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HVAC集总参数优化控制

Energy and Buildings xxx(2011)xxx–xxx

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Energy and Buildings

j o u r n a

l h o m e p a g e:w w w.e l s e v i e r.c o m/l o c a t e/e n b u i l d

Calibration of HVAC equipment PID coef?cients for energy conservation

A.P.Wemhoff

Dept.of Mechanical Engineering,Villanova University,Villanova,PA19085,United States

a r t i c l e i n f o

Article history:

Received7June2011

Received in revised form30August2011

Accepted10October2011

Keywords:

PID Control

Energy minimization

HVAC system

optimization

a b s t r a c t

The combination of proportional–integral–derivative(PID)coef?cients for a set of equipment in a heating,

ventilating,and air conditioning(HVAC)system has an impact on the overall system energy consumption

as well as the ability for the system to maintain temperature setpoints.A simple calibration methodology

is discussed where successive optimization on the set of proportional,integral,and derivative coef?cients

is performed to reduce the energy consumption of the system.The calibration methodology discussed

here is applied to a two-zone building for a summer design day.The results show that calibration of

proportional coef?cients can reduce the system energy consumption by up to29%and can improve

meeting temperature setpoints by up to45%.Successive calibration of integral coef?cients can increase

the energy savings up to35%and can improve meeting temperature setpoints by up to52%.The successive

calibration of derivative coef?cients has a negligible impact on the energy conservation and the ability

to meet temperature setpoints.The re-calibration of proportional coef?cients with the new values of

integral and derivative coef?cients yields an additional2.3%increase in energy savings.

1.Introduction

The Department of Energy states that household heating,venti-

lating,and air conditioning(HVAC)systems consumed356billion

kWh in2001[1].Traditional HVAC design focuses solely on

attaining spatial comfort requirements regardless of the energy

cost.Recently,more attention has been focused on the reduction

of HVAC energy costs while maintaining comfort requirements,

whether it be in the form of more ef?cient equipment[2–4],novel

approaches to HVAC energy storage[5],or supervisory control tech-

niques[6–8].In addition,novel computational techniques in HVAC

design have emerged for energy usage estimation,data collection

techniques,and data visualization[9].

Supervisory control techniques often involve signi?cant alter-

ations to existing controls technology(e.g.[10–12]),so the ability

to implement these techniques may be dif?cult.Therefore,numer-

ous optimization studies(e.g.[13–24])have been performed to

develop a means to calibrate the existing input parameters for

various HVAC equipment.The majority of these studies involve

the use of an optimization technique to determine the parameters

that minimize energy usage while maintaining constraints related

to comfort requirements.Some of these studies have focused on

the use of an automated approach to tuning the parameters in a

proportional–integral–derivative(PID)controller to achieve opti-

mum performance and to avoid the inherent instabilities in HVAC

systems[25].Early work by Brandt[26]discusses the need for this

E-mail address:aaron.wemhoff@https://www.wendangku.net/doc/3f11188628.html,

optimization as advantageous over the use of manual tuning of

parameters,and Nesler[27]states that computational approaches

are advantageous to completing this task.Pinnella et al.[28]deter-

mine the optimal integral-only control parameters for the system

by achieving a critically damped system response to a step input

change in load.Bi et al.[10]later advance auto-tuning methods

by offering multiple tests and different tuning methods depending

on the number of unknown parameters in the system.In addition,

Wang et al.[29]discuss the incorporation of new auto-tuning PID

design rules for optimization on a system of multiple parameters.

They achieved improved HVAC performance experimentally when

their scheme was applied.

Generally,controllable HVAC equipment follows a PID-type

control schematic that adjusts equipment settings(output)based

on current system conditions(input).For example,in a variable-

air-volume(VAV)control method that is commonly implemented

in modern of?ce buildings,the damper opening is modulated

based on difference between the room and setpoint temperatures

[30].The PID control implementation for these dampers may be

expressed mathematically as

C=C prev+?P T+

T( )d +?D

d( T)

(1)

where the control output C is based on the temperature devia-

tion T=T room?T sp,where T room and T sp are the room and setpoint

temperatures,respectively.The value of C prev is the control output

determined from the previous PID calculation.Eq.(1)shows that

doi:10.1016/j.enbuild.2011.10.021

2 A.P.Wemhoff/Energy and Buildings xxx(2011)xxx–xxx

the PID coef?cients?P,?I,and?D impact how C is updated based on T.

PID control settings may also be implemented on a variable-speed fan or pump.Hartman[31]uses variable speed pumps to improve the chiller ef?ciency relative to constant chiller?ow.The ef?ciency of a variable-speed chiller is more affected by changes in the condenser water temperature than a constant speed chiller, and therefore the adjustment of a variable-speed chiller allows for better energy savings.This result is in agreement with Tei-tel et al.[3],who showed that variable speed fans provide better energy ef?ciency than simple on/off control.In addition,Koh et al.[4]showed that a modular varying refrigerant?ow system can provide up to70%in energy savings by eliminating duct losses, improving control over the air supply temperature,and by provid-ing simultaneous heating and cooling in different regions of the system.

The work presented here discusses a computational tool that determines how to tune the PID control coef?cients such that the setpoint temperature is best maintained while near-optimal energy conservation is achieved.The concept of applying simple adjust-ments to existing equipment for reducing energy consumption has been already performed for cooling towers[32],and a brief sen-sitivity analysis of the Proportional Control Coef?cient has been performed by Krarti and Al-Alawi[33].Here,the concept is applied as a general scheme to a system of dampers,fans,and chillers with the goal of reducing the energy consumption for a summer design day.In this study,the damper setting is expressed as an added minor loss coef?cient in the supply duct.In addition,the fan speed applies Eq.(1)where an effective temperature deviation( T)e is calculated as

( T)e=max( T1, T2,..., T N r)(2) where N r is the number of rooms served by supply air from the fan.

In this study,the values of PID coef?cients may be set inde-pendently for each control or shared among common devices.In previous studies[14,34],only proportional control was considered, and their set of?P values were chosen arbitrarily provided that they allowed the room temperatures to converge to their respective set-point values.In this study,the set of PID coef?cients are calibrated towards reducing energy consumption,yet it will be shown that the reduction of energy consumption also improves the ability for the system to meet setpoint conditions.

2.Modeling

This study applies the PID coef?cient calibration method on a simple system with predictable loads.Transient load distributions may be ascertained through either experiments or via commercial software.In this study,DesignBuilder[35]software was used to develop the loads for the two-room building shown in Figs.1and2. This software has been used in other studies and adheres to the European Parliament Board of Directive(EPBD)Standard[36].The building contains of?ce(18.8m2)and restroom(10.9m2)spaces. The transient activity in these spaces follows templates provided by DesignBuilder.The building contains one internal door between the two spaces,and one door connects the of?ce space to the outside environment.All external walls contain30%glazing.Each exter-nal wall contains0.1m brick,0.0795m extruded polystyrene,0.1m concrete block,and0.013m gypsum board.The internal partition contains two0.025m gypsum boards surrounding a0.1m airgap. The?at roof contains0.01m asphalt,0.145m glass wool,an0.2m air gap,and0.013m plasterboard.The loads and outside air dry-bulb temperature were calculated

in subhourly increments for a summer design day(July5)in Philadelphia,PA.The load calcula-tions included climate,occupancy,

in?ltration,solar,lighting,and Fig.1.An external view of the two-room building in this study.The image was

created using DesignBuilder software.

Fig.2.An open view of the two-room building in this study.The image was created using DesignBuilder software.

Fig.3.The transient system loads and external temperature calculated by Design-Builder.Time zero corresponds to midnight.

equipment loads.The resultant transient loads and external tem-perature for this system are shown in Fig.3.

This study applies the in-house code Lumped HVAC(L-HVAC) [37]on the above system.L-HVAC implicitly solves the coupled

A.P.Wemhoff /Energy and Buildings xxx (2011)xxx–xxx

Fig.4.The two-room system used in this study.All ducts are 5m in length.The abbreviation EXT.refers to the external surrounding ambient air,FCU refers to the fan coil unit,and C and R refer to a control output and room,respectively.

?ow,psychrometric,and thermodynamic physics in the system for either steady-state or transient systems.The code divides the system’s moist air into a series of lumps containing uniform ther-modynamic and psychrometric properties.The lumps transfer air via path connectors of zero volume.The approach to determining the system energy consumption via a lumped parameter model is also used in the codes EnergyPlus [38]and Sinda/Fluint [39].Other HVAC optimization studies have also used the TRNSYS code [40]for system modeling.

The two-room HVAC system in this study was modeled in L-HVAC per Fig.4.Ambient air external to the system (EXT.)at 25?C and 50%relative humidity (RH)is drawn into a fan coil unit (FCU),where it is cooled and directed to the two rooms (R 1and R 2),where it is then either returned to the FCU or exhausted out to the surrounding ambient environment.The FCU features a chiller with an approximate cooling capacity of 1.5kW and a variable-speed fan (Fig.5)with a maximum speed of 3000rpm.The chiller cools 2.52×10?3m 3/s of water to a coil of size 0.762m ×0.762m with 27tubes.Both rooms in the system shown in Fig.4contain T sp =25?C.The damper settings for rooms 1and 2are described by the parameters C 1and C 2,respectively,

and their corresponding PID coef?cients contains subscripts 1and 2,respectively.The fan speed is described by the parameter C c with the PID coef?cients

Fig.5.The fan curve set used in this study.

Table 1

Parameters used in fan curve ef?ciency calculations.

Parameter

Value

a 0.12

b 0.10 30?ámax 85%?Q

c 0.565?H

c 0.630

H max 0.254m of water Q max 2.36m 3/s D

1.2

containing the subscript c .In this study,the controls are adjusted in 15-s increments of simulated time,and the tuned PID coef?cients are subject to the constraint that ?P 1=?P 2,?I 1=?I 2,and ?D 1=?D 2due to the symmetry in Fig.4.

The fan curves follow standard polynomial expressions and sim-ilarity rules [41].The ef?ciency curves for the fan,shown in Fig.5,stem from the formula for an ellipse rotated and translated on the fan curve plot:

á(Q,H )=ámax ?D x 2a 2+

y 2

b 2

(3)

where áis the ef?ciency,ámax is the maximum ef?ciency,a and b

are constants,and x and y are de?ned by

x =cos( )(?Q

??Q c )+sin( )(?H ??H c )(4)

y =?sin( )(?Q

??Q c )+cos( )(?H ??H c )(5)

where ?Q

=Q/Q max ,?H =H/H max ,and ?Q c and ?H c are constants.Q max and H max are the largest possible ?ow rate and pump head provided by the fan,respectively.The chosen parameters are in Table 1.

This paper discusses PID tuning for transient loads.Earlier work applies a series of steady-state simulations to collected data [42],but steady-state simulations are limited to proportional control coef?cient tuning.The optimal values of all parameters could be found by a simultaneous calibration process,but the computa-tional expense for all coef?cient combinations would be too large for practical use.Therefore,the following procedure is used:

1.Set all ?I and ?D to zero.

2.Create a 5×5response surface for ?P 1=?P 2and ?Pc .The response surface should contain a reasonable starting range of potential values for calibration.In this study,the range is 1≤?P ≤5.

3.Expand the window of potential coef?cient values by a reason-able amount,and then apply 3steepest descents steps containing 10bisection steps along the line of motion.This approach has been applied in other studies [43].In this study,the range is expanded by a factor of 10.

4.Set values of ?P to the combination corresponding to mini-mum energy consumption,and repeat the previous 2steps to determine which ?I combination yields the minimum energy consumption.The range of ?I values begins at 0.1times the magnitude of ?P and ends at the magnitude of ?P .

5.Set values of ?I to the combination corresponding to minimum energy consumption,and repeat steps 2and 3to determine which ?D combination yields the minimum energy consump-tion.The range of ?I values used in response surface generation is from 0.1times the magnitude of ?I values to the magnitude of ?I .

Further calibration involves repeating the above process except the starting values of ?I and ?D are the ?nal values from the previ-ous iteration.Results will be shown that the added computational

A.P.Wemhoff /Energy and Buildings xxx (2011)xxx–xxx

Table 2

Effects of parameter calibration.

Coef?cient

Stage

Energy,kWh

,?C

Energy savings a

reduction a

RS b 33.633 4.24322.7%30.2%?P Opt c 30.804 3.28929.2%45.9%RS b 29.647 3.05631.8%49.8%?I Opt c 28.165 2.89135.2%52.5%RS b 27.974 2.87835.7%52.7%?D

Opt c 27.972 2.87835.7%52.7%RS b 26.966 2.74638.0%54.9%?P Recalib d

Opt c

26.966

2.750

38.0%

54.8%

a Compared to the worst case of 43.484kWh, =6.082?C.

b RS:response surface stage.

c Opt:steepest descents/bisection optimization stage.d

Recalib:Recalibration of ?P values.

cost of repeating proportional coef?cient calibration provides small gains in energy ef?ciency.

3.Results

The system energy consumption was calculated for the period from 4:30a.m.until 6:00p.m.The average deviation of the instanta-neous room temperature from the setpoint temperature was found in 5-min increments during this period.The calculation for this deviation, ,is

=n t i =1n r j =1

T room,ij ?T sp,j N r N t

(6)

where N t samples of room temperature where taken for N r rooms

with setpoint T sp ,j .

Adjustment of the proportional coef?cient alone resulted in an improvement of energy savings of over 20%compared to the worst combination of tuned parameters shown in the response surface of Fig.6(?P 1=?P 2=3and ?Pc =5).Table 2shows that each successive optimization step provides an improvement in both energy conser-vation and the ability for the system to meet temperature setpoints.The majority of gains in energy savings and reduction occur in the proportional coef?cient calibration stage,suggesting that propor-tional coef?cient tuning dominates the system response.

The calibrated parameters are shown in Table 3.

Fig.7com-pares the transient temperature pro?les for the system containing these PID coef?cient values as well as the worst case proportional

Fig.6.The response surface of energy consumption in kWh for various proportional coef?cient combinations.Note that all ?I and ?D are zero.

Table 3

Calibrated PID coef?cients.

Coef?cient

Value ?P 1,?P 2 5.622?Pc

0.500?I 1,?I 20.100?Ic

0.876?D 1,?D 20.001?Dc

0.924

coef?cient combination.The ?gure shows that the optimal PID sys-tem converges to setpoint more quickly,reducing the overcooling experienced in the Restroom Space during the startup period.

The proportional response surface of Fig.6shows a variation in HVAC energy consumption for the ranges of parameters shown.The ?gure suggests that this system provides a higher sensitivity than that used in the study by Krarti and Al-Alawhi [33],whose sensitiv-ity analysis of the proportional coef?cient for a two-room system using transient simulations showed a change in energy consump-tion by 2.3%for a variation in proportional coef?cient by 100%.The reasons for this discrepancy may be system-dependent or due to the fact that their analysis on a single PID controller was performed in a non-sensitive portion of their response surface.

Fig.8shows the response surface for for various proportional coef?cient combinations.Note that the contours in Fig.8appear similar to those in Fig.6,suggesting that the overcooling experi-enced in the Restroom Space (Fig.7)is the leading cause of excess energy

usage and setpoint deviation in this system.Figs.6and 8show that the most desired location on the response surface is for

Fig.7.Transient response for system containing optimized and worst case PID parameter values.

A.P.Wemhoff /Energy and Buildings xxx (2011)xxx–xxx

Fig.8.The response surface of in ?C for various proportional coef?cient combina-tions.Note that all ?I and ?D are zero.

?P 1=?P 2=5and ?Pc =1,and this point acted as the starting location for the subsequent local optimization.Note that the variation in the contours is small enough to justify the use of a local optimization routine since no hidden local minima are seen.

Figs.9and 10show the response surface for energy consump-tion and for integral parameter calibration.Again,the contours in these response surfaces appear similar,and the smooth con-tours of the response surface also suggest the viability of a local optimization scheme.The response surfaces show that minimiz-ing ?I 1and ?I 2while maximizing ?Ic improves energy savings and reduces the temperature deviation from setpoint.Therefore,the point ?I 1=?I 2=0.56and ?Ic =0.5were used as the starting point for optimization.

Figs.11and 12show response surfaces for ?D variation.The ?gures show that variations in ?D have little impact on the energy savings,and that energy savings are more dependent on ?Dc than ?D 1or ?D 2.Furthermore,the choice of ?D has little in?uence on for the parameter range chosen.The ?gures show

that ?D 1and ?D 2have more in?uence on than on energy savings,but ?Dc still has more in?uence on .

Fig.9.The response surface of energy consumption

in kWh for various integral coef?cient combinations.Note that ?P 1=?P 2=5.622,?Pc =0.500,and all ?D are zero.

Fig.10.The response surface of

in ?C for various integral coef?cient combinations.Note that ?P 1=?P 2=5.622,?Pc =0.500,and all ?D are zero.

Fig.11.The response surface of energy consumption in kWh for various derivative

coef?cient combinations.Note that ?P 1=?P 2=5.622,?Pc =0.500,?I 1=?I 2=0.100,and ?Ic =0.876.

Fig.12.The response surface of in ?C for various derivative coef?cient combina-tions.Note that ?P 1=?P 2=5.622,?Pc =0.500,?I 1=?I 2=0.100,and ?Ic =0.876.

6 A.P.Wemhoff/Energy and Buildings xxx(2011)xxx–xxx

Fig.13.The response surface of energy consumption in kWh for recalibration of pro-portional coef?cients.Note that?I1=?I2=0.100,?Ic=0.876,?D1=?D2=0.001,and ?Dc=0.924.

The proportional calibration process was repeated using the calibrated values of?I and?D.The starting range was±50%of the previously calibrated?P values.The calculated response sur-face for energy consumption,shown in Fig.13,contains much less variation than in Fig.6.Therefore,only an additional2.3%energy savings and2.2%reduction in were achieved as shown in Table3. The best parameters from the re-calibration were?P1=?P2=7.027,?Pc=0.25.The table also shows that applying the local optimization methodology resulted in no additional energy savings beyond this value.

4.Conclusions

This study provides a methodology to tune PID parameters for both energy conservation and a better attainment of setpoint condi-tions.The effectiveness of this method is likely system-dependent and will also depend on the reliability of the modeling software in both load prediction and system response.Fortunately,many commercial software packages follow ASHRAE recommended guidelines for load prediction,and therefore these transient load predictions are generally viable.Furthermore,lumped parame-ter codes such as L-HVAC and EnergyPlus have been validated to experimental data to provide reliability in modeling the system response to different PID coef?cients.Therefore,the method in this study provides a reasonable basis for PID tuning in a given sys-tem.The method discussed here provides a considerable amount of energy savings,but more work is required to determine the type of system(e.g.,highly dynamic versus minimally dynamic)which bene?ts the most from the PID coef?cient calibration method in this study.

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