Building Energy Model (MATLAB)

It is a small software which is developed by MATLAB for modeling the energy system of a building or a HVAC system.

Method of Solution

In this code, the temperatures are considered variables of the problem, which are solved implicitly by solving a system of linear equations based on energy equations of each element.

Elements Classes

Boiler

The boiler contains an inlet fluid pipe, an outlet fluid pipe, a fluid tank which is heated up, and the rest. The class of boiler receives input values including the id of the inlet, the id of outlet, the solver, the specific heat capacity of the rest, the mass of the rest, specific heat capacity of the fluid, mass of the fluid, the boiler power, the mass flow rate, and the status. The inlet and outlet should be outlet and inlet of pipes which are connected to the boiler respectively. The solver is the class of the solver that is used. Next, there are specific heat capacity and mass of the boiler except containing fluid. Then, there are those of the fluid. The next argument is the power of the boiler. The mass flow rate also should be given as an input value. The status works as a switch in the boiler which can be controlled by the smart controller in the next stages of the project.

Equations

Variables

Symbol	Description	Unit
m	Mass	kg
C	Specific Heat Capacity	J/(K.kg)
T	Temperature	K
E.	Energy Rate	W

Subscript	Description
b	Boiler
f	fluid
b,f	Fluid inside Boiler
b,i	Boiler Inlet
b,o	Boiler Outlet

Code

Construction

boiler = Boiler(id_inlet, id_outlet, solver, specific_heat_capacity, mass, specific_heat_capacity_fluid, mass_fluid, power, mass_flow_rate, status);

Input	Description	Type	Unit
id_inlet	Boiler Inlet ID	integer	-
id_outlet	Boiler Outlet ID	integer	-
solver	Class of the Solver	solver	-
specific_heat_capacity	Specific Heat Capacity of the Boiler (without fluid)	double	J/(K.kg)
mass	Mass of the Boiler (without fluid)	double	kg
specific_heat_capacity_fluid	Specific Heat Capacity of the Fluid	double	J/(K.kg)
mass_fluid	Mass of Fluid inside the Boiler	double	kg
power	Power of the Boiler	double	W
mass_flow_rate	Mass Flow Rate of the Boiler	double	kg/s
status	Status of the Boiler (ON/OFF)	boolean	-

Create Matrix

create(solver)

Input	Description	Type	Unit
solver	Class of the Solver	solver	-

---

Pipe

Another element in the model is the pipe. The input values of the pipe class are the id of inlet, the id of outlet, the id of zone, the solver, specific heat capacity of the pipe wall, density of the pipe wall, specific heat capacity of the fluid, density of the fluid, mass flow rate of the fluid, inner heat transfer coefficient, outer heat transfer coefficient, thermal conductivity of the tube wall, inner radius of the pipe, outer radius of the pipe, and length of the pipe. The inlet and outlet of the pipe are the elements which are connected to the pipe. The zone which is in contact with the outer side of the pipe is also the argument of the class.

Equations

Variables

Symbol	Description	Unit
h	Heat Transfer Coefficient	W/(m2K)
r	Radius	m
D	Diameter	m
k	Thermal Conductivity	W.m-1.K-1
L	Length	m
U	equivalent heat transfer coefficient	W/(m2K)
Nu	Nusselt Number	-
Re	Reynolds Number	-
Pr	Prandtl Number	-
Ra	Rayleigh Number	-
g	Gravitational Acceleration	m/s2
&‌beta;	Coefficient of Volume Expansion	1/K
&‌nu;	Kinematic Viscosity	m2/s
&‌mu;	Dynamic Viscosity	kg·m−1·s−1

Subscript	Description
t	Pipe
t,f	Fluid inside Pipe
t,i	Pipe Inlet
t,o	Pipe Outlet
t,in	Pipe Inner Side
t,out	Pipe Outer Side

Code

Construction

pipe = Pipe(id_inlet, id_outlet, id_zone, solver, specific_heat_capacity, density, specific_heat_capacity_fluid, density_fluid, mass_flow_rate,thermal_conductivity,thermal_conductivity_fluid,radius_inner,radius_outer,length,dynamic_viscosity_fluid,dynamic_viscosity_air,density_air,specific_heat_capacity_air,thermal_conductivity_air);

Input	Description	Type	Unit
id_inlet	Pipe Inlet ID	integer	-
id_outlet	Pipe Outlet ID	integer	-
id_zone	Zone ID	integer	-
solver	Class of the Solver	solver	-
specific_heat_capacity	Specific Heat Capacity of the Pipe (without fluid)	double	J/(K.kg)
density	Density of the Pipe (without fluid)	double	kg/m3
specific_heat_capacity_fluid	Specific Heat Capacity of the Fluid	double	J/(K.kg)
density_fluid	Density of Fluid inside the Pipe	double	kg/m3
mass_flow_rate	Mass Flow Rate of the Pipe	double	kg/s
thermal_conductivity	Thermal Conductivity of the Pipe	double	W.m-1.K-1
thermal_conductivity_fluid	Thermal Conductivity of the Fluid	double	W.m-1.K-1
radius_inner	Inner Radius of the Pipe	double	m
radius_outer	Outer Radius of the Pipe	double	m
length	Length of the Pipe	double	m
dynamic_viscosity_fluid	Dynamic Viscosity of the Fluid	double	N·s/m2
dynamic_viscosity_air	Dynamic Viscosity of the Air	double	N·s/m2
density_air	Density of the Air	double	kg/m3
specific_heat_capacity_air	Specific Heat Capacity of the Air	double	J/(K.kg)
thermal_conductivity_air	Thermal Conductivity of the Air	double	W.m-1.K-1

Create Matrix

create(solver)

Input	Description	Type	Unit
solver	Class of the Solver	solver	-

---

Radiator

The input values of the radiator class are the id of inlet, the id of outlet, the id of zone, the solver, specific heat capacity of the radiator except containing fluid, mass of the radiator except containing fluid, specific heat capacity of the fluid, mass of fluid, mass flow rate of the fluid, heat transfer coefficient of the radiator to the zone, the surface of the radiator which is in contact to the air of the zone.

Equations

Variables

Subscript	Description
r	Radiator
r,f	Fluid inside Radiator
r,i	Radiator Inlet
r,o	Radiator Outlet
z	Zone

Code

Construction

radiator = Radiator(id_inlet, id_outlet, id_zone, solver, specific_heat_capacity, mass, specific_heat_capacity_fluid, mass_fluid, mass_flow_rate,heat_transfer_coefficient,surface);

Input	Description	Type	Unit
id_inlet	Radiator Inlet ID	integer	-
id_outlet	Radiator Outlet ID	integer	-
id_zone	Zone ID	integer	-
solver	Class of the Solver	solver	-
specific_heat_capacity	Specific Heat Capacity of the Radiator (without fluid)	double	J/(K.kg)
mass	Mass of the Radiator (without fluid)	double	kg
specific_heat_capacity_fluid	Specific Heat Capacity of the Fluid	double	J/(K.kg)
mass_fluid	Mass of Fluid inside the Radiator	double	kg
mass_flow_rate	Mass Flow Rate of the Radiator	double	kg/s
heat_transfer_coefficient	Heat Transfer Coefficient of the Radiator	double	W/(m2K)
surface	Surface of the Radiator	double	m2

Create Matrix

create(solver)

Input	Description	Type	Unit
solver	Class of the Solver	solver	-

---

Mixer

The mixer is an element that works as a mixer or manifold. It can mix multiple flowing fluids to multiple outlets. For the input arguments of the related class, there are the ids of inlets, the ids outlets, the solver, specific heat capacities of the inlets, mass flow rates of the inlets, and the fractions of outlets.

Equations

Variables

Subscript	Description

Code

Construction

mixer = Mixer(id_inlets, id_outlets, solver, specific_heat_capacity_inlets, mass_flow_rate_inlets, fracrion_outlets);

Input	Description	Type	Unit
id_inlets	Array of Mixer Inlet ID	array(integer)	-
id_outlets	Array of Mixer Outlet ID	array(integer)	-
solver	Class of the Solver	solver	-
specific_heat_capacity_inlets	Specific Heat Capacity of the Mixer Inlets	array(double)	J/(K.kg)
mass_flow_rate_inlets	Mass Flow Rate of the Mixer Inlets	array(double)	kg/s
fracrion_outlets	Heat Transfer Coefficient of the Radiator	array(double)	W/(m2K)

Create Matrix

create(solver)

Input	Description	Type	Unit
solver	Class of the Solver	solver	-

---

Zone

The zone class contains arguments including the id of the zone, the ids of neighbor zones as an array, the ids of radiators inlets as an array, the ids radiators outlets as an array, the solver, thickness of walls as an array, surface of the walls as an array, thickness of the windows as an array, surface of the windows as an array, surface of radiators as an array, heat transfer coefficient radiators as an array, density of the air, volume of the air, specific heat capacity of the air, density of the wall, volume of the wall, specific heat capacity of the wall, mass of the equipment, specific heat capacity of the equipment, thermal conductivity of the wall, thermal conductivity of the window.

Equations

Variables

Subscript	Description

Code

Construction

zone = Zone(id_zone, id_zones, id_radiator_inlets, id_radiator_outlets, solver, thickness_walls, surface_walls, thickness_windows, surface_windows, surface_radiators, heat_transfer_coefficient_radiators, density_air, volume_air, specific_heat_capacity_air, density_wall, volume_wall, specific_heat_capacity_wall, mass_equipment, specific_heat_capacity_equipment, thermal_conductivity_wall, thermal_conductivity_window);

Input	Description	Type	Unit
id_zone	Zone ID	integer	-
id_zones	Array of Neigthbors' Zones IDs	array(integer)	-
id_radiator_inlets	Array of Radiators Inlets IDs	array(integer)	-
id_radiator_outlets	Array of Radiators Outlets IDs	array(integer)	-
solver	Class of the Solver	solver	-
thickness_walls	Array of Walls Thicknesses	array(double)	m
surface_walls	Array of Walls Surfaces	array(double)	m2
thickness_windows	Array of Windows Thicknesses	array(double)	m
surface_windows	Array of Windows Surfaces	array(double)	m2
surface_radiators	Array of Radiators Surfaces	array(double)	m2
heat_transfer_coefficient_radiators	Array of Heat Transfer Coefficient of Radiators	array(double)	W/(m2K)
density_air	Air Density	double	kg/m3
volume_air	Volume of the Air	double	m3
specific_heat_capacity_air	Air Specific Heat Capacity	double	J/(K.kg)
density_wall	Wall Density	double	kg/m3
volume_wall	Volume of the Wall	double	m3
specific_heat_capacity_wall	Wall Heat Transfer Coefficient	double	J/(K.kg)
mass_equipment	Mass of Equipment	double	kg
specific_heat_capacity_equipment	Equipment Specific Heat Capacity	double	J/(K.kg)
thermal_conductivity_wall	Wall Thermal Conductivity	double	W.m-1.K-1
thermal_conductivity_window	Window Thermal Conductivity	double	W.m-1.K-1

Create Matrix

create(solver)

Input	Description	Type	Unit
solver	Class of the Solver	solver	-

---

Same

Code

Construction

same = Same(id_1, id_2, solver);

Input	Description	Type	Unit
id_1	First Element ID	integer	-
id_2	Second Element ID	integer	-
solver	Class of the Solver	solver	-

Create Matrix

create(solver)

Input	Description	Type	Unit
solver	Class of the Solver	solver	-

---

HeatExchanger

The class of heat exchanger contains the id of supply inlet, the id of supply outlet, the id of demand inlet, the id of demand outlet, the solver, specific heat capacity of the supply, specific heat capacity of the demand, mass flow rate of the supply, mass flow rate of the demand, heat transfer coefficient of the heat exchanger, and contact surface of the heat exchanger as inputs.

Equations

Variables

Variable	Description
Rc	Capacity Ratio
NTU	Number of Transfer Units
?	Effectiveness

Subscript	Description
s	Supply
d	Demand
i	Inlet
o	Outlet
min	Minimum
max	Maximum

Code

Construction

heatExchanger = HeatExchanger(id_supply_inlet, id_supply_outlet, id_demand_inlet, id_demand_outlet, solver, specific_heat_capacity_supply, specific_heat_capacity_demand, mass_flow_rate_supply, mass_flow_rate_demand, heat_transfer_coefficient, surface);

Input	Description	Type	Unit
id_supply_inlet	Supply Inlet Element ID	integer	-
id_supply_outlet	Supply Outlet Element ID	integer	-
id_demand_inlet	Demand Inlet Element ID	integer	-
id_demand_outlet	Demand Outlet Element ID	integer	-
solver	Class of the Solver	solver	-
specific_heat_capacity_supply	Specific Heat Capacity of the Supply	double	J/(K.kg)
specific_heat_capacity_demand	Specific Heat Capacity of the Demand	double	J/(K.kg)
mass_flow_rate_supply	Mass Flow Rate of the Supply	double	kg/s
mass_flow_rate_demand	Mass Flow Rate of the Demand	double	kg/s
heat_transfer_coefficient	Heat Transfer Coefficient of the Heat Exchanger	double	W/(m2K)
surface	Surface of the Heat Exchanger	double	m2

Create Matrix

create(solver)

Input	Description	Type	Unit
solver	Class of the Solver	solver	-

---

Chiller

The chiller class needs the following arguments as input: the id of condenser inlet, the id of condenser outlet, the id evaporator inlet, the id of evaporator outlet, the solver, specific heat capacity of the fluid, the cooling power, the coefficient of performance, mass flow rate of the condenser, mass flow rate of the evaporator, and the status of chiller.

Equations

Variables

Variable	Description
Q.	Heat Transfer Rate
P	Electrical Power (input)
COP	Coefficient of Performance
C	Water Specific Heat Capacity

Subscript	Description
e	Evaporator
c	Condenser
i	Inlet
o	Outlet

Code

Construction

chiller = Chiller(id_condenser_inlet, id_condenser_outlet, id_evaporator_inlet, id_evaporator_outlet, solver, specific_heat_capacity_fluid, power, coefficient_of_performance, mass_flow_rate_condenser, mass_flow_rate_evaporator, status);

Input	Description	Type	Unit
id_condenser_inlet	Condenser Inlet Element ID	integer	-
id_condenser_outlet	Condenser Outlet Element ID	integer	-
id_evaporator_inlet	Evaporator Inlet Element ID	integer	-
id_evaporator_outlet	Evaporator Outlet Element ID	integer	-
solver	Class of the Solver	solver	-
specific_heat_capacity_fluid	Specific Heat Capacity of Water	double	J/(K.kg)
power	Electrical Power	double	W
coefficient_of_performance	Coefficient of Performance	double	-
mass_flow_rate_condenser	Mass Flow Rate of the Condenser	double	kg/s
mass_flow_rate_evaporator	Mass Flow Rate of the Evaporator	double	kg/s

Create Matrix

create(solver)

Input	Description	Type	Unit
solver	Class of the Solver	solver	-

---

FanCoil

The fan coil class contains the id of heating inlet, the id of heating outlet, the id of cooling inlet, the id of cooling outlet, the id of air inlet, the id of air outlet, the id of zone which under effect, the solver, specific heat capacity of the air, specific heat capacity of the cooling fluid, specific heat capacity of the heating fluid, mass flow rate of the air, mass flow rate of the cooling, mass flow rate of the heating, status of the heating system, status of the cooling system, heat transfer coefficient of the heating coil, heat transfer coefficient of the cooling coil, surface of the heating coil, and surface of the cooling coil.

Equations

Variables

Variable	Description
C.	Capacitance Flows
Z	Capacitance Flows Ratio
NTU	Number of Transfer Unit
?	Effectiveness

Subscript	Description
a	Air
w	Heating Water
min	Minimum
max	Maximum
i	Inlet
o	Outlet

Code

Construction

fanCoil = FanCoil(id_heating_inlet, id_heating_outlet, id_cooling_inlet, id_cooling_outlet, id_air_inlet, id_air_outlet, id_zone, solver, specific_heat_capacity_air, specific_heat_capacity_cooling, specific_heat_capacity_heating, mass_flow_rate_air, mass_flow_rate_cooling, mass_flow_rate_heating, status_heating, status_cooling, heat_transfer_coefficient_heating, heat_transfer_coefficient_cooling, surface_heating, surface_cooling);

Input	Description	Type	Unit

Create Matrix

create(solver)

Input	Description	Type	Unit
solver	Class of the Solver	solver	-

---

AirHeatExchanger

Next, air heat exchanger class needs data of the id of supply inlet, the id of supply outlet, the id of exhaust inlet, the id of exhaust outlet, the solver, nominal mass flow rate of the supply, specific heat capacity of the supply, specific heat capacity of the exhaust, mass flow rate of the supply, mass flow rate of the exhaust, sensible effectiveness of 75%, sensible effectiveness of 100%, latent effectiveness of 75%, and latent effectiveness of 100% as inputs.

Equations

Variables

Variable	Description
C.	Capacitance Flows
HX	Average Operating Volumetric to Nominal Supply Air Flow Rate
?	Effectiveness
avg	Average
Q.	Heat Transfer Rate

Subscript	Description
sensible	Sensible
operating	Operating
75% flow	75% Flow Rate
100% flow	100% Flow Rate
s	Supply
e	Exhaust
i	Inlet
o	Outlet
min	Minimum

Code

Construction

airHeatExchanger = AirHeatExchanger(id_supply_inlet, id_supply_outlet, id_exhaust_inlet, id_exhaust_outlet, solver, mass_flow_rate_supply_nominal, specific_heat_capacity_supply, specific_heat_capacity_exhaust, mass_flow_rate_supply, mass_flow_rate_exhaust, sensible_effectiveness_75, sensible_effectiveness_100, latent_effectiveness_75, latent_effectiveness_100);

Input	Description	Type	Unit

Create Matrix

create(solver)

Input	Description	Type	Unit
solver	Class of the Solver	solver	-

---

Constant

Equations

Variables

Variable	Description

Subscript	Description

Code

Construction

constant = Constant(id, solver, temperature);

Input	Description	Type	Unit
id	Element ID	integer	-
solver	Class of the Solver	solver	-
temperature	The Constant Temperature	double	K

Create Matrix

create(solver)

Input	Description	Type	Unit
solver	Class of the Solver	solver	-

Controllers Classes

SetpointController

Code

Construction

setpointController = SetpointController(minimum, maximum, mode, status);

Input	Description	Type	Unit
minimum	Minimum Temperature	double	K
minimum	Maximum Temperature	double	K
mode	Heating (=1) or Cooling (=2) Modes	integer	-
status	Status of the Controller	boolean	-

Check

status = check(obj, temperature);

Input	Description	Type	Unit
temperature	Temperature	double	K
status	Status of the Controller	boolean	-

Solvers Classes

Solver

The solver class inputs include time step, matrix size, and initial temperature. There is a freedom of use of multiple solvers for the model in order to solve the equations in different implicit level. For instance, in this project for each water loop separate solver will be considered.

Equations

Code

Construction

Solver(time_step, matrix_size, initial_temperature)

Input	Description	Type	Unit
time_step	Time Step	double	s
matrix_size	Number of Variables of System of Linear Equations	integer	-
initial_temperature	Array of Initial Temperatures	array(double)	K

Iterate

[solver, boilers, pipes, radiators, mixers, zones, sames, heatExchangers, chillers, fanCoils] = solver.iterate(boilers, pipes, radiators, mixers, zones, sames, heatExchangers, chillers, fanCoils);

---

Bridge

This class connects two different elements in different solvers, which has same temperatures.

Code

Construction

bridge = Bridge(id, id_bridge, solver, solver_bridge);

Input	Description	Type	Unit
id	Element ID in the first solver	integer	-
id_bridge	Element ID in the second solver	integer	-
solver	Class of the first Solver	solver	-
solver_bridge	Class of the second Solver	solver	-

Create Matrix

create(solver)

Input	Description	Type	Unit
solver	Class of the first Solver	solver	-

License

GNU GENERAL PUBLIC LICENSE Version 2, June 1991