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Model-Based Potential Analysis of Demand-Controlled Ventilation in Buildings
Proceedings of the 9th Vienna International Conference on Mathematical Proceedings ofModelling the 9th Vienna International Conference on Mathematical Proceedings ofModelling the 9th Vienna International Conference on Vienna, Austria, February Mathematical Modelling Vienna, Austria, February 21-23, 21-23, 2018 2018 Available online at www.sciencedirect.com Mathematical Modelling Vienna, Austria, February 21-23, 2018 Vienna, Austria, February 21-23, 2018
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IFAC PapersOnLine 51-2 (2018) 85–90 Model-Based Potential Analysis of Model-Based Potential Analysis of Model-Based Potential Analysis of Model-Based Potential Analysis of Demand-Controlled Ventilation in Demand-Controlled Ventilation in Demand-Controlled Ventilation in Demand-Controlled Ventilation in Buildings Buildings Buildings Buildings∗ ∗ ∗∗
K. K. Ben Ben Jemaa Jemaa ∗ P. P. Kotman Kotman ∗ K. K. Graichen Graichen ∗∗ K. Ben Jemaa ∗∗ P. Kotman ∗∗ K. Graichen ∗∗ K. Ben Jemaa P. Kotman K. Graichen ∗∗ ∗ ∗ Robert Bosch GmbH, Future Systems for Building Technology, Robert Bosch GmbH, Future Systems for Building Technology, ∗ Bosch GmbH,Germany Future Systems Building Technology, 71272 Renningen, (e-mail: {Karim.Benjemaa; ∗ Robert 71272 Renningen, (e-mail:for Robert GmbH,Germany Future Systems for{Karim.Benjemaa; Building Technology, 71272Bosch Renningen, Germany (e-mail: {Karim.Benjemaa; Philipp.Kotman}@bosch.de.com) Philipp.Kotman}@bosch.de.com) 71272 Renningen, Germany (e-mail: {Karim.Benjemaa; ∗∗ Philipp.Kotman}@bosch.de.com) ∗∗ Ulm University, Institute of Measurement, Control and Institute of Measurement, Control and Philipp.Kotman}@bosch.de.com) ∗∗ Ulm University, University, Institute Measurement, Control and Microtechnology, 89081 Ulm, Germany ∗∗ Ulm Microtechnology, 89081 of Ulm, Germany (e-mail: (e-mail: Ulm University, Institute of Measurement, Control and Microtechnology, 89081 Ulm, Germany (e-mail: [email protected]) [email protected]) Microtechnology, 89081 Ulm, Germany (e-mail: [email protected]) [email protected]) Abstract: This paper proposes a Abstract: This paper proposes a model-based model-based framework framework to to estimate estimate the the theoretical theoretical energy energy Abstract: This paper proposes a model-based framework to estimate the theoretical energy saving potential offered by CO -based demand-controlled ventilation systems in For 2 saving potential offered by CO2 -based demand-controlled ventilation systems in buildings. buildings. For Abstract: This paper proposes a model-based framework to estimate the theoretical energy -based demand-controlled ventilation systems in buildings. For saving potential offered by CO this purpose, the energy consumption of different heating air conditioning (HVAC) 2 this purpose, the energy consumption of different heating ventilation air conditioning (HVAC) -based demand-controlled ventilation systems in buildings. For saving potential offered by CO 2 this purpose, the energy consumption of different heating ventilation air conditioning (HVAC) system configurations is compared for different occupancy scenarios. Physics-based models are system configurations is compared for of different occupancy scenarios. Physics-based models are this purpose, the energy consumption different heating ventilation air conditioning (HVAC) system configurations is compared for different occupancy scenarios. Physics-based models are used to describe the environmental conditions in the building and to estimate the energy used toconfigurations describe the is environmental conditions in the building andPhysics-based to estimate the energy system compared for different occupancy scenarios. models are used to describe the environmental conditions in the building and to estimate the energy consumption of the HVAC system. In order to guarantee optimality, the HVAC system is consumption of the HVAC system. In order to inguarantee optimality, the HVACthe system is used to describe the environmental conditions the building and to estimate energy consumption of the HVAC system. In order to guarantee optimality, the consumption HVAC systemand is controlled by an optimal control approach aiming to minimize the energy controlled by an optimal control approach aiming to minimize the energy consumption and consumption of the HVAC system. In order to guarantee optimality, the HVAC system is controlled by an optimal control approach aiming to minimize the energy consumption and to satisfy the comfort requirements. to satisfy the comfort requirements. controlled by an optimal control approach aiming to minimize the energy consumption and to satisfy the comfort requirements. to satisfy the(International comfort requirements. © 2018, IFAC Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: CO CO2 -based demand controlled ventilation, HVAC systems, model based control, Keywords: 2 -based demand controlled ventilation, HVAC systems, model based control, HVAC systems, model based control, Keywords: CO2 -based optimal control, energy efficient buildings, user optimal control, energydemand efficientcontrolled buildings,ventilation, user comfort comfort HVAC systems, model based control, Keywords: CO2 -based optimal control, energydemand efficientcontrolled buildings,ventilation, user comfort optimal control, energy efficient buildings, user comfort 1. However, 1. INTRODUCTION INTRODUCTION However, little little information information is is available available on on the the performance performance 1. INTRODUCTION However, little information is available on the performance that can be achieved with different CO -based DCV 2 -based that can be achieved with different CO DCV syssys2 1. INTRODUCTION However, little information is available on-based the performance that can be achieved with different CO DCV system configurations. 2 tem configurations. that can be achieved with different CO -based DCV sys2 Heating, Heating, Ventilation Ventilation and and Air Air Conditioning Conditioning (HVAC) (HVAC) syssys- tem configurations. In this work, the energy saving potential of five different tem configurations. Heating, Ventilation and Air Conditioning (HVAC) systems to thermal comfort and air this work, the energy saving potential of five different tems are are used used to guarantee guarantee thermal comfort (HVAC) and good goodsysair In Heating, Ventilation and account Air Conditioning In this work, the energy saving potential of five two-zone different system configurations for tems arein used to guarantee thermal comfort andhalf good air ventilation quality buildings. They for more than of the ventilation system configurations for aa generic generic quality in buildings. They account for more than half of the In this system work, the energy saving potential of five two-zone different tems are used to guarantee thermal comfort andhalf good air ventilation system configurations for generic two-zone HVAC is investigated investigated based on asimulation simulation studies. quality in buildings. They account for more than of the energy consumption in buildings (L.P´ e rez-Lombard et al., HVAC system is based on studies. energy consumption in buildings (L.P´ e rez-Lombard et al., ventilation system configurations for a generic two-zone quality in buildings. They account for more thanoften half varies of the HVAC system is configurations investigated based on simulation studies. The considered feature different numbers energy consumption in buildings (L.P´ e rez-Lombard et al., 2009). One reason is that, although occupancy The considered configurations feature different numbers 2009). One reason is that, although occupancy often varies HVAC systemofis volume investigated based on simulation studies. energy consumption in buildings (L.P´ e rez-Lombard et al., The considered configurations feature different numbers and locations flow controllers and CO sensors. 2009). One reason is that, although occupancy often varies 2 strongly during typical office days, most systems and locations of volume flow controllers and CO2numbers sensors. strongly during typical office days,occupancy most HVAC HVAC systems The considered configurations feature different 2009). One reason is that, although often varies and locations ofoptimal volumecontrol flow controllers and CO2 to sensors. model-based framework aiming ministrongly duringat office air days, most HVAC systems A today operate a exchange rate A model-based framework aiming to minitoday operate attypical a constant constant exchange rate (Erickson (Erickson and locations ofoptimal volumecontrol flow controllers and CO sensors. strongly during typical office air days, most HVAC systems A model-based optimal control framework aiming minimize the energy energy consumption while satisfying the2 to comfort today operate at a constant air exchange rate (Erickson and Cerpa, 2010). As a consequence, overventilation durmize the consumption while satisfying the comfort and Cerpa, 2010). As a consequence, overventilation durA model-based optimal control framework aiming to minitoday operate at a constant air exchange rate (Erickson mize the energy consumption while satisfying the comfort requirements is proposed. In order to assess the highest and Cerpa, of 2010). As a consequence, overventilation dur- requirements ing low and during is proposed. In while order satisfying to assess the the comfort highest ing periods periods of low occupancy occupancy and underventilation underventilation during mize the energy consumption and Cerpa, 2010). As a consequence, overventilation durrequirements is proposed. In order to assess highest offered by perfect knowledge ing periods of low occupancy underventilation during potential periods of high high occupancy areand inevitable. While overvenovervenpotential offered by each each configuration, configuration, perfectthe knowledge periods of occupancy are inevitable. While requirements isand proposed. In order to assess the highest ing periods of to low occupancy and underventilation during potential offered by each configuration, perfect knowledge of the models of the disturbances is assumed. The periods of high occupancy are inevitable. While overventilation leads energy wastage, indoor comfort can be of the models and of theconfiguration, disturbancesperfect is assumed. The tilation leads tooccupancy energy wastage, indoor comfort can be potential offered by each knowledge periods of high are inevitable. While overvenof the models and of the disturbances is assumed. The configurations are are then then compared compared based based on on their their energy energy tilation leads to energy wastage, indoor comfort can be significantly reduced in case of underventilation. configurations significantly reduced in case of underventilation. of the models and of the disturbances is assumed. The tilation leads to energy wastage, indoor comfort can be configurations are then compared based on their energy saving potentials. significantly reduced in case of underventilation. saving potentials. configurations are then compared based on their energy A demand-controlled ventilation (DCV) system attempts significantly reduced in case of underventilation. A demand-controlled ventilation (DCV) system attempts saving potentials. This paper is saving potentials. A demand-controlled attempts to achieve air (IAQ) reduced energy paper is structured structured as as follows: follows: In In Section Section 2, 2, the the to achieve high high indoor indoorventilation air quality quality (DCV) (IAQ) at atsystem reduced energy This A demand-controlled ventilation (DCV) system attempts This paper is structured as follows: In Section 2, venthe generic two-zone HVAC system and the considered to achieve high indoor air quality (IAQ) at reduced energy consumption by modulating the air exchange rate based on generic two-zone HVAC system and the considered venconsumption byindoor modulating the air exchange rate based on This paper is configurations structured as are follows: In considered Section 2, venthe to achieve high air quality (IAQ) at reduced energy generic two-zone HVAC system and the tilation system presented. In Section 3, consumption by modulating the air exchange rate based on a measured measured parameter parameter (Emmerich (Emmerich et et al., al., 2001). 2001). Over Over the the generic tilation system configurations areand presented. In Section 3, a two-zone HVAC system the considered venconsumption by modulating the air exchange rate based on tilation system configurations are presented. In Section 3, physics-based models of the building and of the HVAC a measured parameter (Emmerich et al., 2001). Over the last years, CO has been proposed as an acknowledged criphysics-based models of the building and of the HVAC 2 has been proposed as an acknowledged crilast years, CO tilation system configurations are presented. In Section 3, 2 a measured parameter (Emmerich et al., 2001). Over the physics-based models of the building and of the HVAC system components are described. Section 4 presents the last years, CO2 indoor has been proposed as an acknowledged cri- system terion to assess air quality and to estimate the numcomponents are described. Section 4 presents the terion to assess indoor air quality and to estimate the numphysics-based models of the building and of the HVAC last years, CO2 indoor has(Persily, been as an acknowledged cri- mathematical system components are described. Section HVAC 4 presents the formulation of control terion assess airproposed quality to estimate the number occupants 1997). A demandmathematical formulation of the the optimal optimal HVAC control 2 -based ber of of to occupants (Persily, 1997).and A CO CO demandsystem components are described. Section 4presented presents the 2 -based the terion to assess indoor air quality and to estimate nummathematical formulation of the optimal HVAC control problem. In Section 5, simulation results are and ber of occupants (Persily, 1997). A CO -based demandcontrolled ventilation consists therefore in adjusting the 2in adjusting the problem. In Section 5, simulation results areHVAC presented and controlled ventilation consists therefore mathematical formulation of the optimal control ber of occupants (Persily, 1997). A CO -based demand2 problem. In Section 5, simulation results are presented and Section 66 concludes the paper. controlled ventilation consists in adjusting the discussed, ventilation rate based on discussed,Inbefore before Section concludes theare paper. ventilation rate over over time time basedtherefore on CO CO2 measurements. measurements. Section 5, simulation results presented and controlled consists in adjusting the problem. discussed, before Section 6 concludes the paper. ventilation ventilation rate over time basedtherefore on CO22 measurements. discussed, before Section 6 concludes the paper. Equipping the duct system with additional volume flow ventilation rate over time based on CO measurements. 2 Equipping the duct system with additional volume flow 2. Equipping the duct with additional volume flow controllers and CO sensors is the first step towards 2system 2. THE THE GENERIC GENERIC TWO-ZONE TWO-ZONE HVAC HVAC SYSTEM SYSTEM controllers and CO sensors is the first step towards 2 Equipping the duct system with additional volume flow 2. THE GENERIC TWO-ZONE HVAC SYSTEM controllers and CO sensors is the first step towards CO -based DCV. Thereby, the question arises about the 2 2 CO Thereby, the question arises about the 2. THE GENERIC TWO-ZONE HVAC SYSTEM 2 -based DCV. controllers and CO sensors is the first step towards 2 location CO2 -basednumber DCV. Thereby, the question arisesand about the In this work, aa generic two-zone HVAC system is adequate and of actuators sensors In this work, generic two-zone HVAC system is used used as as a a adequate number and location of actuators and sensors CO -based DCV. Thereby, the question arises about the 2 this work, a generic two-zonethe HVAC system is used as a adequate number and location of actuators and sensors In prototype system to investigate potential of CO leading to a profitable configuration of the ventilation 2 -based prototype system to investigate the potential of CO leading to a profitable configuration of the ventilation -based 2 In this work, a generic two-zone HVAC system is used as a adequate number and location of actuators and sensors investigate the potential of CO leading to a profitable configuration the ventilation system. Available literature on controlled systems DCV, Fig. After discussing its principle 2 -based system. Available literature on demand demand of controlled systems prototype DCV, see see system Fig. 1. 1.to After discussing its working working principle prototype system to investigate the potential of CO leading to a profitable configuration of the ventilation -based 2 system. Available on demandof DCV, see 2.1, Fig. different 1. After configurations discussing its for working principle is focussed on different control the is mainly mainly focussedliterature on the the evaluation evaluation ofcontrolled different systems control in in Section Section 2.1, different configurations the ventilation ventilation system. Available literature on demand controlled systems DCV, see Fig. 1. After discussing its for working principle is mainly focussed on the evaluation of different control in Section 2.1, different configurations for the ventilation strategies for a given ventilation system configuration. system are presented in Section 2.2. strategies for a given ventilation system configuration. system are 2.1, presented in Section 2.2. is mainly focussed on the evaluation of different control in Section different configurations for the ventilation strategies for a given ventilation system configuration. system are presented in Section 2.2. strategies for a given ventilation system configuration. system are presented in Section 2.2.
Copyright © 2018 1 Copyright 2018 IFAC IFAC 1 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Copyright ©under 2018 responsibility IFAC 1 Control. Peer review of International Federation of Automatic Copyright © 2018 IFAC 1 10.1016/j.ifacol.2018.03.015
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2.1 System Description
Table 1. Summary of configurations Configuration (0,0) (1,1) (1,2) (2,1) (2,2)
The working principle of the HVAC system depicted in Fig. 1 is as follows. The supply duct is equipped with a supply fan (SF) allowing the intake of fresh air from the ambience. The incoming fresh air enters a heat exchanger (HX) with the temperature TA , exits it with the temperature TR , is induced to a heating/cooling coil (HCC) to reach the supply temperature TS and finally distributed to the zones Z1 and Z2 . The Radiators R1 and R2 allow to heat up the air in zones Z1 and Z2 , respectively. The exhaust air extracted from the zones through the exhaust fan (EF) enters the heat exchanger with the temperature TE and transfers a part of its heat to the fresh air. EF HX
R1 HCC TA XA
TR Q˙ HC
2
1
2
The main goal of demand-based ventilation is to achieve some predefinded comfort requirements at minimum costs. The higher investment costs related to DCV are then recovered through lower operating costs. In order to estimate the profitability of DCV, the related energy saving potential ought to be examined. In this work, the theoretical energy saving potential offered by four different configurations of CO2 -based DCV system are investigated for different occupancy scenarios. The main goal is to assess the highest potential of each configuration when the comfort requirements are fully achieved.
Zone 2 TZ2 X Z2
3. MODELING In this section, a zone model describing the temperature and the CO2 concentration in a building’s zone is derived in Section 3.1, followed by simplified models for the HVAC system components in Section 3.2.
R2
SF TS
1
Measured quantities TZ1 ,TZ2 TZ1 ,TZ2 ,XE TZ1 ,TZ2 ,XZ1 ,XZ2 TZ1 ,TZ2 ,XE TZ1 ,TZ2 ,XZ1 ,XZ2
2.3 Problem Formulation
TE XE Zone 1 TZ 1 XZ1
Control inputs Q˙ R1 ,Q˙ R2 ,Q˙ HC Q˙ R1 ,Q˙ R2 ,Q˙ HC ,m ˙ Q˙ R1 ,Q˙ R2 ,Q˙ HC ,m ˙ ˙ Z2 ˙ Z1 ,m Q˙ R1 ,Q˙ R2 ,Q˙ HC ,m Q˙ R ,Q˙ R ,Q˙ HC ,m ˙ Z ,m ˙Z
m ˙
3.1 Zone Model
Fig. 1. Illustration of the generic two-zone HVAC system.
A zone denotes a building’s area that can be conditioned separately through its own controlling devices. The zone model proposed in this work to describe the internal conditions is composed of two parts: the thermal model and the CO2 model.
2.2 System Configurations In this work, five different configurations for the ventilation system of the two-zone HVAC system are considered, see Fig 2. Each configuration is defined by the number of CO2 sensors and air flow controllers. As mathematical notation, an ordered pair (na , ns ) is allocated to each configuration, where na is the number of actuators (volume flow controllers) and ns is the number of sensors (CO2 sensors).
Thermal Model: A thermodynamic model describing the air temperature in the zone is derived on the basis of the mass and energy balances as well as the ideal gas law. The mass balance for the air in the zone reads as dmZ =m ˙ in (1) ˙ out Z −m Z , dt where mZ is the mass of the air in the zone Z and m ˙ in Z out and m ˙ Z are the incoming and outgoing air mass flow, respectively. The first law of thermodynamics is given by (Kreider and Rabl, 1994) dUZ = H˙ Zin − H˙ Zout + Q˙ R + Q˙ O + Q˙ S + Q˙ W dt in out =m ˙ in ˙ out + Q˙ R + Q˙ O + Q˙ S + Q˙ W , Z cp TZ − m Z cp TZ (2) where UZ is the internal energy stored in the zone, H˙ Zin and H˙ Zout are the enthalpy flows associated with the mass ˙ flows m ˙ in ˙ out Z and m Z , respectively, QR is the heat transferred from the radiator to the zone, Q˙ O is the occupancy heat, Q˙ S is the radiation heat stemming from the sun and Q˙ W is the heat exchanged with the walls. The temperature TZout of the outgoing mass flow is equal to the temperature TZ inside the zone. The isobaric heat capacity cp of the air is assumed to be constant. Furthermore, the time derivative of the internal energy UZ stored in the zone is
• Configuration (0,0): reference configuration. The ventilation rate is constant. • Configuration (1,1): a volume flow controller adjusts the overall fresh air supply (m) ˙ of the ventilation system. The distribution of the fresh air between the two zones is static. A CO2 sensor measures the CO2 concentration XE in the exhaust duct. • Configuration (2,1): two volume flow controllers adjust the fresh air supply for each zone (m ˙ Z1 and m ˙ Z2 ) individually. A CO2 sensor measures the CO2 concentration XE in the exhaust duct. • Configuration (1,2): a volume flow controller adjusts the overall fresh air supply of the ventilation system. The distribution of the fresh air between the two zones is static. Two CO2 sensors measure the CO2 concentration in each zone. • Configuration (2,2): two volume flow controllers adjust the fresh air supply for each zone individually. Two CO2 sensors measure the CO2 concentration in each zone. 2
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CO2 sensor
Configuration (0,0)
Configuration (1,1)
Configuration (2,1)
Configuration (1,2)
volume flow controller
Configuration (2,2)
Fig. 2. Ventilation sytem configurations. d(uZ mZ ) dUZ = dt dt
TA − TW , Q˙ A = (10) RE with the ambient temperature TA and the resistance RE for the heat transfer to the exterior. Taking this into consideration, the dynamics of the air temperature in the zone finally take the form TW − TZ 1 dTZ m ˙ Z cp TZin − TZ + = dt CZ RI (11) ˙ ˙ ˙ + QR + QO + QS ,
(3) duZ , − + mZ = dt where uZ is the specific internal energy of the air in the zone. For ideal gases the specific internal energy is only a function of the temperature (Bejan, 2016), i.e. (m ˙ in Z
m ˙ out Z )uZ
uZ = cv TZ , with the isochoric heat capacity cv of the air in zone. After some algebraic reformulation combining and (4), the ordinary differential equation (ODE) for temperature TZ is obtained, i.e. 1 in dTZ = m ˙ Z (cp TZin − cv TZ ) − m ˙ out Z RTZ dt mZ cv + Q˙ R + Q˙ O + Q˙ S + Q˙ W ,
(4) the (3) the
with
1 dTW = dt CW
TA − TW T Z − TW + RI RE
.
(12)
CO2 Model: A mathematical model describing the CO2 concentration in the zone is derived based on the mass balance for CO2 . The CO2 concentration XZ in the zone Z is given by XZ = m∗Z /mZ , (13) ∗ where mZ and mZ are the mass of CO2 and the total mass of the air in the zone, respectively. The mass balance of CO2 in the zone reads as dm∗Z =m ˙ ∗Z,in − m (14) ˙ ∗Z,out . dt ∗ ∗ The quantities m ˙ Z,in and m ˙ Z,out are the incoming and outgoing mass flow of CO2 , respectively. The incoming flow of CO2 in the zone depends on the incoming air flow and its CO2 concentration as well as on the amount of CO2 exhaled by the occupants, i.e. (15) ˙ O + XA m ˙ in m ˙ ∗Z,in = m Z, where m ˙ O is the CO2 mass flow exhaled by the occupants in the zone and XA is the CO2 concentration of the incoming air mass flow. It is assumed that XA is equal to the outdoor CO2 concentration and has a constant value. The CO2 generation rate m ˙ O is modeled as a linear function of the number of occupants, i.e. (16) m ˙ O = gCO2 \occ · Nocc , where the CO2 generation rate per occupant gCO2 \occ is assumed to be constant. The outgoing mass flow of CO2 is given by m ˙ ∗Z,out = XZ m ˙ out (17) Z . Deriving the CO2 concentration over the time leads to 1 dXZ = m ˙ O−m ˙ in (18) Z (XZ − XA ) . dt mZ
(5)
with R the universal gas constant. Assuming that the incoming and the outgoing mass flows have the same ˙ in ˙ out the temperature absolute value, i.e. m ˙Z = m Z = m Z ODE simplifies to 1 dTZ = m ˙ Z cp (TZin − TZ ) + Q˙ R + Q˙ O + Q˙ S + Q˙ W , dt CZ (6) where CZ = mZ cv is the heat capacity of the zone. The internal heat gains Q˙ O are modeled as a linear function of the number of occupants Nocc , i.e. (7) Q˙ O = gocc · Nocc , where the heat generation per occupant gocc is assumed to be constant. A differential equation for the wall temperature is introduced in order to quantify Q˙ W . Since the mass of the wall does not change with time, the derivation of the defining ODE of the wall temperature TW is based on the energy balance only and directly leads to 1 ˙ dTW = QZ + Q˙ A . (8) dt CW The quantities Q˙ Z and Q˙ A are the heat transferred to the zone and to the ambience, respectively, and the parameter CW is the heat capacity of the wall. The heat Q˙ W = −Q˙ Z flowing from the wall to the air in the zone is defined by the simple conduction equation TW − TZ , Q˙ W = −Q˙ Z = (9) RI where RI is the resistance for the heat transfer to the interior. Similarly, the heat flow between the wall and the ambience is described by
3.2 HVAC System Components
The HVAC system contains several components, see Fig. 1, that are individually modeled in the following lines. 3
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Heat Exchanger Model The counter-flow heat exchanger (HX) is modeled with the effectiveness-NTU method, see Incropera et al. (2005). Only heat transfer and no mass transfer takes place at the heat exchanger, i.e. the fresh and exhaust air flows are not mixed. According to the effectiveness-NTU method, the effectiveness of a counterflow heat exchanger is given by NTU , (19) ε= 1 + NTU where the number of transfer N T U is expressed by UA , NTU = (20) mc ˙ p with the overall heat transfer coefficient U A of the heat exchanger. The effectiveness of the heat exchanger can finally be described as a function of the mass flow ε = ε(m) ˙ UA (21) · = mc ˙ p + UA
curve of the ventilation system, which is often described by the parabolic function (Ihle, 1997) ∆p = kvent V˙ 2 , (29) where kvent is the characteristic constant of the duct system. Thus, the electrical fan power can be described as a cubic function of the volume flow V˙ , i.e. kvent V˙ 3 Pfan,el = · (30) ηfan
Heating/Cooling Coil Model The power Q˙ HC used by the heating/cooling coil (HCC) to enduce a temperature variation ∆T in the fresh air is expressed by ˙ p ∆T . (22) Q˙ HC = mc
In order to identify the potential offered by each ventilation system configuration, an optimal control approach is followed. The optimal control problem consists in fulfilling the comfort requirements in the building with minimal energy consumption. In this work, two parameters define the comfort range: the indoor zone temperature and the indoor CO2 level. Concerning the thermal comfort, the main goal is to ascertain that the temperature of the zone remains within certain bounds. To ensure a good indoor air quality, the CO2 concentration in the zone has to be kept under some upper bound. Physical limitations stemming from the limited powers of the HVAC system components have to be respected.
Radiator Model The radiators are supplied from a boiler with hot water. The boiler’s energy consumption is assumed to be equal to its gas consumption Pb,fuel , calculated as Q˙ R1 + Q˙ R2 Pb,fuel = · (31) ηb The efficiency ηb of the boiler is assumed to be constant. 4. OPTIMAL HVAC CONTROL PROBLEM
In this work, the heating/cooling coil is assumed to be connected to a reversible heat pump with a constant performance coefficient COP . Thus, the electrical power consumed by the heat pump to adjust the temperature of the fresh air is given by | Q˙ HC | · (23) Php,el = COP Duct Model The temperature of the air flow in the exhaust duct is the weighted average of the zone temperatures, where the weighting factors are the corresponding outgoing air mass flows. Mathematically, the temperature of the exhaust air is given by m ˙ Z1 TZ1 + m ˙ Z2 TZ 2 TE = · (24) m ˙ Z1 + m ˙ Z2 Similarly, the CO2 concentration in the exhaust duct reads as m ˙ Z1 X Z1 + m ˙ Z2 X Z2 XE = · (25) m ˙ Z1 + m ˙ Z2 The temperature of the fresh air flow leaving the heat exchanger is expressed by ˙ (26) TR = ε(m)(T E − TA ) + T A , ˙ Z2 . Finally, the temperature of the where m ˙ = m ˙ Z1 + m supply air is given by Q˙ HC TS = TR + · (27) mc ˙ p
In mathematical terms, the optimal HVAC control problem can be written as a constrained dynamic optimization problem of the form tf Ptot (τ )dτ (32a) min u(t)
ts
s.t. x(0) = x0 (32b) x˙ = f (x, u, d, t) (32c) x∈X (32d) u∈U (32e) where Ptot is the total power consumption of the HVAC system. The state constraints (32d) stem from the comfort requirements and the input constraints (32e) are given by the physical limitations of the HVAC system components. The resulting constrained dynamic optimization problem is solved numerically. To this purpose, a direct approach via partial discretization of the inputs is chosen (Bryson, 1975): the time intervall [ts ,tf ] is discretized into N subintervals and the inputs are parametrized through constant values on these subintervals. The continuous states are evaluated by numerical integration. The resulting discrete static optimization problem is solved using the nonlinear programming solver fmincon of the Matlab Optimization Toolbox.
Fan Model The electrical fan power is calculated as the product of the volume flow V˙ and the pressure difference ∆p (Ihle, 1997), i.e. ∆pV˙ , (28) Pfan,el = ηfan where the overall efficiency ηfan of the fan is assumed to be constant. The relationship between the pressure drop and the volume flow is given by the characteristic pressure
Depending on the configuration of the ventilation system, the formulation of the dynamic optimization problem is slightly changed to suit the available control inputs and measurements. 4
Proceedings of the 9th MATHMOD Vienna, Austria, February 21-23, 2018
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5.1 Test scenario and data generation
Cost Function The cost function is a purely energetic function and describes the energy consumption of the HVAC components.
In this work, an office building is simulated in a cold climate. The weather datasets, which include the ambient temperature and the solar heat gains, were obtained from the Meteonorm 1 data available within TRNSYS 2 . The occupancy profile for each zone corresponds to a typical working day in offices and meets the allowed occupant density in office buildings in Germany.
In case of a static ventilation (configuration (0,0)), the energy consumption through the fan is constant and the cost function reads as Ptot = Pb,fuel + Php,el .
89
(33)
In case of a demand-based ventilation, the energy consumption through the fans can be optimized. Therefore, the cost function is given by (34)
In order to investigate the impact of an asymmetric occupancy of the zones on demand-based ventilation, following occupancy scenarios are considered:
Input Constraints Input constraints related to the power delivered by the radiators and the heating/cooling coils are defined for all configurations. They are given by Q˙ R .min ≤Q˙ R ≤ Q˙ R .max , (35a)
• Scenario I: symmetric occupancy. The two zones have the same number of occupants at each time step. • Scenario II: Zone 1 has two times more occupants in each time step than Zone 2. • Scenario III: Zone 1 has four times more occupants in each time step than Zone 2.
Ptot = Pfan,el + Pb,fuel + Php,el .
1
1
1
Q˙ R2 .min ≤Q˙ R2 ≤ Q˙ R2 .max , Q˙ HC.min ≤Q˙ HC ≤ Q˙ HC.max .
(35b)
To investigate the influence of the ventilation rate on the results, different constant ventilation rates for configuration (0,0) are tested. Similarly, different minimum values for the ventilation rates are simulated for demand-based ventilation.
(35c)
Input constraints for the fans are given in terms of an upper bound for the overall mass flow delivered by the fan. In order to ensure a minimum ventilation rate, a lower bound for the mass flow is defined. In case of one volume flow controller, the input constraint reads as m ˙ min ≤ m ˙ ≤m ˙ max .
(36)
m ˙ min ≤ m ˙ Z1 + m ˙ Z2 ≤ m ˙ max .
(37)
A violation of the comfort requirements related to the CO2 concentration in each zone occurs when no or only one CO2 sensor is used, if a low ventilation rate is used. In order to exclude the effect of a comfort violation on the potential offered by each configuration, the minimum ventilation rate should be chosen suitably. In this context, only ventilation rates above 1 h−1 are simulated for the configurations (0,0), (2,1) and (1,1) to ascertain a fulfillement of the comfort requirements related to admissible CO2 concentration in each zone.
In case of two volume flow controllers, the input constraint takes this form
State Constraints Thermal comfort requirements have to be fulfilled by each configuration, i.e. the zone temperatures are maintened within a comfort range and the temperature of the supply air should remain in the admissible range. Mathematically, thermal comfort requirements are given by TZ1 .min ≤TZ1 ≤ TZ1 .max , TZ2 .min ≤TZ2 ≤ TZ2 .max , TS.min ≤TS ≤ TS.max .
In order to assess the performance of each configuration, a simulation of one year is performed for each configuration with the occupancy scenarios I,II, and III. The configurations are compared based on their annual energy consumption.
(38a) (38b) (38c)
5.2 Potential of DCV compared to constant ventilation
State constraints related to CO2 concentration depend on the configuration, i.e. the number of CO2 sensors. In case of two CO2 sensors, the state constraints read as XZ1 ≤ XZ1 .max , XZ2 ≤ XZ2 .max .
(39a) (39b)
XE ≤ XE.max .
(40)
In this section the relative energy savings per year of the demand-based configurations in comparison to the reference configuration are presented. The elements of the triples in the tables represent the relative energy savings of the considered configuration for a given minimum ventilation rate nmin in comparison to the reference configuration driven by a given constant ventilation rate n, in the occupancy scenarios I, II and III, respectively.
The control strategy ascertains therefore that the comfort requirements related to an admissible CO2 concentration are fulfilled in each zone. In case of one CO2 sensor in the exhaust duct, the state constraint takes the form
Table 2. Relative energy savings of configuration (2,2) in comparison to the reference configuration.
nmin 0 h−1 n −1
In this case, the control strategy ensures that the CO2 concentration in the exhaust duct remains under some upper bound. However, an achievement of the comfort requirements in each zone is not guaranteed.
1h 2 h−1 3 h−1
1 h−1
1 2
5
3 h−1
(32,35,37)% (6,12,9)% (58,58,59)% (42,43,40)% (2,1,0)% (76,76,76)% (67,67,66)% (45,44,43)% (0,0,0)%
5. RESULTS AND ANALYSIS This section gives an overview of the obtained results.
2 h−1
http://www.meteonorm.com https://sel.me.wisc.edu/trnsys/
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Table 3. Relative energy savings of configuration (1,2)
nmin n 1 h−1 2 h−1 3 h−1
RES[%] Scenario I 15
in comparison to the reference configuration. 0 h−1 (25,26,26)% (39,53,50)% (74,73,72)%
1 h−1 2 h−1 3 h−1 (1,2,2)% (40,39,36)% (2,1,2)% (66,65,63)% (45,45,44)% (0,1,0)%
in comparison nmin 0 h−1 n −1 1h 2 h−1 3 h−1
2 h−1
3 h−1 0
(1,2,2)% (40,39,36)% (2,2,2) (66,65,63)% (45,47,44)% (0,1,0)%
in comparison nmin 0 h−1 n 1 h−1 2 h−1 3 h−1
1
2
h−1
3
1
2
3
0
1
2
3
0
1
2
3 nmin[h−1 ]
of the zones (scenario I). The energy saving potential of configuration (2,2) in comparison to configuration (1,1) is estimated by 10% in this case. Although configuration (2,1) has one more actuator than configuration (1,1), setting the minimum ventilation rate to 0 h−1 leads to a violation of the comfort requirements in all scenarios. We can conclude that configuration (2,2), the most expensive configuration, is well suited for zones with considerably differing occupancy scenarios. Configurations (1,2) and (1,1) present a cheaper alternative to this configuration in case of a symmetric occupancy of the zones. However, configuration (2,1) is the least profitable configuration.
to the reference configuration. h−1
0
Fig. 3. Relative energy savings of configuration (2,2).
Table 5. Relative energy savings of configuration (1,1)
(2, 2)/(1, 2) (2, 2)/(1, 1) (2, 2)/(2, 1)
5
to the reference configuration. 1 h−1
Scenario III
10
Table 4. Relative energy savings of configuration (2,1)
Scenario II
h−1
(2,10,6)% (40,41,39)% (1,3,2)% (66,66,65)% (44,45,45)% (0,0,0)%
Clearly, the best potential for energy saving can be achieved by setting the minimum ventilation rate to zero, i.e. if the ventilation system can be completely shut down when it is not needed. Setting the minimum ventilation rate to zero while satisfying the comfort requirements in both zones can only be achieved by the configurations (2,2) and (1,2), where the CO2 concentration is measured in each zone. Going from a constant ventilation of 3 h−1 to a variable one with a minimum value of 0 h−1 , more than 70% of energy saving can be achieved while comfort requirements are still maintained. The energy savings offered by configuration (2,2) when using a minimum ventilation rate equal to zero are slightly better than those offered by the configuration (1,2).
6. CONCLUSION In this paper, the energy saving potential of four different CO2 -based DCV system configurations for a generic twozone building are investigated. A model-based optimal control problem is proposed to assess the best performance of each configuration for different occupancy scenarios. The main goal of the optimal control approach is to fulfill the comfort requirements at minimum .
The potential for energy savings offered by the different configurations starting from a minimum ventilation rate of 1 h−1 are very similar. Due to the higher installation costs related to the configuration (2,1) in comparison to the configuration (1,1), it can be concluded that configuration (2,1) is the least suited configuration of the considered ventilation system. Roughly speaking, the potential offered by a high degree of freedom (2 volume flow controllers) with a low amount of information (only one CO2 sensor) is quite modest.
The configurations featuring more sensors offer the highest energy saving potential while respecting the comfort requirements. It is concluded that a large number of sensors is crucial to guarantee optimal comfort and to reduce energy consumption. If in addition a large number of actuators is employed, the maximum energy savings can be obtained. However, a system featuring more actuators than sensors leads to poor results.
5.3 Comparison between DCV system configurations
REFERENCES Bejan, A. (2016). Advanced Engineering Thermodynamics. Wiley. Bryson, A. (1975). Applied Optimal Control: Optimization, Estimation and Control. Taylor & Francis. Emmerich, S.J., Persily, A.K., Evans, D.L., Emmerich, S.J., and Persily, A.K. (2001). State-of-the-Art Review of CO2 Demand Controlled Ventilation Technology and Application. In NISTIR. Erickson, V.L. and Cerpa, A.E. (2010). Occupancy based demand response hvac control strategy. In Proceedings of the 2Nd ACM Workshop on Embedded Sensing Systems for Energy-Efficiency in Building, BuildSys ’10. ACM, NY, USA. Ihle, C. (1997). L¨ uftung und Luftheizung (German book). Werner. Incropera, F., Dewitt, D., Bergman, T., and Lavine, A. (eds.) (2005). Fundamentals of Heat and Mass Transfer. John Wiley & Sons. Kreider, J. and Rabl, A. (1994). Heating and Cooling of Buildings: Design for Efficiency. McGraw-Hill. L.P´ erez-Lombard, J.Oritz, and C.Pout (2009). A review on buildings energy consumption information. Energy and Buildings. Persily, A. (1997). Evaluating building IAQ and ventilation with indoor carbon dioxide. AHRAE, Inc., Atlanta, GA (US).
As shown in Section 5.2, configuration (2,2), i.e. the configuration with the highest number of sensors and actuators, offers the highest potential for energy savings. In this section, the potential offered by configuration (2,2) in comparison to the other demand-based configurations is investigated for the occupancy scenarios I, II and III and for different minimum ventilation rate values, see Fig. 3. The potential offered by configuration (2,2) in comparison to configuration (1,2) increases with rising asymmetry in the zones’ occupancy (8 % in scenario I, 12 % in scenario II and 16 % in scenario III, with minimum ventilation rate of 0 h−1 ). However, this energy saving potential decreases with rising minimum ventilation rate, as already shown in Section 5.2. A fulfillement of the comfort requirements by configuration (1,1) with a minimum ventilation rate of 0 h−1 , is only achieved in case of a symmetric occupancy 6
ScienceDirect
IFAC PapersOnLine 51-2 (2018) 85–90 Model-Based Potential Analysis of Model-Based Potential Analysis of Model-Based Potential Analysis of Model-Based Potential Analysis of Demand-Controlled Ventilation in Demand-Controlled Ventilation in Demand-Controlled Ventilation in Demand-Controlled Ventilation in Buildings Buildings Buildings Buildings∗ ∗ ∗∗
K. K. Ben Ben Jemaa Jemaa ∗ P. P. Kotman Kotman ∗ K. K. Graichen Graichen ∗∗ K. Ben Jemaa ∗∗ P. Kotman ∗∗ K. Graichen ∗∗ K. Ben Jemaa P. Kotman K. Graichen ∗∗ ∗ ∗ Robert Bosch GmbH, Future Systems for Building Technology, Robert Bosch GmbH, Future Systems for Building Technology, ∗ Bosch GmbH,Germany Future Systems Building Technology, 71272 Renningen, (e-mail: {Karim.Benjemaa; ∗ Robert 71272 Renningen, (e-mail:for Robert GmbH,Germany Future Systems for{Karim.Benjemaa; Building Technology, 71272Bosch Renningen, Germany (e-mail: {Karim.Benjemaa; Philipp.Kotman}@bosch.de.com) Philipp.Kotman}@bosch.de.com) 71272 Renningen, Germany (e-mail: {Karim.Benjemaa; ∗∗ Philipp.Kotman}@bosch.de.com) ∗∗ Ulm University, Institute of Measurement, Control and Institute of Measurement, Control and Philipp.Kotman}@bosch.de.com) ∗∗ Ulm University, University, Institute Measurement, Control and Microtechnology, 89081 Ulm, Germany ∗∗ Ulm Microtechnology, 89081 of Ulm, Germany (e-mail: (e-mail: Ulm University, Institute of Measurement, Control and Microtechnology, 89081 Ulm, Germany (e-mail: [email protected]) [email protected]) Microtechnology, 89081 Ulm, Germany (e-mail: [email protected]) [email protected]) Abstract: This paper proposes a Abstract: This paper proposes a model-based model-based framework framework to to estimate estimate the the theoretical theoretical energy energy Abstract: This paper proposes a model-based framework to estimate the theoretical energy saving potential offered by CO -based demand-controlled ventilation systems in For 2 saving potential offered by CO2 -based demand-controlled ventilation systems in buildings. buildings. For Abstract: This paper proposes a model-based framework to estimate the theoretical energy -based demand-controlled ventilation systems in buildings. For saving potential offered by CO this purpose, the energy consumption of different heating air conditioning (HVAC) 2 this purpose, the energy consumption of different heating ventilation air conditioning (HVAC) -based demand-controlled ventilation systems in buildings. For saving potential offered by CO 2 this purpose, the energy consumption of different heating ventilation air conditioning (HVAC) system configurations is compared for different occupancy scenarios. Physics-based models are system configurations is compared for of different occupancy scenarios. Physics-based models are this purpose, the energy consumption different heating ventilation air conditioning (HVAC) system configurations is compared for different occupancy scenarios. Physics-based models are used to describe the environmental conditions in the building and to estimate the energy used toconfigurations describe the is environmental conditions in the building andPhysics-based to estimate the energy system compared for different occupancy scenarios. models are used to describe the environmental conditions in the building and to estimate the energy consumption of the HVAC system. In order to guarantee optimality, the HVAC system is consumption of the HVAC system. In order to inguarantee optimality, the HVACthe system is used to describe the environmental conditions the building and to estimate energy consumption of the HVAC system. In order to guarantee optimality, the consumption HVAC systemand is controlled by an optimal control approach aiming to minimize the energy controlled by an optimal control approach aiming to minimize the energy consumption and consumption of the HVAC system. In order to guarantee optimality, the HVAC system is controlled by an optimal control approach aiming to minimize the energy consumption and to satisfy the comfort requirements. to satisfy the comfort requirements. controlled by an optimal control approach aiming to minimize the energy consumption and to satisfy the comfort requirements. to satisfy the(International comfort requirements. © 2018, IFAC Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: CO CO2 -based demand controlled ventilation, HVAC systems, model based control, Keywords: 2 -based demand controlled ventilation, HVAC systems, model based control, HVAC systems, model based control, Keywords: CO2 -based optimal control, energy efficient buildings, user optimal control, energydemand efficientcontrolled buildings,ventilation, user comfort comfort HVAC systems, model based control, Keywords: CO2 -based optimal control, energydemand efficientcontrolled buildings,ventilation, user comfort optimal control, energy efficient buildings, user comfort 1. However, 1. INTRODUCTION INTRODUCTION However, little little information information is is available available on on the the performance performance 1. INTRODUCTION However, little information is available on the performance that can be achieved with different CO -based DCV 2 -based that can be achieved with different CO DCV syssys2 1. INTRODUCTION However, little information is available on-based the performance that can be achieved with different CO DCV system configurations. 2 tem configurations. that can be achieved with different CO -based DCV sys2 Heating, Heating, Ventilation Ventilation and and Air Air Conditioning Conditioning (HVAC) (HVAC) syssys- tem configurations. In this work, the energy saving potential of five different tem configurations. Heating, Ventilation and Air Conditioning (HVAC) systems to thermal comfort and air this work, the energy saving potential of five different tems are are used used to guarantee guarantee thermal comfort (HVAC) and good goodsysair In Heating, Ventilation and account Air Conditioning In this work, the energy saving potential of five two-zone different system configurations for tems arein used to guarantee thermal comfort andhalf good air ventilation quality buildings. They for more than of the ventilation system configurations for aa generic generic quality in buildings. They account for more than half of the In this system work, the energy saving potential of five two-zone different tems are used to guarantee thermal comfort andhalf good air ventilation system configurations for generic two-zone HVAC is investigated investigated based on asimulation simulation studies. quality in buildings. They account for more than of the energy consumption in buildings (L.P´ e rez-Lombard et al., HVAC system is based on studies. energy consumption in buildings (L.P´ e rez-Lombard et al., ventilation system configurations for a generic two-zone quality in buildings. They account for more thanoften half varies of the HVAC system is configurations investigated based on simulation studies. The considered feature different numbers energy consumption in buildings (L.P´ e rez-Lombard et al., 2009). One reason is that, although occupancy The considered configurations feature different numbers 2009). One reason is that, although occupancy often varies HVAC systemofis volume investigated based on simulation studies. energy consumption in buildings (L.P´ e rez-Lombard et al., The considered configurations feature different numbers and locations flow controllers and CO sensors. 2009). One reason is that, although occupancy often varies 2 strongly during typical office days, most systems and locations of volume flow controllers and CO2numbers sensors. strongly during typical office days,occupancy most HVAC HVAC systems The considered configurations feature different 2009). One reason is that, although often varies and locations ofoptimal volumecontrol flow controllers and CO2 to sensors. model-based framework aiming ministrongly duringat office air days, most HVAC systems A today operate a exchange rate A model-based framework aiming to minitoday operate attypical a constant constant exchange rate (Erickson (Erickson and locations ofoptimal volumecontrol flow controllers and CO sensors. strongly during typical office air days, most HVAC systems A model-based optimal control framework aiming minimize the energy energy consumption while satisfying the2 to comfort today operate at a constant air exchange rate (Erickson and Cerpa, 2010). As a consequence, overventilation durmize the consumption while satisfying the comfort and Cerpa, 2010). As a consequence, overventilation durA model-based optimal control framework aiming to minitoday operate at a constant air exchange rate (Erickson mize the energy consumption while satisfying the comfort requirements is proposed. In order to assess the highest and Cerpa, of 2010). As a consequence, overventilation dur- requirements ing low and during is proposed. In while order satisfying to assess the the comfort highest ing periods periods of low occupancy occupancy and underventilation underventilation during mize the energy consumption and Cerpa, 2010). As a consequence, overventilation durrequirements is proposed. In order to assess highest offered by perfect knowledge ing periods of low occupancy underventilation during potential periods of high high occupancy areand inevitable. While overvenovervenpotential offered by each each configuration, configuration, perfectthe knowledge periods of occupancy are inevitable. While requirements isand proposed. In order to assess the highest ing periods of to low occupancy and underventilation during potential offered by each configuration, perfect knowledge of the models of the disturbances is assumed. The periods of high occupancy are inevitable. While overventilation leads energy wastage, indoor comfort can be of the models and of theconfiguration, disturbancesperfect is assumed. The tilation leads tooccupancy energy wastage, indoor comfort can be potential offered by each knowledge periods of high are inevitable. While overvenof the models and of the disturbances is assumed. The configurations are are then then compared compared based based on on their their energy energy tilation leads to energy wastage, indoor comfort can be significantly reduced in case of underventilation. configurations significantly reduced in case of underventilation. of the models and of the disturbances is assumed. The tilation leads to energy wastage, indoor comfort can be configurations are then compared based on their energy saving potentials. significantly reduced in case of underventilation. saving potentials. configurations are then compared based on their energy A demand-controlled ventilation (DCV) system attempts significantly reduced in case of underventilation. A demand-controlled ventilation (DCV) system attempts saving potentials. This paper is saving potentials. A demand-controlled attempts to achieve air (IAQ) reduced energy paper is structured structured as as follows: follows: In In Section Section 2, 2, the the to achieve high high indoor indoorventilation air quality quality (DCV) (IAQ) at atsystem reduced energy This A demand-controlled ventilation (DCV) system attempts This paper is structured as follows: In Section 2, venthe generic two-zone HVAC system and the considered to achieve high indoor air quality (IAQ) at reduced energy consumption by modulating the air exchange rate based on generic two-zone HVAC system and the considered venconsumption byindoor modulating the air exchange rate based on This paper is configurations structured as are follows: In considered Section 2, venthe to achieve high air quality (IAQ) at reduced energy generic two-zone HVAC system and the tilation system presented. In Section 3, consumption by modulating the air exchange rate based on a measured measured parameter parameter (Emmerich (Emmerich et et al., al., 2001). 2001). Over Over the the generic tilation system configurations areand presented. In Section 3, a two-zone HVAC system the considered venconsumption by modulating the air exchange rate based on tilation system configurations are presented. In Section 3, physics-based models of the building and of the HVAC a measured parameter (Emmerich et al., 2001). Over the last years, CO has been proposed as an acknowledged criphysics-based models of the building and of the HVAC 2 has been proposed as an acknowledged crilast years, CO tilation system configurations are presented. In Section 3, 2 a measured parameter (Emmerich et al., 2001). Over the physics-based models of the building and of the HVAC system components are described. Section 4 presents the last years, CO2 indoor has been proposed as an acknowledged cri- system terion to assess air quality and to estimate the numcomponents are described. Section 4 presents the terion to assess indoor air quality and to estimate the numphysics-based models of the building and of the HVAC last years, CO2 indoor has(Persily, been as an acknowledged cri- mathematical system components are described. Section HVAC 4 presents the formulation of control terion assess airproposed quality to estimate the number occupants 1997). A demandmathematical formulation of the the optimal optimal HVAC control 2 -based ber of of to occupants (Persily, 1997).and A CO CO demandsystem components are described. Section 4presented presents the 2 -based the terion to assess indoor air quality and to estimate nummathematical formulation of the optimal HVAC control problem. In Section 5, simulation results are and ber of occupants (Persily, 1997). A CO -based demandcontrolled ventilation consists therefore in adjusting the 2in adjusting the problem. In Section 5, simulation results areHVAC presented and controlled ventilation consists therefore mathematical formulation of the optimal control ber of occupants (Persily, 1997). A CO -based demand2 problem. In Section 5, simulation results are presented and Section 66 concludes the paper. controlled ventilation consists in adjusting the discussed, ventilation rate based on discussed,Inbefore before Section concludes theare paper. ventilation rate over over time time basedtherefore on CO CO2 measurements. measurements. Section 5, simulation results presented and controlled consists in adjusting the problem. discussed, before Section 6 concludes the paper. ventilation ventilation rate over time basedtherefore on CO22 measurements. discussed, before Section 6 concludes the paper. Equipping the duct system with additional volume flow ventilation rate over time based on CO measurements. 2 Equipping the duct system with additional volume flow 2. Equipping the duct with additional volume flow controllers and CO sensors is the first step towards 2system 2. THE THE GENERIC GENERIC TWO-ZONE TWO-ZONE HVAC HVAC SYSTEM SYSTEM controllers and CO sensors is the first step towards 2 Equipping the duct system with additional volume flow 2. THE GENERIC TWO-ZONE HVAC SYSTEM controllers and CO sensors is the first step towards CO -based DCV. Thereby, the question arises about the 2 2 CO Thereby, the question arises about the 2. THE GENERIC TWO-ZONE HVAC SYSTEM 2 -based DCV. controllers and CO sensors is the first step towards 2 location CO2 -basednumber DCV. Thereby, the question arisesand about the In this work, aa generic two-zone HVAC system is adequate and of actuators sensors In this work, generic two-zone HVAC system is used used as as a a adequate number and location of actuators and sensors CO -based DCV. Thereby, the question arises about the 2 this work, a generic two-zonethe HVAC system is used as a adequate number and location of actuators and sensors In prototype system to investigate potential of CO leading to a profitable configuration of the ventilation 2 -based prototype system to investigate the potential of CO leading to a profitable configuration of the ventilation -based 2 In this work, a generic two-zone HVAC system is used as a adequate number and location of actuators and sensors investigate the potential of CO leading to a profitable configuration the ventilation system. Available literature on controlled systems DCV, Fig. After discussing its principle 2 -based system. Available literature on demand demand of controlled systems prototype DCV, see see system Fig. 1. 1.to After discussing its working working principle prototype system to investigate the potential of CO leading to a profitable configuration of the ventilation -based 2 system. Available on demandof DCV, see 2.1, Fig. different 1. After configurations discussing its for working principle is focussed on different control the is mainly mainly focussedliterature on the the evaluation evaluation ofcontrolled different systems control in in Section Section 2.1, different configurations the ventilation ventilation system. Available literature on demand controlled systems DCV, see Fig. 1. After discussing its for working principle is mainly focussed on the evaluation of different control in Section 2.1, different configurations for the ventilation strategies for a given ventilation system configuration. system are presented in Section 2.2. strategies for a given ventilation system configuration. system are 2.1, presented in Section 2.2. is mainly focussed on the evaluation of different control in Section different configurations for the ventilation strategies for a given ventilation system configuration. system are presented in Section 2.2. strategies for a given ventilation system configuration. system are presented in Section 2.2.
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2.1 System Description
Table 1. Summary of configurations Configuration (0,0) (1,1) (1,2) (2,1) (2,2)
The working principle of the HVAC system depicted in Fig. 1 is as follows. The supply duct is equipped with a supply fan (SF) allowing the intake of fresh air from the ambience. The incoming fresh air enters a heat exchanger (HX) with the temperature TA , exits it with the temperature TR , is induced to a heating/cooling coil (HCC) to reach the supply temperature TS and finally distributed to the zones Z1 and Z2 . The Radiators R1 and R2 allow to heat up the air in zones Z1 and Z2 , respectively. The exhaust air extracted from the zones through the exhaust fan (EF) enters the heat exchanger with the temperature TE and transfers a part of its heat to the fresh air. EF HX
R1 HCC TA XA
TR Q˙ HC
2
1
2
The main goal of demand-based ventilation is to achieve some predefinded comfort requirements at minimum costs. The higher investment costs related to DCV are then recovered through lower operating costs. In order to estimate the profitability of DCV, the related energy saving potential ought to be examined. In this work, the theoretical energy saving potential offered by four different configurations of CO2 -based DCV system are investigated for different occupancy scenarios. The main goal is to assess the highest potential of each configuration when the comfort requirements are fully achieved.
Zone 2 TZ2 X Z2
3. MODELING In this section, a zone model describing the temperature and the CO2 concentration in a building’s zone is derived in Section 3.1, followed by simplified models for the HVAC system components in Section 3.2.
R2
SF TS
1
Measured quantities TZ1 ,TZ2 TZ1 ,TZ2 ,XE TZ1 ,TZ2 ,XZ1 ,XZ2 TZ1 ,TZ2 ,XE TZ1 ,TZ2 ,XZ1 ,XZ2
2.3 Problem Formulation
TE XE Zone 1 TZ 1 XZ1
Control inputs Q˙ R1 ,Q˙ R2 ,Q˙ HC Q˙ R1 ,Q˙ R2 ,Q˙ HC ,m ˙ Q˙ R1 ,Q˙ R2 ,Q˙ HC ,m ˙ ˙ Z2 ˙ Z1 ,m Q˙ R1 ,Q˙ R2 ,Q˙ HC ,m Q˙ R ,Q˙ R ,Q˙ HC ,m ˙ Z ,m ˙Z
m ˙
3.1 Zone Model
Fig. 1. Illustration of the generic two-zone HVAC system.
A zone denotes a building’s area that can be conditioned separately through its own controlling devices. The zone model proposed in this work to describe the internal conditions is composed of two parts: the thermal model and the CO2 model.
2.2 System Configurations In this work, five different configurations for the ventilation system of the two-zone HVAC system are considered, see Fig 2. Each configuration is defined by the number of CO2 sensors and air flow controllers. As mathematical notation, an ordered pair (na , ns ) is allocated to each configuration, where na is the number of actuators (volume flow controllers) and ns is the number of sensors (CO2 sensors).
Thermal Model: A thermodynamic model describing the air temperature in the zone is derived on the basis of the mass and energy balances as well as the ideal gas law. The mass balance for the air in the zone reads as dmZ =m ˙ in (1) ˙ out Z −m Z , dt where mZ is the mass of the air in the zone Z and m ˙ in Z out and m ˙ Z are the incoming and outgoing air mass flow, respectively. The first law of thermodynamics is given by (Kreider and Rabl, 1994) dUZ = H˙ Zin − H˙ Zout + Q˙ R + Q˙ O + Q˙ S + Q˙ W dt in out =m ˙ in ˙ out + Q˙ R + Q˙ O + Q˙ S + Q˙ W , Z cp TZ − m Z cp TZ (2) where UZ is the internal energy stored in the zone, H˙ Zin and H˙ Zout are the enthalpy flows associated with the mass ˙ flows m ˙ in ˙ out Z and m Z , respectively, QR is the heat transferred from the radiator to the zone, Q˙ O is the occupancy heat, Q˙ S is the radiation heat stemming from the sun and Q˙ W is the heat exchanged with the walls. The temperature TZout of the outgoing mass flow is equal to the temperature TZ inside the zone. The isobaric heat capacity cp of the air is assumed to be constant. Furthermore, the time derivative of the internal energy UZ stored in the zone is
• Configuration (0,0): reference configuration. The ventilation rate is constant. • Configuration (1,1): a volume flow controller adjusts the overall fresh air supply (m) ˙ of the ventilation system. The distribution of the fresh air between the two zones is static. A CO2 sensor measures the CO2 concentration XE in the exhaust duct. • Configuration (2,1): two volume flow controllers adjust the fresh air supply for each zone (m ˙ Z1 and m ˙ Z2 ) individually. A CO2 sensor measures the CO2 concentration XE in the exhaust duct. • Configuration (1,2): a volume flow controller adjusts the overall fresh air supply of the ventilation system. The distribution of the fresh air between the two zones is static. Two CO2 sensors measure the CO2 concentration in each zone. • Configuration (2,2): two volume flow controllers adjust the fresh air supply for each zone individually. Two CO2 sensors measure the CO2 concentration in each zone. 2
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87
CO2 sensor
Configuration (0,0)
Configuration (1,1)
Configuration (2,1)
Configuration (1,2)
volume flow controller
Configuration (2,2)
Fig. 2. Ventilation sytem configurations. d(uZ mZ ) dUZ = dt dt
TA − TW , Q˙ A = (10) RE with the ambient temperature TA and the resistance RE for the heat transfer to the exterior. Taking this into consideration, the dynamics of the air temperature in the zone finally take the form TW − TZ 1 dTZ m ˙ Z cp TZin − TZ + = dt CZ RI (11) ˙ ˙ ˙ + QR + QO + QS ,
(3) duZ , − + mZ = dt where uZ is the specific internal energy of the air in the zone. For ideal gases the specific internal energy is only a function of the temperature (Bejan, 2016), i.e. (m ˙ in Z
m ˙ out Z )uZ
uZ = cv TZ , with the isochoric heat capacity cv of the air in zone. After some algebraic reformulation combining and (4), the ordinary differential equation (ODE) for temperature TZ is obtained, i.e. 1 in dTZ = m ˙ Z (cp TZin − cv TZ ) − m ˙ out Z RTZ dt mZ cv + Q˙ R + Q˙ O + Q˙ S + Q˙ W ,
(4) the (3) the
with
1 dTW = dt CW
TA − TW T Z − TW + RI RE
.
(12)
CO2 Model: A mathematical model describing the CO2 concentration in the zone is derived based on the mass balance for CO2 . The CO2 concentration XZ in the zone Z is given by XZ = m∗Z /mZ , (13) ∗ where mZ and mZ are the mass of CO2 and the total mass of the air in the zone, respectively. The mass balance of CO2 in the zone reads as dm∗Z =m ˙ ∗Z,in − m (14) ˙ ∗Z,out . dt ∗ ∗ The quantities m ˙ Z,in and m ˙ Z,out are the incoming and outgoing mass flow of CO2 , respectively. The incoming flow of CO2 in the zone depends on the incoming air flow and its CO2 concentration as well as on the amount of CO2 exhaled by the occupants, i.e. (15) ˙ O + XA m ˙ in m ˙ ∗Z,in = m Z, where m ˙ O is the CO2 mass flow exhaled by the occupants in the zone and XA is the CO2 concentration of the incoming air mass flow. It is assumed that XA is equal to the outdoor CO2 concentration and has a constant value. The CO2 generation rate m ˙ O is modeled as a linear function of the number of occupants, i.e. (16) m ˙ O = gCO2 \occ · Nocc , where the CO2 generation rate per occupant gCO2 \occ is assumed to be constant. The outgoing mass flow of CO2 is given by m ˙ ∗Z,out = XZ m ˙ out (17) Z . Deriving the CO2 concentration over the time leads to 1 dXZ = m ˙ O−m ˙ in (18) Z (XZ − XA ) . dt mZ
(5)
with R the universal gas constant. Assuming that the incoming and the outgoing mass flows have the same ˙ in ˙ out the temperature absolute value, i.e. m ˙Z = m Z = m Z ODE simplifies to 1 dTZ = m ˙ Z cp (TZin − TZ ) + Q˙ R + Q˙ O + Q˙ S + Q˙ W , dt CZ (6) where CZ = mZ cv is the heat capacity of the zone. The internal heat gains Q˙ O are modeled as a linear function of the number of occupants Nocc , i.e. (7) Q˙ O = gocc · Nocc , where the heat generation per occupant gocc is assumed to be constant. A differential equation for the wall temperature is introduced in order to quantify Q˙ W . Since the mass of the wall does not change with time, the derivation of the defining ODE of the wall temperature TW is based on the energy balance only and directly leads to 1 ˙ dTW = QZ + Q˙ A . (8) dt CW The quantities Q˙ Z and Q˙ A are the heat transferred to the zone and to the ambience, respectively, and the parameter CW is the heat capacity of the wall. The heat Q˙ W = −Q˙ Z flowing from the wall to the air in the zone is defined by the simple conduction equation TW − TZ , Q˙ W = −Q˙ Z = (9) RI where RI is the resistance for the heat transfer to the interior. Similarly, the heat flow between the wall and the ambience is described by
3.2 HVAC System Components
The HVAC system contains several components, see Fig. 1, that are individually modeled in the following lines. 3
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Heat Exchanger Model The counter-flow heat exchanger (HX) is modeled with the effectiveness-NTU method, see Incropera et al. (2005). Only heat transfer and no mass transfer takes place at the heat exchanger, i.e. the fresh and exhaust air flows are not mixed. According to the effectiveness-NTU method, the effectiveness of a counterflow heat exchanger is given by NTU , (19) ε= 1 + NTU where the number of transfer N T U is expressed by UA , NTU = (20) mc ˙ p with the overall heat transfer coefficient U A of the heat exchanger. The effectiveness of the heat exchanger can finally be described as a function of the mass flow ε = ε(m) ˙ UA (21) · = mc ˙ p + UA
curve of the ventilation system, which is often described by the parabolic function (Ihle, 1997) ∆p = kvent V˙ 2 , (29) where kvent is the characteristic constant of the duct system. Thus, the electrical fan power can be described as a cubic function of the volume flow V˙ , i.e. kvent V˙ 3 Pfan,el = · (30) ηfan
Heating/Cooling Coil Model The power Q˙ HC used by the heating/cooling coil (HCC) to enduce a temperature variation ∆T in the fresh air is expressed by ˙ p ∆T . (22) Q˙ HC = mc
In order to identify the potential offered by each ventilation system configuration, an optimal control approach is followed. The optimal control problem consists in fulfilling the comfort requirements in the building with minimal energy consumption. In this work, two parameters define the comfort range: the indoor zone temperature and the indoor CO2 level. Concerning the thermal comfort, the main goal is to ascertain that the temperature of the zone remains within certain bounds. To ensure a good indoor air quality, the CO2 concentration in the zone has to be kept under some upper bound. Physical limitations stemming from the limited powers of the HVAC system components have to be respected.
Radiator Model The radiators are supplied from a boiler with hot water. The boiler’s energy consumption is assumed to be equal to its gas consumption Pb,fuel , calculated as Q˙ R1 + Q˙ R2 Pb,fuel = · (31) ηb The efficiency ηb of the boiler is assumed to be constant. 4. OPTIMAL HVAC CONTROL PROBLEM
In this work, the heating/cooling coil is assumed to be connected to a reversible heat pump with a constant performance coefficient COP . Thus, the electrical power consumed by the heat pump to adjust the temperature of the fresh air is given by | Q˙ HC | · (23) Php,el = COP Duct Model The temperature of the air flow in the exhaust duct is the weighted average of the zone temperatures, where the weighting factors are the corresponding outgoing air mass flows. Mathematically, the temperature of the exhaust air is given by m ˙ Z1 TZ1 + m ˙ Z2 TZ 2 TE = · (24) m ˙ Z1 + m ˙ Z2 Similarly, the CO2 concentration in the exhaust duct reads as m ˙ Z1 X Z1 + m ˙ Z2 X Z2 XE = · (25) m ˙ Z1 + m ˙ Z2 The temperature of the fresh air flow leaving the heat exchanger is expressed by ˙ (26) TR = ε(m)(T E − TA ) + T A , ˙ Z2 . Finally, the temperature of the where m ˙ = m ˙ Z1 + m supply air is given by Q˙ HC TS = TR + · (27) mc ˙ p
In mathematical terms, the optimal HVAC control problem can be written as a constrained dynamic optimization problem of the form tf Ptot (τ )dτ (32a) min u(t)
ts
s.t. x(0) = x0 (32b) x˙ = f (x, u, d, t) (32c) x∈X (32d) u∈U (32e) where Ptot is the total power consumption of the HVAC system. The state constraints (32d) stem from the comfort requirements and the input constraints (32e) are given by the physical limitations of the HVAC system components. The resulting constrained dynamic optimization problem is solved numerically. To this purpose, a direct approach via partial discretization of the inputs is chosen (Bryson, 1975): the time intervall [ts ,tf ] is discretized into N subintervals and the inputs are parametrized through constant values on these subintervals. The continuous states are evaluated by numerical integration. The resulting discrete static optimization problem is solved using the nonlinear programming solver fmincon of the Matlab Optimization Toolbox.
Fan Model The electrical fan power is calculated as the product of the volume flow V˙ and the pressure difference ∆p (Ihle, 1997), i.e. ∆pV˙ , (28) Pfan,el = ηfan where the overall efficiency ηfan of the fan is assumed to be constant. The relationship between the pressure drop and the volume flow is given by the characteristic pressure
Depending on the configuration of the ventilation system, the formulation of the dynamic optimization problem is slightly changed to suit the available control inputs and measurements. 4
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5.1 Test scenario and data generation
Cost Function The cost function is a purely energetic function and describes the energy consumption of the HVAC components.
In this work, an office building is simulated in a cold climate. The weather datasets, which include the ambient temperature and the solar heat gains, were obtained from the Meteonorm 1 data available within TRNSYS 2 . The occupancy profile for each zone corresponds to a typical working day in offices and meets the allowed occupant density in office buildings in Germany.
In case of a static ventilation (configuration (0,0)), the energy consumption through the fan is constant and the cost function reads as Ptot = Pb,fuel + Php,el .
89
(33)
In case of a demand-based ventilation, the energy consumption through the fans can be optimized. Therefore, the cost function is given by (34)
In order to investigate the impact of an asymmetric occupancy of the zones on demand-based ventilation, following occupancy scenarios are considered:
Input Constraints Input constraints related to the power delivered by the radiators and the heating/cooling coils are defined for all configurations. They are given by Q˙ R .min ≤Q˙ R ≤ Q˙ R .max , (35a)
• Scenario I: symmetric occupancy. The two zones have the same number of occupants at each time step. • Scenario II: Zone 1 has two times more occupants in each time step than Zone 2. • Scenario III: Zone 1 has four times more occupants in each time step than Zone 2.
Ptot = Pfan,el + Pb,fuel + Php,el .
1
1
1
Q˙ R2 .min ≤Q˙ R2 ≤ Q˙ R2 .max , Q˙ HC.min ≤Q˙ HC ≤ Q˙ HC.max .
(35b)
To investigate the influence of the ventilation rate on the results, different constant ventilation rates for configuration (0,0) are tested. Similarly, different minimum values for the ventilation rates are simulated for demand-based ventilation.
(35c)
Input constraints for the fans are given in terms of an upper bound for the overall mass flow delivered by the fan. In order to ensure a minimum ventilation rate, a lower bound for the mass flow is defined. In case of one volume flow controller, the input constraint reads as m ˙ min ≤ m ˙ ≤m ˙ max .
(36)
m ˙ min ≤ m ˙ Z1 + m ˙ Z2 ≤ m ˙ max .
(37)
A violation of the comfort requirements related to the CO2 concentration in each zone occurs when no or only one CO2 sensor is used, if a low ventilation rate is used. In order to exclude the effect of a comfort violation on the potential offered by each configuration, the minimum ventilation rate should be chosen suitably. In this context, only ventilation rates above 1 h−1 are simulated for the configurations (0,0), (2,1) and (1,1) to ascertain a fulfillement of the comfort requirements related to admissible CO2 concentration in each zone.
In case of two volume flow controllers, the input constraint takes this form
State Constraints Thermal comfort requirements have to be fulfilled by each configuration, i.e. the zone temperatures are maintened within a comfort range and the temperature of the supply air should remain in the admissible range. Mathematically, thermal comfort requirements are given by TZ1 .min ≤TZ1 ≤ TZ1 .max , TZ2 .min ≤TZ2 ≤ TZ2 .max , TS.min ≤TS ≤ TS.max .
In order to assess the performance of each configuration, a simulation of one year is performed for each configuration with the occupancy scenarios I,II, and III. The configurations are compared based on their annual energy consumption.
(38a) (38b) (38c)
5.2 Potential of DCV compared to constant ventilation
State constraints related to CO2 concentration depend on the configuration, i.e. the number of CO2 sensors. In case of two CO2 sensors, the state constraints read as XZ1 ≤ XZ1 .max , XZ2 ≤ XZ2 .max .
(39a) (39b)
XE ≤ XE.max .
(40)
In this section the relative energy savings per year of the demand-based configurations in comparison to the reference configuration are presented. The elements of the triples in the tables represent the relative energy savings of the considered configuration for a given minimum ventilation rate nmin in comparison to the reference configuration driven by a given constant ventilation rate n, in the occupancy scenarios I, II and III, respectively.
The control strategy ascertains therefore that the comfort requirements related to an admissible CO2 concentration are fulfilled in each zone. In case of one CO2 sensor in the exhaust duct, the state constraint takes the form
Table 2. Relative energy savings of configuration (2,2) in comparison to the reference configuration.
nmin 0 h−1 n −1
In this case, the control strategy ensures that the CO2 concentration in the exhaust duct remains under some upper bound. However, an achievement of the comfort requirements in each zone is not guaranteed.
1h 2 h−1 3 h−1
1 h−1
1 2
5
3 h−1
(32,35,37)% (6,12,9)% (58,58,59)% (42,43,40)% (2,1,0)% (76,76,76)% (67,67,66)% (45,44,43)% (0,0,0)%
5. RESULTS AND ANALYSIS This section gives an overview of the obtained results.
2 h−1
http://www.meteonorm.com https://sel.me.wisc.edu/trnsys/
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K. Ben Jemaa et al. / IFAC PapersOnLine 51-2 (2018) 85–90
Table 3. Relative energy savings of configuration (1,2)
nmin n 1 h−1 2 h−1 3 h−1
RES[%] Scenario I 15
in comparison to the reference configuration. 0 h−1 (25,26,26)% (39,53,50)% (74,73,72)%
1 h−1 2 h−1 3 h−1 (1,2,2)% (40,39,36)% (2,1,2)% (66,65,63)% (45,45,44)% (0,1,0)%
in comparison nmin 0 h−1 n −1 1h 2 h−1 3 h−1
2 h−1
3 h−1 0
(1,2,2)% (40,39,36)% (2,2,2) (66,65,63)% (45,47,44)% (0,1,0)%
in comparison nmin 0 h−1 n 1 h−1 2 h−1 3 h−1
1
2
h−1
3
1
2
3
0
1
2
3
0
1
2
3 nmin[h−1 ]
of the zones (scenario I). The energy saving potential of configuration (2,2) in comparison to configuration (1,1) is estimated by 10% in this case. Although configuration (2,1) has one more actuator than configuration (1,1), setting the minimum ventilation rate to 0 h−1 leads to a violation of the comfort requirements in all scenarios. We can conclude that configuration (2,2), the most expensive configuration, is well suited for zones with considerably differing occupancy scenarios. Configurations (1,2) and (1,1) present a cheaper alternative to this configuration in case of a symmetric occupancy of the zones. However, configuration (2,1) is the least profitable configuration.
to the reference configuration. h−1
0
Fig. 3. Relative energy savings of configuration (2,2).
Table 5. Relative energy savings of configuration (1,1)
(2, 2)/(1, 2) (2, 2)/(1, 1) (2, 2)/(2, 1)
5
to the reference configuration. 1 h−1
Scenario III
10
Table 4. Relative energy savings of configuration (2,1)
Scenario II
h−1
(2,10,6)% (40,41,39)% (1,3,2)% (66,66,65)% (44,45,45)% (0,0,0)%
Clearly, the best potential for energy saving can be achieved by setting the minimum ventilation rate to zero, i.e. if the ventilation system can be completely shut down when it is not needed. Setting the minimum ventilation rate to zero while satisfying the comfort requirements in both zones can only be achieved by the configurations (2,2) and (1,2), where the CO2 concentration is measured in each zone. Going from a constant ventilation of 3 h−1 to a variable one with a minimum value of 0 h−1 , more than 70% of energy saving can be achieved while comfort requirements are still maintained. The energy savings offered by configuration (2,2) when using a minimum ventilation rate equal to zero are slightly better than those offered by the configuration (1,2).
6. CONCLUSION In this paper, the energy saving potential of four different CO2 -based DCV system configurations for a generic twozone building are investigated. A model-based optimal control problem is proposed to assess the best performance of each configuration for different occupancy scenarios. The main goal of the optimal control approach is to fulfill the comfort requirements at minimum .
The potential for energy savings offered by the different configurations starting from a minimum ventilation rate of 1 h−1 are very similar. Due to the higher installation costs related to the configuration (2,1) in comparison to the configuration (1,1), it can be concluded that configuration (2,1) is the least suited configuration of the considered ventilation system. Roughly speaking, the potential offered by a high degree of freedom (2 volume flow controllers) with a low amount of information (only one CO2 sensor) is quite modest.
The configurations featuring more sensors offer the highest energy saving potential while respecting the comfort requirements. It is concluded that a large number of sensors is crucial to guarantee optimal comfort and to reduce energy consumption. If in addition a large number of actuators is employed, the maximum energy savings can be obtained. However, a system featuring more actuators than sensors leads to poor results.
5.3 Comparison between DCV system configurations
REFERENCES Bejan, A. (2016). Advanced Engineering Thermodynamics. Wiley. Bryson, A. (1975). Applied Optimal Control: Optimization, Estimation and Control. Taylor & Francis. Emmerich, S.J., Persily, A.K., Evans, D.L., Emmerich, S.J., and Persily, A.K. (2001). State-of-the-Art Review of CO2 Demand Controlled Ventilation Technology and Application. In NISTIR. Erickson, V.L. and Cerpa, A.E. (2010). Occupancy based demand response hvac control strategy. In Proceedings of the 2Nd ACM Workshop on Embedded Sensing Systems for Energy-Efficiency in Building, BuildSys ’10. ACM, NY, USA. Ihle, C. (1997). L¨ uftung und Luftheizung (German book). Werner. Incropera, F., Dewitt, D., Bergman, T., and Lavine, A. (eds.) (2005). Fundamentals of Heat and Mass Transfer. John Wiley & Sons. Kreider, J. and Rabl, A. (1994). Heating and Cooling of Buildings: Design for Efficiency. McGraw-Hill. L.P´ erez-Lombard, J.Oritz, and C.Pout (2009). A review on buildings energy consumption information. Energy and Buildings. Persily, A. (1997). Evaluating building IAQ and ventilation with indoor carbon dioxide. AHRAE, Inc., Atlanta, GA (US).
As shown in Section 5.2, configuration (2,2), i.e. the configuration with the highest number of sensors and actuators, offers the highest potential for energy savings. In this section, the potential offered by configuration (2,2) in comparison to the other demand-based configurations is investigated for the occupancy scenarios I, II and III and for different minimum ventilation rate values, see Fig. 3. The potential offered by configuration (2,2) in comparison to configuration (1,2) increases with rising asymmetry in the zones’ occupancy (8 % in scenario I, 12 % in scenario II and 16 % in scenario III, with minimum ventilation rate of 0 h−1 ). However, this energy saving potential decreases with rising minimum ventilation rate, as already shown in Section 5.2. A fulfillement of the comfort requirements by configuration (1,1) with a minimum ventilation rate of 0 h−1 , is only achieved in case of a symmetric occupancy 6