Dish Washer 0.99 1.8 0.0 3.5 1.4 0.8 1.0 2.0 0.0 0.0 0.0
Clothes Washer 0.65 0.08 2.9 1.6 1.8 1.0 — ————
Incandescent Lighting 1.0 1.54 0.0 0.0 0.0 0.0 — ————
Clothes Dryer 0.99 2.0 0.0 3.3 2.6 0.2 1.0 2.0 0.0 0.0 0.0
Colored Television 0.77 2.0 0.0 5.2 4.60.0— ————
Furnace Fan 0.73 0.08 2.9 1.6 1.8 1.0 — ————
Commercial Heat Pump 0.84 0.1 1.0 2.5 1.3 0.9 1.0 2.0 0.0 0.0 0.0
Heat Pump Comm. A=C 0.81 0.1 1.0 2.5 1.31.0— ————
Commercial Central A=C 0.75 0.1 1.0 2.5 1.31.0— ————
Commercial Room A=C 0.75 0.5 0.6 2.5 2.81.0— ————
Fluorescent Lighting 0.90 0.08 1.0 3.0 2.80.0— ————
Pump, Fan, (Motors) 0.87 0.08 2.9 1.6 1.8 1.0 — ————
Electrolysis 0.90 1.8 0.32.2 0.60.0— ————
Arc Furnace 0.72 2.3 1.0 1.61 1.00.0— ————
Small Industrial Motors 0.83 0.1 2.9 0.6 1.81.0— ————
Industrial Motors Large 0.89 0.05 1.9 0.5 1.2 1.0 — ————
Agricultural H 2 O Pumps 0.85 1.4 5.6 1.4 4.2 1.0 — ————
Power Plant Auxiliaries 0.80 0.08 2.9 1.6 1.8 1.0 — ————