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An experimental study on an inferential control scheme for optimising the control of boilers in multi-zone heating system
Energy and Buildings 37 (2005) 55–63
An experimental study on an inferential control scheme for optimising the control of boilers in multi-zone heating system Z. Liao a,∗ , A.L. Dexter b b
a Building Research Establishment, Watford WD25 9XX, UK Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
Received 9 January 2004; received in revised form 7 May 2004; accepted 10 May 2004
Abstract An experiment was carried out over two heating seasons to test the performance of an inferential control scheme (ICS), which was designed to optimise the control of boilers in multi-zone heating systems [Building Services Engineering Research and Technology 4 (2003) 245], in a real installation. This paper presents the development of the prototype controller, method and result of the experimental testing. The experimental results show that the ICS can significantly improve the long-term performance, i.e. energy efficiency and thermal comfort, of the multi-zone heating system compared with conventional control schemes. It also demonstrates that the ICS can be implemented in a microprocessor-based controller and be commissioned using short-term monitoring data, which makes it a practical control technique. © 2004 Elsevier B.V. All rights reserved. Keywords: Inferential model; Inferential control scheme; Heating system; Energy efficiency; Thermal comfort; Solar radiation; Simulation; Experiment
1. Introduction The most important energy end-use in the building sector in the UK is space heating, which is responsible for 25% of carbon emission and counts for over 60% of delivered energy and over 40% of energy costs in the residential sector [2–4]. A study in 1980s indicated that over two-thirds of the energy savings achievable in buildings would come from space heating [2]. The energy efficiency of a heating system depends on a lot of factors, such as the thermal performance of the building envelope, the energy efficiency of the boilers and the distribution system, and the performance of the control system, etc. It was estimated in 1996 that 90% of heating systems were operating inefficiently due to inadequate control, which cost industry and commerce £500 million per annum in additional energy consumption [5]. More recent studies show that no improvement on this situation has been made during the last 7 years [6]. Without an appropriate control system, substantial amount of energy is being wasted even where well-designed, efficient plants have been installed. The authors developed a novel boiler control scheme, referred to as inferential control scheme (ICS), which could ∗ Corresponding author. Tel.: +44-1923-66-44-70; fax: +44-1923-66-47-90. E-mail address: [email protected] (Z. Liao).
0378-7788/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2004.05.009
significantly improve the overall performance of multi-zone heating systems compared with conventional boiler control schemes [1]. This control scheme contains an inferential model for estimating the average room temperature in the building based on the information available in most boiler plants: external temperature, solar radiation, and the boiler firing signal. The estimated average room temperature is compared with the desired room temperature to determine an optimal set-point for the supply water temperature. In earlier papers [1,7], the authors presented the inferential model, simulation study on the performance of this control scheme and validation of the inferential model using experimental data obtained from different sources. This control scheme was developed using the simulation technique [8]. The simulation study shows that this control scheme can significantly improve the overall performance of multi-zone heating systems. Without compromising the thermal comfort, it leads to up to 20% of energy saving in systems with poorly controlled radiators and 5–11% of energy saving in systems with well-controlled radiators. In the paper [1], the inferential model was carefully validated using experimental data obtained from different sources. However, there was no experimental data to validate the whole control scheme. To test the performance of the ICS in real heating systems, a hardware prototype controller was developed and validated with the simulator that was used to develop the control scheme [1]. The prototype was in turn installed in a
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Z. Liao, A.L. Dexter / Energy and Buildings 37 (2005) 55–63
Nomenclature A Ca Ce1 Ce2 Cm Cw f K2 K3
K4 K5
Qc Qd Qi Qr Qs Qsol Ta Te1 Te2 Tm Ts Tr Tw T0
floor area (m2 ) thermal capacity (J/◦ C) of room air thermal capacity (J/◦ C) of inner layer of the envelope thermal capacity (J/◦ C) of outer layer of the envelope thermal capacity (J/◦ C) of radiator shell thermal capacity (J/◦ C) of water the weighting factor for computing the average room temperature heat transfer coefficient (W/◦ C) between the air and the inner layer of the envelope heat transfer coefficient (W/◦ C) of infiltration and light-weighted such as windows heat transfer coefficient (W/◦ C) between the inner and outer layers of the envelope heat transfer coefficient (W/◦ C) between the outer layer of the envelope and external air power (W) of infiltration and light-weighted such as windows power (W) released by radiators power (W) of gas consumption power (W) between the air and the inner layer of the envelope power (W) between the inner and outer layer of the envelope power (W) between the outer layer of the envelope and external air room air temperature (◦ C) temperature at the inner layer of the envelope (◦ C) temperature at the outer layer of the envelope (◦ C) radiator shell temperature (◦ C) supply hot water temperature (◦ C) return hot water temperature (◦ C) water temperature (◦ C) external air temperature (◦ C)
real heating system for testing. The testing has been carried out over two consecutive heating seasons (2002–2003). This paper presents the development of the prototype controller, method for the experiment, commissioning of the inferential model using short term of experimental data, and analysis of the result.
2. The inferential control scheme The inferential control scheme (ICS) is proposed for use in multi-zone buildings where there is no measurement of the internal air temperature in the different zones of the building. As can be seen in Fig. 1, the scheme consists of the three components: an inferential model for estimating the average room temperature in the building, a water temperature set-point resetting module, and boiler control logic: • Inferential model: to estimate the average room temperature in the building (Ta ) based on information available to the boiler controller. This inferential model is described by the following equations: Ca
dTˆ a = βQd + αQsol − K2 (Ta − Te1 ) − K3 (Ta − T0 ) dt (1)
Ce1
dTe1 = (1 − β)Qd + K2 (Ta − Te1 ) − K4 (Te1 − Te2 ) dt (2)
Ce2
dTe2 = (1 − α)Qsol + K4 (Te1 − Te2 ) − K5 (Te2 − T0 ) dt (3)
As shown in Fig. 1, the inferential model has three inputs and one output. The three inputs are: the energy consumption (Qd ) calculated from boiler firing signals, the external temperature (T0 ) and solar radiation (Qsol ). The one output is the estimated average room temperature in the building (Tˆ a ). • Water temperature resetting module: a proportional plus integral algorithm (PI) is used to determine the set-point
Greek letters α constant determining the percentage of solar radiation penetrating into the building (%) β constant determining the percentage of convection heat transfer from radiators to the air (%) τ time (s) ϕ the ratio of the period when the temperature falls within the desired range over the entire period Fig. 1. An overview of the inferential control scheme.
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on a microprocessor. To be described below are three major developments. 3.1. Discrete-time inferential model To embed the ICS in a microprocessor-based controller, the continuous model need to be converted into a discrete-time version. Applying the forward-difference to Eqs. (1)-(3) yields: τ τ τ Te2 (N) = 0 K4 1 − (K4 + K5 ) K5 0 Ce2 Ce2 Ce2 τ · T (N − 1)T (4) (1 − α) Ce2 τ τ τ Te1 (N) = K2 1 − (K2 + K4 ) K4 Ce1 Ce1 Ce1 τ (1 − β) 0 · T (N − 1)T Ce1 Fig. 2. Simulated daily profile of the average room temperature in the building when the boiler is controlled by a Type 1, 2, and ICS boiler controller, respectively (the radiators are controlled by TRVs).
of supply water temperature (TwD ) from the difference between the output of the inferential model (ˆTa ) and the desired room temperature (TaD ). • The boiler control logic: to maintain the supply water temperature (Tw ) at the set-point (TwD ) determined by the water temperature resetting module by firing or turning off the burner. In systems with uncontrolled terminals, this scheme varies the supply water temperature to control the heat emitted by the terminals and maintain the zone temperatures in the desired range. The scheme minimises the probability of under-heating during periods of high heating load in systems with controlled terminals. The ICS was investigated in comparison with conventional ON/OFF boiler controller (Type 1) and external compensating boiler controller (Type 2) using simulation. Fig. 2 shows a comparison of the average room temperature in a multi-zone heating system with the radiators controlled by radiator thermostat valves (TRV) and the boiler controlled by a Type 1, Type 2 and the ICS controller, respectively. It shows that the ICS can always maintain the average room temperature with the desired range under any heating load. In comparison, overheating or under-heating occurs when the boiler is controlled by a Type 1 or Type 2 controller. This study aims to test whether this control scheme works in real installations in the same way that is observed in simulation. 3. Development of the prototype The ICS has been implemented in a hardware prototype for testing in real heating systems. The prototype is based
τ τ Ta (N) = 1 − K2 K2 Ca Ca
0
0
τ τ τ K3 β α Ca Ca Ca
· T (N − 1)T
(5)
(6)
where:
T (N − 1) = [Ta (N − 1) Te1 (N − 1) Te2 (N − 1) ×T0 (N − 1) Qd (N − 1) Qsol (N − 1)]
(7)
3.2. Measurement of the solar radiation Sensors and instruments of different sensitivities and functionality have been developed for measuring the solar radiation since 19th century. Bolometer, absolute cavity radiometer, spectroradiometer, pyranometer, pyrheliometer are among the most commonly used ones. The pyranometer is normally used for measuring direct and diffuse solar irradiance in a typical meteorological station where weather is monitored to produce historical data of climate, which can be used for thermal analysis of the built environment. However, these devices are normally very expensive to install and maintain and therefore are not suitable for use in most industrial controllers such as the one being tested in this study. The interest in measuring the solar radiation without using such expensive devices can be dated back to early 20th century. Kimball first suggested that the sunshine fraction was closely correlated to the daily global solar radiation [9]. This was further studied by Angstrom who proposed a linearly relationship between the two variables [10], which was modified to produce what is well known as Angstrom–Prescott equation [11]. This has been widely used in various fields of science and engineering [12]. However, due to the fact that the relationship between the
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sunshine duration and solar radiation is non-linear, which is treated as linear in Angstrom–Prescott equation, efforts have been continued to improve it. Some non-linear equations have been proposed by later researchers. Suehrcke proposed a quadric sunshine fraction–solar radiation relationship can represent a significant advance over the empirical Angstrom–Prescott equation [13]. These methods are applicable for estimating the solar radiation from the sunshine fraction on a daily basis. When the time constant is short, for example minutes, which is required by the ICS controller, these methods are not applicable. Suehrcke and McCormick analysed instantaneous irradiance recorded in interval of 1 min and tried to correlated this with the average clearness index and air mass [14]. The result was that the sunshine fraction is no longer representative to the solar radiation in short term. Graggs et al. investigated the optimal averaging time for solar irradiance on horizontal and vertical surfaces in the UK using statistic method [15]. They concluded that for detailed system design and load estimation, information on short-term changes is crucial and therefore suggested that 10 min averages were required. Here we used a photodiode to measure the solar radiation. A photodiode has two terminals, a cathode and an anode. It has a low forward resistance (anode positive) and high reverse resistance (anode negative). Silicon photodiodes are constructed from single crystal silicon wafers that are similar to those used to manufacture integrated circuits. The major difference is that photodiodes require higher purity silicon. Typically the spectral response of silicon photodiodes ranges from 350 to 1100 nm. Silicon becomes transparent to radiation of longer than 1100 nm wavelength. Therefore it is not suitable for use at wavelengths longer than this value. For UV detection, a fused silica or UV transmitting glass window is needed. Various filter windows are available to tailor the spectral response to suit the application. For this application, the photodiode is reverse-biased to obtain an output that is linear to the illuminance incident on the photodiode junction. The sensitivity is the ratio of radiant energy (in watts) incident on the photodiode to the photocurrent output (in amperes). The photodiode is calibrated using a pyranometer (CM11). Fig. 3 shows the result
Fig. 3. Calibration of the photodiode as a solar radiation sensor using CM11.
Fig. 4. Testing the prototype controller with the simulator.
of the calibration. It shows that the output of the photodiode can be used to calculate the solar radiation accurately. The measuring error is less than 10% when the solar radiation is greater than 50 W/m2 . 3.3. Debugging the prototype To ensure that the control scheme, which was developed in a simulator, had been properly implemented in the prototype, a special interface was developed to connect the hardware prototype with the simulator for testing, as shown in Fig. 4. The interface exchanges information and synchronizes the timing between the simulator (software) and the prototype
Fig. 5. Comparison of the algorithm implemented in the simulator and in the prototype.
Z. Liao, A.L. Dexter / Energy and Buildings 37 (2005) 55–63
controller (hardware). The simulation is slowed down to real-time so that the simulator runs at the exactly the same speed as the prototype. The heating system and the software ICS are simulated simultaneously in a computer. However the boiler is not controlled by the software ICS. Instead, it is controlled by the hardware prototype controller through the signal, uB , which is also used in the software controller. The climatic information is given to both the software and hardware ICS. Both versions of ICS are commissioned with the same values of the parameters. The outputs of the inferential model in the software and hardware (Tˆ aS and Tˆ aP ) should be the same given the exactly same inputs and internal parameters. Any significant difference between the two variables indicates that the algorithm has not been implemented correctly in the prototype. Fig. 5 shows that the final prototype controller performs exactly the same as the software version implemented in the simulator.
4. Experiment The experiment was carried out in a real heating system in Building Research Establishment (BRE). This is a typical commercial hot water heating system with two gas-burned boilers. Only one boiler is used for normal operation and the other one is used as a back-up. This system provides heating to two buildings that accommodate about 150 working people. There are three types of rooms: offices, small meeting rooms and big lecture theatres. The heat emitting devices are radiators that each is controlled by a TRV. Fig. 6 shows a simplified diagram of the heating system. The existing boiler controller is a thermostat. The heating system
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Fig. 6. A simplified diagram of the heating system.
is continuously running and the set-point of the thermostat is fixed. The boiler is switched between ON/OFF by the controller in order to maintain the temperature of supply water at a set-point, which is fixed when the existing thermostat is in control and is variable when the prototype controller is in control. Fig. 7 shows a photograph of the boiler being controlled during experiment. During the test, the prototype controller logs the following information either at a regular interval (5 min) or whenever the state of the boiler is changed: • • • • • • • •
date and time with resolution of second; external temperature (Te ); solar radiation (Qsol ); burner state (Fire: OFF, Low flame, or High flame); supply water temperature (Tw ); set-point of supply water temperature (TwD ); estimated average air temperature in the building (Tˆ a ); set-point of air temperature in the building (TaD ).
Fig. 7. A photo of the boiler being controlled.
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The test was carried out over two heating seasons, including the following sessions:
5. Result
• Period A: January 28 to February 16, 2003 when the boiler was controlled by the existing thermostat. • Period B: February 16 to March 12, 2003 when the boiler was controlled by the prototype controller. • Period C: October 20 to November 12, 2003 when the boiler was controlled by the prototype controller.
5.1. Performance of the inferential model
In order to obtain information to assess the thermal comfort, the temperature in a number of selected rooms in these two buildings were monitored using a battery-powered instrument, which recorded the temperature at a predefined interval. The recorded room temperature is also needed for commissioning the ICS controller and for evaluating the control performance. Additional information for assessing the thermal comfort was obtained through a survey. On each working day, 25 people were randomly selected to answer the following questions: • How do you feel over the day: too hot, hot, neural, cold, too cold? • When do you feel hot or cold? • What do you wear when staying in your office? The responses collected have been used together the logged room temperature to assess the thermal comfort in the buildings. The set-point of the supply water temperature was: • During Period A: the set-point for Low Flame is 65 ◦ C and for High Flame is 70 ◦ C. • During Periods B and C: the set-point for Low Flame varied from 45 to 80 ◦ C and that for High Flame was 5 ◦ C higher. From March 4 the minimum set-point was changed from 45 to 35 ◦ C.
The inferential model is designed to estimate the average air temperature in the building based on the external temperature (Te ), the solar radiation (Qsol ), and the firing signal (Fire). The output of the inferential model is the estimated average air temperature in the building (Tˆ a ). This is compared with the recorded average air temperature (Ta ) to compute the root mean square of the estimation errors (RMSE): N 2 ˆ i=1 (Ta (i) − Ta (i)) RMSE(P) = (8) N where N is the number of samples. As the on-line measurement of Ta is not available in most application, the ICS replies on the inferential model to estimate Ta . There are a set of parameters that characterise the inferential model. These parameters need to be determined such that the inferential model represents the dynamics of the heating system being controlled. This procedure of determining these parameters is referred to as commissioning. The commissioning is carried out using a short-term monitoring data, which include the inputs and output of the inferential model. The parameters are selected such that RMSE is minimised. In this experiment, the data between January 28 and February 5 is used to commission the inferential model. Fig. 8 compares the average air temperature measured and estimated using the commissioned inferential model. It shows that the inferential model can be accurately parameterised for this period. An important issue here is whether the inferential model, once commissioned using a short-term monitoring data, can produce accurate estimation over a long period. The
Fig. 8. Comparison of the measured and estimated average air temperature in the building from January 28 to February 5.
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Table 1 Daily RMSE of differences between measured and estimated building air temperature Date
Daily RMSE
Date
Daily RMSE
Date
Jan. 28 Jan. 29 Jan. 30 Jan. 31 Feb. 1 Feb. 2 Feb. 3 Feb. 4 Feb. 5 Feb. 6 Feb. 7 Feb. 8 Feb. 9 Feb. 10 Feb. 11 Feb. 12 Feb. 13 Feb. 14
0.67 0.65 0.69 0.71 0.70 0.73 0.72 0.71 0.70 0.74 0.75 0.75 0.76 0.77 0.71 0.72 0.79 0.81
Feb. 15 Feb. 16
0.76 0.81
Feb. 17 Feb. 18 Feb. 19 Feb. 20 Feb. 21 Feb. 22 Feb. 23 Feb. 24 Feb. 25 Feb. 26 Feb. 27 Feb. 28 Mar. 1 Mar. 2 Mar. 3
0.83 0.78 0.71 0.69 0.79 0.77 0.76 0.69 0.68 0.69 0.72 0.76 0.79 0.81 0.82
Mar. Mar. Mar. Mar. Mar. Mar. Mar. Mar. Mar. Mar. Oct. Oct. Oct. Oct. Oct. Oct. Oct.
Daily RMSE
Date
Daily RMSE
4 5 6 7 8 9 10 11 12 13
0.83 0.82 0.83 0.82 0.79 0.78 0.77 0.78 0.83 0.85
20 21 22 23 24 25 26
0.85 0.84 0.84 0.83 0.81 0.82 0.81
Oct. 27 Oct. 28 Oct. 29 Oct. 30 Oct. 31 Nov. 1 Nov. 2 Nov. 3 Nov. 4 Nov. 5 Nov. 6 Nov. 7 Nov. 8 Nov. 9 Nov. 10 Nov. 11 Nov. 12
0.79 0.78 0.76 0.69 0.81 0.82 0.77 0.73 0.69 0.74 0.78 0.81 0.75 0.73 0.69 0.75 0.72
parameters determined through the commissioning was configured in the prototype and has been used for the testing periods B and C. A profile of daily RMSE is given in Table 1. As indicated by a simulation study [1], the accuracy of estimating the average room temperature is required to be within 1.2 ◦ C in order for the controller to perform satisfactorily. Here a maximum RMSE of 0.85 ◦ C was achieved. 5.2. Control performance The boiler was controlled as below: • Period A (from January 28 to February 16): the existing controller. • Period B (from February 16 to March 13): the ICS prototype controller as commissioned using the data from January 28 to February 5. • Period C (from October 20 to November 12): the same as one used in Period B.
Fig. 9. The test results of 4 days during the period B.
It is worth noticing that the Period C belongs to a different heating season from the Periods A and B. Figs. 9 and 10 compares 4 days of the estimated and measured average air temperature in the building during the Periods B and C, respectively. In these figures: • Dashed line: the schedule of desired building air temperature. It is 24 ◦ C for the occupancy (7 am to 9 pm), 19 ◦ C for the setback (9 pm to 7 am). • Solid line: the estimated average air temperature (being controlled close to the dashed line). • Bold solid line: the measured average air temperature. This data was not available to the prototype controller. It was found that the building air temperature could not be maintained at the desired value during the setback from
Fig. 10. The test results of 4 days during the period C.
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Z. Liao, A.L. Dexter / Energy and Buildings 37 (2005) 55–63
d1
3 d=d0 Nd 5 3 r=1 Nd d=d0
ϕ = d 1
(9)
is computed respectively for three periods: A, B and C. The result is shown in Fig. 12. It shows that the percentage of comfort was significantly improved by the prototype controller (Periods B and C) compared with the conventional boiler controller (Period A). Fig. 12 also shows that the percentage of comfort was still fairly low (55.2% the maximum) even when the prototype controller was working. It is because the set-point for the room temperature was set as 24 ◦ C during the occupancy, which is higher than the normal comfort temperature range defined by Fanger [17]. It is reasonable to expect a much better thermal comfort if the set-point for the room temperature was set appropriately. Fig. 11. Daily energy against daily heating degree hour (HDH).
February 24 to March 4. This is because the external temperature was high and a minimum of 45 ◦ C water temperature was not low enough to maintain the building air temperature at 19 ◦ C. Due to this problem, the minimum water setpoint was reduced from 45 to 35 ◦ C on March 4 (around hour 13:50 of the year). Fig. 10 shows that the prototype controller was able to maintain a similar control performance in a different heating season. This suggests that the control scheme is likely to be a practical technique. Overall, the prototype controller was able to control the overall building air temperature as scheduled without experiencing any significant overheating, even though the outdoor temperature was higher during this period than the previous one by about 5 ◦ C. The ability of achieving a good control strongly depends on the accuracy of Ta estimation and the range of water temperature that is allowed in the system. 5.3. Energy and comfort Fig. 11 compares the daily energy consumption against daily heating degree hours between the normal thermostat boiler control and the prototype controller. Using degree hours for short-term comparison of two controllers has been well developed in literatures [16]. The results show that the prototype controller can save energy up to 20% for this heating system. The data collected through the thermal comfort survey is used to analyse the thermal comfort in the buildings during the testing period. In each working day (d), the number of people giving answer (R: 5 = too hot, 4 = hot, 3 = neural, 2 = cold, 1 = too cold) is notated as NdR . The percentage of comfort for a period (d = d0 . . . d1 ) is computed by:
Fig. 12. The thermal comfort calculated from the survey result.
Z. Liao, A.L. Dexter / Energy and Buildings 37 (2005) 55–63
6. Conclusion Based on the results presented above, the following conclusions can be drawn: • The inferential control scheme (ICS) can be implemented in a microprocessor-based control unit although the simulation study shows that it is computational demanding. • A photodiode can be used to measure the solar radiation with the accuracy required by the ICS. However, it is essential to carry out an appropriate calibration using a pyranometer. • The ICS can be commissioned using short-term monitoring data. Once it is commissioned properly, it can maintain a satisfactory performance for the entire heating season and even for a number of seasons as long as the heating system and the building remain the same. In this case, the maximum estimation error is 0.85 ◦ C. • The ICS significantly improves the overall performance of the heating system. The average room temperature has been maintained at the desired value over the testing period. Acknowledgements This study was partially funded by the Foundation for the Built Environment (FBE) and carried out in Building Research Establishment (BRE), UK. The BRE Facility Management Office is thankfully acknowledged for their support in the installation of the prototype controller and during the entire period of the testing. References [1] Z. Liao, A.L. Dexter, An inferential control scheme for optimising the operation of boilers in multi-zone heating systems, Building Services Engineering Research and Technology 24 (4) (2003) 245–256.
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[2] H. Herring, R. Hardcastle, R. Phillipson, Energy Use and Energy Efficiency in UK Commercial and Public Buildings up to the Year 2000, Energy Efficiency Series, Energy efficiency office, UK, 1988, ISBN 0-11-412903-7. [3] T. Fawcett, A. Hurst, B. Boardman, ECI Research Report 25 – Carbon UK, Industrial Sustainable Development Group, Environmental Change Institute, University of Oxford, 2002. [4] DTI (1995–2001), Digest of UK Energy Statistics, Department of Trade and Industry, The Stationery Office, London, UK, 2001. [5] BRECSU, General Information Report No. 40: Heating systems and their control, Energy Efficiency Best Practice Programme, DETR, 1996. [6] BRECSU, Energy Consumption Guide 81: Benchmarking Tool for Industrial Building – Heating and Internal Lighting, Energy Efficiency Best Practice Programme, DTI, 2002. [7] Z. Liao, A.L. Dexter, A simplified physical model for estimating the average air temperature in multi-zone heating systems, Building and Environment 39 (9) (2004) 1009–1018. [8] Z. Liao, F. Parand, Controller Efficiency Improvement for Commercial and Industrial Gas and Oil Fired Boilers, Building Research Establishment (BRE), A CRAFT project, contract JOE-CT98-7010l, 1999–2001, 2001, p. 8. [9] H.H. Kimball, Variations in the total and luminous solar radiation with geographical position in the United States, Monthly Weather Review 47 (1919) 769. [10] A. Angstrom, Sloar and terrstrial radiation, QJR Meteorological Society 50 (1924) 121. [11] J.A. Prescott, Evaporation from a water surface in relation to solar radiation, Transactions of Royal Society of Science Australlia 64 (1940) 114. [12] C. Gueymard, P. Jindra, V. Estrada-Cajigal, The probability density function P(K, K) of the clearness index: a new approach, Solar Energy 54 (1995) 357. [13] H. Suehrcke, On the relationship between duration of sunshine and solar radiation on the earth’s surface: Angstrom’s Equation revisited, Solar Energy 68 (5) (2000) 417–425. [14] H. Suehrcke, P.G. McCormick, The frequency distribution of instantaneous insolation values, Solar Energy 40 (5) (1988) 413–422. [15] C. Graggs, E.M. Conway, N.M. Pearsall, Statistical Investigation of the optimal averaging time for solar irradiance on horizontal and vertical surface in the UK, Solar Energy 68 (2) (2000) 179–187. [16] A.R. Day, T.G. Karayiannis, Identification of the uncertainties in degree-day based energy estimates, Building Service Engineering Research Technology 20 (1999) 165–172. [17] P.O. Fanger, Thermal Comfort, Mcgraw-Hill, New York, 1972.
An experimental study on an inferential control scheme for optimising the control of boilers in multi-zone heating system Z. Liao a,∗ , A.L. Dexter b b
a Building Research Establishment, Watford WD25 9XX, UK Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
Received 9 January 2004; received in revised form 7 May 2004; accepted 10 May 2004
Abstract An experiment was carried out over two heating seasons to test the performance of an inferential control scheme (ICS), which was designed to optimise the control of boilers in multi-zone heating systems [Building Services Engineering Research and Technology 4 (2003) 245], in a real installation. This paper presents the development of the prototype controller, method and result of the experimental testing. The experimental results show that the ICS can significantly improve the long-term performance, i.e. energy efficiency and thermal comfort, of the multi-zone heating system compared with conventional control schemes. It also demonstrates that the ICS can be implemented in a microprocessor-based controller and be commissioned using short-term monitoring data, which makes it a practical control technique. © 2004 Elsevier B.V. All rights reserved. Keywords: Inferential model; Inferential control scheme; Heating system; Energy efficiency; Thermal comfort; Solar radiation; Simulation; Experiment
1. Introduction The most important energy end-use in the building sector in the UK is space heating, which is responsible for 25% of carbon emission and counts for over 60% of delivered energy and over 40% of energy costs in the residential sector [2–4]. A study in 1980s indicated that over two-thirds of the energy savings achievable in buildings would come from space heating [2]. The energy efficiency of a heating system depends on a lot of factors, such as the thermal performance of the building envelope, the energy efficiency of the boilers and the distribution system, and the performance of the control system, etc. It was estimated in 1996 that 90% of heating systems were operating inefficiently due to inadequate control, which cost industry and commerce £500 million per annum in additional energy consumption [5]. More recent studies show that no improvement on this situation has been made during the last 7 years [6]. Without an appropriate control system, substantial amount of energy is being wasted even where well-designed, efficient plants have been installed. The authors developed a novel boiler control scheme, referred to as inferential control scheme (ICS), which could ∗ Corresponding author. Tel.: +44-1923-66-44-70; fax: +44-1923-66-47-90. E-mail address: [email protected] (Z. Liao).
0378-7788/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2004.05.009
significantly improve the overall performance of multi-zone heating systems compared with conventional boiler control schemes [1]. This control scheme contains an inferential model for estimating the average room temperature in the building based on the information available in most boiler plants: external temperature, solar radiation, and the boiler firing signal. The estimated average room temperature is compared with the desired room temperature to determine an optimal set-point for the supply water temperature. In earlier papers [1,7], the authors presented the inferential model, simulation study on the performance of this control scheme and validation of the inferential model using experimental data obtained from different sources. This control scheme was developed using the simulation technique [8]. The simulation study shows that this control scheme can significantly improve the overall performance of multi-zone heating systems. Without compromising the thermal comfort, it leads to up to 20% of energy saving in systems with poorly controlled radiators and 5–11% of energy saving in systems with well-controlled radiators. In the paper [1], the inferential model was carefully validated using experimental data obtained from different sources. However, there was no experimental data to validate the whole control scheme. To test the performance of the ICS in real heating systems, a hardware prototype controller was developed and validated with the simulator that was used to develop the control scheme [1]. The prototype was in turn installed in a
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Nomenclature A Ca Ce1 Ce2 Cm Cw f K2 K3
K4 K5
Qc Qd Qi Qr Qs Qsol Ta Te1 Te2 Tm Ts Tr Tw T0
floor area (m2 ) thermal capacity (J/◦ C) of room air thermal capacity (J/◦ C) of inner layer of the envelope thermal capacity (J/◦ C) of outer layer of the envelope thermal capacity (J/◦ C) of radiator shell thermal capacity (J/◦ C) of water the weighting factor for computing the average room temperature heat transfer coefficient (W/◦ C) between the air and the inner layer of the envelope heat transfer coefficient (W/◦ C) of infiltration and light-weighted such as windows heat transfer coefficient (W/◦ C) between the inner and outer layers of the envelope heat transfer coefficient (W/◦ C) between the outer layer of the envelope and external air power (W) of infiltration and light-weighted such as windows power (W) released by radiators power (W) of gas consumption power (W) between the air and the inner layer of the envelope power (W) between the inner and outer layer of the envelope power (W) between the outer layer of the envelope and external air room air temperature (◦ C) temperature at the inner layer of the envelope (◦ C) temperature at the outer layer of the envelope (◦ C) radiator shell temperature (◦ C) supply hot water temperature (◦ C) return hot water temperature (◦ C) water temperature (◦ C) external air temperature (◦ C)
real heating system for testing. The testing has been carried out over two consecutive heating seasons (2002–2003). This paper presents the development of the prototype controller, method for the experiment, commissioning of the inferential model using short term of experimental data, and analysis of the result.
2. The inferential control scheme The inferential control scheme (ICS) is proposed for use in multi-zone buildings where there is no measurement of the internal air temperature in the different zones of the building. As can be seen in Fig. 1, the scheme consists of the three components: an inferential model for estimating the average room temperature in the building, a water temperature set-point resetting module, and boiler control logic: • Inferential model: to estimate the average room temperature in the building (Ta ) based on information available to the boiler controller. This inferential model is described by the following equations: Ca
dTˆ a = βQd + αQsol − K2 (Ta − Te1 ) − K3 (Ta − T0 ) dt (1)
Ce1
dTe1 = (1 − β)Qd + K2 (Ta − Te1 ) − K4 (Te1 − Te2 ) dt (2)
Ce2
dTe2 = (1 − α)Qsol + K4 (Te1 − Te2 ) − K5 (Te2 − T0 ) dt (3)
As shown in Fig. 1, the inferential model has three inputs and one output. The three inputs are: the energy consumption (Qd ) calculated from boiler firing signals, the external temperature (T0 ) and solar radiation (Qsol ). The one output is the estimated average room temperature in the building (Tˆ a ). • Water temperature resetting module: a proportional plus integral algorithm (PI) is used to determine the set-point
Greek letters α constant determining the percentage of solar radiation penetrating into the building (%) β constant determining the percentage of convection heat transfer from radiators to the air (%) τ time (s) ϕ the ratio of the period when the temperature falls within the desired range over the entire period Fig. 1. An overview of the inferential control scheme.
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on a microprocessor. To be described below are three major developments. 3.1. Discrete-time inferential model To embed the ICS in a microprocessor-based controller, the continuous model need to be converted into a discrete-time version. Applying the forward-difference to Eqs. (1)-(3) yields: τ τ τ Te2 (N) = 0 K4 1 − (K4 + K5 ) K5 0 Ce2 Ce2 Ce2 τ · T (N − 1)T (4) (1 − α) Ce2 τ τ τ Te1 (N) = K2 1 − (K2 + K4 ) K4 Ce1 Ce1 Ce1 τ (1 − β) 0 · T (N − 1)T Ce1 Fig. 2. Simulated daily profile of the average room temperature in the building when the boiler is controlled by a Type 1, 2, and ICS boiler controller, respectively (the radiators are controlled by TRVs).
of supply water temperature (TwD ) from the difference between the output of the inferential model (ˆTa ) and the desired room temperature (TaD ). • The boiler control logic: to maintain the supply water temperature (Tw ) at the set-point (TwD ) determined by the water temperature resetting module by firing or turning off the burner. In systems with uncontrolled terminals, this scheme varies the supply water temperature to control the heat emitted by the terminals and maintain the zone temperatures in the desired range. The scheme minimises the probability of under-heating during periods of high heating load in systems with controlled terminals. The ICS was investigated in comparison with conventional ON/OFF boiler controller (Type 1) and external compensating boiler controller (Type 2) using simulation. Fig. 2 shows a comparison of the average room temperature in a multi-zone heating system with the radiators controlled by radiator thermostat valves (TRV) and the boiler controlled by a Type 1, Type 2 and the ICS controller, respectively. It shows that the ICS can always maintain the average room temperature with the desired range under any heating load. In comparison, overheating or under-heating occurs when the boiler is controlled by a Type 1 or Type 2 controller. This study aims to test whether this control scheme works in real installations in the same way that is observed in simulation. 3. Development of the prototype The ICS has been implemented in a hardware prototype for testing in real heating systems. The prototype is based
τ τ Ta (N) = 1 − K2 K2 Ca Ca
0
0
τ τ τ K3 β α Ca Ca Ca
· T (N − 1)T
(5)
(6)
where:
T (N − 1) = [Ta (N − 1) Te1 (N − 1) Te2 (N − 1) ×T0 (N − 1) Qd (N − 1) Qsol (N − 1)]
(7)
3.2. Measurement of the solar radiation Sensors and instruments of different sensitivities and functionality have been developed for measuring the solar radiation since 19th century. Bolometer, absolute cavity radiometer, spectroradiometer, pyranometer, pyrheliometer are among the most commonly used ones. The pyranometer is normally used for measuring direct and diffuse solar irradiance in a typical meteorological station where weather is monitored to produce historical data of climate, which can be used for thermal analysis of the built environment. However, these devices are normally very expensive to install and maintain and therefore are not suitable for use in most industrial controllers such as the one being tested in this study. The interest in measuring the solar radiation without using such expensive devices can be dated back to early 20th century. Kimball first suggested that the sunshine fraction was closely correlated to the daily global solar radiation [9]. This was further studied by Angstrom who proposed a linearly relationship between the two variables [10], which was modified to produce what is well known as Angstrom–Prescott equation [11]. This has been widely used in various fields of science and engineering [12]. However, due to the fact that the relationship between the
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sunshine duration and solar radiation is non-linear, which is treated as linear in Angstrom–Prescott equation, efforts have been continued to improve it. Some non-linear equations have been proposed by later researchers. Suehrcke proposed a quadric sunshine fraction–solar radiation relationship can represent a significant advance over the empirical Angstrom–Prescott equation [13]. These methods are applicable for estimating the solar radiation from the sunshine fraction on a daily basis. When the time constant is short, for example minutes, which is required by the ICS controller, these methods are not applicable. Suehrcke and McCormick analysed instantaneous irradiance recorded in interval of 1 min and tried to correlated this with the average clearness index and air mass [14]. The result was that the sunshine fraction is no longer representative to the solar radiation in short term. Graggs et al. investigated the optimal averaging time for solar irradiance on horizontal and vertical surfaces in the UK using statistic method [15]. They concluded that for detailed system design and load estimation, information on short-term changes is crucial and therefore suggested that 10 min averages were required. Here we used a photodiode to measure the solar radiation. A photodiode has two terminals, a cathode and an anode. It has a low forward resistance (anode positive) and high reverse resistance (anode negative). Silicon photodiodes are constructed from single crystal silicon wafers that are similar to those used to manufacture integrated circuits. The major difference is that photodiodes require higher purity silicon. Typically the spectral response of silicon photodiodes ranges from 350 to 1100 nm. Silicon becomes transparent to radiation of longer than 1100 nm wavelength. Therefore it is not suitable for use at wavelengths longer than this value. For UV detection, a fused silica or UV transmitting glass window is needed. Various filter windows are available to tailor the spectral response to suit the application. For this application, the photodiode is reverse-biased to obtain an output that is linear to the illuminance incident on the photodiode junction. The sensitivity is the ratio of radiant energy (in watts) incident on the photodiode to the photocurrent output (in amperes). The photodiode is calibrated using a pyranometer (CM11). Fig. 3 shows the result
Fig. 3. Calibration of the photodiode as a solar radiation sensor using CM11.
Fig. 4. Testing the prototype controller with the simulator.
of the calibration. It shows that the output of the photodiode can be used to calculate the solar radiation accurately. The measuring error is less than 10% when the solar radiation is greater than 50 W/m2 . 3.3. Debugging the prototype To ensure that the control scheme, which was developed in a simulator, had been properly implemented in the prototype, a special interface was developed to connect the hardware prototype with the simulator for testing, as shown in Fig. 4. The interface exchanges information and synchronizes the timing between the simulator (software) and the prototype
Fig. 5. Comparison of the algorithm implemented in the simulator and in the prototype.
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controller (hardware). The simulation is slowed down to real-time so that the simulator runs at the exactly the same speed as the prototype. The heating system and the software ICS are simulated simultaneously in a computer. However the boiler is not controlled by the software ICS. Instead, it is controlled by the hardware prototype controller through the signal, uB , which is also used in the software controller. The climatic information is given to both the software and hardware ICS. Both versions of ICS are commissioned with the same values of the parameters. The outputs of the inferential model in the software and hardware (Tˆ aS and Tˆ aP ) should be the same given the exactly same inputs and internal parameters. Any significant difference between the two variables indicates that the algorithm has not been implemented correctly in the prototype. Fig. 5 shows that the final prototype controller performs exactly the same as the software version implemented in the simulator.
4. Experiment The experiment was carried out in a real heating system in Building Research Establishment (BRE). This is a typical commercial hot water heating system with two gas-burned boilers. Only one boiler is used for normal operation and the other one is used as a back-up. This system provides heating to two buildings that accommodate about 150 working people. There are three types of rooms: offices, small meeting rooms and big lecture theatres. The heat emitting devices are radiators that each is controlled by a TRV. Fig. 6 shows a simplified diagram of the heating system. The existing boiler controller is a thermostat. The heating system
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Fig. 6. A simplified diagram of the heating system.
is continuously running and the set-point of the thermostat is fixed. The boiler is switched between ON/OFF by the controller in order to maintain the temperature of supply water at a set-point, which is fixed when the existing thermostat is in control and is variable when the prototype controller is in control. Fig. 7 shows a photograph of the boiler being controlled during experiment. During the test, the prototype controller logs the following information either at a regular interval (5 min) or whenever the state of the boiler is changed: • • • • • • • •
date and time with resolution of second; external temperature (Te ); solar radiation (Qsol ); burner state (Fire: OFF, Low flame, or High flame); supply water temperature (Tw ); set-point of supply water temperature (TwD ); estimated average air temperature in the building (Tˆ a ); set-point of air temperature in the building (TaD ).
Fig. 7. A photo of the boiler being controlled.
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The test was carried out over two heating seasons, including the following sessions:
5. Result
• Period A: January 28 to February 16, 2003 when the boiler was controlled by the existing thermostat. • Period B: February 16 to March 12, 2003 when the boiler was controlled by the prototype controller. • Period C: October 20 to November 12, 2003 when the boiler was controlled by the prototype controller.
5.1. Performance of the inferential model
In order to obtain information to assess the thermal comfort, the temperature in a number of selected rooms in these two buildings were monitored using a battery-powered instrument, which recorded the temperature at a predefined interval. The recorded room temperature is also needed for commissioning the ICS controller and for evaluating the control performance. Additional information for assessing the thermal comfort was obtained through a survey. On each working day, 25 people were randomly selected to answer the following questions: • How do you feel over the day: too hot, hot, neural, cold, too cold? • When do you feel hot or cold? • What do you wear when staying in your office? The responses collected have been used together the logged room temperature to assess the thermal comfort in the buildings. The set-point of the supply water temperature was: • During Period A: the set-point for Low Flame is 65 ◦ C and for High Flame is 70 ◦ C. • During Periods B and C: the set-point for Low Flame varied from 45 to 80 ◦ C and that for High Flame was 5 ◦ C higher. From March 4 the minimum set-point was changed from 45 to 35 ◦ C.
The inferential model is designed to estimate the average air temperature in the building based on the external temperature (Te ), the solar radiation (Qsol ), and the firing signal (Fire). The output of the inferential model is the estimated average air temperature in the building (Tˆ a ). This is compared with the recorded average air temperature (Ta ) to compute the root mean square of the estimation errors (RMSE): N 2 ˆ i=1 (Ta (i) − Ta (i)) RMSE(P) = (8) N where N is the number of samples. As the on-line measurement of Ta is not available in most application, the ICS replies on the inferential model to estimate Ta . There are a set of parameters that characterise the inferential model. These parameters need to be determined such that the inferential model represents the dynamics of the heating system being controlled. This procedure of determining these parameters is referred to as commissioning. The commissioning is carried out using a short-term monitoring data, which include the inputs and output of the inferential model. The parameters are selected such that RMSE is minimised. In this experiment, the data between January 28 and February 5 is used to commission the inferential model. Fig. 8 compares the average air temperature measured and estimated using the commissioned inferential model. It shows that the inferential model can be accurately parameterised for this period. An important issue here is whether the inferential model, once commissioned using a short-term monitoring data, can produce accurate estimation over a long period. The
Fig. 8. Comparison of the measured and estimated average air temperature in the building from January 28 to February 5.
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Table 1 Daily RMSE of differences between measured and estimated building air temperature Date
Daily RMSE
Date
Daily RMSE
Date
Jan. 28 Jan. 29 Jan. 30 Jan. 31 Feb. 1 Feb. 2 Feb. 3 Feb. 4 Feb. 5 Feb. 6 Feb. 7 Feb. 8 Feb. 9 Feb. 10 Feb. 11 Feb. 12 Feb. 13 Feb. 14
0.67 0.65 0.69 0.71 0.70 0.73 0.72 0.71 0.70 0.74 0.75 0.75 0.76 0.77 0.71 0.72 0.79 0.81
Feb. 15 Feb. 16
0.76 0.81
Feb. 17 Feb. 18 Feb. 19 Feb. 20 Feb. 21 Feb. 22 Feb. 23 Feb. 24 Feb. 25 Feb. 26 Feb. 27 Feb. 28 Mar. 1 Mar. 2 Mar. 3
0.83 0.78 0.71 0.69 0.79 0.77 0.76 0.69 0.68 0.69 0.72 0.76 0.79 0.81 0.82
Mar. Mar. Mar. Mar. Mar. Mar. Mar. Mar. Mar. Mar. Oct. Oct. Oct. Oct. Oct. Oct. Oct.
Daily RMSE
Date
Daily RMSE
4 5 6 7 8 9 10 11 12 13
0.83 0.82 0.83 0.82 0.79 0.78 0.77 0.78 0.83 0.85
20 21 22 23 24 25 26
0.85 0.84 0.84 0.83 0.81 0.82 0.81
Oct. 27 Oct. 28 Oct. 29 Oct. 30 Oct. 31 Nov. 1 Nov. 2 Nov. 3 Nov. 4 Nov. 5 Nov. 6 Nov. 7 Nov. 8 Nov. 9 Nov. 10 Nov. 11 Nov. 12
0.79 0.78 0.76 0.69 0.81 0.82 0.77 0.73 0.69 0.74 0.78 0.81 0.75 0.73 0.69 0.75 0.72
parameters determined through the commissioning was configured in the prototype and has been used for the testing periods B and C. A profile of daily RMSE is given in Table 1. As indicated by a simulation study [1], the accuracy of estimating the average room temperature is required to be within 1.2 ◦ C in order for the controller to perform satisfactorily. Here a maximum RMSE of 0.85 ◦ C was achieved. 5.2. Control performance The boiler was controlled as below: • Period A (from January 28 to February 16): the existing controller. • Period B (from February 16 to March 13): the ICS prototype controller as commissioned using the data from January 28 to February 5. • Period C (from October 20 to November 12): the same as one used in Period B.
Fig. 9. The test results of 4 days during the period B.
It is worth noticing that the Period C belongs to a different heating season from the Periods A and B. Figs. 9 and 10 compares 4 days of the estimated and measured average air temperature in the building during the Periods B and C, respectively. In these figures: • Dashed line: the schedule of desired building air temperature. It is 24 ◦ C for the occupancy (7 am to 9 pm), 19 ◦ C for the setback (9 pm to 7 am). • Solid line: the estimated average air temperature (being controlled close to the dashed line). • Bold solid line: the measured average air temperature. This data was not available to the prototype controller. It was found that the building air temperature could not be maintained at the desired value during the setback from
Fig. 10. The test results of 4 days during the period C.
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d1
3 d=d0 Nd 5 3 r=1 Nd d=d0
ϕ = d 1
(9)
is computed respectively for three periods: A, B and C. The result is shown in Fig. 12. It shows that the percentage of comfort was significantly improved by the prototype controller (Periods B and C) compared with the conventional boiler controller (Period A). Fig. 12 also shows that the percentage of comfort was still fairly low (55.2% the maximum) even when the prototype controller was working. It is because the set-point for the room temperature was set as 24 ◦ C during the occupancy, which is higher than the normal comfort temperature range defined by Fanger [17]. It is reasonable to expect a much better thermal comfort if the set-point for the room temperature was set appropriately. Fig. 11. Daily energy against daily heating degree hour (HDH).
February 24 to March 4. This is because the external temperature was high and a minimum of 45 ◦ C water temperature was not low enough to maintain the building air temperature at 19 ◦ C. Due to this problem, the minimum water setpoint was reduced from 45 to 35 ◦ C on March 4 (around hour 13:50 of the year). Fig. 10 shows that the prototype controller was able to maintain a similar control performance in a different heating season. This suggests that the control scheme is likely to be a practical technique. Overall, the prototype controller was able to control the overall building air temperature as scheduled without experiencing any significant overheating, even though the outdoor temperature was higher during this period than the previous one by about 5 ◦ C. The ability of achieving a good control strongly depends on the accuracy of Ta estimation and the range of water temperature that is allowed in the system. 5.3. Energy and comfort Fig. 11 compares the daily energy consumption against daily heating degree hours between the normal thermostat boiler control and the prototype controller. Using degree hours for short-term comparison of two controllers has been well developed in literatures [16]. The results show that the prototype controller can save energy up to 20% for this heating system. The data collected through the thermal comfort survey is used to analyse the thermal comfort in the buildings during the testing period. In each working day (d), the number of people giving answer (R: 5 = too hot, 4 = hot, 3 = neural, 2 = cold, 1 = too cold) is notated as NdR . The percentage of comfort for a period (d = d0 . . . d1 ) is computed by:
Fig. 12. The thermal comfort calculated from the survey result.
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6. Conclusion Based on the results presented above, the following conclusions can be drawn: • The inferential control scheme (ICS) can be implemented in a microprocessor-based control unit although the simulation study shows that it is computational demanding. • A photodiode can be used to measure the solar radiation with the accuracy required by the ICS. However, it is essential to carry out an appropriate calibration using a pyranometer. • The ICS can be commissioned using short-term monitoring data. Once it is commissioned properly, it can maintain a satisfactory performance for the entire heating season and even for a number of seasons as long as the heating system and the building remain the same. In this case, the maximum estimation error is 0.85 ◦ C. • The ICS significantly improves the overall performance of the heating system. The average room temperature has been maintained at the desired value over the testing period. Acknowledgements This study was partially funded by the Foundation for the Built Environment (FBE) and carried out in Building Research Establishment (BRE), UK. The BRE Facility Management Office is thankfully acknowledged for their support in the installation of the prototype controller and during the entire period of the testing. References [1] Z. Liao, A.L. Dexter, An inferential control scheme for optimising the operation of boilers in multi-zone heating systems, Building Services Engineering Research and Technology 24 (4) (2003) 245–256.
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[2] H. Herring, R. Hardcastle, R. Phillipson, Energy Use and Energy Efficiency in UK Commercial and Public Buildings up to the Year 2000, Energy Efficiency Series, Energy efficiency office, UK, 1988, ISBN 0-11-412903-7. [3] T. Fawcett, A. Hurst, B. Boardman, ECI Research Report 25 – Carbon UK, Industrial Sustainable Development Group, Environmental Change Institute, University of Oxford, 2002. [4] DTI (1995–2001), Digest of UK Energy Statistics, Department of Trade and Industry, The Stationery Office, London, UK, 2001. [5] BRECSU, General Information Report No. 40: Heating systems and their control, Energy Efficiency Best Practice Programme, DETR, 1996. [6] BRECSU, Energy Consumption Guide 81: Benchmarking Tool for Industrial Building – Heating and Internal Lighting, Energy Efficiency Best Practice Programme, DTI, 2002. [7] Z. Liao, A.L. Dexter, A simplified physical model for estimating the average air temperature in multi-zone heating systems, Building and Environment 39 (9) (2004) 1009–1018. [8] Z. Liao, F. Parand, Controller Efficiency Improvement for Commercial and Industrial Gas and Oil Fired Boilers, Building Research Establishment (BRE), A CRAFT project, contract JOE-CT98-7010l, 1999–2001, 2001, p. 8. [9] H.H. Kimball, Variations in the total and luminous solar radiation with geographical position in the United States, Monthly Weather Review 47 (1919) 769. [10] A. Angstrom, Sloar and terrstrial radiation, QJR Meteorological Society 50 (1924) 121. [11] J.A. Prescott, Evaporation from a water surface in relation to solar radiation, Transactions of Royal Society of Science Australlia 64 (1940) 114. [12] C. Gueymard, P. Jindra, V. Estrada-Cajigal, The probability density function P(K, K) of the clearness index: a new approach, Solar Energy 54 (1995) 357. [13] H. Suehrcke, On the relationship between duration of sunshine and solar radiation on the earth’s surface: Angstrom’s Equation revisited, Solar Energy 68 (5) (2000) 417–425. [14] H. Suehrcke, P.G. McCormick, The frequency distribution of instantaneous insolation values, Solar Energy 40 (5) (1988) 413–422. [15] C. Graggs, E.M. Conway, N.M. Pearsall, Statistical Investigation of the optimal averaging time for solar irradiance on horizontal and vertical surface in the UK, Solar Energy 68 (2) (2000) 179–187. [16] A.R. Day, T.G. Karayiannis, Identification of the uncertainties in degree-day based energy estimates, Building Service Engineering Research Technology 20 (1999) 165–172. [17] P.O. Fanger, Thermal Comfort, Mcgraw-Hill, New York, 1972.