Functional Design of the mCCHP-RES System - Design for Micro-Combined Cooling, Heating and Power Systems - page 291

Fig. 31 Evolution of the
energy accumulated in the
battery

10 x 10 7

Energy accumulated in the battery

9.5

9

8.5

8

7.5

0 2 4 6 8

x 10 4

Time [s]

4.3.2 Thermal Subsystem

The mathematical model is determined based on the thermal balances of the
accumulation tank and the residence. The equation of the thermal balance of the
thermal accumulator is:

m w c w dT c

dt ¼

P Stir þ P pel P tv

ð Þ

P am 54

where m w , c w are the mass, the speci c heat of the water accumulated in the tank,

respectively, T c - the temperature of the water in the tank, P Stir - the thermal power of

the Stirling engine, P pel - the power

consumed in the residence aiming to cover the losses through transmission and
ventilation, and P am -

the power delivered by the pellet boiler, P tv -

the power consumed in the domestic water circuit.
The balance between the thermal power delivered by the sources (Stirling engine
and pellet boiler) and the power consumed for the residence heating and for the
domestic hot water is achieved by the control of the water temperature in the
accumulation tank (setpoint equal to T re c ). Since the thermal power of the Stirling
engine is a random value (given by the voltage controller), the temperature control
of the thermal agent in the accumulation tank is done by the power control of the
pellet boiler.
The second thermal balance equation is:

m a c a dT a

dt ¼

k c T c ð T a Þ P tv ð 55 Þ

where m a , c a are the mass and the speci c heat of the air in the residence, respec-

tively, k c - cient through convection, and P tv is the power consumed

in the residence to compensate the losses through transmission and ventilation. The

transfer coef