Development of hybrid numerical and statistical short term horizon weather prediction models for building energy management optimisation

Building and Environment 90 (2015) 82e95

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Development of hybrid numerical and statistical short term horizon weather prediction models for building energy management optimisation Dimitris Lazos*, Alistair B. Sproul, Merlinde Kay The University of New South Wales, School of Photovoltaics and Renewable Energy Engineering, Australia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 30 December 2014 Received in revised form 22 March 2015 Accepted 23 March 2015 Available online 1 April 2015

Modern building system optimisation frameworks are able to utilise forecasts of generation and load to achieve financial and energy savings. To that end, weather variable predictions of various horizons are particularly useful, as major components of the energy system depend directly or indirectly on prevalent weather conditions. Instead of obtaining weather prediction inputs from an external entity, such as a meteorological office this work proposes the use of a hybrid model that is able to generate localised predictions for ambient temperature, relative humidity and wind speed. A weighted regression and an autoregressive process were implemented in order to develop two hybrid models. The models produce forecasts in a horizon of six hours ahead, with an hourly temporal resolution and are based on two components. The persistence component assumes stationarity of the conditions in the atmosphere, while the numerical component downscales synoptic scale weather observations to a localised region. In this study the persistence will be used as both the reference model to determine the skill of the numerical and the hybrid models, as well as an input component with decreasing weighting for the hybrid models. The hybrid models show notable improvements in skill over both individual components up to 38% for temperature, 28% for relative humidity and 9% for wind speed respectively. More frequent update of reference component inputs, improved the accuracy of the hybrid models even further. Specifically, when the update intervals of the reference component occurred twice as often, the predictions improved by up to 50% compared to the original models. Furthermore, the hybrid models were adjusted to develop forecasts useful for building energy system management, such as the occurrence of a sudden change or a peak temperature. This novel approach is relatively simple to implement and unlike previous works, focuses on high spatial resolution regions and metrics tailored to the optimisation framework of energy management of buildings. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Weather forecasting Numerical prediction models Temperature Relative humidity Predictive control Building energy management

1. Introduction The energy management of commercial buildings is often associated with the prediction of the load and, where available, onsite generation from renewable sources. Accurate forecasting information may assist in minimising the energy costs and adding value to the generated energy, especially during peak load periods. In previous work [1], it was concluded that the accuracy of such forecasts can be increased when using weather variable inputs. This

* Corresponding author. 904/6 Lachlan St, Waterloo NSW 2017, Australia. Tel.: þ61 434 077 254. E-mail address: [email protected] (D. Lazos). http://dx.doi.org/10.1016/j.buildenv.2015.03.025 0360-1323/© 2015 Elsevier Ltd. All rights reserved.

is due to the fact that a primary source of unpredictability is the Heating Ventilation and Air Conditioning (HVAC) load and its peaks, which vary according to the evolution of weather conditions [2e4]. Specifically, in studies where optimisation and control frameworks utilised weather inputs, savings in energy costs of up to 30% were reported compared to a deterministic approach without weather inputs. An extended review of weather forecasting techniques was conducted in previous work [1]. The importance of accuracy was highlighted in the review paper, as errors in weather predictions tend to pass on - often magnified e to higher tier modules responsible for predictions and control of load and demand response measures. Typically, building control systems are receiving predictions from external entities, such as weather

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stations, however it was found that studies with onsite weather forecasts reported improvements in accuracy. The reason for this, is that often the stations are not in close proximity to the building and thus there are differences in the magnitude and temporal evolution of the weather variables [8]. In addition to being able to capture the microclimate of the building site, onsite generated forecasts were found to have advantages, such as ability to integrate directly in a broader control system and generation of tailored outputs. Hence, it was concluded that there is potential value in developing localised weather predictions. Short-term horizons of up to few hours ahead are regarded as the most valuable by the literature, as they are associated with peak load prediction and scheduling of energy flows [5e7]. However, day ahead horizons are also valuable especially for buildings with the ability to utilise their thermal mass to control the discharge of energy. Numerical weather predictions based on atmosphere dynamics equations have been proposed as appropriate high accuracy models for such horizons [1,5,9e12]. However, there are limitations to these techniques, since they may be resource intensive and time consuming to run. Based on the findings discussed in the review paper [1] and summarised above, there is potential for adding value to the energy management systems of commercial buildings via a lightweight localised weather prediction model. The work in this study attempts to add value to the energy management of a building by developing a variety of useful weather forecasts, specifically predictions of air temperature, relative humidity and wind speed of up to 6 h ahead. The advantage of 6 hourly intervals is that the use of recent weather observations can be used to improve overall accuracy. Furthermore, it is a horizon that has been used in existing control strategies as it allows for both a reasonable time frame to develop optimal energy management plans, and a margin for adjustments if needed [13,14]. Air temperature and relative humidity directly affect the heat exchange between the building and the environment as well as the HVAC load. Temperature and wind speed also affect the capacity to generate energy onsite from distributed generation systems, where available. Finally, wind speed may affect ventilation effectiveness depending on the building design. The aim of this paper is the development of a hybrid numerical and statistical regression prediction model, which may operate as a part of a broader control and optimisation framework of building energy management. The justification of such a hybridisation is to combine the advantages of individual numerical and regression prediction models. Specifically, numerical models perform better in instances of strong gradients, while regression models enable the utilisation of existing patterns in weather. The hybridisation was based on the outputs of two base components: a reference component which is obtained from onsite observations and assumes that the state of the atmosphere remains unchanged during the next hours and a numerical prediction component, which is able to downscale synoptic data to generate localised forecasts. The model requires onsite weather observations for the statistical post processing, however since many buildings do not have access to weather monitoring it could run with inputs from external entities. This is considered as a significant benefit as the numerical prediction component can generate simulations from synoptic scale data at any location and hence provide the basis for the final outputs. Two approaches were then followed for the development of the hybrid model: a weighted regression and an autoregressive model with external outputs. Furthermore, the effects of updating the reference component inputs more frequently were investigated. All versions of the base and hybrid models were assessed in terms of their accuracy, requirements and limitations.

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The paper begins with a review of relevant recent studies in order to contextualise the proposed algorithms. The details of the development and parameterisation of the hybrid models, as well as their constituent base models is described in section 3. Section 3 also describes the acquisition process and characteristics of data used in this study. The following part (section 4) includes a range of results and useful findings from the simulations, which are discussed and evaluated extensively in section 4. Additionally, there is a discussion of the limitations and next steps in the context of the development of a complete prediction and optimisation model. 2. Background A considerably large part of control systems responsible for the energy management of buildings is based on analysing outputs from physical models. These models are able to account for a range of factors, such as the building structural composition, the building geometry, and the interactions with its surroundings. While the amount of inputs, architecture and layers used to model the building and its zones vary, variables such as the temperature and relative humidity are vital to ensure efficient management of the load and occupancy comfort. Model predictive control (MPC) systems are control frameworks that typically incorporate weather variables to locate optimal solutions of an objective function, considering boundaries for occupant comfort, energy tariffs and the structure/geometry of the zones in short term horizons [15,16]. Accurate information about the evolution of the weather is involved in:  Adjusting the dynamic optimisation of HVAC set points according to the weather conditions and building zone dynamics [16e20]. Most of these methods attempt to operate the HVAC system at the point of maximum efficiency (lowest energy costs) for a certain horizon and within well-defined boundaries of thermal comfort.  Predictions of building load, as besides occupancy patterns the ambient temperature and relative humidity greatly affect the HVAC load (which in turn is a major component of commercial building load) [19,21e25]. Of particular interest in most of these studies are the predictions of peaks in building load, which are often associated with high energy costs.  Predictions of onsite energy generation (where available): solar generation is directly affected by incident radiation and is negatively affected by higher temperatures and cloud formation [26e33]. Furthermore committing on site cogeneration or trigeneration sources may be optimised with predictions of building load on a day ahead horizon [34e36].  Enabling preconditioning (night-control) processes to shave mid-day peaks by shifting some of the load to low tariff off-peak times [37e41]. Preconditioning of a building is based on the principle of using the building's thermal mass to shift some of the load from the middle of the day to the night before and hence achieve peak and energy cost reductions (assuming that the temperature difference is sufficiently high between day and night).  Enabling various demand response measures: MPC systems are able to respond to hourly energy prices more efficiently with accurate weather inputs [34,42e45]. Savings in terms of reduced energy consumption and costs compared to a business as usual scenario with a rule based control system, can be realised in a range of ways from the above processes (often in parallel). More details about the design, application and performance of such models utilising weather information can be found in previous work [1]. The cost and energy savings results vary

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greatly depending on the building characteristics, available infrastructure, controller used and type of measures implemented, but were mostly within the range of 30e50%. Mixed-mode cooling strategies can make use of accurate weather information in particularly successful ways. In such case study buildings with features, such as automatic control of shading devices the building energy consumption was reduced by up to an impressive 80% with a MPC implementation [46]. Furthermore, temperature predictions of appropriate horizons are always required to assess the preconditioning potential savings. Depending on the building model, location and characteristics, savings up to 40% have been realised in many case study buildings around the world [47,48]. Of course, there is inherent uncertainty in weather predictions due to the inability to perfectly model the atmosphere, as well as limitations in the knowledge of the initial conditions at a given time and point. Building controllers have systems in place to quantify and alleviate any such prediction errors. MPC systems in particular, are designed specifically with the capacity to update the optimal state of a building energy system based on rolling weather forecasts and demonstrate tolerance to inaccuracies [16]. One way to deal with prediction inaccuracies is to use autoregressive models and the assumption that noise follows a normal (Gaussian) distribution to estimate errors at a future point in the time series [16,49]. Predictors using an unbiased Gaussian noise assumption with time dependent variance outperformed conventional strategies for estimating the thermal state of a building by up to 18% and were unaffected by forecasting errors [50,51]. It has also been shown that due to the effects of the thermal mass of the building, small forecasting errors (below 2e3  C for temperature) tend to have relatively minor effects in optimisation of the building energy management and the thermal comfort (reductions of up to 20% reported) [46]. In essence, the indoor temperature and relative humidity display a lag e whose magnitude depends on the building envelope e compared to the ambient weather conditions that our models produce as prediction outputs [52]. Hence the error in building zone conditions is relatively smaller (up to 0.5  C) [53]. Most of the results discussed in this section were obtained from case studies or simulations of specific buildings. Hence, the reported savings were related to:    

The building geometry and structure The building modelling tools The type of energy control system in place The available infrastructure for demand response and energy management

Nevertheless, accurate weather forecasts were deemed necessary in all cases in order to maximise the savings. With a better understanding of the value that accurate onsite forecasts can add to the energy management of a building, it is now possible to proceed with the methodology for the development of the proposed models. 3. Weather variable prediction models This section describes the details of each step during the development of the hybrid models. The outputs were tailored in order to be compatible with several types of measures (the ones discussed in section 2). However, before the design analysis, it is deemed necessary to elaborate on the identity and acquisition of data used in this study. Not only the observed data served as a basis for comparison of the accuracy of the developed models, but

certain parameters of the models were estimated using historical archives. The primary data for the development and comparison of models was obtained from weather observations at three locations around Sydney, NSW:  The Sydney Airport Weather Station (33 570 S, 151100 E, elevation 6 m above sea level)  The Bankstown Airport Weather Station (33 550 S, 150 590 E, elevation 6.5 m above sea level)  The Canterbury Racecourse Weather Station (33 550 S, 15170 E, elevation 3 m above sea level) All of the above sites are located in urban or suburban environments, purposefully selected in order to observe the model capability in predicting weather variables in a setting that resembles a typical commercial building locale. The data was taken directly from weather stations operated by the Bureau of Meteorology (BOM) at each location for three years (2005, 2006 and 2010) and were measured at 10 m above ground level. The temporal resolution is half-hourly. It should be noted that the data provided by the BOM database are averaged over the half-hourly period they correspond to. The hybrid prediction models used in this work were designed to receive inputs from two sources: a persistence prediction model and a numerical weather prediction model (NWP). The persistence and NWP models are referred to as the base models and are explained in section 3.1. Both base models were designed to generate hourly forecast outputs for a 6 h horizon. The outputs from base models were then post-processed using three different statistical techniques in order to generate the final prediction models, referred to as the hybrid models. In addition to the data from the BOM weather stations, synoptic scale data for use with the NWP software was required. This project used synoptic data taken from the National Centre for Environmental Prediction (NCEP) databases [54]. It should be noted that data can also be obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF), however formatting them in a way that is compatible for use within the NWP software is more challenging [55] - unlike NCEP data that can be easily imported into the software. Fig. 1 outlines the architecture of the developed prediction framework and the association of the data, base and hybrid models. As explained earlier, observation and synoptic data were used as both input for the persistence model as well as for the estimation of statistical regression parameters of the hybrid models. 3.1. Base prediction models 3.1.1. Persistence prediction model The persistence model assumes that the state of the atmosphere is stationary over short time intervals. As such, weather variables demonstrate only minor variations for short-term horizons up to 3 h ahead [56]; nevertheless, the use of persistence has been justified for even larger temporal scales in the domain of climatology [57]. Persistence is often used as a reference model in studies attempting to validate NWP or statistical models and evaluate their skill e a forecasting term equivalent to forecasting accuracy [58]. Furthermore, it has been used for the determination of individual component model weighting in ensemble predictions [59]. Wind speed predictions are commonly utilising the persistence model for assessment of power output of a wind farm or micro siting of the turbines [60]. However, predictions of other weather variables, such as temperature [61] and rainfall [62], referred to the persistence as well, in order to evaluate the skill of the model of each study.

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Fig. 1. Architecture of the proposed model, able to generate wind speed, temperature, relative humidity and radiation prediction outputs.

The persistence model uses the observations from weather stations as inputs. The weather variable data used included air temperature, relative humidity and wind speed. Each day was segmented into four 6-h long parts, through which the weather variables were assumed to stay constant according to the persistence model. Let Aobs,n be the observed reference value for the variable A from the weather station averaged between hours n-1 and n. For example, the reference temperature at 01:00 is the average temperature observed at the station's location between 00:00 and 01:00. For the following six hours (nþ1 to nþ6) the persistence model assumes that the temperature stays unchanged and is equal to the temperature at reference hour n. The predicted average values of the variable A for each of the following hour intervals (Anþx) are then:

There are four reference hours during a day, at 01:00, 07:00, 13:00 and 19:00. The prediction model consists of four iterations daily running at the reference hours and predicting the hourly values of the weather variables for the following six hours. For instance the first iteration at 01:00 will produce forecasts for 02:00, 03:00, 04:00, 05:00, 06:00 and 07:00. The rationale behind the selection of these particular reference hours is to align the forecasts with the progressively weaker validity of the persistence hypothesis. The further away from the time when a variable was measured, the less likely it will remain constant, due to weather systems evolving over the day. As such, the persistence model will be less capable of accurate predictions for longer horizons than a few hours. For a commercial building system, the most important time frames would be in the middle of the day, as commercial loads typically have a peak in the afternoon and are very low and independent of weather variables outside working hours [43]. The greatest variations of temperature occur during the morning after the sun rises and in the evening as the sun sets. As such, if the reference hour is set at 7:00 it is hypothesised that by the next iteration which occurs at 13:00 the persistence model will have minimum contribution, because the temperature at the middle of

the day is expected to be higher than the early morning temperature. Similarly, the temperature at 19:00 is expected to be notably lower than the midday temperature. This is a necessary assumption in order to maximise the accuracy of the hybrid models as explained in section 3.2. The trend of higher variation of temperature at certain hours in the middle of the day can be justified by the results shown in Fig. 2. The figure shows the average percentage variation of both observed temperature and observed relative humidity at each hour over the course of a day for 3 years. It can be seen that average hourly temperature varies more during the period starting at 8:00 and keeps varying significantly until 13:00 compared to the rest of the day. Practical reasons were considered in addition to modelling requirements for the selection of the reference hours. Since commercial building occupancy is predominantly between 8:00 and 18:00 it would make sense to attempt to produce forecasts as accurately as possible for this period in order to ensure occupant comfort and optimise energy savings. As such the reference hour choice of 7:00 would allow us to produce forecasts for the morning with the most recent observed values taken into consideration. Similarly, the most recent observed values will be used at reference hour 13:00 to produce forecasts for the afternoon period, which is typically associated with high HVAC loads especially in the summer. Furthermore, choosing a reference hour at 1:00 allows us to predict the evolution of weather variables during the night and make choices for preconditioning that will discharge energy during the morning/afternoon periods depending on the building's thermal mass (typically within the range of 6e12 h).

Fig. 2. Percentage hourly variation of temperature and humidity.

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3.1.2. Numerical prediction model Numerical models are able to solve fundamental equations governing the evolution of atmospheric variables and predict its future state. The second base model is based purely on numerical predictions simulated in The Atmospheric Pollution Model (TAPM) platform. TAPM was developed by the Commonwealth Scientific and Industrial Research Organisation (CSIRO). The software was developed mainly for modelling air quality for use within environmental and pollution studies. However, its meteorology component can be utilised to obtain weather variable outputs for any location in the world. The base meteorological variables are determined in TAPM as follows [63]:  The orthogonal horizontal plane components of wind speed (u and v) are determined from the momentum and terrain following vertical wind speed equations  The terrain following vertical velocity vector (s) is determined from the continuity equation  The potential virtual temperature (qv) is determined from the conservation of heat and vapour  The Exner Pressure (p) is determined as the sum of hydrostatic (pH) and non-hydrostatic pressure components (pN); the nonhydrostatic component of the equation is optional The derivation of the above equations can be found in CSIRO's documentation [64]. Apart from the base variable equations and grid resolution, parameterisation affecting the local meteorology includes soil and vegetation types, precipitation micro-physics, radiative and turbulence fluctuations and degree of urbanisation [63]. The derivation of equations for each of the above parameterisations can be also found in CSIRO's documentation [64]. TAPM generates average hourly outputs of a variety of weather variables, which serve as inputs to the hybrid models in this work. As with other modern numerical model platforms, TAPM is able to run simulations in up to five 3-dimensional domains nested within each other. The user can define the size of each domain, as well as the grid points that the simulations take place. The NCEP synoptic data are used to initialise the simulation at every grid point and set the boundary conditions of the external domain with the lowest spatial resolution. The simulations are then in succession at the internal domains with progressively higher spatial resolution. The internal grids use their immediately outer grid to determine the boundary conditions. Thus it is possible to use the synoptic data to generate very highly localised meteorological prognostics in a reasonable amount of time. The simulations are also computationally non-intensive and they can be run on a normal computer. There have been a few studies based on the meteorological component of TAPM. Solar global horizontal irradiance was predicted using a resolution of 45 km and it was found that it was overestimated especially during periods of sky coverage changes [65]. More relevant to this study, temperature and wind speed predictions showed increased skill at high resolution domains when downscaling from synoptic data [66] for grids of 3 km resolution in certain regions in Melbourne. TAPM was able to accurately predict (correlation coefficient of 93%) hourly values of radiation and temperature in a site in Western Australia, even though post-processing was required for certain cases such as cloudy days and high irradiance periods [67]. However, there is so far a lack of studies examining the potential of using TAPM to generate useful outputs for the energy management of commercial buildings. This study attempts to do so by investigating its forecasting skill in a high spatial resolution domain. Furthermore, besides assessing its skill in general predictions, emphasis is placed on predictions of abrupt changes and extreme heat events, as well as

the correlation of temperature and relative humidity. Such findings are of use to energy management systems as with appropriate infrastructure significant savings may be realised (in the ways discussed in section 2). For this work, the simulations were run in hind casting mode and were initialised by the NCEP synoptic data for the same 6hourly intervals as the persistence model. The spatial resolution of the model was configured with the following constraints:  5 grids nested within each other  Ratio of grid dimensions 81:27:9:3:1 (within the recommended limits for optimal simulations from the developer [68])  Outer grid domain resolution of at least 40 km  40 km to remove boundary conditions as far away from the central grid point and to accurately predict radiation e this is necessary as accuracy of TAPM suffers at grid points close to the domain boundaries [69].  Inner grid domain resolution of at most 500 m  500 m to capture localised effects  25  25  25 grid (x,y,z) (recommended for optimal simulations from the developer [68]) The higher the spatial resolution the longer it takes for the simulations to run. However, the forecasting skill was not improved for very high resolutions (down to 100 m  100m inner grids). Thus the domain configuration for this work was selected to be able to produce high forecasting accuracy at a reasonable running time (around 6 min per forecasting day on a middle-end laptop computer):

40:5km : 13:5km : 4:5km : 1:5km : 0:5km TAPM simulations produce predictions of weather variables averaged over one hour periods, which can be directly compared to the measured average hourly temperatures from the weather stations. The selected domain for weather predictions in this work was the high resolution domain #5 (0.5 km), as it is able to capture the localised variations of the variables more accurately. Table 1 shows the mean absolute forecasting error (MAE) and root mean square error (RMSE) of each domain obtained from TAPM, for each variable averaged across the three sites for a yearly set of data. It was observed that the inner grid produced the highest accuracy and this trend was true for all variables and all weather stations. However it should be pointed that the error variation between domains is relatively small e especially for temperature (difference in MAE of 0.1  C and RMSE of 0.3  C) and relative humidity (difference in MAE of 0.75% and RMSE of 1.4%). Statistical post-processing as described in 3.2 is able to reduce the magnitude of errors substantially. As discussed in section 2, there are ways to minimise the effects of errors in forecasting weather variables that are used as input in controlling the operations of a building energy system. In most cases, while the comfort zone is relatively narrow for temperature (between 5 and 7  C) [10,70], errors within the range of 1e2  C in ambient temperature can still enable optimal operation of the energy system. There is higher tolerance for relative humidity errors as the comfort zone lies typically within a wider range (20e80%). Furthermore, as this paper is concerned with the utilisation of the outputs for commercial building energy management, the performance of TAPM domains was evaluated according to their ability to correctly predict bigger changes in the variables. As discussed earlier, such changes and especially ones that result in peak temperatures are significant for the management of energy in buildings. Domain #5 demonstrated slightly higher accuracy for most tests, thus justifying its selection for the analysis of results in

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Table 1 TAPM domain accuracy comparison.

Domain resolution Temperature MAE( C) Temperature RMSE ( C) Humidity MAE (%) Humidity RMSE (%) Wind MAE (m/s) Wind RMSE (m/s)

Domain 1

Domain 2

Domain 3

Domain 4

Domain 5

40.5 km 1.98 2.77 12.50 17.33 3.51 3.99

13.5 km 1.95 2.69 12.41 17.02 2.99 3.86

4.5 km 1.93 2.62 12.25 16.72 2.76 3.85

1.5 km 1.89 2.60 11.98 16.55 2.50 3.72

0.5 km 1.86 2.44 11.75 15.93 2.39 3.31

section 4. Table 2 summarises the findings of each domain's ability to predict bigger changes in temperature and relative humidity. In the context of the evaluation of TAPM domains, all changes resulting in hourly variation of the variable higher than the 90 percentile or lower than the 10 percentile mark were treated as bigger changes. 3.2. Hybrid prediction models 3.2.1. Linear weighted forecasting (WF) model The linear WF model is the first hybrid model and was developed to utilise outputs from both base models with varying weights. The main assumption is that the numerical forecast outputs become progressively more significant for predictions of temperature further away from the reference hour [71]. As discussed earlier, as the day progresses the persistence hypothesis is becoming less valid. For predictions closer to the reference hours, the persistence model is more significant since the state of the atmosphere changes only marginally. However, as time progresses and the effects of daily weather cycles start becoming prevalent, the numerical prediction framework is more valuable. A linear weighting regression was implemented to express the varying weights of the two base models for the six hourly blocks after each reference hour. The forecasts of variable A for each hour (Anþx) were obtained by weighting the observed temperature at reference hour (Aobs,n) by a factor of wnþx and the numerical prediction (ANWP,nþx) at hour n þ x by a factor of (1wnþx). n þ x is the point in the time series with distance of x hours from the reference hour n. Thus the predicted temperatures (Tnþx) use the following equations:

For Anþ1 the weighting factor wnþ1 was set to 100%, representing 100% contribution of the persistence model and then linearly

Fig. 3. Comparison of weighting contribution of each base model to the WF linear prediction model.

decreased by 1/6 for each subsequent point of the time series. Accordingly, the weighting factor 1wnþx started from 0% and increased in a linear fashion by 1/6 for each hourly interval. The 1/6 decrease represents the negative gradient of the linear weighting, as each prediction iteration occurs in a 6 hourly horizon. The weighting factors of both persistence and NWP models over the duration of each six-hourly prediction interval can be seen in Fig. 3. The hybrid WF model resulted in notable improvement of the forecasting accuracy over both the persistence model and TAPM as seen in the results section. 3.2.2. Optimisation algorithm weighted forecasting (WFS) model Rather than assuming a linear decrease of the weighting factor wnþx the further away the time series is from the reference hour, the WFS model uses heuristics to find the optimal weightings for each point in the 6 hourly blocks. This process is carried out by utilising long-term archived observed weather data for each specific location. One training year was used for each site to estimate the weighting factors, and these factors were applied to assess the skill of the WFS model for all data. Otherwise, the hybridisation is carried out using the formulas presented in 2.2.1. The primary optimisation algorithm objective was to minimise the average mean absolute forecast error. To that end, the algorithm used was the generalised reduced gradient algorithm, since it provides a fast and efficient approach to solve linear problems. The algorithm searches for minima where the function gradient is equal to zero, by continuously modifying each of the six weighting factors and examining the effects on the partial derivatives. The central

Table 2 Comparison of each domain's ability to predict bigger changes in temperature and relative humidity. Domain resolution

Dom. #1

Dom. #2

Dom. #3

Dom. #4

Dom. #5

Temperature changes 90-percentile MAE ( C) Temperature changes 10-percentile MAE ( C) Relative humidity changes 90-percentile MAE (%) Relative humidity changes 10-percentile MAE (%)

2.01 1.60 11.42 11.60

2.01 1.61 11.40 11.15

2.04 1.52 11.29 11.11

1.99 1.53 11.34 10.96

1.92 1.53 11.53 10.91

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differencing technique was implemented, which modifies the weighting factors in both directions in an attempt to find an accurate solution. The optimisation algorithm was run multiple times from different starting points in order to avoid local minima and the results converged to the values shown in Figs. 4e6 using one year long data for each site. The results confirm that the initial approach of linear weighting was reasonable for all variables. 3.2.3. ARX prediction model Using the TAPM forecasts as inputs (B(t)) and the past observations (A(t)) it was possible to approach the hybridisation forecasting problem from a different perspective. An auto-regressive model with external output (ARX) was implemented. The ARX correlates the value of the variable at a time t (A(t)) to a finite number of observed outputs A(t-k) and external inputs B(t-k). The order of the model is a set of three integer parameters that dictate the model architecture:  ma is the number of time steps of past output observations used  mb-1 is the number of time steps of past inputs used  mk is the dead-time of the system e in this analysis it is kept at 1 as observed temperature depends on the immediately previous observation The ARX model of order ma:mb:1 can be then written as:

AðtÞ þ a1 Aðt  1Þ þ a2 Aðt  2Þ þ / þ ama Aðt  ma Þ ¼ b1 Bðt  1Þ þ b2 Bðt  2Þ þ / þ bmb Bðt  mb Þ The equation can be rewritten in a simpler form using a timeshift operator q-m representing the difference between the current output and the mth time step:

AðtÞ þ a1 q1 AðtÞ þ a2 q2 AðtÞ þ / þ ama qma AðtÞ ¼ b1 q1 BðtÞ þ b2 q2 BðtÞ þ / þ bmb qmb BðtÞ The ARX model can be then expressed in a compact form with two weighting polynomials and the input/output time series:

AðtÞaðqÞ ¼ BðtÞbðqÞ Finally, a noise component e(t) with constant variance can be added to the model to simulate the random factors contributing to the evolution of the system:

AðtÞaðqÞ ¼ BðtÞbðqÞ þ eðtÞ

Fig. 4. Weights (wx) of the persistence model for temperature for each hybrid model at each location and time series point. The NWP weighting is equal to 1-wx.

Fig. 5. Weights (wx) of the persistence model for relative humidity for each hybrid model at each location and time series point. The NWP weighting is equal to 1-wx.

The weights a(q) ¼ (a1, a2, …, ama) and b(q) ¼ (b1, b2, …, bmb) were estimated for each order using the MATLAB identification system using the observation data for each site. For this project and in order to compare models on the same basis a 6:1:1 ARX model was implemented. 3.3. Forecast sensitivity to output update intervals The hybrid forecast model performance can be enhanced if the input values of the variables from the persistence model are updated in more regular intervals of 3 h (3U), 2 h (2U) and one hour (1U) respectively. The variable values from the numerical model predictions are still obtained from 6 hourly simulations. Of course this may be less practical from a planning point of view, since it means that the building control system will have to be updated more often with weather prediction inputs. The research results demonstrated that the forecasting performance is increased with more frequent updates and more importantly, the forecasts become more responsive and able to detect sudden changes and peaks; however, decisions for demand response measures, scheduling HVAC operations and committing energy sources may have to be changed more frequently. In buildings with limited infrastructure and inflexible decision making policies, this may pose constraints to an implementation with more frequent updates. 4. Results The main metric used for forecast accuracy comparison is the mean absolute error (MAE). This is preferred over percentage errors (MAPE), as MAE is able to compare variable prediction on a normalised basis across the year. For instance, a temperature error of 1

Fig. 6. Weights (wx) of the persistence model for wind speed for each hybrid model at each location and time series point. The NWP weighting is equal to 1-wx.

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Table 3 MAE of each prediction model for temperature. Prediction model MAE

Persistence

TAPM

WF

WFS

ARX

Average Airport ( C) Average Canterbury ( C) Average Bankstown ( C) Average Total ( C) Accuracy increase from persistence

1.93 2.59 2.81 2.44 e

1.69 1.99 1.92 1.86 23.69%

1.32 1.74 1.82 1.62 33.52%

1.30 1.61 1.64 1.52 37.88%

1.51 1.89 1.76 1.72 29.60%

Average error across three sites and average forecasting skill performance comparison in bold.

Table 4 RMSE of each prediction model for temperature. Prediction model RMSE

Persistence

TAPM

WF

WFS

ARX

Average Airport ( C) Average Canterbury ( C) Average Bankstown ( C) Average Total ( C) Accuracy increase from persistence

2.88 3.56 4.04 3.49 e

2.22 2.63 2.47 2.44 30.27%

1.86 2.16 2.41 2.14 38.73%

1.79 2.16 2.14 2.03 41.81%

2.17 2.51 2.40 2.36 32.40%

Average error across three sites and average forecasting skill performance comparison in bold.

would produce the same MAE regardless of season; however if MAPE was used the winter value would be significantly higher as the temperatures are generally lower in the winter. RMSE is also a useful metric, since it allows us to compare the magnitude of variation in errors across models. Tables 3 and 4 show the average MAE and RMSE respectively for each model, year and site. For temperature predictions the results demonstrated a superiority of the WFS hybrid model for the original scenario of 6 hourly updates of the observed values. As seen in Tables 2 and 3, the WFS hybrid model improved the persistence predictions by 37.88% (MAE) and 41.81% (RMSE). Regarding the absolute prediction errors, the WFS model improved the persistence predictions by 1.52  C (MAE) and 2.03  C (RMSE). The effects of more frequent updates as discussed in section 4.3 can be seen in Table 5. It is worth noting that the greatest improvement compared to the 6U models occurred for the ARX model. In fact, for the 3U, 2U and 1U models the ARX outperformed the WFS in terms of prediction accuracy (MAE) across all sites. While the difference in performance appears to be modest, selecting the ARX model over the WFS is preferred under the assumptions discussed in section 3.3. Further discussion about the advantages and disadvantages of each model can be found in part 5 (Discussion and Conclusions). Fig. 7 displays a comparison of the effects of update frequency of the persistence model to the WFS and ARX models. Tables 6 and 7 show the MAE and RMSE for the predictions of relative humidity across all sites. The numerical model did not perform as well for predictions of humidity as it did for predictions of temperature, however the WFS was still the superior model with an overall improvement compared to persistence of 27.54% (MAE) and 28.59% (RMSE).

Fig. 7. Comparison of effects of update frequency of the persistence model on the accuracy of temperature prediction.

The effects of more frequent updates of persistence to the accuracy of the WFS and ARX models can be seen in Table 8. A similar trend as the one observed for temperature predictions was seen for relative humidity predictions. The ARX model demonstrated the most significant improvement with more frequent persistence updates and outperformed the WFS for the 3U, 2U and 1U models. Fig. 8 summarises the above results. Finally the summary accuracy results for wind speed can be seen in Tables 9 and 10. TAPM appeared to show less skill in wind speed predictions and in fact was significantly less accurate than the persistence model in all instances. Among the hybrid models, WF and WFS only resulted in minor accuracy increases compared to persistence, and in fact ARX generated less skilful forecasts compared to persistence.

Table 5 Comparison of persistence update frequency for temperature. Prediction model

6 hourly updates (6U)

3 hourly updates (3U)

2 hourly updates (2U)

1 hourly updates (1U)

Persistence MAE ( C) Relative accuracy increase from 6U WFS MAE ( C) Relative accuracy increase from 6U ARX MAE ( C) Relative accuracy increase from 6U

2.44 e 1.60 e 1.72 e

1.53 37.21% 1.25 22.08% 1.10 36.24%

1.20 50.89% 1.09 31.88% 0.90 47.67%

0.86 64.57% 0.84 47.50% 0.66 61.43%

Average error across three sites and average forecasting skill performance comparison in bold.

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Table 6 MAE of each prediction model for relative humidity. Prediction model MAE

Persistence

TAPM

WF

WFS

ARX

Average Airport (%) Average Canterbury (%) Average Bankstown (%) Average Total (%) Accuracy increase from persistence

9.48 12.29 11.93 11.17 e

12.74 12.37 10.82 11.75 ¡5.18%

8.03 8.97 8.16 8.26 26.03%

7.66 8.91 8.12 8.09 27.54%

8.55 9.35 8.95 8.95 20.32%

Average error across three sites and average forecasting skill performance comparison in bold.

Table 7 RMSE of each prediction model for relative humidity. Prediction model RMSE

Persistence

TAPM

WF

WFS

ARX

Average Airport ( C) Average Canterbury ( C) Average Bankstown ( C) Average Total ( C) Accuracy increase from persistence

13.45 17.81 17.14 16.13 e

15.93 15.71 16.14 15.93 1.27%

10.96 12.23 11.99 11.73 27.31%

10.62 11.99 11.95 11.52 28.59%

12.09 13.18 14.89 13.39 17.00%

Average error across three sites and average forecasting skill performance comparison in bold.

Table 8 Comparison of persistence update frequency for relative humidity. Prediction model

6 hourly updates (6U)

3 hourly updates (3U)

2 hourly updates (2U)

1 hourly updates (1U)

Persistence MAE (%) Relative accuracy increase from 6U WFS MAE (%) Relative accuracy increase from 6U ARX MAE (%) Relative accuracy increase from 6U

11.24 e 8.23 e 8.95 e

7.24 35.59% 6.37 22.60% 6.24 30.32%

5.84 48.07% 5.41 34.26% 5.14 42.53%

4.33 61.51% 4.22 48.76% 3.89 56.57%

Average error across three sites and average forecasting skill performance comparison in bold.

As temperature and to an extent relative humidity are the variables of highest significance in the context of building load prediction, further results were generated to illustrate the performance of the base and hybrid models. Fig. 9 shows the average MAE for each hour of day as obtained for the airport site for each of the base and hybrid models. TAPM generates consistent predictions and in fact is superior to other models for the morning hours (9AM to 1PM). This can be explained due to the presence of relatively high gradients at that times (since the temperature typically rises faster as seen in Fig. 2). This has implications for load correlation as raw TAPM forecasts could be used in place of either the WF or WFS models during those times for any optimisation routines. Archived data of onsite observations need to be analysed

Fig. 8. Comparison of effects of update frequency of the persistence model on the accuracy of relative humidity prediction.

to assess the frequency of these instances, as well as their magnitude and time of occurrence. These factors are site specific and subject to both the landscape (proximity to the coast, shading, terrain roughness) as well as the microclimate of the region in question. Furthermore, the numerical predictions appear to be slightly less accurate during the summer months, while the persistence model is less accurate during the rest of the year. No clear trends could be recognised for the hybrid models. The comparison per month can be seen in Fig. 10. Besides forecasting skill, the ability to predict sudden changes in weather variables is significant for the energy management of commercial buildings as they may contribute to unforeseen load spikes and lead to deviations from the optimal planning. Figs. 11 and 12 show the performance of the hybrid models (WFS and ARX respectively) during a hot day with a sudden drop in temperature (between 14:00 and 15:00) by 17  C. In both figures the BOM curve represents the measured hourly average temperature, while the rest of the values are the predicted values of temperature as generated by the prediction models. As both WFS and ARX models receive inputs from recent observations with a delay of up to 6 h for the 6U versions and up to 3 h for the 3U versions (depending on the time compared to reference hour), it follows that if a sudden change occurs in the meantime it will be difficult to predict. This can be seen in the Figs. 11 and 12, where both WFS and ARX predictions of the sudden change lag behind the actual sudden change that occurred at 15:00. Table 11 summarises the results for the accuracy of predictions of sudden changes. The results are related to hourly changes over the three sites for the three years. In the context of this study, the following changes are considered abrupt:

D. Lazos et al. / Building and Environment 90 (2015) 82e95

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Table 9 MAE of each prediction model for wind speed. Prediction model MAE

Persistence

TAPM

WF

WFS

ARX

Average Airport (m/s) Average Canterbury (m/s) Average Bankstown (m/s) Average Total (m/s) Accuracy increase from persistence

1.72 1.53 1.71 1.65 e

3.52 1.77 1.89 2.39 ¡44.61%

1.99 1.36 1.50 1.62 2.20%

1.68 1.34 1.49 1.50 9.20%

2.71 1.54 1.68 1.98 ¡19.41%

Average error across three sites and average forecasting skill performance comparison in bold.

Table 10 RMSE of each prediction model for wind speed. Prediction model RMSE

Persistence

TAPM

WF

WFS

ARX

Average Airport ( C) Average Canterbury ( C) Average Bankstown ( C) Average Total ( C) Accuracy increase from persistence

2.96 1.98 1.94 2.29 e

5.23 2.28 2.43 3.31 ¡44.46%

3.04 1.80 1.80 2.22 3.44%

2.94 1.75 1.75 2.15 6.39%

3.54 1.92 1.89 2.45 ¡6.78%

Average error across three sites and average forecasting skill performance comparison in bold.

 Rise or drop of hourly average temperature of more than 10  C  Rise or drop of hourly average relative humidity of more than 10%  Rise or drop of hourly average wind speed of more than 6 m/s [72]. It can be seen in Table 11 that TAPM performs better than the rest of the models in almost all instances. Another notable observation is that using more frequent inputs in the 3U model improves the performance of the WFS and ARX for temperature and relative humidity skill, but not for wind speed. It should however be noted, that this type of abrupt changes is relatively rare. Specifically, in 9 years’ worth of hourly historical observations across the three sites, there were in total:  225 cases of abrupt changes in temperature, spread almost evenly across the three sites (representing 0.3% of a year's worth of observations)  179 cases of abrupt changes in relative humidity, spread almost evenly across the three sites (representing 0.23% of a year's worth of observations)  304 cases of abrupt changes in wind speed, the majority of which were observed at the Bankstown site (representing 0.23% of a year's worth of observations (representing 0.39% of a year's worth of observations)

systems in buildings. In this context, particular emphasis is placed on the prediction of periods of high temperatures as they are responsible for major peaks in HVAC loads and related to the potential activation of demand response measures. Furthermore, during hot days generation plants, such as cogeneration or solar panels may need to shut down or operate at reduced output mode. For the three sites, it was found that periods of temperature of more than 32  C were just above the 97 percentile mark and represent a meaningful value for defining an extreme day. This value of course could be adjusted according to the climate of the location the model is applied, as well as the specific demand response requirements and automation processes of the energy system. Table 12 summarises the results of the skill of each model in predicting such events and compares it to the prediction skill throughout the year. As seen in Table 12, both the persistence and TAPM models experience a significant decrease in skill when predicting the magnitude of extreme events. Accordingly the hybrid models demonstrate a similar decrease in forecasting accuracy. The ARX 3U model appears to be the best performing model for this type of forecasts. The main reason for this trend is that both the base models tend to underestimate the magnitude of such high temperatures. Specifically, TAPM underestimates the temperature of such periods around 91% of the time and persistence underestimates the temperature around 77% of the time.

Apart from sudden changes, information about the occurrence of extreme events is of interest for the optimisation of energy

Fig. 9. Comparison of hourly performance of the four prediction models (airport site).

Fig. 10. Comparison of monthly performance of the four prediction models (airport site).

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D. Lazos et al. / Building and Environment 90 (2015) 82e95

Fig. 11. Performance of WFS model during a typical hot day with a sudden change in temperature.

Fig. 13. Correlation of temperature and humidity for a 9 year period for the airport site.

shows the distribution of temperature-humidity pairs as obtained from the data over a period of 9 years at the airport site. It was found that extremely high temperatures (over 32  C) always occurred under low relative humidity conditions (lower than 50%). With that correlation in consideration it was possible to improve the skills of the hybrid models. Specifically, for the prediction intervals that WFS showed both a drop in humidity below 50% and a rise of temperature above 32  C, the peak temperature prediction was adjusted according to the average error found in Table 12. Fig. 14 shows the flowchart of the process used to take into account the temperature-humidity correlation. Table 13 shows the MAE of each hybrid model (the persistence and TAPM predictions remain unchanged) after adjusting for low humidity. Another interesting metric is the temperature peak temporal difference. As commercial building energy management is greatly concerned with peak load prediction, forecast models can be validated according to their ability to accurately forecast when a peak in temperature will occur. The time when the daily peak occurred was found and then compared with the predicted daily peak of each base and hybrid model. The differences between the actual and predicted peak were then averaged over two years. Table 14 shows the results that demonstrate a superiority of WFS model, as it was able to predict peaks slightly more accurately than the rest of the models, on average 1.72 h away from the actual peak. The numerical model (TAPM) had an average difference of 1.77 h and the ARX model an average difference of 2.23 h. Both the hybrid models were improved by changing the update interval to 3 h (3U).

Fig. 12. Performance of ARX model during a typical hot day with a sudden change in temperature.

In order to enhance the accuracy of the prediction models for extreme events, the raw weather data from the stations were used. This allowed us to provide a better statistical understanding of the correlation between temperature and relative humidity. In turn, this proved useful for assessing the probability of a peak load in addition to the results of the proposed prediction models. Fig. 13

Table 11 Comparison of performance of prediction models in forecasting sudden hourly changes. Type of abrupt change

Persistence MAE

TAPM MAE

WF MAE

WFS 6U MAE

ARX 6U MAE

WFS 3U MAE

ARX 3U MAE

Temperature rises ( C) Temperature drops ( C) Humidity rises (%) Humidity drops (%) Wind speed rises (m/s) Wind speed drops (%)

6.09 6.86 16.8 19.7 5.91 3.82

2.30 4.29 11.9 11.5 5.41 2.08

4.89 5.82 12.5 14.7 5.71 2.74

3.94 5.40 12.5 15.2 5.67 2.25

4.98 5.60 15.5 18.2 5.88 3.11

3.72 4.35 14.1 14.0 5.98 3.77

4.00 4.47 12.4 14.0 5.91 2.57

Table 12 Comparison of accuracy of predictions of each model for extreme heat events (temperatures over 32  C).



MAE of extreme events ( C) Average yearly MAE ( C)

Persistence

TAPM

WF

WFS 6U

ARX 6U

WFS 3U

ARX 3U

5.03 2.44

3.64 1.86

3.16 1.62

2.94 1.52

3.18 1.72

2.40 1.25

1.70 1.10

D. Lazos et al. / Building and Environment 90 (2015) 82e95

Fig. 14. Flowchart of adjusting TAPM predictions of high temperatures according to predicted humidity.

5. Discussion and conclusions The evaluation of the models and modifications described in the previous section has to be carried out not just in terms of their skill, but taking into consideration their usefulness and limitations of their application in a building energy management framework. In this context, it is concluded that both versions of the hybrid models (WFS and ARX) provide significant increase in skill and applicability over the base models in most of the cases. Specifically, for all variables considered, WFS skill was superior to both the base models (reference and TAPM) as well as the linear WF and ARX models under the initial 6-hourly update assumption. Since WFS weighting factors are calculated from archived observations on site, it is expected that using longer databases may improve the skill further. In this paper, the weighting was conducted using one year long data, and the model performed consistently for the other two test years. The ARX model on the other outperformed the WFS in any situation where the reference input was shorter than 3 h. More frequent updates of the reference component resulted into higher skill not just for the ARX, but across all models. While three different variations were tested (3, 2 and 1 hourly update intervals), it was mainly the 3-hourly model that was considered for practical reasons. Updating the reference component requires inputs from onsite observations and may lead to adjustments in demand responses or HVAC setpoints that take some time to implement.

93

Certain dynamic optimisation systems may have the ability to utilise shorter update horizons, improving the potential benefits even further. For instance, modules responsible for adjusting the HVAC setpoints could foresee a peak in temperature larger than initially estimated and attempt to bring the setpoint closer to the upper bound of the comfort zone before the peak occurs (resulting in peak load reduction). While the computation time of the simulations by the proposed models is short, dynamic energy system optimisation may be limited by various factors in a building, such as decision making policies and lack of infrastructure allowing to adjust the energy flows in a dynamic manner. Thus, while shorter update intervals may produce more accurate predictions, they may be inapplicable if the energy system cannot respond in a timely manner to the new outputs. Regarding the prediction of abrupt changes, TAPM appeared to have the highest skill overall even compared to the hybrid models. This is justified by the fact that usually these changes are caused by larger scale weather phenomena, such as cold fronts which TAPM can model better from the synoptic data. On the other hand the hybrid models show inferior skill in predictions of sharp gradients, as they include a component that assumes a steady state of the atmosphere. To address this issue, and in line with the rationale of hybridisation, a simple algorithm must be incorporated in the control system that uses 100% weighting of the numerical prediction component if it indicates that such an abrupt change will occur within the next period. As seen in Table 11, this results in substantial error decrease, especially for sudden rises of temperature, which are majorly responsible for unforeseen load peaks (from 4 to 5  C for the hybrid models to 2.3  C with 100% numerical weighting). Furthermore, as discussed in section 4, while abrupt changes leading to peaks are of great importance to building energy management, our analysis showed that they do not occur that often. As such, the advantage of a hybrid model becomes clear, since it is able to outperform in accuracy the numerical model for the majority of the days within a year (when gradients are low); but can also handle the abrupt change predictions by using the simple algorithm described above. Another algorithm that can be used and shows the value of hybridisation was described in Fig. 14. The statistical adjustment was used to significantly improve the accuracy of the models in predicting extreme heat events and the presence of peaks in temperature as it reduced the error by 1  C in most cases (Table 13). Overall, while both WFS and ARX perform better than the base models in most metrics, it was found that the WFS is more consistent and able to generate more accurate predictions. However, instead of suggesting the use of a single model for all purposes, different modules of a control system may utilise the outputs from the various components, which is after all a benefit of

Table 13 Comparison of accuracy of predictions of each model for extreme heat events (temperatures over 32  C) with consideration of temperature-humidity correlation.



MAE of extreme events ( C) without humidity correlation MAE of extreme events ( C) with humidity correlation

WFS 6U

ARX 6U

WFS 3U

ARX 3U

2.94 1.76

3.18 2.13

2.40 1.35

1.70 1.18

Table 14 Comparison of absolute peak temporal difference for all models. Prediction model

TAPM

WF

WFS

WFS 3U

ARX 6U

ARX 3U

Average peak difference 2010 (hours) Average peak difference 2006 (hours) Average peak difference (hours)

1.77 2.00 1.89

1.73 1.65 1.69

1.72 1.56 1.64

1.60 1.46 1.53

2.23 2.01 2.12

1.80 1.56 1.68

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D. Lazos et al. / Building and Environment 90 (2015) 82e95

Table 15 Comparison of the skill of each model according to the results obtained from the simulations. Model

Persistence

TAPM

WF/WFS

ARX

Forecasting skill (temperature) Forecasting skill (humidity) Forecasting skill (wind speed) Effects of persistence input frequency Abrupt changes skill Extreme heat events skill (default) Extreme heat events skill (with algorithm) Peak time prediction skill

Low Low Low Very Very Very N/A Very

Moderate Low Very low N/A High Low N/A Moderate

High High Moderate Positive Low Low High High

High Moderate Low Very positive Low Low High Moderate

positive low low low

hybridisation since each model complements the other. Depending on what outputs are needed, certain components may be called by the controller for input. For instance, the 3U ARX generated better predictions of extreme heat events especially after considering the humidity correlation, while WFS was better in predicting the timing of such peak events. It should be noted that while TAPM performed relatively well individually in predictions of temperature, it was actually not as skilful in predictions of relative humidity and wind speed compared to the reference model. The hybridisation value was realised in both cases, where application of the regression algorithms improved the forecasting accuracy by up to 28%. The domain selection in TAPM was carried out in order to provide both high spatial resolution and minimise running times. As such, the computational resources necessary to run the simulations and generate the 6 hourly forecasts are very low. On a typical office computer, it took no longer than 5 min to run each iteration, which is significant for the timely adjustments and optimisation of energy management in a building. Table 15 shows a qualitative comparison of the performance of each individual component as well as the hybrid models as obtained from the quantitative results in the previous section. The main advantage of the models analysed in this paper is that they are able to provide a comprehensive set of hourly weather predictions for short-term horizons with relatively low computational needs. While it is beyond the scope of this paper to generate a model for estimation of the savings (especially since savings when using weather forecasts can be realised in various ways), studied discussed in part 2 indicate savings in the range of 10e40% from optimisation of load management alone, compared to a deterministic strategy without any weather inputs. If the building system has the capacity to generate energy onsite, conduct preconditioning and other demand response measures, the savings are cumulative. Another advantage is that the error of the onsite generated predictions may be substantially smaller than the error of predictions taken from a weather station, albeit the magnitude depends on the distance of the station as well as the environment around the building. There are certain limitations to the models proposed in this paper. Firstly, the necessity of archived observations are required to evaluate the weightings of the hybrid models. This issue is not however as troublesome, since using a linear regression for hybridising the reference and TAPM outputs as explained in the WF model still produces good results. In fact, for most metrics the improvement with WFS over WF is in the range of 5e10%. More importantly, the application of the hybrid models implies the presence of onsite weather monitoring equipment, which may not be available in certain buildings. Future work will examine the effects of using data from weather stations that are not onsite, which will assist in assessing the value of localisation. An additional issue is that TAPM uses synoptic data inputs, which have to be obtained from entities like NCEP. While the hybridisation can be carried out

in a variety of common commercial database platforms, TAPM licenses have to be obtained further increasing the total cost of the model. Future work will assess the ability to predict radiation as well as examine different forecasting horizons that may be useful for building energy management. Both are expected to increase the usefulness of the proposed models. Also the value of localisation will be examined, by comparing the performance of the onsite models against external station predictions for buildings with onsite weather monitoring at varying distances from the stations. Finally, as TAPM was designed originally for modelling of atmospheric pollution, there is room for research that may improve its meteorological prediction capacity. A tailored numerical prediction model for energy management could be integrated into a control framework and improve the potential value of the energy system.

References [1] Lazos D, Sproul AB, Kay M. Renew Sustain Energy Rev 2014;39:587e603. [2] Lu N, Taylor T, Jiang W, Correia J, Leung LR, Wong PC. In: 2009 IEEE power and energy society general meeting, PES '09, July 26, 2009-July 30, 2009. Calgary, AB, Canada: IEEE Computer Society; 2009. [3] Perez-Lombard L, Ortiz J, Pout C. Energy Build 2008;40:394e8. [4] Steinfeld J, Bruce A, Watt M. Energy Build 2011;43:2179e87. [5] Zavala VM, Constantinescu EM, Krause T, Anitescu M. J Process Control 2009;19:1725e36. [6] Taylor JW. J Operational Res Soc 2003;54:799e805. [7] Taylor JW. IEEE Trans Power Syst 2012;27:458e64. [8] Kruger E, Lima L. In: Healthy buildings: creating a healthy indoor environment for people, HB 2006, June 4, 2006-June 8, 2006. Lisboa, Portugal: International Society of Indoor Air Quality and Climate; 2006. p. 213e7. [9] Zavala VM. Industrial Eng Chem Res 2013;52:3137e50. [10] Zavala VM, Constantinescu EM, Anitescu M. In: Innovative smart grid technologies conference, ISGT 2010, January 19, 2010-January 21, 2010, IEEE computer society. Gaithersburg, MD, United states: IEEE; IEEE PES - Power and Energy Society; 2010. [11] Kwak Y, Seo D, Jang C, Huh J-H. Energy Build 2013;57:250e60. [12] Nagai T. In: Building simulation 2007, BS 2007, September 3, 2007-September 6, 2007. Beijing, China: International Building Performance Simulation Association; 2007. p. 245e52. [13] Candanedo JA, Dehkordi VR, Stylianou M. Appl Energy 2013;111:1032e45. [14] Hazyuk I, Ghiaus C, Penhouet D. Build Environ 2012;51:388e94. [15] Gunay HB, Bursill J, Huchuk B, O'Brien W, Beausoleil-Morrison I. Build Environ 2014;82:408e19. [16] Oldewurtel F, Parisio A, Jones CN, Gyalistras D, Gwerder M, Stauch V, et al. Energy Build 2012;45:15e27. [17] Cooperman A, Dieckmann J, Brodrick J. ASHRAE J 2010;52:130e2. [18] Lehmann B, Gyalistras D, Gwerder M, Wirth K, Carl S. Energy Build 2013;58: 250e62. [19] Li N, Kwak J-Y, Becerik-Gerber B, Tambe M. In: 30th international symposium on automation and robotics in construction and mining, ISARC 2013, held in conjunction with the 23rd world mining congress, August 11, 2013-August 15, 2013. Montreal, QC, Canada: Canadian Institute of Mining, Metallurgy and Petroleum; 2013. p. 987e94. [20] Ferreira PM, Silva SM, Ruano AE. In: 1st IFAC conference on embedded systems, computational intelligence and telematics in control, CESCIT 2012, April 3, 2012-April 5, 2012. Wurzburg, Germany: IFAC Secretariat; 2012. p. 236e41. [21] Zhou Q, Wang S, Xu X, Xiao F. Int J Energy Res 2008;32:1418e31. [22] Kyungtae Y, Luck R, Mago PJ, Heejin C. Energy Build 2012;54:225e33. [23] Borges CE, Penya YK, Fernandez I. In: IEEE power and energy society'sinnovative smart grid technologies Asia 2011 conference,ISGT Asia 2011, November 13, 2011-November 16, 2011, IEEE computer society. Perth, WA, Australia: IEEE Power and Energy Society; 2011.

D. Lazos et al. / Building and Environment 90 (2015) 82e95 [24] Penya YK, Borges CE, Agote D, Fernandez I. In: 2011 IEEE International symposium on industrial electronics, ISIE 2011, June 27, 2011-June 30, 2011. Gdansk, Poland: IEEE Computer Society; 2011. p. 1359e64. [25] Cherkassky V, Roy Chowdhury S, Landenberger V, Tewari S, Bursch P. In: 2011 international joint conference on neural network, IJCNN 2011, July 31, 2011August 5, 2011. San Jose, CA, United states: Institute of Electrical and Electronics Engineers Inc.; 2011. p. 666e72. [26] Suzuki R, Hayashi Y, Fujimoto Y. In: 2012 IEEE international conference on power and energy, PECon 2012, December 2, 2012-December 5, 2012. Kota Kinabalu, Malaysia: IEEE Computer Society; 2012. p. 343e7. [27] Zong Y, Mihet-Popa L, Kullmann D, Thavlov A, Gehrke O, Bindner HW. In: 2012 3rd IEEE PES innovative smart grid technologies Europe, ISGT Europe 2012, October 14, 2012-October 17, 2012, Berlin, Germany. IEEE Power and Energy Society; Technische Universitat Berlin - SENSE Lab; 2012. [28] Chow SKH, Lee EWM, Li DHW. Energy Build 2012;55:660e7. [29] Yang C, Xie L. In: 2012 North American power symposium, NAPS 2012, September 9, 2012-September 11, 2012. Champaign, IL, United states: IEEE Computer Society; 2012. [30] Al-Messabi N, Li Y, El-Amin I, Goh C. In: 2012 annual international joint conference on neural networks, IJCNN 2012, part of the 2012 IEEE world congress on computational intelligence, WCCI 2012, June 10, 2012-June 15, 2012. , Brisbane, QLD, Australia: Institute of Electrical and Electronics Engineers Inc.; 2012 [IEEE Computational Intelligence Society (CIS); International Neural Network Society (INNS)]. [31] Huang CY, Chen HJ, Chan CC, Chou CP, Chiang CM. In: 1st international conference on smart grid and clean energy technologies, ICSGCE 2011, September 27, 2011-September 30, 2011. Chengdu, China: Elsevier Ltd; 2011. p. 531e7. [32] Bacher P, Madsen H, Perers B. In: 30th ISES biennial solar world congress 2011, SWC 2011, August 28, 2011-September 2, 2011. Kassel, Germany: International Solar Energy Society; 2011. p. 4579e89. [33] Chen C, Duan S, Cai T, Liu B. Sol Energy 2011;85:2856e70. [34] Luo Q, Ariyur KB, Mathur A. In: 2009 ASME dynamic systems and control conference, DSCC2009, October 12, 2009-October 14, 2009. Hollywood, CA, United states: American Society of Mechanical Engineers; 2010. p. 157e64. [35] Collazos A, Marechal F, Gahler C. Comput Chem Eng 2009;33:1584e92. [36] Cho H, Luck R, Eksioglu SD, Chamra LM. Energy Build 2009;41:445e51. [37] Spindler HC, Norford LK. Build Environ 2009;44:750e61. [38] Greensfeldera EM, Henzea GP, Felsmannb C. J Build Perform Simul 2011;4: 91e104. [39] Xu P, Haves P. 2006 winter meeting of the american society of heating, refrigerating and air-conditioning engineers, ASHRAE, January 21, 2006January 25, 2006. Chicago, IL, United states: Amer. Soc. Heating, Ref. AirConditoning Eng. Inc.; 2006. p. 572e80. [40] Rabl A, Norford LK. Int J Energy Res 1991;15:781e98. [41] Ruud MD, Mitchell JW, Klein SA. In: 1990 annual meeting of the American society of heating, refrigerating and air-conditioning engineers, technical and symposium papers, June 10, 1990-June 13, 1990. St. Louis, MO, USA: ASHRAE; 1990. p. 820e9. [42] Candanedo JA, Paradis E, Stylianou M. In: 4th symposium on simulation for architecture and urban design, SimAUD 2013, part of the 2013 Spring

[43] [44]

[45] [46] [47] [48] [49]

[50] [51] [52]

[53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72]

95

simulation multiconference, springsim 2013, April 7, 2013-April 10, 2013. San Diego, CA, United states: The Society for Modeling and Simulation International; 2013. p. 22e7. Mathieu JL, Price PN, Kiliccote S, Piette MA. IEEE Trans Smart Grid 2011;2: 507e18. Hagras H, Packham I, Vanderstockt Y, McNulty N, Vadher A, Doctor F. In: 2008 IEEE international conference on fuzzy systems, FUZZ 2008, June 1, 2008-June 6, 2008. Hong Kong, China: Institute of Electrical and Electronics Engineers Inc.; 2008. p. 156e62. Lee K-h, Braun JE. In: Proceedings of simbuild; 2004. p. 1e12. Hu J, Karava P. Build Environ 2014;71:233e44. May-Ostendorp P, Henze GP, Corbin CD, Rajagopalan B, Felsmann C. Build Environ 2011;46:428e37. Karava P, Athienitis AK, Stathopoulos T, Mouriki E. Build Environ 2012;57: 313e26. Oldewurtel F, Jones CN, Morari M. In: 47th IEEE conference on decision and control, CDC 2008, December 9, 2008-December 11, 2008. Cancun, Mexico: Institute of Electrical and Electronics Engineers Inc.; 2008. p. 4731e6. Henze GP, Kalz DE, Liu S, Felsmann C. HVAC R Res 2005;11:189e213. Henze GP, Krarti M. In: ASHRAE annual meeting, June 18, 1999-June 23, 1999. Seattle, WA, USA: ASHRAE; 1999. PART 2. Kruger E, Fernandes L. In: Healthy buildings: creating a healthy indoor environment for people, HB 2006, June 4, 2006-June 8, 2006. Lisboa, Portugal: International Society of Indoor Air Quality and Climate; 2006. p. 167e72. Spindler HC, Norford LK. Build Environ 2009;44:736e49. Kalnay MKE, Kistler R, Collins W, Deaven D, Gandin L, Iredell M, et al. Amer Meteor. Soc 1996;77:437e70. ECMWF, 2015. Nielsen TS, Joensen A, Madsen H, Landberg L, Giebel G. Wind Energy 1998;1: 29e34. Bunde A, Havlin S. Phys A Stat Mech Its Appl 2002;314:15e24. Mittermaier MP. Weather Forecast 2008;23:1022e31. Greybush SJ, Haupt SE, Young GS. Weather Forecast 2008;23:1146e61. rez A, Palomares-Salas JC, Gonza lez de la Rosa JJ, Moreno-Mun ~ oz A. Agüera-Pe J Wind Eng Ind Aerodyn 2013;119:48e52. Abdel-Aal RE. Eng Appl Artif Intell 2004;17:543e56. Landman S, Engelbrecht FA, Christien E, Dyson L, Willem L. Water SA 2012;38: 765e74. Hurley PJ, Physick WL, Luhar AK. Environ Model Softw 2005;20:737e52. Hurley P, CSIRO. CSIRO marine and atmospheric research paper no. 25. 2008. Dehghan A, Prasad AA, Sherwood SC, Kay M. Sol Energy 2014;107:668e80. Thatcher M, Hurley P. Environ Model Softw 2010;25:82e92. Hibberd M. Department of environment and conservation. WA. 2011. Hurley P. TAPM V4. User manual, CSIRO. CSIRO; 2008. Marine and Atmospheric Research Internal Report No. 5. Zoras S, Triantafyllou AG, Hurley PJ. Environ Model Softw 2007;22:33e9. Mishra AK, Ramgopal M. Build Environ 2014;71:223e32. Bacher P, Madsen H, Nielsen HA. Sol Energy 2009;83:1772e83. Xinmei Huang YM, Mills Graham. CAWCR technical report no.008. Melbourne: CSIRO & BOM; 2008.