**1. Introduction**

Ventilation fans are energy-demanding equipment that stands for a significant share of a building's total energy consumption. Improving energy efficiency of ventilation fans is thus important. Fans used for demand controlled ventilation (DCV) are intended to deliver a specific flow rate derived from the actual load in the building. This chapter is about how to deliver the required air flow rate to all rooms, without wasting energy on throttling. There are several ways to control the flow rate in a ventilation system. The most common ways are (1) pure throttling, (2) constant differential pressure and (3) constant duct static pressure. In some situations, (4) direct fan control are used as a control strategy (DDCV). The latter is known to be efficient, as it will provide only the required air flow at all times, without the need for any throttling. It needs however more extensive instrumentation, and flow rates to and from all zones in a building have to be continually recorded and fed back to the central flow controller. A simulation study shows that by introducing a relatively simple control procedure, the fan can be controlled more efficient and energy consumption can be reduced to a significant degree, also for alternative (2) and (3), without the need for added control equipment.

Pressure energy used for throttling of air in the ventilation system is transformed to heat by friction. Thus the ventilation air is heated by the 'wasted' pressure energy. For this reason it can be argued that throttling is just as good as pure speed regulation. However, this makes sense only if a demand for heating exists. During periods with cooling demands, throttling is a true waste of energy since the heat produced from it cannot be exploited. If there is local cooling of air within the zones, throttling is even worse since energy must be used to remove the 'throttling' heat. Throttling also produces noise. Hence, the degree of throttling in ventilation systems should be as low as possible.

© 2012 Sørensen, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In this study a different approach of controlling the static pressure difference of a fan is suggested. The study is based on a detailed dynamic simulation system that was presented in (Sørensen, 2006, 2010). Controlling static pressure difference of the fan to a fixed set point is a compromise between pure throttling and pure speed regulation. Seen from an energy consumption perspective, control is not optimal. To make control more optimized energywise, while still retaining proper pressure control, the static pressure set point should be altered automatically, along a predefined path.

Energy Efficient Control of Fans in Ventilation Systems 137

The direction of path 1-3 must be very carefully assessed. Choosing a too slack slew rate is not critical, but then there will be room for more energy savings still. Choosing a too steep curve is however critical. A too steep curve will affect the available maximum air flow rate for the local zones in the building. The risk of getting too little air to some zones is then

The algorithm for resetting the set point along path 1-3 is presented below. The following

• The set point to which the fan pressure difference normally would have been controlled

• Lowest airflow rate at Δp1,2 (all local dampers closed) - Q2,3,4. This will be the minimum

The parameters can be found for instance during the commissioning process, by measurements or from the fan characteristics. In addition to these parameters, a gain (Kpath) must be carefully selected. Kpath determines the steepness of the path 1-3 (refer to Fig. 1) and is in the range between 0 and 1. A value of zero means no adjustment of the set point, and a value of one means nearly pure fan speed control. The reset algorithm was obtained through a linear curve fit of the above parameters, and requires continuous measurements of the

> SP 1,2 path 1 1 2,3,4

To avoid that the set point moves to a very low or high value, it should be saturated at a maximum value. Stopping the set point from moving to a too high or too low value can be

The pressure and flow characteristics produced by the fan model, are crucial for the simulation results. Thus quite much effort has been put into the development of a proper fan model. The model is based on a backward curved, inclined radial fan, and takes into

p p p pK Q(t) Q Q Q Δ −Δ

Δ =Δ + ⋅ <sup>−</sup> <sup>−</sup>

achieved by implementing the following algorithm in the controller:

( ) 1,2 4

(1)

• Pressure difference at minimum fan speed (all local dampers open) - Δp4.

present.


main air flow rate:

if ΔpSP > Δp1,2

then ΔpSP = Δp1,2

**3.1. Fan model** 

if ΔpSP < Δp4 + (1-Kpath)·(Δp1,2-Δp4)

then ΔpSP = Δp4 + (1-Kpath)·(Δp1,2-Δp4)

**3. Simulation system description** 

account fan efficiency and mechanical losses.

parameters have to be found or known:

• Design airflow rate (all local dampers open) - Q1.

flow rate from the fan during operation.

The developed simulation systems used as basis for this study cannot at this stage account for heating of air due to friction and throttling in the system. The error introduced by this is assessed not to be very significant due to other more dominant loads.

The following sections will explain the models and simulation systems used to demonstrate the possible benefits of the reset algorithm in practice. Furthermore, a case study will be carried out and discussed.

## **2. Procedure to reset of static pressure difference set point**

The study presented in this section is based on (Sørensen 2011). Fig. 1 shows three different paths from one flow rate to another in the fan diagram. In this diagram, we consider pressure difference along the y-axis, and flow rate along the x-direction. Path 1-2 is the normal path to follow during constant fan pressure difference control. Pressure variations due to throttling in the duct system are then compensated for by adjusting the fan speed. Path 1-4 is obtained while there is no throttling going on in the duct system and thus no static pressure control is needed. This is the optimal path from an energy consumption perspective. Path 1-4 is used in a variable air volume ventilation system addressing a DDCV control strategy. Path 1-3 represents a compromise between path 1-2 and 1-4. This means more speed regulation and less throttling than 1-2. The path 1-3 was used in this study to reset the set point as a function flow rate.

**Figure 1.** Three different paths of getting from one flow rate to another in the fan diagram (n=fan speed, Q=flow rate, p=pressure)

The direction of path 1-3 must be very carefully assessed. Choosing a too slack slew rate is not critical, but then there will be room for more energy savings still. Choosing a too steep curve is however critical. A too steep curve will affect the available maximum air flow rate for the local zones in the building. The risk of getting too little air to some zones is then present.

The algorithm for resetting the set point along path 1-3 is presented below. The following parameters have to be found or known:


The parameters can be found for instance during the commissioning process, by measurements or from the fan characteristics. In addition to these parameters, a gain (Kpath) must be carefully selected. Kpath determines the steepness of the path 1-3 (refer to Fig. 1) and is in the range between 0 and 1. A value of zero means no adjustment of the set point, and a value of one means nearly pure fan speed control. The reset algorithm was obtained through a linear curve fit of the above parameters, and requires continuous measurements of the main air flow rate:

$$
\Delta \mathbf{p}\_{\rm SP} = \Delta \mathbf{p}\_{1,2} + \mathbf{K}\_{\rm path} \cdot \frac{\Delta \mathbf{p}\_{1,2} - \Delta \mathbf{p}\_4}{\dot{\mathbf{Q}}\_1 - \dot{\mathbf{Q}}\_{2,3,4}} \left( \dot{\mathbf{Q}}(\mathbf{t}) - \dot{\mathbf{Q}}\_1 \right) \tag{1}
$$

To avoid that the set point moves to a very low or high value, it should be saturated at a maximum value. Stopping the set point from moving to a too high or too low value can be achieved by implementing the following algorithm in the controller:

if ΔpSP > Δp1,2 then ΔpSP = Δp1,2 if ΔpSP < Δp4 + (1-Kpath)·(Δp1,2-Δp4) then ΔpSP = Δp4 + (1-Kpath)·(Δp1,2-Δp4)

#### **3. Simulation system description**

#### **3.1. Fan model**

136 Energy Efficiency – The Innovative Ways for Smart Energy, the Future Towards Modern Utilities

assessed not to be very significant due to other more dominant loads.

**2. Procedure to reset of static pressure difference set point** 

altered automatically, along a predefined path.

carried out and discussed.

reset the set point as a function flow rate.

Q=flow rate, p=pressure)

In this study a different approach of controlling the static pressure difference of a fan is suggested. The study is based on a detailed dynamic simulation system that was presented in (Sørensen, 2006, 2010). Controlling static pressure difference of the fan to a fixed set point is a compromise between pure throttling and pure speed regulation. Seen from an energy consumption perspective, control is not optimal. To make control more optimized energywise, while still retaining proper pressure control, the static pressure set point should be

The developed simulation systems used as basis for this study cannot at this stage account for heating of air due to friction and throttling in the system. The error introduced by this is

The following sections will explain the models and simulation systems used to demonstrate the possible benefits of the reset algorithm in practice. Furthermore, a case study will be

The study presented in this section is based on (Sørensen 2011). Fig. 1 shows three different paths from one flow rate to another in the fan diagram. In this diagram, we consider pressure difference along the y-axis, and flow rate along the x-direction. Path 1-2 is the normal path to follow during constant fan pressure difference control. Pressure variations due to throttling in the duct system are then compensated for by adjusting the fan speed. Path 1-4 is obtained while there is no throttling going on in the duct system and thus no static pressure control is needed. This is the optimal path from an energy consumption perspective. Path 1-4 is used in a variable air volume ventilation system addressing a DDCV control strategy. Path 1-3 represents a compromise between path 1-2 and 1-4. This means more speed regulation and less throttling than 1-2. The path 1-3 was used in this study to

**Figure 1.** Three different paths of getting from one flow rate to another in the fan diagram (n=fan speed,

The pressure and flow characteristics produced by the fan model, are crucial for the simulation results. Thus quite much effort has been put into the development of a proper fan model. The model is based on a backward curved, inclined radial fan, and takes into account fan efficiency and mechanical losses.

The model presented below refers to a fan which has no mechanical losses, which applies to incompressible flow and on which the mathematical description is purely based on the fan laws. Losses, in terms of fan efficiency, is added to the model later, thus enabling computation of the required fan power and energy usage and also the fraction of fan power which goes into heating of ventilated air.

For simulation of flow distribution throughout the ventilation system, a function which expresses the relationship between pressure difference, air flow rate and fan speed is required. This function can be derived, using a second order parabolic polynomial, as follows:

$$\frac{\Delta \mathbf{p}\_2}{\Delta \mathbf{p}\_1} = \left(\frac{\mathbf{n}\_2}{\mathbf{n}\_1}\right)^2 = \left(\frac{\dot{\mathbf{Q}}\_2}{\dot{\mathbf{Q}}\_1}\right)^2 = \mathbf{K}\_{\mathbb{A}} \cdot \left(\frac{\mathbf{n}\_2}{\mathbf{n}\_1}\right)^2 + \mathbf{K}\_{\mathbb{B}} \cdot \left(\frac{\dot{\mathbf{Q}}\_2}{\dot{\mathbf{Q}}\_1}\right)^2 + \mathbf{K}\_{\mathbb{C}} \cdot \left(\frac{\dot{\mathbf{Q}}\_2}{\dot{\mathbf{Q}}\_1}\right) \cdot \left(\frac{\mathbf{n}\_2}{\mathbf{n}\_1}\right) \tag{2}$$

Energy Efficient Control of Fans in Ventilation Systems 139

(6)

2

max 2

<sup>2</sup> p max

max max max p max

The total efficiency of the fan must be known to compute the total fan power and energy

This means that if the flow obstacles in the ventilation system are kept unchanged, the fan efficiency is constant, even if the fan speed is altered. Note that since the mechanical losses are directly proportional to the fan speed, the total efficiency of the fan is not constant.

Below, the terms fan efficiency and total fan efficiency are addressed. For a VAV system in which the air flow is controlled by a fan only (a single zone system or a DDCV system), the fan efficiency is approximately constant. In more complex systems, control dampers and VAV boxes continuously change the flow resistance and hence the system pressure (or working) characteristics. Then the fan efficiency is a variable which depends on both the

Fan efficiency can be modelled in a similar manner as the pressure drop shown earlier, using a second order polynomial to fit two arbitrary chosen data points from the fan characteristics; η1 = f(n1, Q1) and η2 = f(n1, Q2). The resulting expression for the fan efficiency

( ) ( )

The total efficiency *�t* at any speed *n* can be related to a reference mechanical efficiency

η ⋅η

mech,0 mech,0

Since fans are installed and connected to the air handling unit or ducts in different manners,

Furthermore, to simulate fan acceleration, a rate limiter has been added to the relative speed input (i.e. input 2). The fan drive speed input is in itself equal to the controller output (or the frequency inverter output), and must be limited. Typical acceleration times for common

(t) (t)

entrance and discharge losses are normally not included in the fan efficiency.

η =

f mech,0 t 2

η + −η ⋅

<sup>n</sup> (1 ) n(t)

12 21 12 21 2 f1 1 12 1 2 12 1 2 Q Q Q(t) Q Q Q(t) (t) <sup>n</sup> <sup>n</sup> QQ Q Q QQ Q Q n(t) n(t) η ⋅ −η ⋅ η ⋅ −η ⋅ η = ⋅⋅ − ⋅ ⋅ ⋅⋅ − ⋅⋅ −

<sup>2</sup> 2 2

(7)

0

(8)

p n Q Q

= − <sup>Δ</sup> <sup>−</sup>

Qmax, Qpmax and nmax can be found from fan product catalogues.

It is based on the following assumption:

flow rate and the fan speed.

�mech,0 at a reference speed n0 as follows (Eck, 1973):

HVAC fans are in the range of 5 - 20 sec (Daly, 1988).

then becomes:

usage. In this section, a simplified model of fan efficiency is presented.

• Fan efficiency scale to the system pressure (or working) characteristic.

n(t) Q(t) Q p(t) n(t) <sup>n</sup>

− ⋅ <sup>Δ</sup>

This relation is developed from the general polynomial model presented by (Lorenzetti, 1993). The factors KA, KB and KC can be found by specifying certain boundary conditions of the fan characteristics. If assuming that the maximum pressure difference Δpmax is present at an air flow rate of Qpmax, and that the maximum air flow rate Qmax is found at the minimum pressure difference (that is a pressure difference of zero), the boundary conditions of the characteristic are:

Δp2 =Δpmax for Q2 = Qpmax and n2 = nmax Δp2 = 0 for Q2 = Qmax and n2 = nmax

In addition, the following constraint must be fulfilled:

$$\frac{\partial \left(\Delta \mathbf{p}\_2\right)}{\partial \dot{\mathbf{Q}}\_2}\Big|\_{\mathbf{n}\_2 \text{-const}} = 0 \quad \text{for} \qquad \mathbf{Q}\_2 \equiv \mathbf{Q}\_{\text{pmax}} \qquad \qquad \text{and} \qquad \mathbf{n}\_2 \equiv \mathbf{n}\_{\text{max}}.$$

Solving eq. NN for the factors KA, KB and KC gives:

$$\mathbf{K}\_{\lambda} = \frac{\Delta \mathbf{p}\_{\text{max}}}{\Delta \mathbf{p}\_{1}} \cdot \left(\frac{\mathbf{n}\_{1}}{\mathbf{n}\_{\text{max}}}\right)^{2} \cdot \left(1 - \frac{\dot{\mathbf{Q}}\_{\text{p}\,\text{max}}^{2}}{\left(\dot{\mathbf{Q}}\_{\text{max}} - \dot{\mathbf{Q}}\_{\text{p}\,\text{max}}\right)^{2}}\right) \tag{3}$$

$$\mathbf{K}\_{\rm B} = -\frac{\Delta \mathbf{p}\_{\rm max}}{\Delta \mathbf{p}\_1} \cdot \left(\frac{\dot{\mathbf{Q}}\_1^{\prime 2}}{\left(\dot{\mathbf{Q}}\_{\rm max} - \dot{\mathbf{Q}}\_{p\rm max}\right)^2}\right) \tag{4}$$

$$\mathbf{K}\_{\text{C}} = \frac{\Delta \mathbf{p}\_{\text{max}}}{\Delta \mathbf{p}\_{1}} \cdot \frac{\mathbf{n}\_{1}}{\mathbf{n}\_{\text{max}}} \cdot \frac{\mathbf{2} \cdot \dot{\mathbf{Q}}\_{1} \cdot \dot{\mathbf{Q}}\_{\text{p}\_{\text{max}}}}{\left(\dot{\mathbf{Q}}\_{\text{max}} - \dot{\mathbf{Q}}\_{\text{p}\_{\text{max}}}\right)^{2}} \tag{5}$$

where for instance Δp1, Q1 and n1 refer to the point at which Δpmax, Qpmax and nmax occur. Hence, the governing (ideal) fan model can be expressed by:

Energy Efficient Control of Fans in Ventilation Systems 139

$$\frac{\Delta\mathbf{p}(\mathbf{t})}{\Delta\mathbf{p}\_{\text{max}}} = \left(\frac{\mathbf{n}(\mathbf{t})}{\mathbf{n}\_{\text{max}}}\right)^{2} - \left(\frac{\dot{\mathbf{Q}}(\mathbf{t}) - \dot{\mathbf{Q}}\_{\text{pmax}} \cdot \frac{\mathbf{n}(\mathbf{t})}{\mathbf{n}\_{\text{max}}}}{\dot{\mathbf{Q}}\_{\text{max}} - \dot{\mathbf{Q}}\_{\text{pmax}}}\right)^{2} \tag{6}$$

Qmax, Qpmax and nmax can be found from fan product catalogues.

The total efficiency of the fan must be known to compute the total fan power and energy usage. In this section, a simplified model of fan efficiency is presented.

It is based on the following assumption:

138 Energy Efficiency – The Innovative Ways for Smart Energy, the Future Towards Modern Utilities

which goes into heating of ventilated air.

In addition, the following constraint must be fulfilled:

2 2

Solving eq. NN for the factors KA, KB and KC gives:

Hence, the governing (ideal) fan model can be expressed by:

n const

<sup>p</sup> <sup>0</sup> Q <sup>=</sup>

( )

2

follows:

characteristic are:

The model presented below refers to a fan which has no mechanical losses, which applies to incompressible flow and on which the mathematical description is purely based on the fan laws. Losses, in terms of fan efficiency, is added to the model later, thus enabling computation of the required fan power and energy usage and also the fraction of fan power

For simulation of flow distribution throughout the ventilation system, a function which expresses the relationship between pressure difference, air flow rate and fan speed is required. This function can be derived, using a second order parabolic polynomial, as

> 1 1 1 1 1 1 1 pn Q n Q Qn KKK p n Q n Q Q n Δ = = = ⋅ +⋅ +⋅ ⋅ <sup>Δ</sup>

This relation is developed from the general polynomial model presented by (Lorenzetti, 1993). The factors KA, KB and KC can be found by specifying certain boundary conditions of the fan characteristics. If assuming that the maximum pressure difference Δpmax is present at an air flow rate of Qpmax, and that the maximum air flow rate Qmax is found at the minimum pressure difference (that is a pressure difference of zero), the boundary conditions of the

Δp2 =Δpmax for Q2 = Qpmax and n2 = nmax

Δp2 = 0 for Q2 = Qmax and n2 = nmax

∂ Δ <sup>=</sup> <sup>∂</sup> for Q2 = Qpmax and n2 = nmax

max p max 1 A 2 1 max max p max

p n Q Q <sup>Δ</sup> = ⋅ ⋅− <sup>Δ</sup> <sup>−</sup>

max 1 B 2 <sup>1</sup> max p max

p Q Q <sup>Δ</sup> =− ⋅ <sup>Δ</sup> <sup>−</sup>

p n Q Q <sup>Δ</sup> ⋅ ⋅ = ⋅⋅ <sup>Δ</sup> <sup>−</sup>

where for instance Δp1, Q1 and n1 refer to the point at which Δpmax, Qpmax and nmax occur.

( ) max 1 p max <sup>1</sup> C 2 1 max max p max

<sup>p</sup> <sup>n</sup> <sup>Q</sup> K 1

<sup>p</sup> <sup>Q</sup> <sup>K</sup>

<sup>p</sup> <sup>n</sup> 2Q Q <sup>K</sup>

( )

(3)

(4)

(5)

2 2

( )

2

AB C

(2)

2 2 2 2 22 2 2 2 22

• Fan efficiency scale to the system pressure (or working) characteristic.

This means that if the flow obstacles in the ventilation system are kept unchanged, the fan efficiency is constant, even if the fan speed is altered. Note that since the mechanical losses are directly proportional to the fan speed, the total efficiency of the fan is not constant.

Below, the terms fan efficiency and total fan efficiency are addressed. For a VAV system in which the air flow is controlled by a fan only (a single zone system or a DDCV system), the fan efficiency is approximately constant. In more complex systems, control dampers and VAV boxes continuously change the flow resistance and hence the system pressure (or working) characteristics. Then the fan efficiency is a variable which depends on both the flow rate and the fan speed.

Fan efficiency can be modelled in a similar manner as the pressure drop shown earlier, using a second order polynomial to fit two arbitrary chosen data points from the fan characteristics; η1 = f(n1, Q1) and η2 = f(n1, Q2). The resulting expression for the fan efficiency then becomes:

$$\boldsymbol{\eta}\_{t}(\mathbf{t}) = \frac{\boldsymbol{\eta}\_{1} \cdot \dot{\mathbf{Q}}\_{2}^{2} - \boldsymbol{\eta}\_{2} \cdot \dot{\mathbf{Q}}\_{1}^{2}}{\dot{\mathbf{Q}}\_{1} \cdot \dot{\mathbf{Q}}\_{2} \cdot \left(\dot{\mathbf{Q}}\_{1} - \dot{\mathbf{Q}}\_{2}\right)} \cdot \mathbf{n}\_{1} \cdot \frac{\dot{\mathbf{Q}}(\mathbf{t})}{\mathbf{n}(\mathbf{t})} - \frac{\boldsymbol{\eta}\_{1} \cdot \dot{\mathbf{Q}}\_{2} - \boldsymbol{\eta}\_{2} \cdot \dot{\mathbf{Q}}\_{1}}{\dot{\mathbf{Q}}\_{1} \cdot \dot{\mathbf{Q}}\_{2} \cdot \left(\dot{\mathbf{Q}}\_{1} - \dot{\mathbf{Q}}\_{2}\right)} \cdot \mathbf{n}\_{1}^{2} \cdot \left(\frac{\dot{\mathbf{Q}}(\mathbf{t})}{\mathbf{n}(\mathbf{t})}\right)^{2} \tag{7}$$

The total efficiency *�t* at any speed *n* can be related to a reference mechanical efficiency �mech,0 at a reference speed n0 as follows (Eck, 1973):

$$\eta\_{\rm t}(\mathbf{t}) = \frac{\eta\_{\rm t}(\mathbf{t}) \cdot \eta\_{\rm mech, 0}}{\eta\_{\rm mech, 0} + (1 - \eta\_{\rm mech, 0}) \cdot \left(\frac{\mathbf{n}\_{\rm o}}{\mathbf{n}(\mathbf{t})}\right)^2} \tag{8}$$

Since fans are installed and connected to the air handling unit or ducts in different manners, entrance and discharge losses are normally not included in the fan efficiency.

Furthermore, to simulate fan acceleration, a rate limiter has been added to the relative speed input (i.e. input 2). The fan drive speed input is in itself equal to the controller output (or the frequency inverter output), and must be limited. Typical acceleration times for common HVAC fans are in the range of 5 - 20 sec (Daly, 1988).

#### **3.2. Fan model validation**

Most of the component models used in the study have been validated through comparison with either measurements or product data, and show good agreement with real life equipment. See for instance (Sørensen, 2006, 2008, 2010) for a complete overview.

Energy Efficient Control of Fans in Ventilation Systems 141

The study addressed a CO2 controlled VAV system serving four similar classrooms in a

**Figure 4.** The investigated scenario; four classrooms in a school. Two rooms are facing west and two

The dynamic simulation system (Fig. 5) was built of four main subsystems:

The tool used for modeling and simulation was Matlab Simulink, developed by Mathworks. Matlab Simulink enables a visual programming technique, and is well suited for dynamic (time dependent) modeling. The program facilitates a modular approach, giving the user

The flow/pressure supply air subsystem is shown by Fig. 6. A steady state approach was chosen for the flow/pressure subsystem because changes to the parameters will have almost immediate effect on other connected subsystems. While for instance the thermal systems use considerable time to stabilize its outputs after a change on the inputs, the flow/pressure system outputs will change without any delay caused by inertia. The only dynamic elements of the flow/pressure subsystems are pure time delays caused by transportation of air in the ducts, time dependent ramp functions to model opening/closing time of dampers and ramp

Each of the blocks of Fig. 6 represents a component model describing the air flow and pressure loss through that component. To calculate pressure loss of ducts, duct fittings, dampers and so on, flow (velocity) dependent functions of friction and single loss factors have been implemented in the various component models. Flow rates are fed forward through the systems (from main duct to terminals), while pressures are summarized backwards. The total pressure loss is compared to the set point of the fan controller, and based on this, fan speed is either increased or decreased. This creates a simulation system

**3.3. Simulation system** 

school (Fig. 4).

are facing east

possibility to re-use models in other simulations.

• a dynamical contaminant building system.

• a dynamical thermal air handling unit (AHU) system

• a steady state flow/pressure system • a dynamical thermal building system

functions modulating fan speed.

The non dynamical qualities of the pressure/flow fan model were examined by comparing the model output with data from fan product catalogues (fan characteristics) Such comparisons was made for two non ducted real fans. Both were backward inclined radial fans, but of different size and capacity. Fig. 2 and Fig. 3 show comparisons of the output from the model and data from the real fan characteristic.

**Figure 2.** Comparison of pressure and flow rate produced by model to real fan data (small fan).

**Figure 3.** Comparison of pressure and flow rate produced by model to real fan data (large fan).

## **3.3. Simulation system**

140 Energy Efficiency – The Innovative Ways for Smart Energy, the Future Towards Modern Utilities

from the model and data from the real fan characteristic.

equipment. See for instance (Sørensen, 2006, 2008, 2010) for a complete overview.

**Figure 2.** Comparison of pressure and flow rate produced by model to real fan data (small fan).

**Figure 3.** Comparison of pressure and flow rate produced by model to real fan data (large fan).

Most of the component models used in the study have been validated through comparison with either measurements or product data, and show good agreement with real life

The non dynamical qualities of the pressure/flow fan model were examined by comparing the model output with data from fan product catalogues (fan characteristics) Such comparisons was made for two non ducted real fans. Both were backward inclined radial fans, but of different size and capacity. Fig. 2 and Fig. 3 show comparisons of the output

**3.2. Fan model validation** 

The study addressed a CO2 controlled VAV system serving four similar classrooms in a school (Fig. 4).

**Figure 4.** The investigated scenario; four classrooms in a school. Two rooms are facing west and two are facing east

The tool used for modeling and simulation was Matlab Simulink, developed by Mathworks. Matlab Simulink enables a visual programming technique, and is well suited for dynamic (time dependent) modeling. The program facilitates a modular approach, giving the user possibility to re-use models in other simulations.

The dynamic simulation system (Fig. 5) was built of four main subsystems:


The flow/pressure supply air subsystem is shown by Fig. 6. A steady state approach was chosen for the flow/pressure subsystem because changes to the parameters will have almost immediate effect on other connected subsystems. While for instance the thermal systems use considerable time to stabilize its outputs after a change on the inputs, the flow/pressure system outputs will change without any delay caused by inertia. The only dynamic elements of the flow/pressure subsystems are pure time delays caused by transportation of air in the ducts, time dependent ramp functions to model opening/closing time of dampers and ramp functions modulating fan speed.

Each of the blocks of Fig. 6 represents a component model describing the air flow and pressure loss through that component. To calculate pressure loss of ducts, duct fittings, dampers and so on, flow (velocity) dependent functions of friction and single loss factors have been implemented in the various component models. Flow rates are fed forward through the systems (from main duct to terminals), while pressures are summarized backwards. The total pressure loss is compared to the set point of the fan controller, and based on this, fan speed is either increased or decreased. This creates a simulation system

which has to be solved by iteration for each time step. The computed airflow rates from the pressure/flow system were fed into the other systems, and the room CO2 and temperature responses were computed.

Energy Efficient Control of Fans in Ventilation Systems 143

**Figure 6.** The pressure/flow supply system model (steady state). Each block represents a component

model.

**Figure 5.** Main simulation system.

The thermal subsystem (AHU – air handling unit, ducts and rooms) was implemented to be able to calculate energy consumption from the dynamical system states. The AHU simulation subsystem, shown in Fig. 7, contains fan, water based heating coil, cooling coil and rotary heat recovery unit (HRU). It also contains thermal models for pipes, ducts, shunt, actuator and controls. Heating coil, het recovery unit and cooling coil are controlled by a sequential PID controller, which ensures that operation of these units is not overlapping. The sequence PID has three sets of controller parameters to ensure proper control of all the units.

The contaminant subsystem considers CO2 room responses from human presence. The model is a simple dynamic mass balance of CO2 in a room that accounts for infiltration/exfiltration, ventilation efficiency, and through a contaminant model of a rotary heat exchanger, also for leakage of exhaust air to the supply. Based on the supply air CO2 concentration and the chosen set point of the rooms, flow rates will by varied. For instance, if room concentration is too high in a room, i.e. above set point, flow rate to the room will be increased until the concentration falls below the set point again. If concentration continues to fall, flow rate will be decreased accordingly. At zero occupancy, flow rate will decrease to a minimum level. For more details, refer to Sørensen 2006, 2008, 2010.

responses were computed.

**Figure 5.** Main simulation system.

units.

which has to be solved by iteration for each time step. The computed airflow rates from the pressure/flow system were fed into the other systems, and the room CO2 and temperature

The thermal subsystem (AHU – air handling unit, ducts and rooms) was implemented to be able to calculate energy consumption from the dynamical system states. The AHU simulation subsystem, shown in Fig. 7, contains fan, water based heating coil, cooling coil and rotary heat recovery unit (HRU). It also contains thermal models for pipes, ducts, shunt, actuator and controls. Heating coil, het recovery unit and cooling coil are controlled by a sequential PID controller, which ensures that operation of these units is not overlapping. The sequence PID has three sets of controller parameters to ensure proper control of all the

The contaminant subsystem considers CO2 room responses from human presence. The model is a simple dynamic mass balance of CO2 in a room that accounts for infiltration/exfiltration, ventilation efficiency, and through a contaminant model of a rotary heat exchanger, also for leakage of exhaust air to the supply. Based on the supply air CO2 concentration and the chosen set point of the rooms, flow rates will by varied. For instance, if room concentration is too high in a room, i.e. above set point, flow rate to the room will be increased until the concentration falls below the set point again. If concentration continues to fall, flow rate will be decreased accordingly. At zero occupancy, flow rate will decrease to

a minimum level. For more details, refer to Sørensen 2006, 2008, 2010.

**Figure 6.** The pressure/flow supply system model (steady state). Each block represents a component model.

Energy Efficient Control of Fans in Ventilation Systems 145

The outdoor CO2 level was considered to be constant at 400 ppm. In all cases the occupant load varied as shown in Tab. 1. It was assumed that the time used by occupants to enter or

The building was considered to be multi storey, wherein the simulated rooms had only one exterior surface each. Moreover, terrain was assumed to be completely flat on the west side of the building. On the east side there was an obstruction of angle 20° in the two middle 45° view sectors (the 180° horizontal view from the windows was divided into four 45° sectors) (Sørensen, 2006). As shown in Fig. 2, classroom 1 and 2 were facing west and classroom 3 and 4 were facing east. There was no external shading. Windows were internally shaded (light curtains, 50% reflection) between hour 09.00 and 12.00 in classroom 2 and 4, and from 14.00 to 17.00 in classroom 1 and 3. Window U-value and solar factor were respectively 2.0 W/m2K and 0.7. Total window area of each room was 9 m2. The external wall had a U-value of 0.3 W/m2K and a time constant of 15 hours. Internal walls, floor and ceiling had U-values of 0.7 W/m2K and a time constant of 10 hours (light inner structure). Heat capacity of the interior was set to 10000 J/m2K. The shares of radiation onto the walls from persons, internal equipment and external radiation (both atmospheric and solar) were respectively 0.5, 0.5 and 0.8. Heat from lights was specified to 10 W/m2 and the lights were on between 07.00 and

> **Hour of day Room 1 Room 2 Room 3 Room 4** 07.00 0 0 0 0 08.00 25 0 25 15 10.00 0 0 0 0 10.30 25 25 30 30 12.00 0 0 0 5 13.00 15 25 25 25 15.00 8 3 5 25 17.00 0 0 0 0 18.00 0 0 0 0

Flow regulation was achieved through static pressure difference control of the fan and CO2 control of the room airflow via local dampers. To account for steady state offset and to avoid too aggressive control, a PI controller was used on the fan. Pure P control was used locally. Maximum set point for the fan pressure difference control was 450 Pa. At this point the fan provided the design flow rate (at which the system was balanced and all local dampers were fully opened). To reduce throttling, and to ensure sufficient minimum flow rates to all zones, minimum damper positions were set to 30% of maximum. The correction gain of the

leave the rooms was 5 seconds per occupant.

**Table 1.** Occupant load of selected four classrooms

**4. Control strategy** 

18.00 only.

**Figure 7.** Simulation model (block diagram) of the air handling unit model.
