EDITING IN PROGRESS

The purpose of the range model in GridLAB-D is to facilitate the real representation of the oven and cooktop energy consumptions profile.

## General Description

Electric range has oven and an electronic control for the cooktop. It converts electrical energy into heat to cook and bake.

### Oven

The food in the oven is heated by an electrical element and is controlled by a thermostat. Oven element capacity (wattage) ranges from about 500[[Units|W] to 2500W, with 1000W being common. It heats to the temperature that the user sets it to. Thermostatic controls have a deadband associated with the setpoint to prevent rapid cycling of power to the elements, which would result if the turn-on temperature equaled the turn-off temperature. The deadband is typically a few degrees above and below the nominal setpoint.

The oven GridLAB-D model is similar to that of GridLAB-D waterheater one-node model.

### Cooktop

The cooktop has burners on the top and is usually installed into a countertop. These are essentially perfectly resistive loads. Each burner on a cooktop can be controlled by the user-controlled knob settings.

# Modeling Assumptions

• The temperature inside the oven is considered to be uniform throughout.
• Three cooktop settings are considered for the cooktop model.
• The cooktop is a timer-based model. This implies that the operating time of the cooktop depends on time settings rather than on system voltage.

# Equations

## Oven Equations

Table 1: Equation Notation
Variable Definition
$T_{on}$ Lower setpoint temperature of oven (degF)
$T_{off}$ Upper setpoint temperature of oven (degF)
$\dot{m}$ mass flow (lb/hr)
$T_{amb}$ Ambient temperature (degF)
$GALPCF$ Gallons to cubic foot conversion factor
$BTUPHPKW$ Btu/hr to kw conversion factor
$\Delta_{t}$ The time required to change the oven's temperature from an intial temperature ($T_0$) to a new temperature ($T_1$)
$C_w$ Thermal capacitance
ovenUA Thermal Conductance
$P_l$ Load power
$I_l$ Load current
$Z_l$ Load admittance
$V_l$ Load voltage factor
$C_{heat}$ Heating element capacity
$p_l$ Load power fraction
$i_l$ Load current fraction
$z_l$ Load impedance fraction
$P_{total}$ Total power
$E_{total}$ Energy used
$T_{set}$ Oven setpoint
$db$ Thermostat deadband
ovenDemand oven demand in gal/min
$\rho$ density of food in pounds per cubic feet (lb/cf)
$C_p$
$c_{food}$ Specific heat of the food

### Total Power Calculation

\begin{align}P_l &= C_{heat} \cdot p_l\\ I_l &= C_{heat} \cdot i_l\\ Z_l &= C_{heat} \cdot z_l\end{align}

$P_{total} = (P_l + (I_l + Z_lV_l) \cdot V_l) \cdot 1000$
$E_{total} = \frac{P_{total}}{1000} \cdot \frac{\Delta t}{3600}$

### Thermostat Setpoint Temperatures

\begin{align}T_{on}&=T_{set}-\frac{db}{2}\\ T_{off}&=T_{set}-\frac{db}{2}\end{align}

### New Time Calculation

Estimate mass flow:

$\dot{m}= \text{ovenDemand} \cdot 60 \cdot \frac{\rho}{GALPCF}$

Calculate new time

\begin{align}\Delta t &= \frac{\text{log}(c_1+c_2T_1)-\text{log}(c_1+c_2T_0)}{c_2}\\ c_{11}&=\frac{\text{ovenUA} + \dot{m}_{C_p}}{C_w}\\ c_{22}&=\frac{(P_{total}\cdot BTUPHPKW) + (\dot{m}\cdot c_{food})+(\text{ovenUA} \cdot T_{amb})}{\text{ovenUA}+(\dot{m} \cdot c_{food})}\\ T_{new}&=c_{22}-(c_{22}-T_0) \cdot exp(-c_{11} \cdot \Delta t)\end{align}

where

\begin{align}c_1 &= \frac{(P_{total} \cdot BTUPHPKW + ovenUA \cdot T_{amb} + \dot{m} \cdot C_p \cdot T_{inlet})}{C_w}\\ c_2&=\frac{-(ovenUA+\dot{m}\cdot c_{food})}{C_w}\\ C_w &= \frac{v_{oven}}{GALPCF} \cdot \rho \cdot c_{food}\end{align}

# Solver

## Interfacing Overview

### Published Inputs

The user may input values for the following variables related to the oven model.

Table 2: Oven inputs
Variable Type Units Default Definition
oven_volume double gal 5 Volume of oven
heating_element_capacity double kw 1 Power rating of heating element
oven_setpoint double degF 100 Setpoint temperature of oven
temperature double degF 70 Initial temperature
thermostat_deadband double degF 8 Deadband around oven_setpoint temperature (half above, half below)
location bool n/a INSIDE location of oven
oven_UA double BTU/hr.F 2.9 Thermal conductance of the oven
food_density double lb/cf 5 Density of the food
specificheat_food double Btu/lb.degF 1 Specific heat of the food
time_oven_setting double s 3600 Cycle time of oven
load_impedence_fraction double n/a 1 Constant impedance component fraction
load_current_fraction double n/a 0 Constant current component fraction
load_power_fraction double n/a 0 Constant power component fraction
queue_oven double n/a 0.85 Oven is placed in its 'queue' and awaiting to be turned on
demand_oven double n/a RANGE * 20 The probability that a given oven is turned on depends on demand_oven, and the value of the normalized oven load shape at any given time. The higher these quantities are, the higher the probability of the given appliance turning on (GE CRADA report)
Table 3: Cooktop inputs
Variable Type Units Default Definition
cooktop_energy_baseline double kwh 0.5 The amount of energy needed for a cooktop event
cooktop_coil_setting_1 double W 2 Power rating of the cooktop's high level setting
cooktop_coil_setting_2 double W 1 Power rating of the cooktop's low leven setting
cooktop_coil_setting_3 double W 1.7 Power rating of the cooktop's medium level setting
cooktop_interval_setting_1 double s 240 Cook time of setting 1
cooktop_interval_setting_2 double s 900 Cook time of setting 2
cooktop_interval_setting_3 double s 120 The amount of energy needed for a cooktop event
time_cooktop_setting double s 2000 Cycle time of cooktop
demand_cooktop double n/a RANGE* 35 The probability that a given cooktop is turned on depends on demand_cooktop and the value of the normalized appliance load shape at any given time. The higher these quantities are, the highter the probability of the given appliance turning on (GE CRADA report)
queue_cooktop double n/a 0.99 Cooktop is placed in its 'queue' and awaiting its turn to be ON
queue_min double n/a 0 Minimum 'queue' value considered
queue_max double n/a 2 Maximum 'queue' value considered

### Published Outputs

Table 4: Range Outputs
Variable Type Units Definition
total_power_oven double kw Total power required during the oven cycle
total_power_cooktop double kw Total power required during the cooktop cycle
cooktop_energy_used double kwh Total energy consumed for cooktop cycle
time_cooktop_operation double s Duration of cooktop in each setting
Toff double degF Upper setpoint temperature
Ton double degF Lower setpoint temperature
time_oven_operation double s Incremental change of oven operation time when it is ON
time_oven_setting double s Total ON time for electric oven

### Data Structure

To facilitate data operations between the individual objects and the dynamic solver capability, a common data structure will be used to pass information back and forth. This data structure should contain information and pointers to the following elements.

Table 5: Range interface elements
Variable Definition
timestamp Pointer to current timestamp of the solution
timestamp_change Pointer to the difference between the last and current timestamp
energy Pointer to accumulated energy consumption of the system
voltage Pointer to complex voltage values of the object
current Pointer to complex current values of the object
power Pointer to complex power contributions of the object
impedance Pointer to complex impedance contributions of the object

## Solver Timing

The range model will need to be properly timed with the powerflow solution, as well as the requirements of the individual range components.

### Solver Passes

The oven model follows these steps:

1. Solve the time required to change the oven's temperature if the oven's inside temperature is lower than the lower setpoint temperature.
2. Solve the oven interface components based on its settings.
3. Update the energy calculation.

After these steps are complete, the simulation advances to the next timestamp. This sequence will repeat until the next GridLAB-D overall timestamp is encountered. At that point, the changes will be reflected into the quasi-steady state powerflow solution, and the process will repeat until the given energy consumption is elapsed.

The cooktop model follows these steps:

1. Solve the cooktop interface conponents based on its settings.
2. Update energy calculation.

### Solution Timesteps

TODO: Add description like in Spec:Microgrids.

### Solver Call Timing

TODO: Add description like in Spec:Microgrids.

# Testing And Validation

TODO: Include finalized testing and validation.

# References

1. IEEE power & energy magazine; May/June 2010