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Industrial and agricultural loads are implemented using a parametric load model, calculating the real and imaginary current, power, and resistance load components based on the time and existing weather data.

Parametric Loads

Parametric loads can be defined using the pqload object, which is derived from powerflow::load. A pqload object has varying contributions to constant impedance, current, and power depending on prevailing time and weather conditions, such as sunlight, temperature, humidity, wind speed, and rainfall. Each load component (Z, I, P) is nominally computed based on the prevailing weather and adjusted based on the time.

The weather load is computed from a linear transformation as a function of weather as follows:

[math] \begin{bmatrix} Z_p \\ Z_q \\ I_m \\ I_a \\ P_p \\ P_q \end{bmatrix} = \begin{bmatrix} Zp_T & Zp_H & Zp_S & Zp_W & Zp_R & Zp \\ Zq_T & Zq_H & Zq_S & Zq_W & Zq_R & Zq \\ Im_T & Im_H & Im_S & Im_W & Im_R & Im \\ Ia_T & Ia_H & Ia_S & Ia_W & Ia_R & Ia \\ Pp_T & Pp_H & Pp_S & Pp_W & Pp_R & Pp \\ Pq_T & Pq_H & Pq_S & Pq_W & Pq_R & Pq \end{bmatrix} \ \begin{bmatrix} T_t \\ H_t \\ S_t \\ W_t \\ R_t \\ 1 \end{bmatrix} [/math]


  • [math]Z[/math], [math]I[/math], [math]P[/math] are the constant impedance, current and power components of the load, with [math]_p[/math] and [math]_q[/math] indicated the real and reactive parts and [math]m[/math] and [math]a[/math] are the magnitude and angle, respectively;
  • [math]T[/math] is the outdoor temperature at the time [math]t[/math] in °F;
  • [math]R[/math] is the relative humidity at the time [math]t[/math] in %;
  • [math]S[/math] is the solar gains at the time [math]t[/math] in Btu/h;
  • [math]W[/math] is the wind speed at the time [math]t[/math] in mph;
  • [math]R[/math] is the rainfall at the time [math]t[/math] in inch/h;


The pqload object publishes the following variables, in addition to those published by powerflow::load.

Table 1 - pqload properties
Property Type Unit Default Description
schedule char1024 - * * * * *:1.0; The load schedule (default is always 1.0)
weather object - NULL The climate object to use for this load. If NULL, the temperature coefficients will be ignored.
Zp_T double ohm/degF 0 Resistance response to temperature
Zp_H double ohm/% 0 Resistance response to humidity
Zp_S double ohm.h/Btu 0 Resistance response to solar gains
Zp_W double ohm/mph 0 Resistance response to wind
Zp_R double ohm.h/in 0 Resistance response to rainfall
Zp double ohm Invariant resistance
Zq_T double F/degF 0 Capacitance response to temperature
Zq_H double F/% 0 Capacitance response to humidity
Zq_S double F.h/Btu 0 Capacitance response to solar gains
Zq_W double F/mph 0 Capacitance response to wind
Zq_R double F.h/in 0 Capacitance response to rainfall
Zq double F 0 Invariant capacitance
Im_T double A/degF 0 Current magnitude response to temperature
Im_H double A/% 0 Current magnitude response to humidity
Im_S double A.h/Btu 0 Current magnitude response to solar gains
Im_W double A/mph 0 Current magnitude response to wind
Im_R double A.h/in 0 Current magnitude response to rainfall
Im double A 0 Invariant current magnitude
Ia_T double deg/degF 0 Current angle response to temperature
Ia_H double deg/% 0 Current angle response to humidity
Ia_S double deg.h/Btu 0 Current angle response to solar gains
Ia_W double deg/mph 0 Current angle response to wind
Ia_R double deg.h/in 0 Current angle response to rainfall
Ia double deg 0 Invariant current angle
Pp_T double W/degF 0 Real power response to temperature
Pp_H double W/% 0 Real power response to humidity
Pp_S double W.h/Btu 0 Real power response to solar gains
Pp_W double W/mph 0 Real power response to wind
Pp_R double W.h/in 0 Real power response to rainfall
Pp double W 0 Invariant real power
Pq_T double VAr/degF 0 Reactive power response to temperature
Pq_H double VAr/% 0 Reactive power response to humidity
Pq_S double VAr.h/Btu 0 Reactive power response to solar gains
Pq_W double VAr/mph 0 Reactive power response to wind
Pq_R double VAr.h/in 0 Reactive power response to rainfall
Pq double VAr 0 Invariant Reactive power
input_temp double degF -- Observed temperature. Read only.
input_humid double % -- Observed humidity. Read only.
input_solar double Btu/h -- Observed solar gains. Read only.
input_wind double mph -- Observed wind speed. Read only.
input_rain double in/h -- Observed rainfall. Read only.
output_admit_p double Ohm -- Observed resistance. Read only.
output_admit_q double Ohm -- Observed capacitance. Read only.
output_current_m double A -- Observed current magnitude. Read only.
output_current_a double degrees -- Observed current angle. Read only.
output_power_p double W -- Observed real power. Read only.
output_power_q double VAr -- Observed reactive power. Read only.
output_admittence complex Ohm -- Observed impedance. Read only.
output_current complex A -- Observed complex current. Read only.
output_power complex W -- Observed complex power. Read only.

The schedule is defined based the POSIX standard for crontab. The general syntax is

moh hod dom moy dow[ lpu][; ...]


  • moh is the minute of hour;
  • hod is the hour of day;
  • dom is the day of month;
  • moy is the month of year;
  • dow is the day of week;
  • lpu is the load per unit (optional, 1.0 if omitted);

The block may be repeated as many times as needed to complete the schedule. Any unscheduled time interval is assumed to be 0.