The following subsections develop the methodology in this study. First the base modeling platform to study the two-way interaction of building systems and outdoor climate-weather will be introduced. Then the modification of this modeling platform for the inclusion of renewable and alternative building energy systems will be discussed. The building system configuration and control strategies are provided in detail. Further, the governing equations and physical processes for each renewable or alternative building energy system will be offered. Next the economic framework for feasibility of the building energy system will be established. Finally, an optimization process is implemented to allow minimizing multi-objective functions pertaining to building energy consumption and cost.
2.1. The Vertical City Weather Generator (VCWG)
The Vertical City Weather Generator (VCWG) is a computationally-efficient urban micro-scale and multi-physics simulation platform that predicts the temporal and vertical variation of potential temperature, wind speed, specific humidity, and turbulence kinetic energy in the outdoor environment, temperatures on indoor and outdoor surfaces, and temporal variation of building performance metrics such as indoor air temperature and specific humidity, sensible cooling/heating loads, humidification/dehumidification loads, and more variables [
39]. As shown in
Figure 1, it is composed of several sub-models: a rural model, a one-dimensional urban vertical diffusion model, a radiation model, and a building energy model. VCWG is forced with weather data from a rural site at the vicinity of the urban area. The rural model is used to solve for the vertical profiles of potential temperature, specific humidity, and friction velocity at 10 m a.g.l. The rural model also calculates a horizontal pressure gradient. The rural model outputs are forced on the urban vertical diffusion model that solves vertical transport equations for potential temperature, momentum, specific humidity, and turbulence kinetic energy. This vertical diffusion model is coupled to the radiation and building energy models using two-way interaction. The aerodynamic and thermal effects of urban elements, surface vegetation, and trees are considered. The feedback interaction coupling scheme among the building energy model, radiation model, and the urban one-dimensional vertical diffusion model is designed to update the boundary conditions, surface temperatures, and the source/sink terms in the transport equations in successive time step iterations.
The two-way interaction between the building energy systems and the outdoor environment is determined by the term
[W m
] which is the sensible waste heat of the building that is rejected to the outside environment. It is calculated by the building energy model as [
39]:
under cooling and heating modes, respectively. In these equations all symbols represent positive terms, unless a negative term is emphasized by the negative sign in front of the symbol. Under cooling mode,
[W m
] is computed by adding the cooling demand (
[W m
]), consisting of surface cooling demand, ventilation demand, infiltration (or exfiltration) demand, and internal energy demand (lighting, equipment, and occupants), energy consumption of the cooling system (
[W m
]) (accounting for
[-]), dehumidification demand (
[W m
]), energy consumption by gas combustion (e.g., cooking) (
[W m
]), and energy consumption for water heating (
[W m
]). Under heating mode,
[W m
] is computed by adding heating demand (
[W m
]), consisting of surface heating demand, ventilation demand, infiltration (or exfiltration) demand, and internal energy demand (lighting, equipment, and occupants) (divided by thermal efficiency of the heating system (
[-])), subtracting the heating demand, adding the dehumidification demand (
[W m
]), energy consumption by gas combustion (e.g., cooking) (
[W m
]), and energy consumption for water heating (
[W m
]).
In VCWG, the balance equation for indoor convection, conduction, and radiation heat fluxes is applied to all building elements (wall, roof, floor, windows, ceiling, and internal mass) to calculate the indoor air temperature. Then, a sensible heat balance equation, between convective heat fluxes released from indoor surfaces and internal heat gains and sensible heat fluxes from the HVAC system and infiltration (or exfiltration), is solved to obtain the time evolution of indoor temperature as [
34,
45]:
where
V [m
m
] is indoor volume per building footprint area,
[K] is the indoor air temperature, and the heat fluxes on the right hand side are specified in Equations (
1) and (
2). More details on the parameterization of the terms in Equation (
3) can be found in the literature [
34,
35,
36,
37,
38,
39]. In this convention all symbols represent positive terms however, in the equation either positive or negative signs should be used to emphasize if a term contributes to indoor temperature increase or decrease, depending on the operation mode (cooling versus heating) and environmental conditions (indoor, outdoor, and surface temperatures). Similar equations are solved for the calculation of the dehumidification load (for system under cooling mode) and indoor specific humidity; however, since the dehumidification load is usually less than 10% of the cooling load, it is not reported in this study [
34,
35,
36,
37,
38].
The earlier version of VCWG (v.1.3.2) is fully described in the literature [
39], while in the present study its implementation to simulate renewable and alternative energy systems is explored. The newly-developed VCWG v.1.4.4 is forced with meteorological data obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 data product for Guelph, Canada, in 2015 (
https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5 (accessed 15 March 2021)).
2.3. System Integration in VCWG v1.4.4
The active thermal storage is considered as the main paradigm in this study, supplemented by other building renewable energy systems.
Figure 2 shows the building systems via integration of Solar Thermal (ST), PhotoVoltaic (PV), Wind Turbine (WT), Building Integrated Thermal Energy Storage (BITES) system, Phase Change Material (PCM), Heat Pump (HP), and heat recovery systems as well as the utilization of ground thermal energy. The space heating and cooling can be supplemented via a HP. In this configuration, the BITES system is charged or discharged using the ST collector, HP, exhaust air, supply water, or grey water. Concrete is considered due to its common use in building structures and convenience of heat transfer optimization via embedded pipe design with liquid or air as heat transfer fluids [
12,
25]. The BITES system acts as either a cold (under heating mode) or warm (under cooling mode) reservoir of heat for the HP system. Energy recovery can be considered via the exhausted ventilation air. Another heat recovery system allows ejection of thermal energy from used domestic (grey) water into the BITES system under the heating mode. The system is equipped with a WT. PCM technology is considered to modulate the BITES temperature if temperatures are favorable, supported by successful evidence of using PCM with concrete for thermal storage [
16]. Water heating can be achieved using the BITES system if its temperature is greater than the water temperature to be heated. Ground thermal energy in the form of heat flux can be exchanged between the deep soil and the BITES system. This flux could be either desirable or undesirable for a given season and system configuration.
Table 2 shows the system design parameters.
The control design for thermally-activated buildings is very important via the setting of temperatures, mass flow rates, and operation of various building systems [
10].
Figure 3 shows the control algorithm for the system under heating mode. The ST collector attempts to heat the BITES system and raise its temperature when solar thermal energy is available. If BITES is to be used as a heat source for the HP, then the BITES temperature determines the
of HP. Furthermore, the fraction of the sensible heating demand to be supplied by the HP is determined using this temperature-dependent
. The BITES system is not permitted to reach a temperature below the minimum temperature required for the HP to operate. If this occurs, or if any fraction of heat is not to be supplied by the HP, then the required heating demand is supplied by the standard heating furnace that relies on natural gas. Heat recovery from the exhausted ventilated air is possible if the exit indoor air temperature is greater than the BITES temperature. A key variable to track is the fraction of the PCM that is melted. If this fraction is between 0 and 1, the heat exchanged with the PCM occurs by either melting the PCM (adding heat to BITES) or solidifying PCM (extracting heat from BITES) while keeping the BITES temperature the same. If the fraction of melted PCM reaches 0, there is no more solidification possible, where the removed heat will contribute to lowering the BITES temperature by sensible cooling. Likewise, if the fraction of the melted PCM reaches 1, there is no more melting possible, where the added heat will contribute to increasing the BITES temperature by sensible heating. The amount of heat used from BITES for water heating is determined by the building water usage schedule and the water inlet temperature. The BITES system can only warm up the water to its current temperature, while any further heating of the water must be achieved by auxiliary natural gas combustion in the hot water tank. Heat recovery by used domestic water is achieved if waste water temperature is greater than the BITES temperature. The ground heat flux is computed and its effect on BITES temperature or PCM melt fraction is accounted for.
Figure 4 shows the control algorithm for the system under cooling mode. The ST collector attempts to cool the BITES system and lower its temperature when thermal energy can be lost via the collector. If BITES is to be used as a heat sink for the HP, then the BITES temperature determines the
for the HP. Furthermore, the entire amount of sensible cooling demand is set to be met by the HP using this temperature-dependent coefficient of performance. The BITES system is not permitted to reach a temperature above the maximum temperature required for the HP to operate. If this occurs, the standard air conditioning unit is operated. Heat recovery from the exhaust ventilated air is possible if the exit indoor air temperature is less than the BITES temperature. The same logic holds for utilizing PCM and water heating under the cooling mode as in the heating mode. There is no heat recovery from used domestic water under cooling mode. The ground heat flux is computed and its effect on BITES temperature or PCM melt fraction is accounted for.
2.3.1. Solar Thermal Collectors
The Hottel–Whillier–Bliss model is commonly used for the design and analysis of free-standing (i.e., not building integrated) flat plate solar thermal collectors [
48]. This model considers an energy balance consisting of shortwave radiation gain, longwave radiation loss, and convective loss to air at ambient conditions to determine the available solar energy
[W m
] for a flat plate collector [
48]:
where
[-] is the heat removal factor,
[m
m
] is the collector area per building footprint area,
[-] is the effective transmittance-apsorptance product,
I [W m
] is the incident shortwave radiation flux normal to the collector,
[W m
K
] is the convective and radiative heat loss coefficient,
[K] is the inlet fluid temperature to the collector,
[K] is the outlet fluid temperature from the collector,
[K] is the ambient atmospheric temperature,
[kg s
m
] is the mass flow rate of the fluid through the collector per unit building footprint area, and
[J kg
K
] is the heat capacity of the fluid at constant pressure.
If the collector tilt angle is
[
], the zenith angle is
, the azimuth angle is
[
], the direct shortwave radiation flux vector from the sky is
[W m
], and the diffuse shortwave radiation flux vector from the sky is
[W m
], the incident shortwave radiation flux normal to the collector
I [W m
] is [
49]:
2.3.2. Photovoltaic Collectors
It is true that the conversion efficiency of a solar photovoltaic cell depends modestly on ambient temperature. However, in practical modeling, a constant conversion efficiency can be considered. The electricity power conversion of a photovoltaic system per building footprint area can be calculated as [
49]:
where
[m
m
] is the collector area per building footprint area,
[-] is conversion efficiency, and
[
] is the tilt angle of the photovoltaic system.
2.3.3. Wind Turbines
The most generic wind turbine equation for electricity production
per building footprint area is employed and valid when wind speed is within a specified operational range of minimum and maximum possible wind speeds. The equation is given as [
50]:
where
[-] is the turbine efficiency,
[kg m
] is the air density, and
S [m s
] is the wind speed near the roof level of a building, and
[m
m
] is the swept area of the turbine per building footprint area [
50].
2.3.4. Heat Exchangers
A typical heat exchanger that is used in building energy systems is the counter-flow heat exchanger. In the present model, such a heat exchanger is needed to transfer the thermal energy between the working fluid of the solar thermal collector and the air stream that is circulating through the BITES system. The objective of a simplistic model for a heat exchanger is to find a relationship between inlet and outlet temperatures for the two streams of the fluids. This relationship can be given using the efficiency of the heat exchanger:
From the energy balance of a heat exchanger and knowing the efficiency of a heat exchanger, it is possible to arrive at an equation for
[K] given other inlet temperatures (
and
[K]), mass flow rates (
and
[kg s
m
]), and heat capacities (
and
[J kg
K
]):
2.3.5. Building Envelop
The resistance value of a building construction material is calculated by dividing the construction material thickness
[m] by the thermal conductivity
k [W m
K
]:
For a multi-layer construction material, the total resistance value is computed by adding the individual resistances:
By the same approach the total conductivity can be calculated as:
The volumetric heat capacity for the total envelop of interest (e.g., wall, roof, or floor) can be computed by weighted averaging using the layer thicknesses:
Table 3 shows the details of the construction layers for external walls, roof, and floor that are associated with a high-performance building envelop based on Expanded PolyPropylene (EPP). The total volumetric heat capacity for the external walls, roof, and floor are computed as
289,010.9,
195,080, and
1,258,814 [J m
K
], respectively.
2.3.6. Thermal Energy Storage
A simple way to model thermal energy storage is to ignore PCMs and to consider a lump system with uniform temperature
[K] throughout the BITES system. With these assumptions, using energy balance, the change in temperature of a BITES system over finite time
[s], subject to heat gains
[W m
], heat losses
[W m
], and ground heat transfer
[W m
] can be written as:
where
[K] is a change in the temperature of the BITES system,
[m
m
] is the volume of the BITES system per unit building footprint area, and
[J m
K
] is the volumetric heat capacity of the BITES system. It is interesting to note that the BITES system can be thermally charged or discharged using multiple sources and sinks of energy, so the gains and losses are shown using a summation notation. The availability of heat gains and losses are strongly dependent on temperatures of the surrounding systems that the BITES is interacting with. A source of energy for the BITES system (e.g., solar thermal system) should be at a higher temperature, while a sink of energy for the BITES system (e.g., ground) should be at a lower temperature.
The ground heat flux is computed by having a resistance
[m
K W
] between the BITES temperature
[K] and the deep soil temperature
[K]. This heat flux could act as a source (warming BITES) or sink (cooling BITES) of thermal energy for the BITES. The ground heat flux can be calculated as:
When PCMs are used, the net heat transfer to the material results in either melting or solidifying a portion of the volume of the material without changing the temperature of the thermal storage system. This can be given by:
where
[m
m
] is the change in volume of PCM melted (positive) or solidified (negative) per unit building footprint area and
[J m
] is the volumetric latent heat of melting/solidification.
2.3.7. Heat Pumps
The first law of thermodynamics can be expressed for the HP, which states that the electricity consumption (
) plus the heat removed from a cold reservoir of heat (
) should be equal to the heat forced into a warm reservoir of heat (
). Furthermore, the
for the HP is defined differently under heating or cooling modes. The following three equations are relevant [
21]:
2.4. Economic Assessment
Economic analysis is an essential part of system optimization since cost is usually an important objective function. The European Committee for Standardization (CEN), offers the standard prEN 15459-1 (economic evaluation procedure for energy systems in buildings), which provides the Global Cost method for assessment of relative economic feasibility of multiple building energy configurations with respect to one another [
2,
51]. This method considers all costs associated with a building energy configuration, including initial investment cost, operation and maintenance cost, fuel cost, and more. It also accounts for a discount rate over an investment period of usually
years. This method can calculate three alternative cost metrics: (1) present value of the global cost, which moves all costs in time to the present time; (2) annualized cost, which distributes all costs to an equal annual value; and (3) pay-back period, which provides the number of years in which the marginal initial cost of a building configuration system will be balanced by the accumulation of annual savings. All three metrics are useful, but in this study we mainly report the annualized cost, as the primary metric, given by:
where
is the annualized initial investment for system installation and commissioning,
is the annualized cost of gas consumption,
is the annualized cost of electricity consumption,
is the annualized cost of operation and maintenance, and
is the annualized revenue of discarding the system, which has a salvage value. All costs in this equation are per unit building footprint area [
$ m
].
In the present analysis, it is important to know the marginal annualized cost, which is the difference in cost of a system retrofitted with renewable energy and a pre-existing system, on top of which the renewable energy systems are added. In other words, since the building is not completely net-zero, it still requires a standard water heater, furnace, air conditioner, etc. From here forward, any cost computed will correspond to this marginal annualized cost.
Without any renewable energy, the marginal initial cost for a conventional system is
[
$ m
]. This cost is non-zero since without renewable energy, the conventional system should be over-sized to meet the energy demand of the building. This annualized cost can be given by [
49]:
The capital recovery factor computes the annual payment required to form a total present worth of an amount given an effective interest rate
i and the number of years
N. The capital recovery factor and effective interest rate are given by [
49]:
where
is the nominal interest rate and
j is the inflation rate.
The annualized initial investment for renewable energy systems can be computed by adding the price of equipment, subtracting the government rebate (or incentive) for retrofitting the house with renewable energy, and annualizing the cost using the capital recovery factor:
where
represents the unit installation cost for a given system and
R represents the unit rebate value. For PV collectors,
[
$ m
] is provided per unit collector area; for WT,
[
$ m
] is provided per unit swept area of wind; for ST, collectors
[
$ m
] is provided per unit collector area; for BITES,
[
$ m
] is provided per unit volume; for PCM,
[
$ m
] is provided per unit volume; for HP,
[
$ m
] is provided per unit building footprint area; for the building envelop
, [
$ m
] is provided per unit building footprint area; and for the rebate
R, [
$ m
] is provided per unit building footprint area.
The annualized cost of gas consumption, for both the base energy system and the system using renewable energy, should be computed by considering the annual rate of increase in gas price
and the present worth factor
, given by [
49]:
where
and
[m
m
] are total annual gas consumption per building footprint area required for space and water heating, respectively, and
[
$ m
] is the current gas price per cubic meter at standard pressure.
The annualized cost of electricity consumption for the base energy system should be computed by considering the annual rate of increase in electricity price
:
where
and
[kW hr m
] are total annual electricity consumption per building footprint area required for space cooling and domestic use, respectively, and
[
$ kW
hr
] is the current electricity price.
The annualized cost of electricity consumption for the renewable energy system should consider more terms that relate to electricity required for heating by the HP
[kW hr m
] and electricity generated by the PV collector
[kW hr m
] and WT
[kW hr m
] such that:
The annualized marginal cost of operation and maintenance for the base system may be assumed to equal to
$ m
, which would be lower than the same cost for the renewable energy system, given by:
where
[
$ m
] is the operation and maintenance cost for the PV collector per unit collector area;
[
$ m
] is the cost for WT per unit swept area of wind;
[
$ m
] is the cost for the ST collector per unit collector area;
[
$ m
] is the cost for BITES per unit volume;
[
$ m
] is the cost for PCM per unit volume; and
[
$ m
] is the cost for HP per unit building footprint area.
The annualized revenue of discarding the system, which has a salvage value, can be computed by assuming a salvage factor,
or
for the base and renewable energy systems, respectively, and applying the
and
for the full period of
N years:
The payback period can be calculated by equating the present worth of the difference in annual cost of running the systems (base minus renewable energy) to the difference in the initial cost of the systems (renewable energy minus the base) [
51]:
where
[
$ m
] is the difference in the annual cost of running the systems (base minus renewable energy). At
, this equality is satisfied.
The initial price of a high performance building envelop can be calculated by considering the unit price of Expanded PolyPropylene (EPP) and dimensions of the house. Consider the house footprint to be 200 m
with horizontal dimensions of 10 m × 20 m and a height of 6 m. This requires, approximately, 360 m
of walls, 200 m
of floor, and 200 m
of roof areas. The installation cost of a single layer EPP panel shown in
Table 3, including assembly and labor, is
$ m
. Usually the walls require two layers of EPP, while the floor and roof require only a single layer of EPP. Given these assumptions, the cost of EPP per unit building footprint area [
$ m
] can be calculated as:
Various government rebates and incentives exist in Canada to assist home owners to improve the energy efficiency of their homes. For instance The Ontario Renovates Program provides up to
$25,000 in forgivable loan assistance to low- and moderate-income households to assist them in upgrading the energy efficiency of their homes (
https://dnssab.ca/housing-services/programs/ontario-renovates-program/ (accessed 14 April 2021)). The Enbridge Home Efficiency Rebate provides up to
$5000 for home energy upgrades, including insulation, air sealing, window replacement, heating and cooling, hot water, and more (
https://windfallcentre.ca/energy/incentives/ (accessed 14 April 2021)). The Enbridge Home Winter Proofing Insulation rebate offers
$500 for improving the thermal insulation of homes in critical areas (
https://www.hometradestandards.com/rebates (accessed 14 April 2021)). The Union Gas Home Reno Rebate offers
$5000 for switching to two or more energy-efficient HVAC units (
https://www.hometradestandards.com/rebates (accessed 14 April 2021)). The Grey water Reuse System program at the City of Guelph provides a credit of
$1000 for systems that collect and use grey water from household showers and baths (
https://showmethegreen.ca/ (accessed 14 April 2021) ). These rebates can be assumed to apply to the economic analysis for a total rebate value of
$36,500. Assuming the footprint of a two-storey house to be 200 m
, the rebate value per unit building footprint area is
$ m
.
The operation and maintenance cost of each renewable energy system can be scaled using the initial system cost [
2]. Some systems are known to require higher operation and maintenance costs, such as the HP and WT, while other systems impose lower costs. The salvage factor for the base system can be assumed to be lower than the renewable energy system.
2.5. System Optimization
A key optimization problem arises when sizing the components of the renewable energy system. On the one hand, sizing up a component of the system would likely result in greater energy savings and possibly fuel costs; on the other hand, however, the energy savings may impose a greater price premium due to larger capital investment, operation, and maintenance required.
The weighted-sum approach is a common technique for multi-objective optimization [
53]. In our case, the multi-objective function to be minimized is given by the utility function as [
53]:
where
,
, and
are the gas consumption [m
m
], electricity consumption [kW hr m
], and cost [
$ m
] objective functions, respectively; and
,
,
are the corresponding weights. Here
is the vector of design parameters that is subject to constraints
. The design parameters of choice are
,
,
,
,
,
,
, and
, which is the combination of wall-roof-floor thermal resistances (conductivities). Note that
is defined as a combined parameter so that all resistances (conductivities) would change by the same percentage.
The utility function minimum is dependent on the choice of the set of weights, and for a given set, the solution to the optimization problem is pareto optimal. On a pareto front, the optimization has been reached, i.e., the utility function has been minimized, at least locally, and moving on this front may improve (reduce) one objective function while degrading (increasing) another objective function [
53]. One common problem is the choice of the weights, since there is usually arbitrariness in the choice given the user (or decision maker) preferences to weigh some objective functions higher than the others. However, it is recommended that the weights (1) be all positive, (2) usually consider the magnitude of each objective function, and (3) be ranked according to a well-established method to prefer some objectives over the others. Although there is no strict requirement, it is recommended that
[
53].
One way to consider the magnitude of each objective function is to normalize it by its maximum possible value. In our case, the maximum values for
,
, and
are not trivial, so alternatively the objective functions can be normalized by the starting value of the initial solution to the optimization, i.e., the utility function can be written as:
where
,
, and
refer to the values associated with case 1. Note that in this representation, the design parameters are also normalized by the starting solution such that
. To weigh each objective function equally we can set
. Then using the method of steepest gradient successive number of solutions can be found to reach a local minimum, or so the pareto front. Theoretically the direction for each successive solution should be along the following vector:
However, the exact functional form of
is not known. Instead, the vector can be approximated by computing partial derivatives given 20% variation in
from the current value of
:
This vector can be expressed as a unit vector, whose magnitude is equal to 1 with components given by
. Having this unit vector, it is possible to find a new solution from the design parameters in the down-gradient direction by a fixed amount
. For example, corresponding to a total change in solution by 20%, we can set
and find the new solution by:
where
is the vector of design parameters for the current solution. Using this method, if a constraint limit for a parameter is reached, the solution cannot be changed for that parameter. This process can be repeated until the computed value for magnitude of
reaches an arbitrary lower threshold, e.g., 0.1 or 10%, at which point a pareto front has been reached and the utility function is locally minimized. A few iterations are carried out to improve the solution.
Table 5 shows the limits for design parameters.