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One_Stock_Systems

by Marcus D. Gabriel (Submitted: 05/11/2010)

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WHAT IS IT?

A one-stock model of a thermostat/furnance/room system. Using the System Dynamics Modeler, this model captures the essential design and behaviour of a Viessmann gas furnance being used in the Bas-Rhin of Alsace in France during winter. All temperatures are in centigrade and initial values and ranges have been choosen for a typical winter season in this region of the world.

HOW IT WORKS

Open the System Dynamics Model from the menu item

- Tools -> System Dynamics Model

and note that there are one stock, one inflow, one outflow, four variables, and eight links:

- Stocks: ROOM-TEMPERATURE;

- Inflows: HEAT-TO-ROOM;

- Outflow: HEAT-FROM-ROOM;

- Variables: THERMOSTAT-SETTING, OUTSIDE-TEMPERATURE, ROOM-LEAKAGE-FACTOR, and ROOM-FURNACE-SIZE;

- Links to HEAT-TO-ROOM from: THERMOSTAT-SETTING, ROOM-TEMPERATURE, ROOM-FURNACE-SIZE, and HEAT-FROM-ROOM; and

- Links to HEAT-FROM-ROOM from: OUTSIDE-TEMPERATURE, ROOM-TEMPERATURE, ROOM-FURNACE-SIZE, and ROOM-LEAKAGE-FACTOR.

The outflow HEAT-FROM-ROOM is proportional to the descrpency between the OUTSIDE-TEMPERATURE and the ROOM-TEMPERATURE, is proportional to the ROOM-LEAKAGE-FACTOR, and is inversely proportional to the ROOM-FURNACE-SIZE (that is, the heat capacity of the room).

The ROOM-LEAKAGE-FACTOR inversely models the insolation of the room, the R factor. The lower the ROOM-LEAKAGE-FACTOR, the smaller the loss of heat to the outside per unit time. The greater the ROOM-LEAKAGE-FACTOR, the greater the loss of heat to the outside per unit time. The ROOM-LEAKAGE-FACTOR is a percentage where 0% means no leakage and 100% means complete leakage, that is, at 100% leakage the furnance must add as much heat to the room as is leaving the room per unit time so as to maintain the current room temperature.

The ROOM-FURNACE-SIZE is a unitless quantity in this model. It is proportional to the size of the room and inversely propotional to the strength (size) of the furnace, that is, increasing the ROOM-FURNACE-SIZE means the room is larger relative to the size (strength) of the furnance and decreasing it means the room is smaller relative to the size (strength) of the furnance.

The thermostat/furnance/room system monitors the descrepency between the THERMOSTAT-SETTING and the ROOM-TEMPERATURE and also monitors the HEAT-FROM-ROOM outflow, which is dependent on the OUTSIDE-TEMPERATURE, so as to bring the ROOM-TEMPERATURE to or above the THERMOSTAT-SETTING if required.

Pay particular attention to DELTA-TEMPERATURE-TO-ROOM since this is where all the feedback logic of the thermostat/furnance/room system resides, this is where the action is.

Finally, in this model, MAXIMUM-DELTA-TEMPERATURE-TO-ROOM varies as the ROOM-FURNACE-SIZE-SLIDER varies. The larger the room, the smaller MAXIMUM-DELTA-TEMPERATURE-TO-ROOM a given furnance can supply, and the smaller the room, the larger MAXIMUM-DELTA-TEMPERATURE-TO-ROOM the given furnance can supply.

HOW TO USE IT

To start the model for the first time, click on INITIALISE, and then GO to start the model, and then once again GO to stop the model.

The Interface tab consists of the following elements:

- INTIALISE: Equivalent to SETUP and RESET-SLIDERS.

- SETUP: Clears all plots and sets the ROOM-TEMPERATURE to the INITIAL-ROOM-TEMPERATURE (5).

- GO: Starts and stops the model.

- RESET-SLIDERS: Resets all sliders to their default values:
-- Set OUTSIDE-TEMPERATURE-SLIDER to INTIIAL-OUTSIDE-TEMPERATURE (0);
-- Set THERMOSTAT-SETTING-SLIDER to INTIIAL-THERMOSTAT-SETTING (21);
-- Set ROOM-LEAKAGE-FACTOR-SLIDER to INTIIAL-ROOM-LEAKAGE-FACTOR (30%, that is, 30% is a leaky room, 10% is good, and 50% is a very leaky room).
-- Set ROOM-FURNACE-SIZE-SLIDER to INITIAL-ROOM-FURNACE-SIZE (550, i.e., 100 is a small room relative to the furnance, 1000 is a larger room relative to the furnance, and 550 is in the middle).

- INSIDE TEMPERATURE MONITOR: Display the inside ROOM-TEMPERATURE.

- TIME MONITOR: Number of ticks so far.

- OUTSIDE-TEMPERATURE-SLIDER: Adjusts the OUTSIDE-TEMPERATURE from MINIMUM-OUTSIDE-TEMPERATURE (-25) to MAXIMUM-OUTSIDE-TEMPERATURE (45).

- THERMOSTAT-SETTING-SLIDER: Adjusts the THERMOSTAT-SETTING from MINIMUM-THERMOSTAT-SETTING (5) to MAXIMUM-THERMOSTAT-SETTING (25).

- ROOM-LEAKAGE-FACTOR-SLIDER: Adjusts the ROOM-LEAKAGE-FACTOR from MINIMUM-ROOM-LEAKAGE-FACTOR (5%) to MAXIMUM-ROOM-LEAKAGE-FACTOR (95%).

- ROOM-FURNACE-SIZE-SLIDER: Adjusts the ROOM-FURNACE-SIZE from MINIMUM-ROOM-FURNACE-SIZE (100) to MAXIMUM-ROOM-FURNACE-SIZE (1000).

- INSIDE TEMPERATURE PLOT: A plot of the inside room temperature versus time.

- RATE OF HEAT CONSUMPTION PLOT: A plot of heat, that is, energy or monetary consumption versus time. It is scaled from 0 to 100. 0 means the furnance is not supplying heat to the room in order to maintain the rooms temperature, and 100 means the furmance is working at 100% of its maximum capacity.

- MAXIMUM-DELTA-TEMPERATURE-TO-ROOM MONITOR: The furnance/thermostat/room system has been sized to handle at most a given maximum temperature difference between the inside room temperature and the outside temperature, for a given efficiency of insolation of the room, and for a given size of the room relative to the size (strength) of the furnance.

- DELTA-TEMPERATURE MONITOR: The temperature change needed for the room only due to the discrepancy between theromostat setting and room temperatures.

- DELTA-TEMPERATURE-FROM-ROOM MONITOR: The temperature change of the room due to heat leaking from the room to the outside. It can be negative, positive, or zero.

- DELTA-TEMPERATURE-TO-ROOM MONITOR: The temperature of the room from the furance adding heat to the room. This takes into account the discrepancy between theromostat setting and room temperatures, DELTA-TEMPERATURE, and the heat lost to the outside, DELTA-TEMPERATURE-FROM-ROOM. If this delta is to large for the furnance, then MAXIMUM-DELTA-TEMPERATURE-TO-ROOM is used instead.

THINGS TO NOTICE

To return to a known, default starting point, one must click on INITIALISE, otherwise clicking on SETUP allows one to keep the current slider settings and observe the model once again or adjust one of the sliders to observe how this variable affects the run of the model. One can click on RESET-SLIDERS in the middle of a run of the model to return to a know point after adjusting several sliders at once.

THINGS TO TRY

Run the model serveral times and only adjust the ROOM-FURNACE-SIZE-SLIDER. Do different values of the ROOM-FURNACE-SIZE change the shape of the two plots of this model? Does it change the rate at which the room reaches dynamic equilibrium? Adjust the ROOM-FURNACE-SIZE-SLIDER while the model is running. Is the ROOM-FURNACE-SIZE variable interesting?

During a run of the model, try raising and lowering the THERMOSTAT-SETTING-SLIDER to observe the result. During another run of the model, try raising and lowering the OUTSIDE-TEMPERATURE-SLIDER to observe the result. Place the OUTSIDE-TEMPERATURE above the THERMOSTAT-SETTING.

Try a high THERMOSTAT-SETTING and a low OUTSIDE-TEMPERATURE so as to overwhelm the furnance and to force the ROOM-TEMPERATURE below the THERMOSTAT-SETTING. Now try adjusting the ROOM-LEAKAGE-FACTOR-SLIDER and observe changes in the plots.

Run the model serveral times while only adjusting the ROOM-LEAKAGE-FACTOR-SLIDER before and during the run of the model. What is the affect on the rate of heat consumption?

Does your intuition agree with the plots during runs of the model? If not, is your intuition wrong or incomplete, does the model have a defect in one of the procedures, or is the model wrong or incomplete?

EXTENDING THE MODEL

If outside conditions are dry and with little wind, many individuals will open many windows so as to air out the room. Add a switch WINDOWS-OPEN such that ON means that they are open and OFF means that they are closed. (Hint: think about the ROOM-LEAKAGE-FACTOR.)

Extend the model so that ROOM-FURNACE-SIZE is replaced by the independent concepts of
ROOM-SIZE (heat capacity of the room) and FURNANCE-SIZE (strength of the furnance). Of these two new variables, which one or ones affect the inflow and which one or ones affect the outflow? How many links would one have given this change above?

Instead of the previous suggestion for extending the model, what about extending the model to include a sunny day warming the room via its windows?

NETLOGO FEATURES

All parameters can be changed in the SET-GLOBALS procedure, nothing is hard-coded outside of this procedure.

The procedure DO-PLOTS was needed to coordinate the two plots, MINIMUM-VALUE and MAXIMUM-VALUE were added for convenience, SAFE-ROOM-FURNANCE-SIZE was added to avoid dividing by zero, and RATE-OF-CONSUMPTION is an alias.

Version 1.19 of this model was tested under Netlogo 4.1.0, Java 1.6.0_18-b07, and Ubuntu 8.04.

RELATED MODELS

Other one stock models:

File -> Models Library -> Exponential Growth

File -> Models Library -> Logistic Growth

CREDITS AND REFERENCES

Author Marcus D. Gabriel at marcus@gabriel.name.
Copyright (c) 2010. All rights reserved.

See "Thinking in Systems, A primer" by Donella H. Meadows, ISBN 978-1-84407-726-7, chapter 2.

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