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Re: [EnergyPlus_Support] energy balance equation
Hello,
This section of the engineering documentation is an excerpt from
published papers:
 Taylor, R. D., Pedersen, C. O., Fisher, D. F., Lawrie, L., and
Liesen, R. J., ?Impact of Simultaneous Simulation of Buildings and
Mechanical Systems in a Heat Balance Based energy Analysis Programs on
System Response and Control?, Proceedings of Building Simulation ?91,
International Building Performance Simulation Association, August 2022,
1991, SophiaAntipolis, Nice France.
 Taylor, R. D., Pedersen, C. O., and Lawrie, L., ?Simultaneous
Simulation of Buildings and Mechanical Systems in Heat Balanced Based
energy Analysis Programs?, Proceedings of Building Simulation ?90,
International Building Performance Simulation Association, December 35,
1990, Liege, Belgium.
These papers can take you through the derivation in even more
excruciating detail.
To answer your question Equation 1.8 is the Euler Formulation and
is not what was finally chosen to be used. The Third Order
substitution for the temperature was found to be stable, therefore
equation 1.11 is what is currently implemented as the air heat balance
equation. Then all the variables are used from the current time
step except for 3 zone air temperature from 3 previous time steps that
are weighted in according to the third order formulation.
 heating/cooling load at time step t is calculated on the basis
of set point temperature at time step t and heat transfer
(internal surfaces, air mixing with other zones, infiltration from
outside, internal convective gains etc..) at time step (tdt)
This would be at the current time step t, not
(tdt).
 if the system is able to provide such load (as by definition for a
Purchased Air system) the zone temperature at time t matches
exactly the set point scheduled for time t
Correct.
 if the system is not able to provide all the required load (as for a
real system), zone temperature is updated on the basis of the difference
between the cooling/heating load calculated at time step (tdt)
and the system power at time t
If there is not enough capacity then Tz at t is updated with the
current conditions for infiltration, loads, etc. and the current system
capacity. The history is preserved in the old zone air temps and
the capacitance from the zone surfaces.
My interest is in the meaning of
"Zone/Sys Sensible Cooling (Heating) Rate" output at time
t for a Purchased Air system.
Is it the cooling (heating) load calculated at time t or (tdt) or what
is the time shift?
That would be at time t.
Thanks Richard Liesen
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