Demand forecast of PV integrated bioclimatic buildings using ensemble framework

Applied Energy 208 (2017) 1626–1638 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Demand forecast of PV integrated bioclimatic buildings using ensemble framework MARK Muhammad Qamar Raza , Mithulananthan Nadarajah, Chandima Ekanayake ⁎ School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, QLD 4072, Australia School of Engineering, Griffith University, Gold Coast 422, Australia H I G H L I G H T S ensemble forecasting framework for PV integrated bioclimatic buildings. • AFivenovel different predictors along with their wavelet transformed are combined. • Bayesian model averaging technique is used to aggregate the multiple predictors. • Forecast framework is analyzed for multiple forecast horizons and buildings. • Significant error reduction in different test case studies using the framework. • A R T I C L E I N F O A B S T R A C T Keywords: Smart building Ensemble predictors Neural network Particle swarm optimization Bayesian model averaging Wavelet transform Buildings are one of the major sources of electricity and greenhouse gas emission (GHG) in urban areas all around the world. Since a large integration of solar energy is observed in the form of rooftop photovoltaic (PV) units, electricity use of buildings is highly uncertain due to intermittent nature of solar output power. This leads to poor energy management for both network operators and building owners. In addition, uncertain metrological conditions, diversity and complexity of buildings are big hurdles to accurate prediction of the demand. To improve accuracy of load demand forecast of PV integrated smart building, a hybrid ensemble framework is proposed in this paper. This is based on a combination of five different predictors named as backpropagation neural network (BPNN), Elman neural network (EN), Autoregressive Integrated Moving Average (ARIMA), feed forward neural network (FNN), radial basis function (RBF) and their wavelet transform (WT) models. WT is applied to historical load data to remove the spikes and fluctuations. FNN and RBF network were trained with particle swarm optimization (PSO) for higher forecast accuracy. The output of each predictor in the ensemble network is combined using Bayesian model averaging (BMA). The proposed framework is tested using real data of two practical PV integrated smart buildings in a big university environment. The results indicate that the proposed framework show improvement in average forecast normalized root mean square error (nRMSE) around 17% and 20% in seasonal daily and seasonal weekly case studies, respectively. In addition, proposed framework also produces lowest of nRMSE about 3.88% in seasonal monthly forecast of smart buildings with rooftop PV as compared to benchmark model. The proposed forecast framework provides consistent forecast results for global change institute (GCI) and advance engineering building (AEB) during seasonal daily and weekly comparison. 1. Introduction The built environment is one of the major consumers of energy and source of environmental pollution. One study highlights that, worldwide the energy demand of buildings is up to 32% and it’s up to 40% of total demand in the United States [1]. It is reported for densely populated cities that buildings account for a staggering 94% of electricity use and the greenhouse gas emission (GHG) is up to 75% [1]. Buildings ⁎ contributed about 36% of CO2 emission in Europe [2]. Therefore, in order to address this issue, European Union (EU) has set an energy target for 2020 with emission reduction. The target is to reduce the EU greenhouse emission equal to the level in 1990 and improvement in energy efficiency by 20% [3]. Therefore, characterizing and forecasting the demand of smart building will reduce the excess usage of electricity and consequently environmental pollution. In addition, accurate load demand forecasting will help the design of more effective energy Corresponding author at: Power and Energy System Group, School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, QLD 4072, Australia. E-mail addresses: Qamar.raza@uq.edu.au (M.Q. Raza), mithulan@itee.uq.edu.au (M. Nadarajah), c.ekanayake@griffith.edu.au (C. Ekanayake). http://dx.doi.org/10.1016/j.apenergy.2017.08.192 Received 5 May 2017; Received in revised form 29 July 2017; Accepted 18 August 2017 Available online 09 September 2017 0306-2619/ © 2017 Elsevier Ltd. All rights reserved. Applied Energy 208 (2017) 1626–1638 M.Q. Raza et al. model. Such a combination of networks is also referred as aggregation, combination, and fusion. In order to overcome the limitation of single model and enhancement in predictive accuracy, network ensembles based forecast models are suggested by many researchers [26]. The ensembles based forecast model for wind speed is presented in [27]. The performance of ensemble based forecast model demonstrate the possibility to apply ensemble models to load demand forecasts. Therefore, five independent predictors in ensemble network along with their WT based approach is proposed and implemented for load demand forecast of a PV integrated smart building in this work. The proposed NN ensembles based forecast framework is designed in multiple phases. In first phase, the historical load demand data is preprocessed with the wavelet transform technique. An ensemble framework is made by designing multiple predictors in it. However, the number of predictors in an ensemble network may be varied depending on the nature and complexity of forecasting problem. Then, wavelet transformed load demand data and correlated metrological variables were applied as forecast model inputs. In next stage, the individual network produced forecasted output, which is reconstructed using WT reconstruction process. After that, generated output of each predictor will be combined using aggregation techniques. In this research study, Bayesian model averaging technique is used to integrate the output of individual predictors and to generate forecast output. The details of each phase are discussed in later section of the paper. The major contributions of the proposed novel ensemble approach are highlighted as follows: management system. It will be beneficial to implement energy efficiency programs with greater outcome. Accurate demand forecast of PV integrated smart buildings is also important due to higher penetration of solar energy. However, it is a difficult task to precisely forecast the load demand as several factors affect it. These factors are uncertain PV output power, meteorological conditions, uncertain occupant’s usage behavior, building comfort level and structure. In the last decade, a large number of accurate load demand forecast models have been developed and deployed. The forecasting models are based on statistical forecast [4], support vector machine (SVM) based models [5], fuzzy logic [6], grey model [7] and artificial neural networks (ANN) [8]. Among the reported load demand forecasting techniques, ANN is the most widely used technique with various degrees of success. Neural networks (NN) have been found as a worthwhile competitor to several conventional time series models [9,10]. Therefore, NN has received considerable attention by researchers due to numerous advancements in the model performance and suitability for different prediction, optimization, and classification problems. However, there are some drawbacks of NN based models for load demand forecast. The output performance of NN is greatly affected by the learning of the network, learning rates, network structures, number and quality of forecast model inputs. In addition, the output performance of NN forecast model also varies due to change in evaluation metrics and the sites of data collection. The poor learning of the NN leads to lower generalization capability of the network [11]. Therefore, it is difficult to declare that, a single NN model will outperform the other forecast models for different predictions applications and forecast conditions [12]. In [13], authors suggest a short term load demand forecast model based on NN method for bioclimatic building. The investigation of this study finds that, the load demand of a building varies with change in outdoor solar radiation and temperature. However, a single NN model cannot provide a higher level of generalization and prediction performance in PV integrated smart buildings. Some research studies proposed hybrid models to enhance the forecast accuracy by overcoming the drawback of single model. For example in [14], authors present a SVM and self-organized map (SOM) based two-stage hybrid load forecast model. The proposed model demonstrates better results than single SVM model for different time series data sets. A chaotic particle swarm optimization (CPSO) with ANN based forecast model is proposed in [15]. The prediction results demonstrate that, proposed model produces better forecast accuracy compared with Levenberg Marquardt (LM) NN model. A number of other techniques was applied to forecast the load demand of buildings [16–23]. However, there is still room to enhance the forecast accuracy, especially in PV integrated smart building. It is a difficult task due to higher uncertainty of PV output power and volatility of building load demand. In previously reported research, the hybrid model tries to precisely forecast with two or more models that depends on each other. As a result, the overall forecast accuracy is affected due to bad performance of any of the models. Therefore, there is a need to design multi predictor based forecast model, in which each predictor doesn’t affect the performance of each other. It is also reported that, the forecast performance of independent predictors, even with low quality solutions in ensemble network will increase the forecast accuracy [24,25]. The individual predictor produces different forecast output with the same input data due to different operational principles. The diverse output of individual independent predictor provides an opportunity to enhance the overall forecast output by exploring other possible solutions. The NN ensemble is a method to aggregate the multiple models or predictors to generate the output accurately rather than relying on a single model. Neural network ensemble is a method for creating a multiple NN and train them individually. After that, the outputs of all individual networks are combined to generate output of ensemble (1) Development and integration of the five neural networks and time series predictors along with the WT models in ensemble network. (2) Aggregation of predicators output using Bayesian model averaging for efficient selection and contribution of each of them in final forecast results. (3) Implementation of proposed forecast framework on two real PV integrated smart buildings to achieve the long-term net-zero energy building (NZEB) goal. (4) Training of neural predictors (FNN and RBF) using particle swarm optimization (PSO) for higher forecast accuracy of individual predictor. (5) Incorporating the wavelet transformed historical load demand data with metrological variables such as wind speed (Ws), temperature (T), humidity (H) and exogenous variables (type, week and hour of the day) as forecast model inputs. (6) Improvement in average forecast normalized root mean square error (nRMSE) more than 17% in seasonal daily and 20% in seasonal weekly evaluation case studies in comparison with the existing model. Rest of the paper is organized as follows. Section 2 describes a typical load profile of PV integrated smart building. Section 3 highlights the major components of proposed framework. The proposed hybrid framework for demand forecast of PV integrated smart building is discussed in Section 4. Numerical results and discussion are presented in Section 5. The conclusions of the paper are summarized in Section 6. 2. Load profile of PV integrated smart building 2.1. Practical PV integrated smart buildings In this study, two practical PV integrated bioclimatic buildings at The University of Queensland (UQ), Australia namely GCI and AEB are selected for validation of proposed forecast framework. The design objective of GCI building is to closely work with the natural environment. It is also aimed to achieve the target of zero carbon emission and zero net energy building. The GCI building is equipped with modern sun shading, which tracks the sunlight and provide the natural air ventilation for reduction in energy demand. The net zero energy 1627 Applied Energy 208 (2017) 1626–1638 M.Q. Raza et al. Fig. 1. Electrical power flow diagram of GCI building. management system. However, PV output power is available from 7am to 5 pm due to absence of solar radiations. The PV output power other than 7 am to 5 pm is considered zero or not significant. There are 219,000, 43,800 and 7300 measurements in the 1-min, 5-min and 30min dataset within the range of 7am to 5 pm. However, 0.62% of data is missing in online data management system, which might be due to instrumental and other errors. Therefore, the missing data is replaced with average value of last 4 weeks at same time. It can be observed from Fig. 2, that the PV output power is highest during the first 100 days of the year. The PV output goes down to lowest level in next 125 days of the year. Afterwards, PV output power start climbing and reached up to medium level. This indicates that, the PV output varies throughout the year with change in season and environmental conditions. The solar output power rose to a maximum level in December and January due to increase in solar irradiation and temperature. A real-time data of PV output power and respective weather variables with one-minute resolution were recorded to train and validate the proposed framework. Electrical power is fed to AEB distribution network using four feeder lines called 49.1, 49.2, 49.3 and 49.7 of UQ internal grid network. In AEB power distribution network, 49.7 is connected with AEB roof top PV unit and other three feeders are connected with UQ internal grid. The PV output power is variable and uncertain due to different factors. Therefore, the additional power supply from UQ internal grid fulfills AEB load demand. Fig. 3 illustrates the hourly load profile of AEB for 2014. It can be observed that, the load demand of AEB varies throughout the year in different season. The load demand of this building varies due to change of metrological conditions and occupant’s usage pattern. The load demand is at medium level during the month of December and January (Summer) as the regular semester is off. However, due to raise in temperature in summer season, air conditioning load takes it to medium level with start of new semester. The load demand is relatively at higher level in February due to increase in occupants’ usage and fairly higher temperature. The load demand of AEB building is reduced from higher to medium level in autumn season and it further deceased in winter season. The peak load demand of AEB is reached at 0.9 normalized value between October and November 2014. Fairly similar seasonal load demand pattern is observed for GCI building. The higher level of fluctuations in load demand can be observed from AEB and GCI building load profiles. The variability of PV output power also adds more uncertainty in load demand from grid side. It will lead towards lower power system reliability and quality. In addition, the higher level of fluctuations can be observed at building than the electrical grid due to sharp changes in metrological conditions and occupants’ usage. This makes it more objective is achieved by cross ventilation system (natural air circulation), shading control from solar gain, optimal lighting and solar PV integration. These PV arrays are connected with batteries and solar hot water. 138 kW rooftop PV is installed at GCI building and excess energy is stored in batteries. Electrical energy flow diagram of GCI building is shown in Fig. 1. AEB is the second smart building, which is considered in this study. AEB is designed in energy efficient way by implementing the mix mode of air conditioning system. In this building, 95.75 kW rooftop PV system comprises of tilt mounted 383 modules. AEB is connected with 11 kV UQ internal grid and rooftop PV. The voltage is step down to 415 V for AEB distribution network. In addition, PV is connected to low voltage (LV) distribution network of AEB. The electrical power is absorbed by the electrical load and water production system. The pure electrical load consists of building lighting, lifts, fans etc. In addition, chilled water production system that consists of a chiller station is also run using electrical power. 2.2. Historical load data and PV output profile Fig. 2 represents the PV output power profile of year 2014 from 1 January to 31 December. In this graph, number of days on X axis, solar data points in a day on Y axis and magnitude of power on Z axis. The solar output power is available for 24 h of the day in solar data Fig. 2. Aggregated solar output power profile of UQ solar of year 2014. 1628 Applied Energy 208 (2017) 1626–1638 M.Q. Raza et al. Fig. 3. Advance Engineering Building (AEB) hourly load profile during 2014. use and CO2 emission of buildings. difficult to forecast accurately the load demand due to higher fluctuations. Figs. 4 and 5 depict the hourly load profile of AEB for one month (January 2014) and one week (January 1 to 7, 2014) respectively. It can be observed from one week and month hourly load profile that the load demand of AEB is highly fluctuating. The load demand varies through the month of January 2014 and it goes to peak of the month during the last week. In addition, the demand varies throughout the day and it is also different between hours. It is observed from load profile analysis that load demand curve was much more stable than PV integrated smart buildings. On the other hand, the load demand of buildings is highly volatile in comparison with grid load demand profile. Therefore, the load demand forecast of PV integrated smart buildings is more difficult and forecast models are less accurate. There is a need to accurately forecast the load demand of buildings in order to correctly characterize, reduce energy 3. Components of ensemble forecast framework Proposed forecast framework components such as wavelet transform, ensemble predictors, particle swarm optimization and Bayesian model averaging (BMA) are described below in detail. 3.1. Wavelet transform It can be observed that from historical load demand, time series data contains oscillations, peaks, and different types of non-stationary data components. These are due to variable PV output power as a result of sudden changes in metrological conditions and exogenous variables. The PV output varies throughout the day due to above mentioned factors. The forecast accuracy of prediction model can be enhanced by Fig. 4. AEB Load profile of one month, January 2014. 1629 Applied Energy 208 (2017) 1626–1638 M.Q. Raza et al. Fig. 5. AEB Load profile of one week, January 1 to 7, 2014. named as w D1, D2 and D3. The approximate component (low frequency components) A3 is obtained by down sampling with low pass filters. These detailed and approximate components of historical load demand data signals (A3, D1, D2 and D2) were applied as forecast model inputs along with other variables. The output of predictor is reconstructed using reconstruction process. In reconstruction process is applied to detailed (D1̂ ,D2̂ and D3̂ ) and approximate A3̂ components to generate the predictor output. smoothing the historical demand data, which is applied as forecast model to train it. Therefore, Wavelet transform (WT) technique has potential to apply on historical data in order to treat as forecast model inputs for higher forecast accuracy. The WT can be separated into two groups known as continuous WT (CWT) and discrete WT (DWT). The historical demand data can be decomposed into a series of constitutive components using wavelet transform. These transformed constitutive components demonstrate more stable behavior with less variations, which can contribute to better forecast accuracy. The two basic functions of WT are mother wavelet signal ψ (t ) and scaling function ϕ (t ) . The series of function can be derived as given below in Eq. (1) and (2) [28]. φj,k (t ) = 2 j /2 ∗φ (2 j /2t −k ) (1) ψj,k (t ) = 2 j /2 ∗ψ (2 j /2t −k ) (2) 3.2. Ensemble predictors ANN consists of different layers such as input, hidden and output layer. ANN models attempt to achieve the best performance through densely interconnected small processing units called neurons. The network of artificially interconnected neurons explores multiple competing hypotheses by simultaneously massive processing for the better results. In this research, five different types of predictors are applied to forecast the load demand. These predictors are backpropagation neural network (BPNN), Elman neural network (EN), Autoregressive Integrated Moving Average (ARIMA), feed forward (FNN) and radial basis function (RBF). The purpose of different predictor’s in ensemble network is based on their applicability for forecast application and achieve the diverse forecast output. This diverse forecast output is combined using aggregation technique. Therefore, the overall forecast accuracy of ensemble network will be increased as each predictor will dissimilar forecast results. The details of predictors are given below. where scaling and translating integer variables are j and k. The φ and ψ represents the scaling and wavelet function. The signal S(t) can be expressed by using the scaling φj,k and wavelet function ψj,k as given in Eq. (3). S (t ) = ∑ k C j0 (k )2 j0 /2φ (2 j0 t −k ) + ∞ ∑ ∑ k j = j0 dj (k )2 j /2ψ (2 jt −k ) (3) where dj (k ) and C j0 represents the detailed and approximations coefficients of the signal respectively. The symbol j0 represents pre-scaling coefficient in the above signal equation. Mallat’s algorithm is a method to implement the wavelet transform using different high and low pass filters [29]. In this algorithm, firstly the original signal is decomposed into different detailed and approximation components by using low and high pass filters as shown in Fig. 6.lefttop A research study utilize the wavelet transform (WT) for short-term load forecast. In this study, two-level decomposition is used for preprocessing historical load data [28]. In [30], authors used threelevel WT decomposition for electricity price forecasting. The forecast results demonstrate the effectiveness of three-level WT decomposition in terms of model predication performance. Therefore, the three-level decomposition is applied on historical load data in this study. However, WT is not applied to other forecast model input variables. During the decomposition process of WT, high pass (H.P.) filter generates the high frequency or detailed components of the signal 3.2.1. BPNN The first predictor is BPNN. In the last decade, BPNN is applied to vast range of forecast applications such as electrical load, price and wind forecast with good level of success. In BPNN, backpropagation process tries to determine the nodes connections weights values. The weights values of the network are updated using error function. The network learning error is calculated with difference of network predicted and actual. The error between the predicted and actual output values is back-propagated and weight values are updated based on network learning error. Therefore, the network learning error is minimized by back propagating the error and updating the connections weight values. 1630 Applied Energy 208 (2017) 1626–1638 M.Q. Raza et al. Fig. 6. Wavelet Transformation process of signal. 3.3. Particle swarm optimization 3.2.2. EN EN is considered as another type of recurrent neural network. In EN, special copy layer of hidden layer is connected through linking path. Therefore, the Elman neural network training process depends on three processes named as previous state, current inputs of the system and network output. The standard backpropagation algorithm can also be used for training of the neural network as the special layer treated as another set of inputs [31,32]. The performance of NN predictor is highly dependent on network training. The objective of neural network training is to find the optimum values of weights. It is reported that, backpropagation learning algorithm is used for training neural networks. However, backpropagation learning technique of the NN uses gradient learning technique. It has drawbacks such as slow convergence, higher probability to become trapped in local minima and inefficient training of the network [33]. In order to obtain an accurate forecast output, network should converge to global optimum solution rather than local optimum. In addition, BP algorithm is highly dependent on learning rate, momentum, initial weight and biases values. PSO is one of the most efficient training techniques, which can be utilized for NN training. Therefore, PSO is utilized in this study to enhance the forecast performance of neural predictors. PSO is population based optimization technique which inspired by sociological behavior of flock of birds or school of fishes moving in search for food. The birds or fishes try to find the food by own best search experience as well as social experience. In PSO population based optimization technique, in which each candidate of population is called particle and each particle tends to find the best solution based on own and neighbor experience in a multidimensional search space. A group of particles is called swarm and swarm tends to find the optimal solution for certain objective function. The one major advantage of PSO techniques is to adjust only two parameters which are velocity and position of particles. Each particle updates his position and velocity based on his own and social experience according to Eqs. (4) and (5) [33]. 3.2.3. ARIMA ARIMA is the third predictor employed for load demand forecast in ensemble network. In ARIMA based forecast model, differenced series appearing in the forecasting equation and lags of the forecast errors are named as autoregressive and moving average respectively. The purpose of including a time series predictors in ensemble network is to achieve the diverse forecast output. In ensemble network, each standalone predictor will explore the different forecast possibilities. As a result, the overall forecast accuracy of the proposed ensemble would be enhanced by integrating the each predictor. 3.2.4. FNN FNN is the third neural and fourth ensemble predictor in the network. In FFN, the input information of the network is proceeded in forward direction only. The input data of NN is applied to input layer and pass to network output layer though hidden layer. There is no backward path for the information like backpropagation network. In the study, a three-layer FNN is used which contains one input, hidden and output layer. Hyperbolic tangent (tansig) and linear (purelin) functions activation functions were used for hidden and output layer respectively. vi(k + 1) = wvik + c1 r1 (Pbestik−x ik ) + c2 r2 (gbest k −x ik ) (4) x ik + 1 = x ik + vik + 1 (5) where 3.2.5. RBF The fourth neural and fifth ensemble network predictor is RBF neural network. It consists of three layers named as input, hidden and output layer. Gaussian function is chosen as the radial basis function and network output is expressed in the form of Gaussian function. The training algorithm is applied to RBF network learning and it tries to find the optimum values of connection weights to reduce the learning error of the network in iterative manner. c1 and c2 are positive constants which control the personal and global component of algorithm, r1 and r2 are randomly generated numbers within a range of [0,1], w is the inertia weight, Pbest ki is the personal particle best position achieved, which is based on its own experience, gbestk is the global particle best position achieved by the all particle, 1631 Applied Energy 208 (2017) 1626–1638 M.Q. Raza et al. Fig. 7. Schematic diagram of the proposed ensemble framework. weight for the BMA technique. Let b will represent the coefficients/ weight of BMA model. The j number of models in M model space as Mj = (1,2,3,…,J ) and these are predicting the PV output y . Fj is the output of forecast model j and D denotes the training data of each network [40]. The average of posterior distributions of each model is P = (Mj |D) and weighted by their posterior probabilities P = (y |Mj,D) for probability density function. The calculation of the BMA probabilistic forecast are given in Eq. (6). which is based on overall swarm’s experience, k is the iteration index. vik Current velocity of the particle. vi(k + 1) New velocity of the particle. x ki Current of the position. x ki +1 New particle position. 3.4. Ensemble network aggregation using Bayesian model averaging (BMA) p (y |D) = The objective of ensemble network aggregation process is to combine the individual predictors output in an optimal way for final accurate forecast. In NN ensemble based forecast method, each predictor forecast the load demand, which is independent from each other. Each ensemble predictors will also produce the forecast error according to individual predictor performance. The idea is to combine individual result together in an intelligent manner. This allows to compensate individual predictor errors using better performing aggregation technique. In this way, the final prediction error of ensemble will be reduced. One of the simplest ways to aggregate the outcomes of all applied predictors is averaging. However, individual predictor averaging is not the optimal way as the equal weightage is given to bad and good performing models. As a result, it leads to higher forecast error. Several studies have reported that, the BMA has potential to be used as good aggregation tool. It can produce more adaptive and reliable predictions results as demonstrated for different applications in [34–37]. BMA is a statistical procedure to infer consensus results of different predictors to combine them. Recently, BMA techniques is used to aggregate the output of the neural network ensembles for different forecast applications [36]. The results of proposed framework demonstrate the significance of BMA aggregation in terms forecast accuracy. BMA technique opposes the individual model dependence and entire data set take part in inference making process. Based on posterior model probabilities, the combinational weights are assigned to each individual network in aggregation process of BMA method. Weights values of any individual NN model are based on the network performance. The higher weight values are assigned to better performing forecast models as compared to lower performing models [36,37]. In [38,39], authors present the method to estimate the coefficients/ j ∑ wj∗p (y |Mj,D) j=1 (6) The BMA forecast posterior mean and variance can be calculated as: E [y |D] = j ∑ j ∑ p (Mj |D) ∗E [y |Mj,D] = j=1 Var [y |D] = wj∗fj j=1 j ∑ j=1 2 ⎞ ⎛ Wj ⎜fj− ∑ wifi⎟ + i=1 ⎠ ⎝ j j ∑ j=1 (7) wj ∗σ j2 (8) For training data D, the variance associated with model prediction fj is σ j2 . The posterior probability of the jth model is wj−p(fi|d ) for steady observations. The average by weighting each forecast with corresponding posterior model probability represents the BMA combination. The forecast is basically combination of different model components. The calculation of posterior model probability is one of the most important parts of BMA combination process. The estimated coefficients and errors are put into a matrix called coefficient matrix b. After that, estimated BMA weight coefficients are multiplied with individual output of the individual predictor in order obtain the combined forecast using BMA model. The Youtput is the output of each NN forecast model. BMA output can be calculated as given in Eq. (9). YBMA = Youtput ∗b (9) This aggregation technique is also known as BMA combination algorithm. It is also applied to different forecast applications [27]. 1632 Applied Energy 208 (2017) 1626–1638 M.Q. Raza et al. 4. Proposed ensemble forecast framework particle with the best fitness value of all the particles is selected as the Gbest. The “Pbest” and “Gbest” values are used to calculate the new velocity according to Eq. (5) for new position of particle for targeted learning error. The new calculated particle positions (weight, bias of NN). The new velocity is added in old position according to Eq. (4). These new set of positions are applied to network and it will produce the new learning error. The flow chart of PSO trained predictors in the proposed framework is shown in Fig. 9. Fig. 7 depicts the schematic diagram of the proposed framework for load forecast of smart building using neural ensemble predictors, Bayesian model averaging and WT. The load forecast procedure, which consists of six phases, for a PV integrated smart building is explained as follows: Phase 1: The first phase of the forecast process is to select the most influential model input variables. The forecast input variables of individual neural predictors are hourly historical load data values of smart building, day of the week (DW), type of the day (D) (i.e. working or holyday), and hour of the day (H). In addition, temperature (T), humidity (HDt), and wind speed (WSt) are also applied as predictors inputs [41]. Hourly historical load and metrological data is used to train the predictors at t hour for accuracy forecast. Phase 2: WT technique is applied to historical load data. The historical load series is decomposed into three detailed and one approximate component. The detailed or high-frequency components named as D1, D2, and D3 are obtained using high pass filter. The approximate or low frequency component (A3) is obtained by down sampling with low pass filter. The schematic diagram of individual predictor is shown in Fig. 8. Phase 3: The connection weight vectors of neural predictors are initialized using the PSO algorithm. Initial particle position of PSO algorithm is assigned as initial weight values of NN. These weight values are used during the training process of NN based predictors. The network is trained using initial weights values (particle positions). The network will generate learning error on the basis of provided network weight values during training process. Phase 4: The neural predictors are initialized in ensemble network. These predictors are BPNN, EN, ARIMA, FNN, and RBF. The learning of parameters and network configuration of each predictor is different from each other. Therefore, the performance of each predictor is different due to individual network performance. A diverse range of forecast output is obtained using these predictors. As a result, the overall forecast performance of ensemble network is enhanced by combining them. The historical load data wavelet transformed components and exogenous variables are applied as each predictor’s model input. This process will be repeated until NN termination criteria are met. In this research, RBF and FNN were trained using PSO algorithm in order to enhance the forecast accuracy of individual predictors. As a result, the overall forecast accuracy of ensemble network will be enhanced by aggregating the individual predictor output. Phase 5: The output components of each NN predictor is reconstructed as shown in Fig. 8. The output decomposed components named as approximation ( A2̂ ) and detailed signals (D1̂ ,D2̂ and D2̂ ) are reconstructed by up sampling using combination of low and high pass filters. The individual ensemble predictors output is reconstructed. Phase 6: The output forecast of each predictor is combined using ensemble network aggregator as shown in Fig. 7. Averaging model is used to aggregate the output of ensemble network. However, the forecast accuracy of ensemble model is affected due to equal weight assignment to bad and good performing models. Therefore, BMA technique is used to aggregate the output of ensemble network in proposed framework. The particle positions (weight and bias) are updated in order to minimize the learning error of the network. Fitness function of NN (network learning error which is mean square error, MSE) is calculated. The lowest error of each particle’s is Pbest value of PSO. The lowest learning error achieved during the entire learning process is considered as gbest in swarm. If the fitness value is better than the best fitness value (Pbest) in a search history, then current value is set as the new Pbest. The Fig. 8. Schematic diagram of individual Predictor in the proposed framework. Load Demand Ldt Wavelet decomposition D1 D2 D3 A3 Tt Day of the Week (DW) Type of the Day (D) WSt Predictor HDt Hour of the Day(H) Wavelet reconstruction Predicted Load Demand 1633 Temprature Wind Speed Humidity Applied Energy 208 (2017) 1626–1638 M.Q. Raza et al. Fig. 9. Flowchart for the neural predictor trained with PSO in a proposed framework. START Forecast model Input Selection Wavelet Decomposition Forecast Model Inputs D1,D2,D3,A1 Ensemble Network Initialization NN weight vectors Initialization using PSO PSO algorithm Update Weight vectors NO Network MSE<NN criteria Yes Wavelet Reconstruction Predicted Output Y1,Y2,Y3,…,Y3 END 5. Numerical results and discussion to similar pattern of results only four randomly selected days and weeks are presented in this paper. In addition, MATLAB® and its neural network tool is used to do simulations. The proposed ensemble forecast framework is tested using recorded data by building management system (BMS) of AEB and GCI building at UQ, Australia. In order to evaluate the performance of proposed framework, the forecast results are compared with persistence forecast and individual predictors such as BPNN, EN, ARIMA, FNN, and RBF models. WT is applied to each individual predictor in the ensemble network. The forecast results of each predictor with and without WT are presented in order to analyse the effectiveness of the WT techniques. The historical load values, wind speed (WSt), humidity (HDt), Temperature (Tt), Type (D), Day (DW) and hour of the day are applied as inputs of neural predictors in ensemble network. The output of each independent predictors in ensemble is combined using aggregation techniques as discussed earlier. In this study, normalized root-mean-square error (NRMSE) is calculated to evaluate the performance of predictors as given in Eq. (10) [42]. NRMSE (%) = LD Actual−LDtForecast ⎞ 1 ∗ ∑ ⎜⎛ t ⎟ ∗ 100 N t=1 ⎝ LDtPeak ⎠ N 5.1. Seasonal daily forecast case study In order to assess the forecast models’ performance, one day is selected from each season of the year 2014. In this study, one day is selected from each season such as summer (December 15), autumn (April 2), winter (July 16) and spring (October 30) of 2014. The 24 h ahead load demand forecast case studies were designed for AEB and GCI PV integrated smart buildings. The historical one year historical data with 30 min. resolution were used to train the forecast model. The actual data of 30 min. resolution data of forecasted days were used to validate the performance of proposed framework. The nMAE and nRMSE is calculated for each individual predictor and ensemble network. In addition, proposed forecast framework results are also compared with persistence model for all test case studies. Table 1 presents the seasonal daily forecast nRMSE and nMAE comparison of proposed ensemble forecast framework with persistence model and other individual predictors for AEB. It can be observed that, the persistence method produces higher nRMSE (8.81%, 7.92%, 9.12% and 8.78%) in comparison of proposed framework (4.48%, 4.11%, 4.61% and 4.21%) for selected seasonal forecast days of AEB. In order to assess, similar forecast models were applied to GCI building, where nRMSE values were obtained from persistence method are also higher (9.36%, 9.11%, 8.36%, and 7.86%) compared to proposed model (5.27%, 4.99%, 4.16% and 4.17%) for under consideration seasonal days. In addition, in seasonal daily load forecast case study, BPNN predictors produces higher forecast nRMSE than the persistence method for all seasonal days as given in Table 1. Fig. 10 highlights the comparison of different predictors with proposed framework. The designed framework is more close to actual load demand in comparison with other models. 2 (10) where N is number of load demand data points. The N = 24 for daily load demand (LD) forecast and N = 168 for the week LD forecast. The LDtActual is actual demand at time t, LDtForecast is forecasted demand and LDtPeak represents peak demand at tth hour. In addition, normalized mean absolute error (NMAE) is calculated for each predictor and case study in order to assess the forecast performance of proposed and other predictors. NMAE (%) = N 1 ∗∑ N t=1 LDtActual−LDtForecast ∗100 LDtPeak (11) In this study, seasonal one day, seasonal one week and month ahead forecast case studies were designed in order to assess the performance proposed forecast model along with other comparative predictors. Due 1634 Applied Energy 208 (2017) 1626–1638 M.Q. Raza et al. Table 1 Daily forecast error comparison for AEB. Summer M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 N12 Autumn Table 2 Daily forecast error comparison of GCI building. Winter Spring Avg. E1 E2 E1 E2 E1 E2 E1 E2 8.81 9.92 8.15 7.23 6.42 6.52 8.96 7.23 6.56 5.46 5.67 4.48 6.78 7.86 6.56 5.38 4.94 5.16 7.18 5.63 4.78 3.96 4.12 3.26 7.92 8.36 6.94 7.09 6.13 5.96 7.81 6.38 6.29 5.74 5.46 4.11 5.96 6.73 5.11 5.24 4.56 4.42 6.11 4.24 4.28 4.16 3.92 3.06 9.12 9.26 7.68 8.16 7.13 7.19 8.62 6.79 7.34 6.54 6.32 4.61 7.19 7.35 5.98 6.62 5.57 5.83 7.16 5.05 5.68 4.83 4.98 3.43 8.78 8.81 7.19 6.86 6.06 5.91 8.14 6.36 6.46 5.76 5.64 4.21 6.91 7.12 5.29 5.11 4.18 4.26 6.38 4.47 4.43 3.87 3.92 2.95 Summer 8.65 9.08 7.49 7.33 6.43 6.39 8.38 6.69 6.66 5.87 5.77 4.35 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 Autumn Winter Spring Avg. E1 E2 E1 E2 E1 E2 E1 E2 9.36 9.82 8.02 7.96 7.19 7.36 8.8 7.55 6.92 6.16 5.98 5.27 7.12 7.76 6.59 6.45 6.03 5.95 7.12 6.04 5.71 4.92 4.84 3.79 9.11 9.38 7.92 7.48 6.94 6.73 8.56 7.16 6.86 5.98 5.82 4.96 6.84 7.11 6.53 6.31 5.39 5.08 6.45 5.94 5.61 4.51 4.39 3.41 8.26 8.65 7.92 7.47 6.56 6.48 7.81 6.61 6.56 5.72 5.79 4.42 6.71 7.46 6.26 5.84 5.17 5.31 6.47 5.33 5.16 4.51 4.47 3.21 7.86 8.57 7.72 6.76 6.14 5.85 7.97 7.37 6.02 5.57 5.38 4.27 6.72 7.09 5.91 5.37 4.92 4.64 6.56 5.51 4.79 4.28 4.03 3.12 8.64 9.10 7.89 7.41 6.70 6.60 8.28 7.17 6.59 5.85 5.7 4.73 M1 = Persistence, M2 = BPNN, M3 = EN, M4 = ARIMA, M5 = RBF + PSO, M6 = FNN + PSO, M7 = WT + BPNN, M8 = WT + EN, M9 = WT + ARIMA, M10 = WT + RBF + PSO, M11 = WT + FNN + PSO, M12 = Proposed, E1 = nRMSE, E2 = nMAE. M1 = Persistence, M2 = BPNN, M3 = EN, M4 = ARIMA, M5 = RBF + PSO, M6 = FNN + PSO, M7 = WT + BPNN, M8 = WT + EN, M9 = WT + ARIMA, M10 = WT + RBF + PSO, M11 = WT + FNN + PSO, M12 = Proposed, E1 = nRMSE, E2 = nMAE. Fig. 10. One day ahead load demand forecast error comparison. pattern of ensemble framework, individual predictor and persistence model were observed for seasonal daily load forecast of GCI building. The forecast nRMSE values obtained from BPNN model are larger (9.38%, 9.82%, 8.65% and 8.57%) than the persistence (9.36%, 9.11%, 8.26% and 7.86%) and proposed method (5.27%, 4.96%, 4.42% and 4.27%) for GCI building. As mentioned earlier, historical load data contains non-stationary components and different spikes. Therefore, WT technique is used to remove the fluctuations and smoothing the model input data. The effectiveness of WT techniques can be observed from AEB and GCI daily forecast error Tables. The EN model gives average nRMSE value 7.89% without WT for GCI building case study. The forecast average nRMSE reduced to 7.17%, when EN is integrated with WT. The average nRMSE indicates that, the proposed hybrid framework outperforms the persistence model and individual predictor in terms of forecast accuracy with average nRMSE 4.35% for GCI building. The forecast nRMSE comparison of persistence, BPNN, FNN+PSO, WT+BPNN, WT+FNN+PSO and proposed framework is presented in Fig. 11. It can be observed form forecast error comparison, that the proposed framework is robust and accurate for load demand forecast of seasonal days. 5.2. Seasonal weekly forecast case study It can be observed that, the prediction performance of models is inconsistent over the different seasonal days. Therefore, average of four season’s nRMSE is calculated for better comparison. In the most of seasonal daily load forecast cases, the prediction performance WT+RBF+PSO and WT+FNN+PSO are found closer to each other. The forecasted output of proposed framework is close to real load and follow the variation pattern in better way. However, average forecast nRMSE results indicate that, the WT+FNN+PSO model produces less forecast error (5.77%) in comparison with WT+RBF+PSO (5.87%). Furthermore, the average forecast nRMSE values of EN and ARIMA model are close with 7.49% and 7.33% respectively. In most of seasonal daily forecast cases of AEB, ARIMA model gives higher forecast accuracy than the EN. The proposed forecast framework produces higher forecast accuracy than the individual predictors and persistence forecast model. It is also observed that, the forecast performance of the proposed ensemble framework and other models varies during seasonal daily case study. It is concluded that from daily seasonal forecast, the forecast model performance is sensitive to seasonal variations. Therefore, inconsistent forecast results are obtained. Table 2 represents the seasonal daily forecast error comparison of GCI building. The proposed framework and persistence model were applied for the same selected seasonal days. The similar forecast error In order to assess the performance of proposed framework, the second case study is designed to forecast the week ahead load demand of different season for AEB and GCI building. In this case study, one week is selected from each season e.g. December 22–27 (summer), April Fig. 11. Daily load demand forecast nRMSE Comparison of AEB. 1635 Applied Energy 208 (2017) 1626–1638 M.Q. Raza et al. Table 3 Weekly forecast comparison of AEB. Summer M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 Autumn Winter Spring Avg. E1 E2 E1 E2 E1 E2 E1 E2 7.96 8.46 7.34 7.12 6.42 6.32 7.62 6.76 6.59 5.73 5.65 4.18 5.89 6.77 5.71 5.41 4.8 4.67 5.86 5.23 4.7 3.98 3.93 3.12 7.92 8.06 7.17 6.78 5.75 5.68 7.71 6.96 5.78 5.21 5.36 4.26 6.1 6.37 5.29 4.93 4.06 4.1 6.01 5.37 4.02 3.63 3.82 3.21 8.59 8.93 7.81 7.66 6.73 6.59 8.21 7.09 6.92 6.18 5.91 4.49 6.92 7.06 6.21 5.91 5.01 4.98 6.35 5.07 5.17 4.29 4.19 3.23 8.18 8.31 7.29 6.61 5.94 5.83 8.11 6.81 6.42 5.71 5.57 4.87 5.95 6.14 5.82 5.26 4.36 4.21 5.91 5.61 5.26 4.02 3.84 3.68 8.16 8.44 7.40 7.04 6.21 6.10 7.91 6.90 6.42 5.70 5.62 4.45 M1 = Persistence, M2 = BPNN, M3 = EN, M4 = ARIMA, M5 = RBF + PSO, M6 = FNN + PSO, M7 = WT + BPNN, M8 = WT + EN, M9 = WT + ARIMA, M10 = WT + RBF + PSO, M11 = WT + FNN + PSO, M12 = Proposed, E1 = nRMSE, E2 = nMAE. Fig. 12. Weekly load demand forecast nRMSE Comparison of GCI Building. seasonal sensitive. Therefore, the forecast results are inconsistent. Table 4 Weekly forecast error comparison of GCI building. Summer M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 N12 Autumn 5.3. Monthly forecast case study Winter Spring Avg. E1 E2 E1 E2 E1 E2 E1 E2 7.71 7.65 7.02 6.91 5.89 6.06 6.84 6.44 6.24 5.19 5.32 4.97 5.91 5.74 5.37 5.1 4.27 4.51 5.24 4.6 4.52 3.48 3.53 2.94 8.07 8.28 7.19 6.79 6.41 6.29 7.83 6.69 6.13 5.61 5.72 4.32 6.36 6.51 6.13 5.37 4.54 4.63 5.92 5.16 4.59 3.89 4.03 3.25 7.86 8.15 6.97 6.47 6.14 5.98 7.24 6.49 5.76 5.32 5.24 4.23 6.04 6.32 5.12 4.58 4.17 4.11 5.67 4.54 3.98 3.46 3.34 3.06 7.83 8.13 6.81 6.56 5.84 5.71 7.48 6.29 5.93 4.98 5.1 4.11 5.81 6.24 5.19 4.84 4.33 3.99 5.63 4.47 4.14 3.16 3.44 3.21 Third case study is designed to forecast the monthly load demand of AEB building to analyze the performance of proposed framework under various weather conditions. Table 5 presents the monthly forecast error comparison of proposed and persistence framework. The proposed forecast framework produce average monthly forecast nRMSE (4.19%) as compared to persistence model (8.20%). Fig. 13 presents the histogram error comparison of proposed and persistence model. It can be observed that, the proposed hybrid framework gives better forecast results than the persistence model in monthly forecast. It can be concluded that from forecast results, the proposed framework highlights significant improvement in load demand forecast of PV integrated smart buildings. 7.86 8.05 6.99 6.68 6.07 6.01 7.34 6.47 6.01 5.27 5.34 4.40 5.4. Forecast error comparison of GCI and AEB M1 = Persistence, M2 = BPNN, M3 = EN, M4 = ARIMA, M5 = RBF + PSO, M6 = FNN + PSO, M7 = WT + BPNN, M8 = WT + EN, M9 = WT + ARIMA, M10 = WT + RBF + PSO, M11 = WT + FNN + PSO, M12 = Proposed, E1 = nRMSE, E2 = nMAE. This case study is designed to compare the prediction median error of proposed forecast framework for AEB and GCI in seasonal daily and weekly scenario. Figs. 14 and 15 represent the box plot of seasonal daily and weekly nRMSE for AEB and GCI respectively. As Fig. 14 highlights that, forecast results of AEB provides steady error in comparison with GCI. It is can also observed from box plot as the size of upper and lower quartile is small. However, GCI forecast results are less steady as compare to AEB in same selected days. Proposed forecast framework produced about 4.70% nRMSE for GCI, while it is less than 4.30% for AEB. Improper training of ensemble predictors and uncertain 7–13 autumn (April 2), July 14–16 (winter) and October 20–26 (spring). Seasonal weekly forecast error comparison of proposed and benchmark model along with individual predictor is presented in Tables 3 and 4 for AEB and GCI building respectively. The persistence, BPNN, EN, ARIMA, RBF+PSO, FNN+PSO models produce average forecast nRMSE values 8.16%, 8.44%, 7.4%, 7.04%, 6.21% an 6.1% respectively without WT for AEB. The forecast nRMSE reduced to 7.91%, 6.90%, 6.42%, 5.70% and 5.62% respectively with WT. Therefore, forecast results indicate the effectiveness of WT in terms of prediction error reduction. The proposed ensemble forecast framework outperform the persistence model with average nRMSE of 4.45% for AEB. Table 4 illustrates the seasonal weekly forecast error comparison of GCI building. The seasonal weekly forecast performance of proposed framework and other comparative model are presented by calculating the nRMSE and nMAE. The results indicate that, proposed ensemble network outperform the comparative models in week ahead forecast case study with nRMSE 3.97%, 4.32%, 4.23% and 4.11%. Furthermore, histogram error plot of persistence, BPNN, FNN+PSO, WT+BPNN, WT+FNN+PSO and proposed framework is presented in Fig. 12. The predicted load using proposed framework is close enough to real load due lower forecast error. This indicates the effectiveness of proposed forecast framework. Seasonal daily and weekly forecast results indicate that, the prediction performance of forecast framework is Table 5 Monthly AEB forecast nRMSE comparison. 1636 Month Persistence model (nRMSE) Proposed framework (nRMSE) January February March April May June July August September October November December 7.75 8.21 8.23 8.07 9.12 7.89 8.18 7.58 8.26 8.62 9.06 7.53 3.94 4.45 4.21 3.91 4.61 4.11 4.36 4.12 3.88 4.11 4.61 3.98 Average 8.20 4.19 Applied Energy 208 (2017) 1626–1638 M.Q. Raza et al. Fig. 13. nRMSE histogram of monthly AEB load demand forecast. occupancy of GCI are potential cause of increased forecast nRMSE. Prediction results of proposed forecast framework for AEB and GCI are more consistent in seasonal weekly case study. Median forecast nRMSE AEB and GCI are about 4.80% and 4.40% respectively in seasonal weekly forecast case study. The distribution of prediction nRMSE of AEB and GCI are also closer to each other. In conclusion, prediction results are more stable in seasonal weekly case study. 5.5. Potential practical applications An accurate forecast of load demand and renewable energy resources can be utilized for smart building demand side management [43]. The power generation at certain instant is matched with by controlling the energy demand of smart buildings are considered as building demand side management. Energy demand of buildings is managed by shifting the appliances time of use from peak to off time. Therefore, peak demand can be shifted by using accurate prediction of building level load demand. It is important to optimize the electricity use in building as they consume more than 30% of total [44]. The proposed framework can also be used in building to optimize the energy use of PV integrated buildings [45]. Furthermore, storage devices can be charged and discharged depending on the availability of PV output power. As a result, this will reduce the building operational cost significantly. In addition, an efficient heating ventilation and air conditioning (HVAC) system can also be designed with minimal electricity use with the help of an accurate forecasting. The proposed forecast can also be utilized for different prediction application such as wind speed, load demand of power grid and PV output power forecast etc. [46–49]. Fig. 14. Seasonal daily nRMSE comparison of AEB and GCI. 6. Conclusions A novel hybrid framework has been proposed in this work for accurate load demand forecast of PV integrated smart buildings. The proposed forecast framework is based on five different predictors named as BPNN, EN, ARIMA, FNN, RBF and their wavelet transformed models in an ensemble network. WT is applied to historical load data to remove the sharp fluctuations and spikes. Individual predictors such as RBF and FNN were trained with PSO algorithm to enhance the prediction performance of individual predictor. The combination of Fig. 15. Seasonal weekly nRMSE comparison of AEB and GCI. 1637 Applied Energy 208 (2017) 1626–1638 M.Q. Raza et al. different independent predictors generates diverse forecast output due its operational principle. After that, the output of each predictor and WT predictors were aggregated using Bayesian model averaging. The objective of aggregation is to achieve higher forecast accuracy of PV integrated smart building’s load demand through selection of better performing models. The overall forecast accuracy is enhanced by combining the predictors in an intelligent manner, in which more weight is given to best performing models. The performance of proposed forecasting framework is tested on two practical PV integrated smart buildings located at a big university campus environment using a massive data captured through building data management system. The performance of the proposed framework is compared with other models such as the persistence model, BPNN, EN, ARIMA, FNN, RBF and their WT models. The forecast results demonstrate that the proposed forecast shows improvement in average forecast nRMSE around 17% in seasonal daily and 20% in seasonal weekly in comparison with each compared models. The proposed framework produces approximately consistent forecast results for GCI and AEB during seasonal daily and weekly forecast comparison. In addition, proposed framework provides minimum nRMSE of 3.88% in monthly forecast. The effectiveness of WT is also observed with forecast error reduction. The proposed hybrid and intelligent forecast framework is significantly increased the prediction accuracy during different seasonal and monthly case studies. In future, the proposed forecast framework can be applied to electrical load, price and PV output power forecast including other prediction applications. 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