Volume 3 solar thermal systems components and applications 3 11 – modeling and simulation of passive and active solar thermal systems

Volume 3 solar thermal systems components and applications 3 11 – modeling and simulation of passive and active solar thermal systems Volume 3 solar thermal systems components and applications 3 11 – modeling and simulation of passive and active solar thermal systems Volume 3 solar thermal systems components and applications 3 11 – modeling and simulation of passive and active solar thermal systems Volume 3 solar thermal systems components and applications 3 11 – modeling and simulation of passive and active solar thermal systems

Systems

A Athienitis, Concordia University, Montreal, QC, Canada

SA Kalogirou, Cyprus University of Technology, Limassol, Cyprus

L Candanedo, Dublin Institute of Technology, Dublin, Ireland

© 2012 Elsevier Ltd All rights reserved

3.11.1 Introduction

3.11.2 Passive Solar Design Techniques and Systems

3.11.2.1 Direct-Gain Modeling

3.11.2.1.1 Transient heat conduction and steady-periodic (frequency domain) solution

3.11.2.1.2 Building transient response analysis

3.11.2.1.3 Simplified analytical direct-gain room model and solution (passive)

3.11.3 PV/T Systems and Building-Integrated Photovoltaic/Thermal (BIPV/T) Systems

3.11.3.1 Integration of Solar Technologies into the Building Envelope and BIPV/T

3.11.3.2 A Simplified Open-Loop PV/T Model

3.11.3.3 Transient and Steady-State Models for Open-Loop Air-Based BIPV/T Systems

3.11.3.3.1 Air temperature variation within the control volume

3.11.3.3.2 Radiative heat transfer

3.11.3.3.3 Inlet air temperature effects

3.11.3.4 Heat Removal Factor and Thermal Efficiency for Open-Loop BIPV/T Systems

3.11.4 Near-Optimal Design of Low-Energy Solar Homes

3.11.4.1 Envelope and Passive Solar Design

3.11.4.1.1 HVAC and renewable energy systems

3.11.4.2 Overview of the Design of Two Net-Zero Energy Solar Homes

3.11.5 Active Solar Systems

3.11.6 The f-Chart Method

3.11.6.1 Performance and Design of Liquid-Based Solar Heating Systems

3.11.6.1.1 Storage capacity correction

3.11.6.1.2 Collector flow rate correction

3.11.6.1.3 Load heat exchanger size correction

3.11.6.2 Performance and Design of Air-Based Solar Heating Systems

3.11.6.2.1 Pebble-bed storage size correction

3.11.6.2.2 Airflow rate correction

3.11.6.3 Performance and Design of Solar Service Water Systems

3.11.8 The Φ¯, f-Chart Method

3.11.8.1 Storage Tank Losses Correction

3.11.8.2 Heat Exchanger Correction

3.11.9 Modeling and Simulation of Solar Energy Systems

3.11.9.1 The F-Chart Program

3.11.9.2 The TRNSYS Simulation Program

3.11.9.3 WATSUN Simulation Program

3.11.10 Limitations of Simulations

References

d tube diameter, m qrec heat recovered in the control volume per unit area,

Fplate,insu view factor between plate and insulation Ra Rayleigh number, GrPr = g% c2p β(Tw –Tbulk)Dh 3/(μk) = g

%

Pelect electrical power per unit area, W m−2

Δt number of seconds during a month the load is

required, s

unit area, W m

ε1, ε2, ε3 long-wave emissivities ρ average air density 1/(T Tw – b) ∫∫T T w bρdT, kg m−3

3.11.1 Introduction

There are two principal categories of building solar heating and cooling systems: passive and active Passive systems integrate into the structure of the building technologies that admit, absorb, store, and release solar energy, thereby reducing the need for electricity use to transport fluids In contrast, active systems also include fans and pumps controlled to move air and heat transfer fluids, respectively, for space heating and/or cooling and domestic hot water (DHW) heating

Current international trends, which are expected to continue, will increasingly rely on a combination of active and passive solar

thermal (PV/T) systems that are described later in this chapter

This section presents approaches that are used for modeling and simulating both passive and active solar systems First, techniques are discussed for modeling direct gains, analyzing transient responses of buildings, and developing simplified analytical thermal models of direct-gain rooms Next, methods are presented for the thermal analysis of hybrid PV/T collectors and building-integrated photovoltaic (BIPV) systems Then, to conclude the section, an overview of the design of two net-zero energy houses is described

In the second part of the chapter, various design methods are presented that include the simplified f-chart method, which is

Φ; f-chart methods Subsequently, various packages for advanced modeling and simulation of active systems are presented Finally, it should be noted that the components and subsystems discussed in other chapters of this volume may be combined to create a wide variety of building solar heating and cooling systems

3.11.2 Passive Solar Design Techniques and Systems

Passive solar technologies do not use fans or pumps in the collection and usage of solar heat Instead, these technologies use the natural modes of heat transfer to distribute the thermal energy of solar gains among different spaces When applied to buildings, this generally refers to passive energy flows among rooms and envelope, such as the redistribution of absorbed direct solar gains or night

Passive technologies are integrated within the building and may include:

amount of direct solar gains into the living space, while reducing envelope heat losses and gains in the heating and cooling seasons, respectively Skylights are often employed for daylighting in office buildings and in sunspaces (solaria)

2 Building-integrated thermal storage Thermal storage, which is commonly referred to as thermal mass, may consist of sensible heat

since it limits the views to the outdoor environment Direct-gain systems are the most common implementation of thermal storage

3 Airtight insulated opaque envelope Such an envelope reduces heat transfer to and from the outdoor environment, but must be chosen to be appropriate for the local climate In most climates, this energy efficiency aspect is an essential part of the passive design A solar technology that may be employed in conjunction with opaque envelopes is transparent insulation combined with thermal mass to store solar gains in a wall so as to turn it into an energy-positive element

4 Daylighting technologies and advanced solar control systems These technologies provide passive daylight transmission They include electrochromic and thermochromic coatings, motorized shading (internal, external) that may be automatically controlled, and fixed shading devices, particularly for daylighting applications in the workplace Newer technologies, such as transparent photovoltaics (PV) panels, can also generate electricity

(a)

qsolar TROMBE

Passive solar heating systems are generally divided into two categories: direct gain and indirect gain Four common types of passive

Direct-gain systems have two essential components: near-equatorial facing windows that transmit incident solar radiation and thermal mass distributed in the interior surfaces of the room to store much of that radiation Since the direct-gain zone

of a building collects, stores, and releases thermal energy from the sun, it is not only technologically simple but also one of

be satisfied and very often visual comfort as well with glare reduction measures Although technologically simple, these systems require proper integration with the active (heating, ventilation, and air-conditioning (HVAC)) systems to achieve

high performance In the case of the workspace such as offices integration with design and operation of the lighting system

In indirect-gain systems, the thermal storage mass is separated from the main building envelope Such systems include Trombe wall (i.e., collector-storage wall) systems, transparent insulation systems, and air heating systems (i.e., airflow windows and solar

3.11.2.1 Direct-Gain Modeling

The primary objective in the design of a direct-gain solar building or thermal zone is to achieve high savings in energy consumption through optimal utilization of passive solar gains, while preventing frequent room overheating above the acceptable comfort limit During the thermal analysis stage of a solar building, it is necessary to determine heating loads and room temperature fluctuations either for design days or with given typical annual weather data For sizing equipment and components, it is desirable

to evaluate the building response under extreme weather conditions for many design options, each time changing only a few of the building parameters, until an optimum or acceptable response is obtained For a solar building that includes direct gain as its main solar energy utilization mechanism, it is also essential to study the free (passive) response of the building as it enables the designer

to determine the relation between room temperature fluctuation and storage of passive solar gains

There are two main steps in creating a mathematical model that describes the heat transfer processes in a solar building First, the thermal exchanges must be modeled as accurately as is practical; while a high level of precision is desired, too much complexity can

room temperature and auxiliary energy loads The type of solution may be numerical or analytical, as long as the variables of interest can be determined As an optional third step, a method of analyzing the system without simulation can be developed

The degree of detail and model resolution required during the analysis of a building depends on the stage of the design For the early stages of design, a steady-state or an approximate dynamic model is often adequate However, more detail is required for a preliminary design, taking into account all objectives of thermal design and the specific characteristics of the system considered Modeling the radiant heat exchanges of the zone interior is more important with direct-gain than with indirect-gain systems and generally requires more modeling detail In designing direct-gain buildings (i.e., a building with at least one direct-gain room), a key objective is to store energy in the walls during the daytime for release at night without having uncomfortable temperature swings

A basic characteristic of passive solar building is the strong convective and conductive coupling between adjacent thermal zones This coupling is very important between equatorial-facing direct-gain rooms that receive a significant amount of solar radiation transmitted through large windows and adjacent rooms that receive very little solar radiation For example, heat transfer by natural convection through a doorway connecting a warm direct-gain room or a solarium and a cool north-facing room can be an effective way of heating the cool room

The design of direct-gain buildings can be separated into two phases First involves the determination of room temperature swings

on relatively clear days during the heating season (assuming no active or passive cooling) in order to decide how much storage mass to include so as to ensure that overheating does not occur frequently Second, to determine the optimum amount of insulation and window area and type, the net increase in the mean (daily or monthly) room temperature above the ambient temperature due to the solar gains is calculated, or auxiliary heating loads are computed until the desired energy savings are achieved

Periodic conditions are usually assumed (explicitly or implicitly) in dynamic building thermal analysis and load calculations Heating or cooling load, that is, the auxiliary heat energy input/removal required to maintain comfort conditions, is usually calculated for a design day The peak heating load is used to size heating equipment and the peak cooling load to size cooling equipment The following three types of approximations are commonly introduced in mathematical models to facilitate the representation

of building thermal behavior:

1 Linearization of heat transfer coefficients Convective and radiative heat transfers are nonlinear processes, and the respective heat transfer coefficients are usually linearized so that equations to derive system energy balance can be solved by direct linear algebraic techniques and possibly represented by a linear thermal network

2 Spatial and/or temporal discretization The equation describing transient heat conduction is a parabolic, diffusion-type partial differential equation Thus, when finite-difference methods are used, a conducting medium with significant thermal capacity such as concrete or brick must be discretized into a number of regions, commonly known as control volumes, which may be modeled by lumped network elements (thermal resistances and capacitances) Also, time domain discretization is required in which an appropriate time step is employed In response factor methods, only time discretization is necessary For frequency domain analysis, none of these approximations are required; in periodic models however, the number of harmonics employed must be kept within reasonable limits

3 Approximations for reduction in model complexity – selecting model resolution These approximations are employed in order to reduce the required data input and the number of simultaneous equations to be solved or to enable the derivation of closed-form analytical solutions They are by far the most important approximations Examples include combining radiative and convective heat transfer coefficients (so-called film coefficients commonly employed in building energy analysis), assuming that many surfaces are at the same temperature, or considering certain heat exchanges as negligible

A major aspect of the modeling process considers heat conduction in the building envelope In most cases relating to heating or cooling load estimations, energy savings calculations, and thermal comfort analysis, it is generally accepted that one-dimensional heat conduction may be assumed Thermal bridges such as those present around corners and at the structure are generally accounted for in calculating the effective thermal resistance of building envelope elements However, the thermal storage process may usually

be adequately modeled as a one-dimensional process for insulated buildings

Direct-gain zone modeling entails certain important requirements in addition to those involved in traditional building modeling In particular, there is an increased need to deal with thermal comfort requirements and a need to allow the room temperature to fluctuate in order to enable storage of direct solar gains in building-integrated exposed thermal mass

account the building thermal storage capacity and dynamic variation of solar radiation and outdoor temperature in order to avoid oversizing of HVAC systems For most mild temperate climates, a heat pump will provide an efficient auxiliary heating and cooling system Well-insulated buildings with effective shading systems and natural ventilation will have a reduced need for auxiliary cooling Similarly, appropriate sizing of the fenestration systems facing the equator will meet most heating requirements on sunny days Frequency domain analysis techniques with complex variables are usually employed for steady-periodic analysis of multilayered walls and zones They provide a convenient mean for periodic analysis, in which parameters like magnitude and phase angle of room temperatures and heat flows are obtained

Generally, materials with significant thermal storage capacity must be modeled, particularly room interior layers The thermal

(for 1 °C temperature rise)

Q ¼ 184 800 J

density and moisture content

3.11.2.1.1 Transient heat conduction and steady-periodic (frequency domain) solution

The equation describing heat conduction is a parabolic, diffusion-type partial differential equation Thus, the use of finite-difference methods requires the discretization of a conducting medium with significant thermal capacity into a number of regions which are modeled by lumped elements Also, time domain discretization is required in which an appropriate time step is employed In response factor methods, only time discretization is necessary

Mass density Thermal conductivity Specific heat

Room side

Tr

Conducted

Figure 2 Heat exchanges in a wall layer with absorption of solar radiation (To, ambient temperature; Teo, sol-air temperature [3])

For frequency domain analysis, none of these approximations are required; in periodic models however, the number of harmonics employed must be kept within reasonable limits Frequency domain analysis techniques with complex variables are usually employed for steady-periodic analysis of multilayered walls They provide a convenient means for periodic analysis, in which the main parameters of interest are the magnitude and phase angle of room temperatures and heat flows

domain variable):

dxThis is an ordinary differential equation which may be solved for T(x) while keeping s as a constant:

rffiffiffiffiffi

s

α

steady-periodic (or frequency domain) solutions

P = 86 400 s For a multilayered wall, the cascade matrices for each successive layer are multiplied to get an equivalent wall cascade matrix that relates conditions at one surface of the wall to those at the other surface, thus eliminating all intermediate nodes with no approximation required and no discretization:

Usually, the variables of primary interest are the surface temperatures of the room interior Consider, for example, a wall made

up of an inner (room side) storage mass layer and insulation on the exterior This can be represented by

3.11.2.1.1(i) Admittance transfer functions for walls

The above cascade equations for walls may be utilized to obtain frequency domain (admittance) transfer functions for walls that can

be used for steady-periodic analysis or controls and system dynamics studies

Simple Fourier series models for outside temperature or sol-air temperature and solar radiation are used for steady-periodic thermal analysis of wall heat flow Frequency domain transfer functions such as the wall admittance are studied in terms of magnitude and phase lag and are then used together with Fourier series models for weather variables to determine the steady-periodic thermal response of walls The technique is applied to passive solar analysis and design

Significant insight into the dynamic thermal behavior of walls may be obtained by studying their admittance transfer functions (magnitude and phase angle) as a function of frequency, thermal properties, and geometry

time lag between the input and output waves For inputs with more than one harmonic, the total response may be obtained by superposition of the response harmonics

The thermal admittance of a wall is a transfer function parameter useful for analysis of the effects on room temperature of cyclic variations in weather variables such as solar radiation, outside temperature, and dynamic heat flows under steady-periodic conditions

resulting heat flow at the inside surface

and thermally nonmassive layers (low thermal capacity) with conductance u per unit area, and a thermally massive layer of thickness L The Norton equivalent network for a wall with a specified temperature on one side (such as basement temperature or sol-air temperature) is obtained from the cascade form of the wall equations which relates temperature and heat flow at one surface to those at the other surface The cascade form of the equations is derived by first taking the Laplace transform of the one-dimensional heat diffusion equation to obtain an ordinary differential equation (as previously described) which can then be readily solved to relate heat flux and temperature at one surface of a one-dimensional medium to those at the other surface as

ROOM SIDE

obtained by multiplying the cascade matrices for consecutive layers Usually, the temperatures of interest are either the inside or the outside temperatures In this way, wall intermediate layer nodes and their temperatures are eliminated A linear subnetwork connected to a network at only two terminals (a port) can be represented by its Norton equivalent, consisting of a heat source

The admittance is the subnetwork equivalent admittance as seen from the connection port (the two terminals), and the heat source is

mass of uniform thermal properties and an insulation layer with negligible thermal capacity, also of uniform thermal properties The

obtaining the total cascade matrix by multiplying the cascade matrix for the storage mass layer by that for u (note: u = U/A):

admittance as seen from the interior surface is obtained, yielding (after multiplying by A)

nodes exterior to the inner glazing An important result is obtained for an infinitely thick wall or a wall with no heat loss at the back

20

Concrete Softwood

Concrete Softwood

Concrete Softwood

45 42.5 40

0

variables

3.11.2.1.1(i)(a) Analysis Substantial insight into wall and building thermal behavior may be gained by studying the magnitude

a sinusoidal input function, such as solar radiation in the case of the room interior surface, and the resulting peak of the interior

frequency (one cycle per day, n = 1) for unit wall area Note that the diurnal (n = 1) frequency is important in the analysis of variables with a dominant diurnal harmonic such as solar radiation High frequencies are important in analyzing the effect of varying heat inputs such as those due to on/off cycling of a furnace

Compare two walls, one with a concrete interior and the other with a softwood interior The exterior insulating layer of both walls has insignificant thermal capacity, and its thermal resistance is 2.5 RSI The concrete is assumed to have a specific heat capacity

The results presented below are specific to this concrete, but they generally indicate the expected trends for concrete, brick, and

corresponding to the maximum admittance Therefore, this is the optimum thermal mass thickness for passive solar design because the dominant harmonic component of solar radiation is that corresponding to one cycle per day

period) The magnitude of wall admittance is also higher for concrete than for softwoods Thus, the inside room temperature fluctuations are smaller for high-frequency fluctuations in internal heat gains in the case of the concrete wall For harmonic numbers

thickness, and therefore, fluctuations in the sol-air temperature are significantly modulated as they are transmitted to the room interior This is a well-known phenomenon, efficiently employed in traditional architecture in adobe buildings The time lag of the heat gains

4000.4

Concrete Softwood

Concrete Softwood

0.2

Concrete Softwood

Concrete Softwood

The time delay in the transmission of a heat wave through a wall is another positive effect of thermal mass in addition to the attenuation of temperature swings Thus, the peak heat gains through the structure coincide with cooler outside conditions when natural ventilation may be employed to reduce total instantaneous cooling loads

decreasing period Thus, the heat gain fluctuations transmitted into the room as a result of sol-air temperature fluctuations are significantly reduced at high frequencies For example, a temperature fluctuation (amplitude of wave) of 10 °C in sol-air tempera­

3.11.2.1.2 Building transient response analysis

Transient thermal analysis of walls or zones may be performed with the following objectives:

1 Peak heating/cooling load calculations

2 Calculation of dynamic temperature variation within walls, including solar effects, room temperature swings, and condensation on wall interior surfaces; two-dimensional steady-state temperature profiles in walls (e.g., for investigation of thermal bridge effects) For a multilayered wall, an energy balance is applied at each node at regular time intervals to obtain the temperature of the nodes as

a function of time These equations may be solved with the implicit method as a set of simultaneous equations or with the explicit method which involves a forward progression in time from a set of initial conditions Mixed differencing schemes are also often used in building simulation

Here we consider the finite-difference thermal network approach In this approach, each wall layer is discretized (divided) into a number of sublayers (regions) Each region is represented by a node and is assumed to be isothermal Each node (i) has a thermal

Wall transient thermal response analysis with finite-difference techniques may generally provide a more accurate estimation of temperatures and heat flows owing to the capability to model nonlinear effects such as convection and radiation One disadvantage

is that the initial conditions are usually unknown Thus, the simulation is repeated until a steady-periodic response is obtained

also known as control volumes Each region is represented by a central node with a thermal capacitance C connected to two thermal

(thickness L)

Concrete modeled

consists of two capacitances for the concrete thermal capacity and interconnecting thermal resistances The energy balance for the thermal network is as follows:

Subscript i indicates the node for which the energy balance is written, and j indicates all nodes connected to node i, while p is the

The time step is selected on the basis of the following condition for numerical stability:

10

j Ri ; j

C

for all nodes i

The explicit finite-difference method is particularly suitable for the modeling of nonlinear heat diffusion problems such as heat transfer through the building envelope It can easily accommodate nonlinear heat transfer coefficients and control actions

Figure 10 Simplified thermal network for Figure 9

system and concrete face)

using the equivalent sol-air temperature and equivalent resistance The simplification and the resulting thermal network are shown

in Figure 10

simulations, a shutter is assumed to be closed in the air cavity, reflecting outwards 90% of transmitted solar gains

3.11.2.1.3 Simplified analytical direct-gain room model and solution (passive)

An analytical model can provide insight into passive solar design and quick comparison of design options A simple analytical

are external) are assumed to be made up of an inner lining of storage mass material of uniform thermal transport properties and outer insulating layers with negligible thermal storage capacity Walls with storage mass are assumed to be at the same surface temperature, and they are thus treated as one exterior wall, which is modeled as a two-port distributed element as previously

incident solar radiation

T4 i = TR+Ri⋅ T3 i − TR

Rc2 + Ri

Ra+ Rb

a uniformly distributed storage mass, by a small extension it can model a situation where some of the walls (normally the ceiling)

outer glazings, respectively

STORAGE MASS

would be felt by an occupant who senses, through radiant exchange, the temperature of the room surfaces, and through convective exchange, the room air temperature

The final simplification is replacement of the wall by its Norton equivalent, which is determined as explained above The variable

� � � �

3.11.2.1.3(i) Important design approximation

For rooms with well-insulated walls and high mass (more than 10 cm of concrete or equivalent), the approximate wall self-admittance can be calculated with the following equation:

For very thick mass (more than 25 cm of concrete or equivalent), the wall may be approximated to a semi-infinite solid with admittance equal to

In both of the above cases, the transfer admittance (for all frequencies apart from the mean) is negligible

3.11.2.1.3(ii) Source models

Steady-state periodic conditions are assumed in computing the room temperature swing (difference between maximum and

preceded by identical days Although deviations from the 1-day periodic assumption (e.g., previous day overcast and current day

not be affected, and therefore, the difference between its maximum and minimum points should be close to the actual swing Another option would have been to include the effect of the previous day, that is, to assume a 2-day periodicity; the present method can be readily generalized to include such a model Note that because of the 1-day periodic assumption, weather input is needed only for the particular day in question

closely modeled over the daytime as a half sinusoid The constraints on the half sinusoid are chosen to satisfy two conditions: first,

� � � �

radiation at sunrise and its more rapid decrease at sunset For windows that are not south-facing, the Fourier coefficients can be determined by direct numerical integration of the instantaneous absorbed irradiation Various methods can be used for determining

index may be used to generate values of the hourly clearness index

The model does not distinguish between the differing orientations of the exterior wall surfaces, and hence, it is not possible

to accurately model the effect of fluctuations in the solar radiation absorbed by the wall exterior surfaces A sensitivity analysis showed that the effect of this absorbed solar radiation on the temperature swing is small, provided there is at least a

3.11.2.1.3(iii) Periodic solution

evaluating magnitudes and phase angles for the complex transfer functions Since the variable of interest here is fluctuations, the

�ΔToUeo � π ΔToYseo1 ðTFÞeis1 XN

4

Yseo1 and φseo1 The variation in Ts is given by

times at which the maximum and minimum temperatures occur, and then substituting these times back into the original equation

3.11.2.1.3(iv) Approximate design method for temperature swings

For a well-insulated room with massive walls, the maximum temperature swings can be estimated with the following approxima­tion that adjusts the response to the first (fundamental) harmonic to include higher harmonic effects:

equivalent to 1 h for a period of 24 h)

3.11.2.1.3(v) Detailed frequency domain zone model and building transfer functions

Building heat exchanges may be represented by a thermal network, and transfer functions are obtained by performing an energy balance at all nodes in the Laplace domain Both lumped and distributed elements can be considered with this approach Simple models, as in the previous section which do not represent in detail infrared radiation heat exchanges between room interior surfaces, can usually be solved analytically

lightweight room contents are modeled by a lumped thermal capacitance Although this capacitance has no effect on load calculations because of the relatively low frequencies involved, it is important to include it for short-term (high frequency) control studies Each two-port element represents the equivalent two-port for each wall, obtained after multiplying the cascade matrices for each massive and nonmassive layer The resistances connecting node 1 (room air) to the interior surfaces represent convective conductances given by

3

The energy balances at the room interior nodes for both models are readily obtained after replacing each wall with its Norton

Coil Fan

PI Control

Floor mass

the sign convention used)

½31a

or

½ Y N  Nf gT N ¼ Qf gN where [Y] is the admittance matrix, {T} is the temperatures vector, and {Q} is the source vector The solution for {T} in the frequency domain is obtained by

heat sources connected to node j (positive if directed to the node) As can be seen, for thermal networks the admittance matrix has

Uij), and (2) all capacitances and all self-admittances appear in the diagonal entries, which are consequently complex The transfer

functions of interest are the elements of the inverse of [Y], that is, the impedance transfer functions Z(i,j) The temperature of node I for each frequency is given by

NX

J ¼ 1 For room air temperature, I is set equal to 1 in the above equation, which is determined for each frequency (harmonic) of interest

temperature change at a node in the thermal network The most important transfer function required in the present method is the impedance transfer function:

TðIÞ

QðJÞ which represents the temperature change for node I due to unit heat input at node J for a given frequency Thus, for heat input Q(J)

It is often useful to determine a transfer function not only for individual room temperatures but also for an effective room

in which an occupant would exchange the same amount of heat by radiation plus convection as in the actual nonuniform environment The operative temperature is given by

respectively, for a person or object (sensor) The operative temperature transfer functions X(I) are given by

QðIÞ and represent the effect of a source Q(I) acting at node I on the operative temperature

3.11.2.1.3(vi) Analysis of building transfer functions

Substantial insight into building thermal behavior may be obtained by studying the magnitude and phase angle of the important transfer functions Consider, for example, the transfer functions Z11 and Z17 in the detailed model (Z11 and Z12, respectively, in the simple model); these represent the effects of heat sources at node 1 (room air) and 7 (floor), respectively, on the temperature of node 1 (in both cases all other sources set to zero):

the floor surface as follows

represents the magnitude of its

significant result is the time delay between the peak of S(t) (noon for south-facing windows) and the resulting peak of the

Im(Z17)/Re(Z17))

the vertical walls and on the ceiling is a 13 mm-thick gypsum board The insulation is 3.5 RSI on the vertical walls, 7.4 RSI on the ceiling, and 1 RSI on the floor, which connects to a basement

shows the Nyquist plot, that is, imaginary versus real components, for Z11 of the room with a concrete floor and for Z17 of the

MR-EXACT PL-FITTED FUNCTION

FREQUENCY (CYCLES PER DAY)

MR FOR FITTED FUNC

PL FOR FITTED FUNC

MR Exact

PL

high-frequency range and a low-frequency range; in the high-frequency short-term dynamics region, the room air thermal capacitance is significant, and the difference between Z11 for the concrete floor and the carpeted one is small in both phase and magnitude, that is, the effect of thermal mass is minimal in this region The separation between short-term and long-term building thermal dynamics begins at frequencies of approximately 35 cycles per day or periods of 41 min The separation is also indicated in

within which the room air (and furniture, etc.) thermal capacity is important Simulations by the authors with different construc­tions showed similar results for Z11, which represents the effects of convective heat gains or losses Short-term dynamics are particularly important for feedback control studies For lower frequencies such as one cycle per day, the magnitude and phase of Z11 and Z17 is a strong function of room construction, and there is a significant difference between the response of the massive (concrete) construction and the nonmassive (carpet) one

third-order fit is good in both magnitude and phase, the error being typically less than 2% The fitted Laplace transfer function for Z17 is

Z17 ðsÞ ¼

3.11.2.1.3(vii) Heating/cooling load and room temperature calculation

Heating/cooling load and associated room temperature calculations are performed with the same building transfer functions employed in frequency response and thermal control studies These computations are performed by means of discrete Fourier series

The building transfer functions are calculated at discrete frequencies (s = jωn), and a discrete Fourier transform (DFT) of the weather data is performed For example, convective auxiliary heating is given by

transform (IDFT) For design day analysis, five to nine harmonics are usually adequate These are the harmonics necessary for adequate representation of the inputs, that is, heat sources such as absorbed solar radiation, internal gains, and ambient

Thus, optimum set-point profile variations may be determined to optimize solar gain utilization The discrete Fourier series

the thermal network and a technique for modeling time-varying parameters, such as a conductance representing infiltration based

on the substitution network theorem

3.11.2.1.3(viii) Discrete Fourier series method for simulation

Steady-periodic conditions are usually assumed; for example, if the simulation is to be performed for a week, it is assumed that all previous weeks have been identical to the week considered The steps needed for a periodic steady-state solution are as follows:

1 Select the number N of harmonics to perform the analysis If n represents a harmonic number and P is the time length of the

2 Obtain the appropriate discrete Fourier series representations for the sources An arbitrary source M(t) is represented by a complex Fourier series (IDFT) of the form

N

n ¼ − N X

P

harmonics N cannot exceed K/2

each source is obtained by superposition of the output harmonics using complex (phasor) multiplication The total response to

the room air temperature T1(t) is obtained by

3.11.3 PV/T Systems and Building-Integrated Photovoltaic/Thermal (BIPV/T) Systems

3.11.3.1 Integration of Solar Technologies into the Building Envelope and BIPV/T

Integration improves the cost-effectiveness by having the PV panels provide additional functions, which involve active solar heating

Montreal with a BIPV/T façade) The following are some recognized methods of beneficial integration:

(a) (b) (c)

08/15/2007

module (c) BIPV/T roof module delivered on-site for assembly of house

TM

right section of façade) and schematic illustrating the system concept: 70% of the transpired collector cladding area (288 m2) is covered by specially designed PV modules; the system generates up to about 25 kW electricity and 75 kW of thermal energy used to directly heat ventilation air [7]

1 Integrating the PV panels into the building envelope (BIPV) This strategy could involve, for example, replacing roof shingles or wall

component (e.g., roof asphalt shingles), but it also eliminates penetrations of a preexisting envelope that are required in order to attach the panel to the building (It is understood that the components replaced are not windows, as this is covered by Method 3, below.) Architectural and aesthetic integration is a major requirement in this type of BIPV system Not only can this strategy lead to much higher levels of overall performance, but it can also provide enhanced durability: one International Energy Agency (IEA) study

2 Integrating heat collection functions into the PV panel (BIPV/T) PV panels typically convert from about 6% to 18% of the incident solar energy to electrical energy, and the remaining solar energy (normally lost as heat to the outdoor environment) is available

to be captured as useful heat In this strategy, a coolant fluid, such as water or air, is circulated next to the panel, extracting useful heat The coolant also serves to lower the temperature of the panel; this is beneficial, because panel efficiency increases at lower panel temperatures This strategy can be adopted in either in an open-loop or closed-loop configuration In one open-loop configuration, outdoor air is passed under PV panels, and the recovered heat can be used for space heating, preheating of

3 Integrating light transmission functions into the PV panel (BIPV/L) This strategy uses special PV panels (semitransparent PV windows) that transmit sunlight As was the case for the previous strategy, this strategy draws on the fact that only a fraction

light, thereby saving on the energy that electrical lights would otherwise draw Thin-film PV cells that let some sunlight through are commercially available for this purpose A major challenge is limiting the temperature rise of the windows and controlling the impact of the associated heat gains during times when building cooling is required Compared with normal windows, these windows have a reduced light transmission and can therefore function as shading devices

Appropriate modeling of building-integrated solar energy systems (thermal, electric, hybrid, daylighting) is essential for the designing of high-performance solar buildings These systems will play a major role in achieving the net-zero energy goal and

need to be carefully selected, modeled, and sized for an accurate design Different simulation tools include different technologies and simulate building-fabric energy transfer with different levels of detail They also utilize different techniques to model the transient response of buildings and their systems to changes in internal and external thermal loads

At the early stage of the design, a simplified software tool may provide enough accuracy to size a BIPV or a solar thermal system

as it provides monthly estimates of energy generated However, a BIPV/T system that generates both electricity and heat requires

heat pump) To properly simulate these systems, tools characterized by a high-integrity representation of the dynamic and connected processes are required

3.11.3.2 A Simplified Open-Loop PV/T Model

A simplified model for a PV/T façade or roof with the exterior layer being PV panels is described below to calculate the PV temperature and the heat recovered

Consider a façade with PV panels as the exterior layer; this façade may be represented by the thermal network model shown in

Figure 24

distance x It is assumed that the air speed is constant, that is, air is drawn into the window by a fan in the HVAC system fresh air

3.11.3.3 Transient and Steady-State Models for Open-Loop Air-Based BIPV/T Systems

BIPV/T systems produce thermal and electrical energy, and have lower effective system costs than do stand-alone PV systems The BIPV/T system absorbs solar energy on the top surface, which includes the PV panels and generates electricity while also heating air

to be an insulating layer with a thermal resistance of RSI 1)

PV module

Air inlet at the soffit

Reflectedradiation

Incoming solar radiation

Insulation

Convective heat losses

Radiative heat losses

Inverter

Section 5

Convective and radiative heat exchanges in the channel

Variable-speed fan

(b)

in the open-loop configuration for solar heating of fresh air used for ventilation)

elements of the building envelope Open-loop air-based BIPV/T systems supply solar-heated air that can be used either for

Accurate convective heat transfer coefficients are essential for solving the energy balance equations used for lumped parameter network modeling of these systems This is necessary to quantify the thermal and electrical energy production, which in turn provides adequate means for sizing associated equipment, such as heat exchangers and electrical inverters The PV module temperatures obtained by solving the energy balance equations for the PV modules are useful in designing the array layout in order to maximize total energy production The forced convection increases the heat transfer rate from the PV modules, lowering their temperature and thus increasing their electrical conversion efficiency Monocrystalline and polycrystalline silicon-based PV

development of control algorithms for the control of the airflow that cools the panels so as to obtain a desired outlet air temperature suitable for the specific application

of the PV module; outdoor air is used to cool the PV modules by convection (commonly, forced convection) The heated air is used

to provide thermal energy to one or more functions in the building before being exhausted to the exterior Open-loop air systems are normally preferred over closed-loop air systems as the latter would likely lead to overheating of the PV module (reducing its

more common and more severe in hot and humid climates, sometimes occurring after less than 5 years of exposure Also, open-loop systems allow for the potential use of preheated fresh air for ventilation Since BIPV/T systems have lower inlet temperatures than those in the case of closed-loop systems, the former system normally operates with higher thermal efficiencies, although its air exit temperatures are lower

BIPV/T systems contain several features that need to be addressed such as heating asymmetry and a relatively complex geometry Mathematical models of different levels of complexity, emphasizing different phenomena, have been developed over the years This section presents two models bringing together some of the ideas presented in previous works by the authors, and the most relevant findings obtained from measurements at the experimental facilities and demonstration projects of the Canadian Solar Buildings

Mathematical models for the particular case of forced-convection open-loop BIPV/T systems have been developed by Clarke et al

collectors – not necessarily installed as a building component – have been developed by several researchers Examples include the

Nusselt numbers are also reported

At Concordia University, different BIPV/T numerical models have been developed both for research on these systems and as

The aforementioned models, based on energy balances in control volumes, have used different levels of complexity to model the energy interactions between the surfaces Some of the most relevant differences in approach are presented below The majority of the

developed a fully explicit finite-difference model for a solar air collector The authors found that the transient model is useful to account for the effects of rapid changes (e.g., variable cloudiness, wind speed fluctuations), and therefore, it can be useful for the development of robust control algorithms for the control of flow rate

3.11.3.3.1 Air temperature variation within the control volume

case, the average air temperature inside the control volume is the arithmetic mean of the inlet and outlet temperatures However, most recent investigations use an exponential air temperature variation, which is the exact solution if the temperatures of the surrounding surfaces are assumed to be uniform inside the control volume The average air temperature (used for energy balances)

3.11.3.3.2 Radiative heat transfer

assuming a view factor of 1 between the plates The radiation exchange difference calculated by using this coefficient, assuming two plates at 350 K and 273 K, is about 1.5% underestimated from the exact value given by the equation

The majority of models assume, often without stating it explicitly, that the view factor between the two surfaces of interest is close to

account

As explained above, heat transfer in a BIPV/T system has several particularities due to the asymmetric heating (i.e., heat transfer occurs mainly through one side of the BIPV/T channel) and the more complex geometry However, most researchers have used Nusselt number correlations developed for pipes and ducts with uniform boundary conditions for a given cross section,

underestimate convective heat transfer coefficients because several heat transfer enhancing factors are not taken into account, such as the presence of the framing structure and surface imperfections (which act as turbulence promoters) and developing flow conditions at the inlet

The determination of heat loss to the surroundings has been carried out through many different approaches The McAdams

layer significantly increases the insulation, and the effect of the exterior heat transfer coefficients becomes less important Most researchers separate exterior heat losses into two components: convection to the exterior air and radiation to a representative sky

roof-mounted flat-plate collector and are preferable to the McAdams formula Both correlations have been used in modeling BIPV/T

can be used to calculate radiative heat transfer losses

‘Moisture’ has an important effect on the physical characteristics of the fluid, in particular on the effective specific heat of the air,

3.11.3.3.3 Inlet air temperature effects

In BIPV/T systems, the inlet air temperature is sometimes slightly higher than the exterior air temperature This is especially true in

Roof metal sheet 0.5 mm

3.11.3.3.3(i) Electrical efficiency modeling

A common approach has been to linearize all the equations and solve the resulting linear system by matrix inversion Since the system of equations is relatively robust, it can be solved by the simple method of assuming guess values and iterating until a convergence criterion is met When the effects of thermal inertia have been considered, a transient method such as the fully explicit finite-difference method has been used

The focus of this section is a BIPV/T system with outdoor air as the cooling fluid The channel is smooth and has an aspect ratio

For the particular BIPV/T design studied here, an amorphous PV module is mounted on a metal roof sheet The amorphous PV module is formed from different layers These are from top to bottom, TEFZEL (an encapsulant layer), antireflective coating,

insulation

module, the middle of the PV module, the interior surface of the metal plate, air node, and the surface of the insulation facing the cavity:

Figure 26 BIPV/T thermal network model showing the interior convective heat transfer coefficients hct and hcb (the configuration shown corresponds to

an experimental prototype studied by Candanedo et al [31])

variables (solar radiation, exterior temperature, mass flow rates, material properties, etc.) are known inputs Several necessary parameters and variables are calculated as follows:

• The absorptance α of the exposed PV surface is corrected as a function of the angle of incidence of beam solar radiation, as

hours For these models, a correction curve developed specifically for the amorphous PV laminate, calculated according to the

πt

12

• The exterior convective heat transfer correlation is obtained using different correlations to compare their effects into the results These

distributions and graphed as a function of the Reynolds number (forced convection)

The Nusselt number distribution (local heat transfer coefficients) for the developing length x has been calculated for the whole

 x

 x

Both correlations represent the convective heat transfer distribution up to the maximum length (about 3 m) of the analyzed BIPV/T

values For the laminar region, the last term represents the Nusselt number for the maximum length It is expected that for larger lengths, the Nusselt number will tend to keep decreasing

associated with the film coefficient under the insulation and plywood has been neglected due to its low value compared with the thermal resistance of the insulation The two models are identical except in one respect: the steady-state model does not consider the thermal capacitance of the PV panel (making it a steady-state model), while the transient model takes into account the thermal inertia (capacitance) of the PV panels In a dynamic simulation, the solution of the equations of the steady-state model is independent of previous conditions In contrast, at every time step, the transient model requires the solution of the previous

solution of both models

As mentioned above, the transient model includes the thermal capacitance of the PV module In this case, a fully explicit scheme has been used (the temperatures for the current time step depend only on the temperatures of the previous time step) The second equation below corresponds to the energy balance in a node associated with a midlayer of the PV module

included only in the top part of PV module, since it is exposed to rapidly changing weather conditions, including wind and irradiance, whereas the bottom of the channel is insulated The equations corresponding to the transient model are as follows: