Formulas

Question 1

The heat pump (HP) power requirement W,el:

Answer 1

W,el = Q,HP / COP

Q,HP = HP condenser capacity (Upper Q)

Question 2

Formula for total annual cost for power plant (energy production):

Answer 2

r(SEK/MW)MW+
+(SEK/MWh)*MWh = SEK

MWh = MWh
(installd capacityrunning time)

Question 3

Formula for calculating how much of maximum energy recovery is done:

Answer 3

Alt 1:
Q,max = sumHR + sumHX - Q,h,min

Alt 2:
Q,max = sumCL + sumHX - Q,c,min

sumHX/Q,max = % of heat recovery

Question 4

Pinch rule violations formulas:

Answer 4

Heaters and coolers (HR, CL):
(Heating below or cooling above pinch:)
Only the part of teh heating/cooling that is a violation:

Ex: hot (bellow pinch)
(T,pinch-T,start) F*Cp = violation kW

HX:
If one side is all above pinch and the other all bellow
= all heat transfer is violation kW

Part of the transfer is on the same side of teh pinch, only the transfer that crosses teh pinch is a violation
= % of teh heat transfer kW
Ex: hot side decides violation:
(T,start - T,pinch) F*Cp = violation kW

Question 5

F*CP constraint above pinch:

Answer 5

FCp,h < FCp,c

Question 6

F*CP constraint below pinch:

Answer 6

FCp,h > FCp,c

Question 7

Electrical efficiency

Total efficiency

Answer 7

El.eff = El out / Fuel in

Tot.eff = (El + useful heat out) / Fuel in

Question 8

COP and COP,carnot

Answer 8

COP = Q,c/W = Q,c/(Q,c - Q,e)
Q,c: condeser
Q,e: evaporator

COP,carnot = T1 / (T1-T2)

COP = eff,c * COP,carnot