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Evaluation of the most influential parameters of heat load in district heating systems
Accepted Manuscript Title: Evaluation of the most influential parameters of heat load in district heating systems Author: Dalibor Petkovi´c Milan Proti´c Shahaboddin Shamshirband Shatirah Akib Miomir Raos Duˇsan Markovi´c PII: DOI: Reference:
S0378-7788(15)30116-X http://dx.doi.org/doi:10.1016/j.enbuild.2015.06.074 ENB 5980
To appear in:
ENB
Received date: Revised date: Accepted date:
31-3-2015 18-6-2015 30-6-2015
Please cite this article as: D. Petkovi´c, M. Proti´c, S. Shamshirband, S. Akib, M. Raos, D. Markovi´c, Evaluation of the most influential parameters of heat load in district heating systems, Energy and Buildings (2015), http://dx.doi.org/10.1016/j.enbuild.2015.06.074 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Evaluation of the most influential parameters of heat load in district heating systems Dalibor Petković*a, Milan Protić**, Shahaboddin Shamshirband***, Shatirah Akib****, Miomir Raos**, Dušan Marković* *
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University of Niš, Faculty of Mechanical Engineering, Department for Mechatronics and Control, Aleksandra Medvedeva 14, 18000 Niš, Serbia. ** University of Niš, Faculty of Occupational Safety, Čarnojevića 10A, 18000 Niš, Serbia *** Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia. **** Department of Civil Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia. corresponding author: [email protected], +381643283048
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Abstract
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The aim of this study is to investigate the potential of soft computing methods for selecting the most relevant variables for predictive models of consumers’ heat load in district heating systems (DHS). Data gathered from one of the heat substations was used for the simulation process. The ANFIS (adaptive neuro-fuzzy inference system) method was applied to the data obtained from these measurements. The ANFIS process for variable selection was implemented in order to detect the predominant variables affecting the short-term multistep prediction of consumers’ heat load in district heating systems. It was also used to select the minimal input subset of variables from the initial set of input variables – current and lagged variables (up to 10 steps) of heat load, outdoor temperature, and primary return temperature. The obtained results could be used for simplification of predictive methods so as to avoid multiple input variables. While the obtained results are promising, further work is required in order to get results that could be directly applied in practice. Keywords: ANFIS, variable selection, district heating systems, heat load, variable selection 1. Introduction
Currently, the fundamental idea of district heating is to recover fuel and heat flows that are otherwise lost, from heat sources both inside and outside the energy system [1]. DHS offers the possibility of using renewable sources (biomass, solar and geothermal energy) as well as cheap, “waste”, heat from industrial plants and power production facilities [2]. As pointed out in [3], a number of recent studies [4-9] found that DHS will play significant role in future sustainable energy systems. However, present DHS will need to undergo substantial changes in order to expand further and effectively compete with other space heating alternatives. 1 Page 1 of 28
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Introduction of intelligent control of heating of buildings is one of the options which could accelerate transition of present DHS systems towards future low-temperature DHS [10]. Consumers’ heat load predictive models are a necessary prerequisite for the realization of novel, intelligent, control strategies, contributing to more efficient use of primary energy. Heat load prediction is very important for optimization and planning in DHS. If credible prediction heat load models could be built, heat production could be matched to the real consumers’ needs. This would result in reduced distribution heat losses, lower return temperatures, and possibility of connecting more consumers to DHS. Additionally, heat suppliers could schedule which production units to activate and avoid the use of peak boilers, which mostly use expensive fossil fuels [11]. In addition, heat load forecasts could be used as input to model predictive control in DHS, effective use of the thermal storage system [12], and peak shaving. In the literature, different approaches were used for DHS heat load modeling and prediction. In one of the earliest studies regarding heat load in DHS, Werner [13] proposed the model of heat load of complete DHS comprising four major components: space heating, preparation of hot consumption water, distribution loss, and additional working load. Space heating load was modeled as a linear combination of the steady heat transmission and the heating of a constant ventilation rate, transient heat transmission, wind-induced air infiltration, and solar gain. In [14] different parametric and non-parametric heat load prediction models were discussed and used. In [15] general transfer function models for different prediction horizons were proposed for control purposes. Dotzauer [16] modeled heat load using the assumption that heat demand can be described sufficiently well as a function of outdoor temperature (piecewise linear function) and the social component. Grey-box approach, combining the relations from the theory of heat transfer, statistical methods, and aggregated data, was used by [17] for modeling heat consumption in entire DHS in Denmark. It was concluded that this approach, even with aggregated data, is powerful. Mesterkemper [18] used dynamic factor models for predicting heat load in the city of Wuppertal in North-Western Germany. Seasonal Autoregressive Integrated Moving Average (SARIMA) heat load models were developed in [19]. Recurrent neural networks were used in [20] for heat load prediction. In [21] an ensemble of decision trees was used for building an online learning algorithm for heat load forecasting in DHS. In the aforementioned studies, versatile sets of input variables were used to build the prediction models. The following variables were primarily indicated as influential for heat load models: outdoor air temperature, insolation, wind direction and velocity, water flow, temperature of supply and return water, and time and type of day (weekend and workdays). When structuring heat load predictive models, it is crucial to include the most influential variables and discard the redundant and non-informative predictors. Additionally, it is important to identify and eliminate the potential multicollinearity between the input variables. Correct variable selection will result in increased model predictability and interpretability. In the literature, different approaches were used for selection of subset of most influential variables, but generally all the methods can be divided in two main categories [22]: 2 Page 2 of 28
filter methods and wrapper methods.
Methodology
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In filter methods the selection of model input variables is made prior to model training and tuning. On the other hand, in the wrapper approach the idea is to assess the predictive ability of various models with different combinations of input variables, using some error metrics, and to select the model producing the best results. While wrappers are more computationally demanding, especially for models having multiple tuning hyper-parameters, they can be regarded as a superior alternative as compared with filters [23]. In this article, we used the wrapper approach to select the most influential variables for DHS heat load predictive models. The Adaptive Neuro-fuzzy Inference Technique (ANFIS) was applied to the available data sets to select the predominant model variables. Current (at moment t) and lagged (up to 10 steps) variables of heat load, outdoor temperature, and primary return temperature were used for structuring the predictive models. An initial set of 33 potential variables was used for experiments. The remainder of the article is organized as follows. First we provide a brief explanation of experimental installation used for gathering the data used for analysis. In the second section we implement ANFIS methodology to select the most influential variables from the model. The third section presents the main results. Finally, the fourth section contains the main concluding remarks.
2.1. System and data description
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Data acquisition was performed in the Novi Sad district heating system. With installed capacity of 877.3 MW, it is the second largest DHS in Serbia, numbering 101,948 consumers, of which 93,971 are residential and 7,977 commercial, connected to the DHS [24]. Heat distribution network is 219.8 km long and 3,832 heating substations are connected to the network. One CHP (combined heat and power) unit and six heat-only boilers plants are used as the heat source. Base heat load is provided from the CHP plant while peak load is covered from heat-only boilers. The data used for this study were gathered from one of the system’s heat substations during the 2010/2011 heating season. This substation is directly connected to the system via a 3pipe system. One supply pipe is used for space heating and another is used for preparation of domestic hot water (using storage tanks placed in the substation). The third pipe is common return. Temperature in consumers’ installations (secondary installations) is regulated by ECL Comfort 300 regulator and motorized control valve, which is positioned in the return pipe. The 3 Page 3 of 28
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regulator is realized as a weather compensator that controls the supply temperature in the secondary installation according to outdoor temperature (“sliding” diagram). Primary supply and return temperatures, thermal energy, power and flow on primary side, as well as outdoor temperature, were measured at 15-minute intervals during the heating season. Outdoor temperature was measured with Danfoss ESMT temperature sensor (Pt 1000, temperature range from -50 °C to 50 °C, time constant ≤ 15 min). Primary supply and return temperatures were measured with immersion Danfoss ESMU 100 sensors (Pt 1000, temperature range from 0 °C to 140 °C, time constant 2 s). Thermal energy and power and flow on primary side were measured with Kamstrup Multical 66C energy meter. All measuring devices were calibrated prior to measurement. Measured values were logged on Danfoss ECA 87 remote control and data log module for ECL Comfort 300 regulator (weather compensator). Measured and stored data from the regulator were regularly downloaded via Danfoss ECL WebAccess module. Prior to analysis, data were averaged at 1-hour intervals. Data cleaning and preprocessing was not performed. For this study, three time series for heat load, outdoor temperature, and primary return temperature were created and used for subsequent analysis. Statistical summary for these time series is presented in Table 1.
Std 62.5 6.5 5.8
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Table 1: Statistical summary of collected data Variable Minimum Maximum Mean value value Heat load [kW] 0.0 298.3 125.2 0 Outdoor temperature [ C] -7.6 24.4 5.7 Primary return temperature 21.1 52.4 37.1 [0C] 2.2. Input variables for model building
For this study predictive models of heat load were developed for 1-5 hours ahead and 8, 10, 12, and 24 hours ahead. Before the analysis we formed the set of potential input variables. In addition to the initial three input variables (outdoor temperature, heat load, and primary return temperature), due to the dynamic nature of DHS, it was important to add the lagged values of these variables in the initial set. Although the initial set with more lagged variables is advantageous, their number is limited by available computation power. In that respect we limited the number of lags to 10. The list of all potential predictors is shown in Table 2. Table 2: List and description of potential input variables for heat load modeling Input variable Input Input variable – Input Input variable – Input – variable Heat load variable Primary return temp. variabl Outdoor ID ID e ID temperature 4 Page 4 of 28
temperature
23 24 25 26 27 28 29 30 31 32 33
Tp(t) Tp(t-1) Tp(t-2) Tp(t-3) Tp(t-4) Tp(t–5) Tp(t-6) Tp(t-7) Tp(t-8) Tp(t-9) Tp(t-10)
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Q(t) Q(t-1) Q(t-2) Q(t-3) Q(t-4) Q(t–5) Q(t-6) Q(t-7) Q(t-8) Q(t-9) Q(t-10)
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12 13 14 15 16 17 18 19 20 21 22
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T(t) T(t-1) T(t-2) T(t-3) T(t-4) T(t–5) T(t-6) T(t-7) T(t-8) T(t-9) T(t-10)
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To build a predictive model with the best characteristics, it is necessary to identify the most relevant and influential subset of variables. This process of selection is usually called variable selection. The purpose of this process is to find a subset from the initial input variables set that best contributes to the model’s predictive power. Essentially, we adopted the wrapper approach with neural network as the foundation. Neural network is an architecture made up of extremely parallel adaptive processing elements, which are interconnected through structured networks. Predictive performance of the neural network models depends heavily on the chosen input variables. To achieve a successful generation and creation of a model that is capable of estimating a special process output, the selection process of the subset of variables that are really pertinent is crucial. This is achieved in the process of variable selection. As mentioned, the purpose of this procedure is to find a subset of the total set of parameters that have been recorded to show good capability of prediction [25-28]. The problems faced in the process of selection of parameters could possibly be resolved by integrating and applying prior knowledge to segregate and remove irrelevant parameters. Otherwise, a more sophisticated approach to the abovementioned problem would be to regard the problem as an optimization procedure through the use of genetic algorithms [29]. The objective here was to select the proper explanatory (input) parameters and thereby minimize the error that exists between the observed values and the model estimations of the explained variables. Among the many neural network systems, one of the most used and powerful is the ANFIS, a hybrid approach, which combines the merits of both neural networks and the fuzzy set theory [30, 31]. In order to determine the main influential variables that most significantly contribute to the predictive power of heat load models of DHS, we conducted a variable search by employing the ANFIS. ANFIS [32], a hybrid intelligent system that increases the capability of learning and adapting automatically, has been used by researchers for many different purposes in a variety of engineering systems, such as modeling [33-36], prediction [37-39], and control [40-44]. The 5 Page 5 of 28
ANFIS methodology aims to organize the FIS (fuzzy inference system) by analyzing the input/output data pairs [45,46]. It gives fuzzy logic the ability to adjust the fuzzy membership function parameters so that it is optimal in allowing the associated FIS to detect and trace the given input/output data [47,48].
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2.3. Variable selection using ANFIS
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Generating predetermined input-output subsets requires the construction of a set of fuzzy ‘IF THEN’ rules with the suitable MFs. The ANFIS can serve as the foundation for such a construction. The input-output data are converted membership functions. In accordance with the collection of input-output data, the ANFIS takes the initial FIS and adjusts it through a back propagation algorithm. The FIS is comprised of three components, (1) a rule base, (2) a database, and (3) a reasoning mechanism. The rule base consists of a choice of fuzzy rules. The database assigns the MFs that are employed in the fuzzy rules. Finally, the last component is the reasoning mechanism, which infers from the rules and input data to reach a feasible outcome. These intelligent systems are a combination of knowledge, methods, and techniques from a variety of different sources. They adjust to perform better in environments that are changing. These systems have similar-human intelligence within a specific domain. The ANFIS recognizes patterns and assists in the revision of environments. FIS integrates human comprehension, does interfacing, and makes decisions. In MATLAB, FIS is employed in the whole process of the FIS training and evaluation. An ANFIS network for two input variables is the most influential parameter of the heat load of DHS. This is depicted in Figure 1.
Figure 1: ANFIS structure The fuzzy IF-THEN rules of Takagi and Sugeno’s class and two inputs for the first-order Sugeno are employed for the purpose of this study: 6 Page 6 of 28
.
(1)
The first layer is made up of input parameters MFs and it provides the input values to the following layer. Each node here is considered an adaptive node having a node function
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and , where and are membership functions. Bell-shaped membership functions having the maximum value (1.0) and the minimum value (0.0) are selected, such as
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is the set of parameters set. The parameters of this layer are designated as
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where
(2)
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premise parameters. Here, and are the inputs to nodes. They represent a combined version of the two most impactful variables on the heat load of DHS. The membership layer is the second layer. It looks for the weights of every membership function. This layer gets the receiving signals from the preceding layer and then it acts as a membership function to the representation of the fuzzy sets of each input variable, respectively. Second layer nodes are non-adaptive. The layer acts as a multiplier for the receiving signals as . Every output node exhibits the firing strength of a rule. The next, third, layer is known as the rule layer. All neurons here act as the pre-condition matching the fuzzy rules, i.e. each rule’s activation level are calculated, whereby the number of fuzzy rules is equal to the quantity of layers. Every node computes the normalized weights. The nodes in the third layer are also considered non-adaptive. Each of the nodes computes the value of the rule’s firing strength over the sum of all rules’ firing strengths in the form of , The outcomes are referred to as the normalized firing strengths. The fourth layer is responsible for providing the output values as a result of the inference of rules. This layer is also known as the defuzzification layer. Every 4th layer node is an adaptive node having the node function . In this layer, the is the variable set. The variable set is designated as consequent parameters. The fifth and final layer is known as the output layer. It adds up all the receiving inputs from the preceding layer. Thereafter, it converts the fuzzy classification outcomes into a binary (crisp). The single node of the fifth layer is considered non-adaptive. This node calculates the total output as the whole sum of all receiving signals,
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3.
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In the process of identification of variables in the ANFIS architectures, the hybrid learning algorithms were applied. The functional signals progress until the fourth layer, where the hybrid learning algorithm passes. Further on, the consequent variables are found by the least squares estimation. In the backward pass, the error rates circulate backwards and the premise variables are synchronized through the gradient decline order. Results
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A comprehensive search was performed using the given set of input variables. The first group of tested models was structured with fixed heat load and outdoor temperature at time step t, while different models were created using the current and lagged values of primary return temperature. The procedure was then performed for all prediction horizons. In the following step, heat load at time step t was fixed and predictive models were built using the current and lagged values of primary return temperature and outdoor temperature. Finally, the procedure in the previous two steps was repeated for all lagged variables of heat load. Basically, an ANFIS model was built by the functions for each combination and then respectively trained for single epoch. Subsequently, the achieved performance was reported. In the beginning only one input parameter influence was examined. From the outset, the most influential input in the prediction of the output was identified and determined, as depicted in Figure 2 for all predictive models. The leftmost input variables have the lowest number of errors (RMSE) or the most relevance (the highest influence on the output parameter) in regards to the outcome (Figure 2).
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(i) Figure 2: Time lagged heat load influence on heat load of DHS prediction
As it can be clearly seen from the function’s plot and the results depicted in Figure 2, the heat load at time step t (i.e. Q(t)) is the most influential for the heat load prediction models of 1, 2, 3, 4, and 24 hours ahead. The fact that both the checking errors and training are comparable is an indirect indication that there is no over-fitting. The results listed in Tables 3-11 show the influence of all 33 input variables for the prediction of DHS heat load for different prediction horizons. Tables 3 and 4 show that for heat load prediction models of 1 and 2 hours ahead, the most influential parameters are not the time lagged parameters. This means that the present 12 Page 12 of 28
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values of heat load are sufficient for prediction. With increased prediction horizon it is noticeable that the most influential parameters become time lagged values (Tables 5-11). However, for 24 hours ahead prediction of heat load of DHS (Table 11) there is only time lagged data for outdoor temperature. Prediction models for 3 and 24 hours ahead have almost static behavior, since only the time lagged parameter for outdoor temperature was selected as the most influential parameter. The results in Table 12 indicate that of all the parameters examined, optimal combination of the present input variables (not time lagged) was indicated only for the 1 hour ahead model, and the best predictor of accuracy was noted for this model. All the other examined models have some dynamical behavior in heat load prediction of DHS, since mostly time lagged values are selected as the most influential variables. A model of such simplicity in terms of structure was always preferable; the use of more than two inputs in the construction of the ANFIS model may not be advisable or appropriate.
trn=35.8629, chk=37.9808
trn=38.2416, chk=42.6324
Tp(t-1)
trn=43.8227, chk=46.5521
trn=38.9838, chk=42.6687
Tp(t-2)
trn=48.9675, chk=51.7906
T(t-3)
trn=39.9060, chk=42.8519
Tp(t-3)
trn=52.2905, chk=54.9052
T(t-4)
trn=40.6690, chk=42.9727
Tp(t-4)
trn=54.3021, chk=56.7889
T(t–5)
trn=41.2124, chk=42.8143
Tp(t–5)
trn=55.2996, chk=57.7248
T(t-6)
trn=41.4268,
Tp(t-6)
trn=55.3915,
T(t-1)
Q(t-3)
Q(t-4)
Q(t–5)
Q(t-6)
trn=38.0195, chk=42.8433
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Tp(t)
T(t-2)
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Q(t-2)
T(t)
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Q(t-1)
trn=23.6298 , chk=28.079 1 trn=35.3664 , chk=39.474 2 trn=42.7475 , chk=46.601 7 trn=47.7557 , chk=50.838 9 trn=51.0669 , chk=53.491 2 trn=53.2792 , chk=55.510 7 trn=54.4660
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Q(t)
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Table 3: ANFIS regression errors for heat load prediction for 1 hour ahead Predictor RMSE Predictor RMSE Predictor RMSE
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Q(t-10)
Tp(t-7)
T(t-8)
trn=41.2261, chk=41.6170
Tp(t-8)
T(t-9)
trn=41.1387, chk=41.5880
Tp(t-9)
T(t-10)
trn=41.2103, chk=42.0237
trn=54.6206, chk=56.8159
ip t
trn=41.3915, chk=41.9661
trn=53.3354, chk=55.5810
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T(t-7)
trn=52.2942, chk=54.5948
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Q(t-9)
chk=57.5593
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Q(t-8)
chk=42.4508
Tp(t-10)
trn=52.0464, chk=54.1897
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Q(t-7)
, chk=56.687 1 trn=54.4929 , chk=56.201 3 trn=53.3418 , chk=55.433 9 trn=51.8334 , chk=54.323 4 trn=50.7159 , chk=53.518 0
trn=35.3286 , chk=39.477 1 trn=42.7233 , chk=46.588 8 trn=47.7474 , chk=50.804 2 trn=51.1002 , chk=53.429 6 trn=53.3091 ,
trn=38.2380, chk=42.6252
Tp(t)
trn=43.8022, chk=46.5454
T(t-1)
trn=38.9820, chk=42.6588
Tp(t-1)
trn=48.9645, chk=51.7654
T(t-2)
trn=39.9047, chk=42.8218
Tp(t-2)
trn=52.3200, chk=54.8561
T(t-3)
trn=40.6636, chk=42.9176
Tp(t-3)
trn=54.3431, chk=56.7267
T(t-4)
trn=41.2056, chk=42.7455
Tp(t-4)
trn=55.3384, chk=57.6657
T(t)
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Q(t)
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Table 4: ANFIS regression errors for heat load prediction for 2 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE
Q(t-1)
Q(t-2)
Q(t-3)
Q(t-4)
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trn=41.3824, chk=41.9423
Tp(t-6)
T(t-7)
trn=41.2166, chk=41.6098
Tp(t-7)
T(t-8)
trn=41.1316, chk=41.5856
Tp(t-8)
trn=52.3372, chk=54.5587
Tp(t-9)
trn=52.0857, chk=54.1542
Tp(t-10)
trn=52.5975, chk=54.6551
T(t-9)
T(t-10)
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Q(t-10)
T(t-6)
ip t
Q(t-9)
trn=55.4304, chk=57.5108
cr
trn=54.6602, chk=56.7764
trn=53.3771, chk=55.5401
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Q(t-8)
Tp(t–5)
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Q(t-7)
trn=41.4189, chk=42.3780
trn=41.2022, chk=42.0272
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Q(t-6)
T(t–5)
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Q(t–5)
chk=55.459 1 trn=54.4970 , chk=56.608 0 trn=54.5230 , chk=56.168 8 trn=53.3781 , chk=55.405 6 trn=51.8721 , chk=54.288 5 trn=50.7544 , chk=53.500 3 trn=50.4848 , chk=53.013 0
trn=41.5696, chk=43.1571
Table 5: ANFIS regression errors for heat load prediction for 3 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE Q(t)
Q(t-1)
Q(t-2)
trn=42.6797 , chk=46.590 4 trn=47.7151 , chk=50.787 1 trn=51.0838 , chk=53.390
T(t)
trn=38.9654, chk=42.6529
Tp(t)
trn=48.9381, chk=51.7549
T(t-1)
trn=39.8902, chk=42.8130
Tp(t-1)
trn=52.3101, chk=54.8264
T(t-2)
trn=40.6487, chk=42.8896
Tp(t-2)
trn=54.3626, chk=56.6735
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Q(t-7)
trn=41.3986, chk=42.3102
Tp(t-4)
trn=55.4566, chk=57.4541
T(t–5)
trn=41.3615, chk=41.8697
Tp(t–5)
T(t-6)
trn=41.1940, chk=41.5885
Tp(t-6)
T(t-7)
trn=41.1083, chk=41.5808
Tp(t-7)
trn=52.3742, chk=54.5250
trn=41.1807, chk=42.0272
Tp(t-8)
trn=52.1233, chk=54.1242
Q(t-9)
T(t-9)
trn=41.5470, chk=43.1625
Tp(t-9)
trn=52.6300, chk=54.6249
Q(t-10)
T(t-10)
trn=42.3937, chk=45.0065
Tp(t-10)
trn=53.7382, chk=55.8719
cr
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T(t-4)
trn=54.6882, chk=56.7346
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T(t-8)
Ac ce p
Q(t-8)
trn=55.3658, chk=57.6018
an
Q(t-6)
Tp(t-3)
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Q(t–5)
trn=41.1861, chk=42.6920
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Q(t-4)
T(t-3)
te
Q(t-3)
0 trn=53.3291 , chk=55.392 6 trn=54.5148 , chk=56.554 1 trn=54.5403 , chk=56.087 9 trn=53.3924 , chk=55.379 3 trn=51.9017 , chk=54.269 4 trn=50.7877 , chk=53.473 8 trn=50.5160 , chk=53.001 5 trn=51.0514 , chk=53.801 0
trn=53.4096, chk=55.5093
Table 6: ANFIS regression errors for heat load prediction for 4 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE Q(t)
trn=47.6960 , chk=50.726 4
T(t)
trn=39.8829, chk=42.7250
Tp(t)
trn=52.3018, chk=54.7999
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Q(t–5)
Q(t-6)
T(t-2)
trn=41.1805, chk=42.6434
Tp(t-2)
trn=55.3929, chk=57.5883
T(t-3)
trn=41.3897, chk=42.2864
Tp(t-3)
T(t-4)
trn=41.3521, chk=41.8553
T(t–5)
trn=41.1842, chk=41.5760
Tp(t–5)
trn=53.4410, chk=55.4581
trn=41.0975, chk=41.5200
Tp(t-6)
trn=52.4095, chk=54.4561
T(t-7)
trn=41.1695, chk=41.9314
Tp(t-7)
trn=52.1618, chk=54.0499
Q(t-8)
T(t-8)
trn=41.5375, chk=43.0616
Tp(t-8)
trn=52.6693, chk=54.5482
Q(t-9)
T(t-9)
trn=42.3835, chk=44.8832
Tp(t-9)
trn=53.7731, chk=55.8063
Q(t-10)
T(t-10)
trn=43.6668, chk=47.1534
Tp(t-10)
trn=54.9893, chk=57.2846
ip t
trn=54.3666, chk=56.6729
cr
trn=55.4872, chk=57.4205
us
T(t-6)
Ac ce p
Q(t-7)
Tp(t-1)
Tp(t-4)
an
Q(t-4)
trn=40.6430, chk=42.8077
M
Q(t-3)
T(t-1)
d
Q(t-2)
trn=51.0699 , chk=53.377 6 trn=53.3278 , chk=55.408 4 trn=54.5416 , chk=56.538 2 trn=54.5638 , chk=56.049 5 trn=53.4137 , chk=55.354 4 trn=51.9208 , chk=54.190 9 trn=50.8185 , chk=53.377 5 trn=50.5508 , chk=52.918 9 trn=51.0851 , chk=53.663 1 trn=52.4701 , chk=55.100 0
te
Q(t-1)
trn=54.7172, chk=56.6951
17 Page 17 of 28
Table 7: ANFIS regression errors for heat load prediction for 5 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE
Q(t-4)
Tp(t-1)
T(t-2)
trn=41.3864, chk=42.2510
T(t-3)
trn=41.3484, chk=41.8427
Q(t-6)
Q(t-7)
Q(t-8)
Q(t-9)
ip t
trn=41.1779, chk=42.5763
trn=54.3626, chk=56.6739
trn=55.3952, chk=57.6094
us
cr
T(t-1)
Tp(t-2)
trn=55.5022, chk=57.4272
Tp(t-3)
trn=54.7342, chk=56.6758
trn=41.1819, chk=41.5718
Tp(t-4)
trn=53.4571, chk=55.4286
trn=41.0962, chk=41.5172
Tp(t–5)
trn=52.4278, chk=54.4145
T(t-6)
trn=41.1673, chk=41.8856
Tp(t-6)
trn=52.1822, chk=53.9932
T(t-7)
trn=41.5342, chk=42.9848
Tp(t-7)
trn=52.6910, chk=54.4904
T(t-8)
trn=42.3787, chk=44.8038
Tp(t-8)
trn=53.7959, chk=55.7512
T(t-9)
trn=43.6612,
Tp(t-9)
trn=55.0097,
T(t-4)
T(t–5)
Ac ce p
Q(t–5)
Tp(t)
an
Q(t-3)
trn=40.6404, chk=42.7364
M
Q(t-2)
T(t)
d
Q(t-1)
trn=51.0621 , chk=53.351 9 trn=53.3217 , chk=55.421 3 trn=54.5409 , chk=56.573 3 trn=54.5780 , chk=56.060 8 trn=53.4252 , chk=55.329 5 trn=51.9306 , chk=54.176 1 trn=50.8276 , chk=53.313 9 trn=50.5664 , chk=52.838 4 trn=51.1036 , chk=53.600 6 trn=52.4891
te
Q(t)
18 Page 18 of 28
chk=47.0595
T(t-10)
trn=45.0621, chk=49.1532
chk=57.2385
Tp(t-10)
trn=55.7488, chk=58.3628
ip t
Q(t-10)
, chk=55.002 5 trn=54.3674 , chk=56.864 6
trn=41.1809, chk=41.6122
Q(t-4)
Q(t–5)
Q(t-6)
Q(t-7)
Tp(t)
trn=54.7618, chk=56.8747
an
us
T(t-1)
Tp(t-1)
trn=53.5019, chk=55.5668
Tp(t-2)
trn=52.4866, chk=54.4673
trn=41.1675, chk=41.9999
Tp(t-3)
trn=52.2487, chk=53.9740
T(t-4)
trn=41.5356, chk=43.0744
Tp(t-4)
trn=52.7591, chk=54.4410
T(t–5)
trn=42.3796, chk=44.8432
Tp(t–5)
trn=53.8669, chk=55.7041
T(t-6)
trn=43.6602, chk=47.0546
Tp(t-6)
trn=55.0841, chk=57.1981
T(t-7)
trn=45.0591, chk=49.1230
Tp(t-7)
trn=55.8249, chk=58.3323
T(t-2)
T(t-3)
Ac ce p
Q(t-3)
trn=41.3484, chk=41.8337
M
Q(t-2)
T(t)
trn=41.0950, chk=41.6095
d
Q(t-1)
trn=54.5813 , chk=56.289 6 trn=53.4481 , chk=55.564 8 trn=51.9682 , chk=54.351 5 trn=50.8745 , chk=53.394 1 trn=50.6123 , chk=52.815 9 trn=51.1507 , chk=53.545 6 trn=52.5436 , chk=54.943 1 trn=54.4289 ,
te
Q(t)
cr
Table 8: ANFIS regression errors for heat load prediction for 8 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE
19 Page 19 of 28
Tp(t-8)
trn=55.6216, chk=58.0292
T(t-9)
trn=47.2279, chk=51.6329
Tp(t-9)
ip t
T(t-10)
trn=47.8853, chk=52.0691
Tp(t-10)
trn=54.5531, chk=56.1642
trn=52.7642, chk=53.3312
an
Q(t-10)
trn=46.2934, chk=50.6651
cr
Q(t-9)
T(t-8)
us
Q(t-8)
chk=56.801 4 trn=55.7351 , chk=58.318 1 trn=55.8477 , chk=58.270 7 trn=55.0368 , chk=56.726 1
Q(t-2)
Q(t-3)
Q(t-4)
Q(t–5)
trn=41.0936, chk=41.5411
Tp(t)
trn=52.4887, chk=54.5494
trn=41.1673, chk=41.9727
Tp(t-1)
trn=52.2691, chk=54.0241
T(t-2)
trn=41.5370, chk=43.0909
Tp(t-2)
trn=52.8052, chk=54.4347
T(t-3)
trn=42.3795, chk=44.8749
Tp(t-3)
trn=53.9237, chk=55.6714
T(t-4)
trn=43.6595, chk=47.0878
Tp(t-4)
trn=55.1427, chk=57.1587
T(t–5)
trn=45.0566, chk=49.1317
Tp(t–5)
trn=55.8887, chk=58.2842
d
T(t)
T(t-1)
Ac ce p
Q(t-1)
trn=51.9598 , chk=54.439 6 trn=50.8692 , chk=53.504 0 trn=50.6320 , chk=52.896 3 trn=51.1906 , chk=53.545 1 trn=52.5829 , chk=54.921 2 trn=54.4724 , chk=56.761
te
Q(t)
M
Table 9: ANFIS regression errors for heat load prediction for 10 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE
20 Page 20 of 28
Q(t-10)
T(t-7)
trn=47.2243, chk=51.6215
Tp(t-7)
trn=54.6266, chk=56.0926
T(t-8)
trn=47.8843, chk=52.0503
Tp(t-8)
T(t-9)
trn=48.2574, chk=51.9141
Tp(t-9)
T(t-10)
trn=48.2828, chk=51.3018
Tp(t-10)
cr
ip t
trn=55.6901, chk=57.9717
trn=52.8385, chk=53.2475
us
Q(t-9)
Tp(t-6)
an
Q(t-8)
trn=46.2895, chk=50.6554
M
Q(t-7)
T(t-6)
trn=50.2114, chk=49.8828
trn=46.7029, chk=45.7276
d
Q(t-6)
2 trn=55.7853 , chk=58.267 5 trn=55.9075 , chk=58.226 4 trn=55.1044 , chk=56.660 5 trn=53.6388 , chk=54.404 5 trn=51.3695 , chk=51.738 8
trn=50.6168 , chk=52.906 0 trn=51.1892 , chk=53.504 9 trn=52.6170 , chk=54.835 4 trn=54.5287 , chk=56.654 4
T(t)
trn=41.5339, chk=43.1127
Tp(t)
trn=52.8112, chk=54.3996
T(t-1)
trn=42.3797, chk=44.8693
Tp(t-1)
trn=53.9579, chk=55.5887
T(t-2)
trn=43.6584, chk=47.0260
Tp(t-2)
trn=55.2082, chk=57.0428
T(t-3)
trn=45.0522, chk=49.0262
Tp(t-3)
trn=55.9656, chk=58.1641
Ac ce p
Q(t)
te
Table 10: ANFIS regression errors for heat load prediction for 12 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE
Q(t-1)
Q(t-2)
Q(t-3)
21 Page 21 of 28
Q(t-8)
Q(t-9)
T(t–5)
trn=47.2187, chk=51.5485
Tp(t–5)
trn=54.7142, chk=56.0300
T(t-6)
trn=47.8796, chk=52.0315
Tp(t-6)
T(t-7)
trn=48.2565, chk=51.9076
T(t-8)
trn=48.2848, chk=51.2993
Tp(t-8)
trn=46.8089, chk=45.7143
trn=47.8538, chk=50.2476
Tp(t-9)
trn=42.5001, chk=40.3925
trn=47.0542, chk=48.7725
Tp(t-10)
trn=38.1975, chk=34.5664
cr
trn=52.9339, chk=53.2032
us
T(t-9)
T(t-10)
ip t
trn=55.7712, chk=57.8739
Ac ce p
Q(t-10)
Tp(t-4)
Tp(t-7)
an
Q(t-7)
trn=46.2842, chk=50.5394
M
Q(t-6)
T(t-4)
d
Q(t–5)
trn=55.8445 , chk=58.121 5 trn=55.9717 , chk=58.114 5 trn=55.1768 , chk=56.599 7 trn=53.7236 , chk=54.352 6 trn=51.4630 , chk=51.711 9 trn=48.2193 , chk=48.099 5 trn=43.8235 , chk=42.764 1
te
Q(t-4)
trn=50.3153, chk=49.8525
Table 11: ANFIS regression errors for heat load prediction for 24 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE Q(t)
Q(t-1)
Q(t-2)
trn=35.5636 , chk=31.995 1 trn=39.0603 , chk=36.400 6 trn=44.7021
T(t)
trn=45.7837, chk=46.0671
Tp(t)
trn=39.3249, chk=34.5699
T(t-1)
trn=45.6952, chk=45.5254
Tp(t-1)
trn=45.1348, chk=42.0252
T(t-2)
trn=45.9545,
Tp(t-2)
trn=50.1689,
22 Page 22 of 28
Q(t-7)
trn=46.9863, chk=45.7115
Tp(t-4)
T(t–5)
trn=47.4259, chk=45.7907
Tp(t–5)
T(t-6)
trn=47.7263, chk=45.7960
Q(t-9)
Q(t-10)
ip t
T(t-4)
trn=53.7760, chk=52.8384
trn=56.2092, chk=55.8128
cr
Tp(t-3)
us
trn=57.7812, chk=57.4859
Tp(t-6)
trn=58.6343, chk=58.2266
trn=47.8672, chk=45.6251
Tp(t-7)
trn=58.8414, chk=58.0522
trn=48.0004, chk=45.2993
Tp(t-8)
trn=58.3689, chk=57.2833
T(t-9)
trn=48.0852, chk=45.2001
Tp(t-9)
trn=57.3964, chk=56.2021
T(t-10)
trn=48.2015, chk=45.3173
Tp(t-10)
trn=56.4651, chk=55.2410
T(t-7)
T(t-8)
Ac ce p
Q(t-8)
trn=46.4530, chk=45.5456
an
Q(t-6)
T(t-3)
M
Q(t–5)
chk=48.3488
d
Q(t-4)
chk=45.4167
te
Q(t-3)
, chk=43.138 9 trn=49.4617 , chk=48.302 2 trn=52.9598 , chk=52.206 5 trn=55.4112 , chk=54.701 7 trn=57.0660 , chk=56.384 0 trn=57.9623 , chk=57.089 3 trn=58.0841 , chk=56.853 9 trn=57.3238 , chk=56.005 6 trn=56.1756 , chk=55.040 7
Table 12: ANFIS regression errors for heat load prediction for two and three input parameter combinations Predictor RMSE
23 Page 23 of 28
Q(t), T(t), Tp(t) Q(t), T(t)
2 hours ahead
Q(t-6), Q(t), T(t)
3 hours ahead
cr
Q(t-7), T(t) Q(t-5), Q(t), T(t) Q(t-7), T(t) Q(t-4), T(t), Tp(t-10)
an
4 hours ahead
M
Q(t-6), T(t) 5 hours ahead
Q(t-3), T(t), Tp(t-10)
d
Q(t), T(t-2)
Q(t-8), Q(t), T(t)
te
8 hours ahead
Ac ce p
T(t-2), Tp(t-10)
10 hours ahead
12 hours ahead
Q(t-10), T(t-1), Tp(t10) T(t), Tp(t-10) T(t-6), T(t), Tp(t-10) Q(t), Tp(t-1)
24 hours ahead
4.
us
1 hour ahead
trn=22.2632, chk=26.9841 trn=20.3209, chk=25.9834 trn=31.7865, chk=36.5678 trn=28.4119, chk=32.2106 trn=35.8337, chk=38.0809 trn=31.9307, chk=36.1877 trn=36.7978, chk=39.4246 trn=32.7425, chk=34.8671 trn=37.7118, chk=39.9263 trn=33.0647, chk=33.8502 trn=38.3282, chk=38.0467 trn=34.4196, chk=35.4864 trn=38.6445, chk=39.2871 trn=35.3245, chk=36.4954 trn=33.8509, chk=32.5914 trn=32.0151, chk=32.8701 trn=34.7263, chk=31.0598 trn=33.0816, chk=32.2453
ip t
Q(t), Tp(t)
Q(t), T(t), Tp(t-5)
Conclusion
24 Page 24 of 28
M
an
us
cr
ip t
There can be problems with the inclusion of multiple input variables in predictive models. Excessive number of input variables will negatively affect interpretability as well as predictive power of constructed models. Additionally, this will reduce the generalization capability of the model. In that respect, methods for selecting the most influential variables from a huge set of potential variables are necessary. In this study, a systematic approach was used to select the most dominant input variables for prediction of heat load in DHS using the ANFIS methodology. The simulations also employed MATLAB, and outcomes were checked on the corresponding output blocks. Wrapper approach was used to select the subset of most influential variables (in the sense of minimal RMSE) from a set of potential input variables. The ANFIS network was used to perform a variable search and then to determine how 33 selected input variables (11 time lagged heat load, 11 time lagged outdoor temperature, 11 time lagged outdoor primary return temperatures) influence prediction of heat load in DHS for different prediction horizons. The results demonstrated that the proposed method has potential, although further refinements are needed in order to practically apply the method. One direction would be to accelerate the process of testing different predictive models. This will open up the possibility of starting the testing process with a greater number of potential input variables and including more lags, which will certainly improve the predictive power of created models.
[3]
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[8]
te
[2]
Gadd, H., Werner, S. (2015). Thermal energy storage systems for district heating and cooling in Advances in Thermal Energy Storage Systems. (pp. 467–478), Elsevier. Rezaie, B., & Rosen, M. A. (2012). District heating and cooling: Review of technology and potential enhancements. Applied Energy, 93, 2-10. Lund, H., Werner, S., Wiltshire, R., Svendsen, S., Thorsen, J. E., Hvelplund, F., & Mathiesen, B. V. (2014). 4th Generation District Heating (4GDH). Energy, 68, 1–11. doi:10.1016/j.energy.2014.02.089 Dyrelund A, Lund H. Heat plan Denmark 2010: a road map for implementing the EU directive on renewable energy (Varmeplan Danmark); 2010. Lund H, Möller B, Mathiesen BV, Dyrelund A. The role of district heating in future renewable energy systems. Energy 2010;35:1381-90. Münster M, Morthorst PE, Larsen HV, Bregnbæk L, Werling J, Lindboe HH, et al. The role of district heating in the future Danish energy system. Energy 2012;48:47-55. Connolly D, Lund H, Mathiesen BV, Werner S, Möller B, Persson U, et al. Heat roadmap Europe: combining district heating with heat savings to decarbonise the EU energy system. Energy Policy 2014;65:475-89. Brand M, Svendsen S. Renewable-based low-temperature district heating for existing buildings in various stages of refurbishment. Energy 2013;62:311-319.
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Sivakumar R, Balu K, ANFIS based Distillation Column Control, IJCA Special Issue on “Evolutionary Computation for Optimization Techniques” (2010), 67-73. Kurnaz S, Cetin O, Kaynak O, Adaptive neuro-fuzzy inference system based autonomous flight control of unmanned air vehicles, Expert Systems with Applications (2010), 37, 1229-1234. Ravi S, Sudha M, Balakrishnan P.A, Design of Intelligent Self-Tuning GA ANFIS Temperature Controller for Plastic Extrusion System, Modelling and Simulation in Engineering (2011), 1-8. Areed F.G, Haikal A.Y, Mohammed R.H, Adaptive neuro-fuzzy control of an induction motor, Ain Shams Engineering Journal (2010), 1, 71-78. Petković, D., Issa, M., Pavlović, N.D., Zentner, L., Ćojbašić, Ž., Adaptive neuro fuzzy controller for adaptive compliant robotic gripper, Expert Systems with Applications, DOI: 10.1016/j.eswa.2012.05.072, Online First. Tian L, Collins C, Adaptive neuro-fuzzy control of a flexible manipulator, Mechatronics (2005), 15, 1305-1320. Aldair A.A, Wang W.J, Design an intelligent controller for full vehicle nonlinear active suspension systems, International Journal on Smart Sensing and Intelligent Systems (2011), 4:2, 224-243. Dastranj M.R, Ebroahimi E, Changizi N, Sameni E, Control DC Motorspeed with Adaptive Neuro-Fuzzy control (ANFIS), Australian Journal of Basic and Applied Sciences (2011), 5:10, 1499-1504. Wahida Banu R.S.D, Shakila Banu A, Manoj D, Identification and Control of Nonlinear Systems using Soft Computing Techniques, International Journal of Modeling and Optimization (2011), 1:1, 24-28. Grigorie T.L, Botez R.M, Adaptive neuro-fuzzy inference system-based controllers for smart material actuator modelling, J. Aerospace Engineering (2009), 655-668. Akcayol M.A, Application of adaptive neuro-fuzzy controller for SRM, Advances in Engineering Software (2004), 35, 129-137.
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[38]
Highlights •
District heating systems for increase in fuel efficiency.
•
Control and prediction future improvement of district heating systems operation.
•
To predict the heat load for individual consumers in district heating systems.
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A process which simulates the head load conditions.
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S0378-7788(15)30116-X http://dx.doi.org/doi:10.1016/j.enbuild.2015.06.074 ENB 5980
To appear in:
ENB
Received date: Revised date: Accepted date:
31-3-2015 18-6-2015 30-6-2015
Please cite this article as: D. Petkovi´c, M. Proti´c, S. Shamshirband, S. Akib, M. Raos, D. Markovi´c, Evaluation of the most influential parameters of heat load in district heating systems, Energy and Buildings (2015), http://dx.doi.org/10.1016/j.enbuild.2015.06.074 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Evaluation of the most influential parameters of heat load in district heating systems Dalibor Petković*a, Milan Protić**, Shahaboddin Shamshirband***, Shatirah Akib****, Miomir Raos**, Dušan Marković* *
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University of Niš, Faculty of Mechanical Engineering, Department for Mechatronics and Control, Aleksandra Medvedeva 14, 18000 Niš, Serbia. ** University of Niš, Faculty of Occupational Safety, Čarnojevića 10A, 18000 Niš, Serbia *** Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia. **** Department of Civil Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia. corresponding author: [email protected], +381643283048
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Abstract
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The aim of this study is to investigate the potential of soft computing methods for selecting the most relevant variables for predictive models of consumers’ heat load in district heating systems (DHS). Data gathered from one of the heat substations was used for the simulation process. The ANFIS (adaptive neuro-fuzzy inference system) method was applied to the data obtained from these measurements. The ANFIS process for variable selection was implemented in order to detect the predominant variables affecting the short-term multistep prediction of consumers’ heat load in district heating systems. It was also used to select the minimal input subset of variables from the initial set of input variables – current and lagged variables (up to 10 steps) of heat load, outdoor temperature, and primary return temperature. The obtained results could be used for simplification of predictive methods so as to avoid multiple input variables. While the obtained results are promising, further work is required in order to get results that could be directly applied in practice. Keywords: ANFIS, variable selection, district heating systems, heat load, variable selection 1. Introduction
Currently, the fundamental idea of district heating is to recover fuel and heat flows that are otherwise lost, from heat sources both inside and outside the energy system [1]. DHS offers the possibility of using renewable sources (biomass, solar and geothermal energy) as well as cheap, “waste”, heat from industrial plants and power production facilities [2]. As pointed out in [3], a number of recent studies [4-9] found that DHS will play significant role in future sustainable energy systems. However, present DHS will need to undergo substantial changes in order to expand further and effectively compete with other space heating alternatives. 1 Page 1 of 28
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Introduction of intelligent control of heating of buildings is one of the options which could accelerate transition of present DHS systems towards future low-temperature DHS [10]. Consumers’ heat load predictive models are a necessary prerequisite for the realization of novel, intelligent, control strategies, contributing to more efficient use of primary energy. Heat load prediction is very important for optimization and planning in DHS. If credible prediction heat load models could be built, heat production could be matched to the real consumers’ needs. This would result in reduced distribution heat losses, lower return temperatures, and possibility of connecting more consumers to DHS. Additionally, heat suppliers could schedule which production units to activate and avoid the use of peak boilers, which mostly use expensive fossil fuels [11]. In addition, heat load forecasts could be used as input to model predictive control in DHS, effective use of the thermal storage system [12], and peak shaving. In the literature, different approaches were used for DHS heat load modeling and prediction. In one of the earliest studies regarding heat load in DHS, Werner [13] proposed the model of heat load of complete DHS comprising four major components: space heating, preparation of hot consumption water, distribution loss, and additional working load. Space heating load was modeled as a linear combination of the steady heat transmission and the heating of a constant ventilation rate, transient heat transmission, wind-induced air infiltration, and solar gain. In [14] different parametric and non-parametric heat load prediction models were discussed and used. In [15] general transfer function models for different prediction horizons were proposed for control purposes. Dotzauer [16] modeled heat load using the assumption that heat demand can be described sufficiently well as a function of outdoor temperature (piecewise linear function) and the social component. Grey-box approach, combining the relations from the theory of heat transfer, statistical methods, and aggregated data, was used by [17] for modeling heat consumption in entire DHS in Denmark. It was concluded that this approach, even with aggregated data, is powerful. Mesterkemper [18] used dynamic factor models for predicting heat load in the city of Wuppertal in North-Western Germany. Seasonal Autoregressive Integrated Moving Average (SARIMA) heat load models were developed in [19]. Recurrent neural networks were used in [20] for heat load prediction. In [21] an ensemble of decision trees was used for building an online learning algorithm for heat load forecasting in DHS. In the aforementioned studies, versatile sets of input variables were used to build the prediction models. The following variables were primarily indicated as influential for heat load models: outdoor air temperature, insolation, wind direction and velocity, water flow, temperature of supply and return water, and time and type of day (weekend and workdays). When structuring heat load predictive models, it is crucial to include the most influential variables and discard the redundant and non-informative predictors. Additionally, it is important to identify and eliminate the potential multicollinearity between the input variables. Correct variable selection will result in increased model predictability and interpretability. In the literature, different approaches were used for selection of subset of most influential variables, but generally all the methods can be divided in two main categories [22]: 2 Page 2 of 28
filter methods and wrapper methods.
Methodology
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In filter methods the selection of model input variables is made prior to model training and tuning. On the other hand, in the wrapper approach the idea is to assess the predictive ability of various models with different combinations of input variables, using some error metrics, and to select the model producing the best results. While wrappers are more computationally demanding, especially for models having multiple tuning hyper-parameters, they can be regarded as a superior alternative as compared with filters [23]. In this article, we used the wrapper approach to select the most influential variables for DHS heat load predictive models. The Adaptive Neuro-fuzzy Inference Technique (ANFIS) was applied to the available data sets to select the predominant model variables. Current (at moment t) and lagged (up to 10 steps) variables of heat load, outdoor temperature, and primary return temperature were used for structuring the predictive models. An initial set of 33 potential variables was used for experiments. The remainder of the article is organized as follows. First we provide a brief explanation of experimental installation used for gathering the data used for analysis. In the second section we implement ANFIS methodology to select the most influential variables from the model. The third section presents the main results. Finally, the fourth section contains the main concluding remarks.
2.1. System and data description
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Data acquisition was performed in the Novi Sad district heating system. With installed capacity of 877.3 MW, it is the second largest DHS in Serbia, numbering 101,948 consumers, of which 93,971 are residential and 7,977 commercial, connected to the DHS [24]. Heat distribution network is 219.8 km long and 3,832 heating substations are connected to the network. One CHP (combined heat and power) unit and six heat-only boilers plants are used as the heat source. Base heat load is provided from the CHP plant while peak load is covered from heat-only boilers. The data used for this study were gathered from one of the system’s heat substations during the 2010/2011 heating season. This substation is directly connected to the system via a 3pipe system. One supply pipe is used for space heating and another is used for preparation of domestic hot water (using storage tanks placed in the substation). The third pipe is common return. Temperature in consumers’ installations (secondary installations) is regulated by ECL Comfort 300 regulator and motorized control valve, which is positioned in the return pipe. The 3 Page 3 of 28
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regulator is realized as a weather compensator that controls the supply temperature in the secondary installation according to outdoor temperature (“sliding” diagram). Primary supply and return temperatures, thermal energy, power and flow on primary side, as well as outdoor temperature, were measured at 15-minute intervals during the heating season. Outdoor temperature was measured with Danfoss ESMT temperature sensor (Pt 1000, temperature range from -50 °C to 50 °C, time constant ≤ 15 min). Primary supply and return temperatures were measured with immersion Danfoss ESMU 100 sensors (Pt 1000, temperature range from 0 °C to 140 °C, time constant 2 s). Thermal energy and power and flow on primary side were measured with Kamstrup Multical 66C energy meter. All measuring devices were calibrated prior to measurement. Measured values were logged on Danfoss ECA 87 remote control and data log module for ECL Comfort 300 regulator (weather compensator). Measured and stored data from the regulator were regularly downloaded via Danfoss ECL WebAccess module. Prior to analysis, data were averaged at 1-hour intervals. Data cleaning and preprocessing was not performed. For this study, three time series for heat load, outdoor temperature, and primary return temperature were created and used for subsequent analysis. Statistical summary for these time series is presented in Table 1.
Std 62.5 6.5 5.8
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Table 1: Statistical summary of collected data Variable Minimum Maximum Mean value value Heat load [kW] 0.0 298.3 125.2 0 Outdoor temperature [ C] -7.6 24.4 5.7 Primary return temperature 21.1 52.4 37.1 [0C] 2.2. Input variables for model building
For this study predictive models of heat load were developed for 1-5 hours ahead and 8, 10, 12, and 24 hours ahead. Before the analysis we formed the set of potential input variables. In addition to the initial three input variables (outdoor temperature, heat load, and primary return temperature), due to the dynamic nature of DHS, it was important to add the lagged values of these variables in the initial set. Although the initial set with more lagged variables is advantageous, their number is limited by available computation power. In that respect we limited the number of lags to 10. The list of all potential predictors is shown in Table 2. Table 2: List and description of potential input variables for heat load modeling Input variable Input Input variable – Input Input variable – Input – variable Heat load variable Primary return temp. variabl Outdoor ID ID e ID temperature 4 Page 4 of 28
temperature
23 24 25 26 27 28 29 30 31 32 33
Tp(t) Tp(t-1) Tp(t-2) Tp(t-3) Tp(t-4) Tp(t–5) Tp(t-6) Tp(t-7) Tp(t-8) Tp(t-9) Tp(t-10)
ip t
Q(t) Q(t-1) Q(t-2) Q(t-3) Q(t-4) Q(t–5) Q(t-6) Q(t-7) Q(t-8) Q(t-9) Q(t-10)
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12 13 14 15 16 17 18 19 20 21 22
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T(t) T(t-1) T(t-2) T(t-3) T(t-4) T(t–5) T(t-6) T(t-7) T(t-8) T(t-9) T(t-10)
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To build a predictive model with the best characteristics, it is necessary to identify the most relevant and influential subset of variables. This process of selection is usually called variable selection. The purpose of this process is to find a subset from the initial input variables set that best contributes to the model’s predictive power. Essentially, we adopted the wrapper approach with neural network as the foundation. Neural network is an architecture made up of extremely parallel adaptive processing elements, which are interconnected through structured networks. Predictive performance of the neural network models depends heavily on the chosen input variables. To achieve a successful generation and creation of a model that is capable of estimating a special process output, the selection process of the subset of variables that are really pertinent is crucial. This is achieved in the process of variable selection. As mentioned, the purpose of this procedure is to find a subset of the total set of parameters that have been recorded to show good capability of prediction [25-28]. The problems faced in the process of selection of parameters could possibly be resolved by integrating and applying prior knowledge to segregate and remove irrelevant parameters. Otherwise, a more sophisticated approach to the abovementioned problem would be to regard the problem as an optimization procedure through the use of genetic algorithms [29]. The objective here was to select the proper explanatory (input) parameters and thereby minimize the error that exists between the observed values and the model estimations of the explained variables. Among the many neural network systems, one of the most used and powerful is the ANFIS, a hybrid approach, which combines the merits of both neural networks and the fuzzy set theory [30, 31]. In order to determine the main influential variables that most significantly contribute to the predictive power of heat load models of DHS, we conducted a variable search by employing the ANFIS. ANFIS [32], a hybrid intelligent system that increases the capability of learning and adapting automatically, has been used by researchers for many different purposes in a variety of engineering systems, such as modeling [33-36], prediction [37-39], and control [40-44]. The 5 Page 5 of 28
ANFIS methodology aims to organize the FIS (fuzzy inference system) by analyzing the input/output data pairs [45,46]. It gives fuzzy logic the ability to adjust the fuzzy membership function parameters so that it is optimal in allowing the associated FIS to detect and trace the given input/output data [47,48].
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2.3. Variable selection using ANFIS
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Generating predetermined input-output subsets requires the construction of a set of fuzzy ‘IF THEN’ rules with the suitable MFs. The ANFIS can serve as the foundation for such a construction. The input-output data are converted membership functions. In accordance with the collection of input-output data, the ANFIS takes the initial FIS and adjusts it through a back propagation algorithm. The FIS is comprised of three components, (1) a rule base, (2) a database, and (3) a reasoning mechanism. The rule base consists of a choice of fuzzy rules. The database assigns the MFs that are employed in the fuzzy rules. Finally, the last component is the reasoning mechanism, which infers from the rules and input data to reach a feasible outcome. These intelligent systems are a combination of knowledge, methods, and techniques from a variety of different sources. They adjust to perform better in environments that are changing. These systems have similar-human intelligence within a specific domain. The ANFIS recognizes patterns and assists in the revision of environments. FIS integrates human comprehension, does interfacing, and makes decisions. In MATLAB, FIS is employed in the whole process of the FIS training and evaluation. An ANFIS network for two input variables is the most influential parameter of the heat load of DHS. This is depicted in Figure 1.
Figure 1: ANFIS structure The fuzzy IF-THEN rules of Takagi and Sugeno’s class and two inputs for the first-order Sugeno are employed for the purpose of this study: 6 Page 6 of 28
.
(1)
The first layer is made up of input parameters MFs and it provides the input values to the following layer. Each node here is considered an adaptive node having a node function
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and , where and are membership functions. Bell-shaped membership functions having the maximum value (1.0) and the minimum value (0.0) are selected, such as
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is the set of parameters set. The parameters of this layer are designated as
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where
(2)
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premise parameters. Here, and are the inputs to nodes. They represent a combined version of the two most impactful variables on the heat load of DHS. The membership layer is the second layer. It looks for the weights of every membership function. This layer gets the receiving signals from the preceding layer and then it acts as a membership function to the representation of the fuzzy sets of each input variable, respectively. Second layer nodes are non-adaptive. The layer acts as a multiplier for the receiving signals as . Every output node exhibits the firing strength of a rule. The next, third, layer is known as the rule layer. All neurons here act as the pre-condition matching the fuzzy rules, i.e. each rule’s activation level are calculated, whereby the number of fuzzy rules is equal to the quantity of layers. Every node computes the normalized weights. The nodes in the third layer are also considered non-adaptive. Each of the nodes computes the value of the rule’s firing strength over the sum of all rules’ firing strengths in the form of , The outcomes are referred to as the normalized firing strengths. The fourth layer is responsible for providing the output values as a result of the inference of rules. This layer is also known as the defuzzification layer. Every 4th layer node is an adaptive node having the node function . In this layer, the is the variable set. The variable set is designated as consequent parameters. The fifth and final layer is known as the output layer. It adds up all the receiving inputs from the preceding layer. Thereafter, it converts the fuzzy classification outcomes into a binary (crisp). The single node of the fifth layer is considered non-adaptive. This node calculates the total output as the whole sum of all receiving signals,
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3.
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In the process of identification of variables in the ANFIS architectures, the hybrid learning algorithms were applied. The functional signals progress until the fourth layer, where the hybrid learning algorithm passes. Further on, the consequent variables are found by the least squares estimation. In the backward pass, the error rates circulate backwards and the premise variables are synchronized through the gradient decline order. Results
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A comprehensive search was performed using the given set of input variables. The first group of tested models was structured with fixed heat load and outdoor temperature at time step t, while different models were created using the current and lagged values of primary return temperature. The procedure was then performed for all prediction horizons. In the following step, heat load at time step t was fixed and predictive models were built using the current and lagged values of primary return temperature and outdoor temperature. Finally, the procedure in the previous two steps was repeated for all lagged variables of heat load. Basically, an ANFIS model was built by the functions for each combination and then respectively trained for single epoch. Subsequently, the achieved performance was reported. In the beginning only one input parameter influence was examined. From the outset, the most influential input in the prediction of the output was identified and determined, as depicted in Figure 2 for all predictive models. The leftmost input variables have the lowest number of errors (RMSE) or the most relevance (the highest influence on the output parameter) in regards to the outcome (Figure 2).
(a)
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(e)
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(h)
(i) Figure 2: Time lagged heat load influence on heat load of DHS prediction
As it can be clearly seen from the function’s plot and the results depicted in Figure 2, the heat load at time step t (i.e. Q(t)) is the most influential for the heat load prediction models of 1, 2, 3, 4, and 24 hours ahead. The fact that both the checking errors and training are comparable is an indirect indication that there is no over-fitting. The results listed in Tables 3-11 show the influence of all 33 input variables for the prediction of DHS heat load for different prediction horizons. Tables 3 and 4 show that for heat load prediction models of 1 and 2 hours ahead, the most influential parameters are not the time lagged parameters. This means that the present 12 Page 12 of 28
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values of heat load are sufficient for prediction. With increased prediction horizon it is noticeable that the most influential parameters become time lagged values (Tables 5-11). However, for 24 hours ahead prediction of heat load of DHS (Table 11) there is only time lagged data for outdoor temperature. Prediction models for 3 and 24 hours ahead have almost static behavior, since only the time lagged parameter for outdoor temperature was selected as the most influential parameter. The results in Table 12 indicate that of all the parameters examined, optimal combination of the present input variables (not time lagged) was indicated only for the 1 hour ahead model, and the best predictor of accuracy was noted for this model. All the other examined models have some dynamical behavior in heat load prediction of DHS, since mostly time lagged values are selected as the most influential variables. A model of such simplicity in terms of structure was always preferable; the use of more than two inputs in the construction of the ANFIS model may not be advisable or appropriate.
trn=35.8629, chk=37.9808
trn=38.2416, chk=42.6324
Tp(t-1)
trn=43.8227, chk=46.5521
trn=38.9838, chk=42.6687
Tp(t-2)
trn=48.9675, chk=51.7906
T(t-3)
trn=39.9060, chk=42.8519
Tp(t-3)
trn=52.2905, chk=54.9052
T(t-4)
trn=40.6690, chk=42.9727
Tp(t-4)
trn=54.3021, chk=56.7889
T(t–5)
trn=41.2124, chk=42.8143
Tp(t–5)
trn=55.2996, chk=57.7248
T(t-6)
trn=41.4268,
Tp(t-6)
trn=55.3915,
T(t-1)
Q(t-3)
Q(t-4)
Q(t–5)
Q(t-6)
trn=38.0195, chk=42.8433
M
Tp(t)
T(t-2)
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Q(t-2)
T(t)
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Q(t-1)
trn=23.6298 , chk=28.079 1 trn=35.3664 , chk=39.474 2 trn=42.7475 , chk=46.601 7 trn=47.7557 , chk=50.838 9 trn=51.0669 , chk=53.491 2 trn=53.2792 , chk=55.510 7 trn=54.4660
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Q(t)
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Table 3: ANFIS regression errors for heat load prediction for 1 hour ahead Predictor RMSE Predictor RMSE Predictor RMSE
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Q(t-10)
Tp(t-7)
T(t-8)
trn=41.2261, chk=41.6170
Tp(t-8)
T(t-9)
trn=41.1387, chk=41.5880
Tp(t-9)
T(t-10)
trn=41.2103, chk=42.0237
trn=54.6206, chk=56.8159
ip t
trn=41.3915, chk=41.9661
trn=53.3354, chk=55.5810
cr
T(t-7)
trn=52.2942, chk=54.5948
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Q(t-9)
chk=57.5593
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Q(t-8)
chk=42.4508
Tp(t-10)
trn=52.0464, chk=54.1897
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Q(t-7)
, chk=56.687 1 trn=54.4929 , chk=56.201 3 trn=53.3418 , chk=55.433 9 trn=51.8334 , chk=54.323 4 trn=50.7159 , chk=53.518 0
trn=35.3286 , chk=39.477 1 trn=42.7233 , chk=46.588 8 trn=47.7474 , chk=50.804 2 trn=51.1002 , chk=53.429 6 trn=53.3091 ,
trn=38.2380, chk=42.6252
Tp(t)
trn=43.8022, chk=46.5454
T(t-1)
trn=38.9820, chk=42.6588
Tp(t-1)
trn=48.9645, chk=51.7654
T(t-2)
trn=39.9047, chk=42.8218
Tp(t-2)
trn=52.3200, chk=54.8561
T(t-3)
trn=40.6636, chk=42.9176
Tp(t-3)
trn=54.3431, chk=56.7267
T(t-4)
trn=41.2056, chk=42.7455
Tp(t-4)
trn=55.3384, chk=57.6657
T(t)
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Table 4: ANFIS regression errors for heat load prediction for 2 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE
Q(t-1)
Q(t-2)
Q(t-3)
Q(t-4)
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trn=41.3824, chk=41.9423
Tp(t-6)
T(t-7)
trn=41.2166, chk=41.6098
Tp(t-7)
T(t-8)
trn=41.1316, chk=41.5856
Tp(t-8)
trn=52.3372, chk=54.5587
Tp(t-9)
trn=52.0857, chk=54.1542
Tp(t-10)
trn=52.5975, chk=54.6551
T(t-9)
T(t-10)
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Q(t-10)
T(t-6)
ip t
Q(t-9)
trn=55.4304, chk=57.5108
cr
trn=54.6602, chk=56.7764
trn=53.3771, chk=55.5401
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Q(t-8)
Tp(t–5)
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Q(t-7)
trn=41.4189, chk=42.3780
trn=41.2022, chk=42.0272
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Q(t-6)
T(t–5)
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Q(t–5)
chk=55.459 1 trn=54.4970 , chk=56.608 0 trn=54.5230 , chk=56.168 8 trn=53.3781 , chk=55.405 6 trn=51.8721 , chk=54.288 5 trn=50.7544 , chk=53.500 3 trn=50.4848 , chk=53.013 0
trn=41.5696, chk=43.1571
Table 5: ANFIS regression errors for heat load prediction for 3 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE Q(t)
Q(t-1)
Q(t-2)
trn=42.6797 , chk=46.590 4 trn=47.7151 , chk=50.787 1 trn=51.0838 , chk=53.390
T(t)
trn=38.9654, chk=42.6529
Tp(t)
trn=48.9381, chk=51.7549
T(t-1)
trn=39.8902, chk=42.8130
Tp(t-1)
trn=52.3101, chk=54.8264
T(t-2)
trn=40.6487, chk=42.8896
Tp(t-2)
trn=54.3626, chk=56.6735
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Q(t-7)
trn=41.3986, chk=42.3102
Tp(t-4)
trn=55.4566, chk=57.4541
T(t–5)
trn=41.3615, chk=41.8697
Tp(t–5)
T(t-6)
trn=41.1940, chk=41.5885
Tp(t-6)
T(t-7)
trn=41.1083, chk=41.5808
Tp(t-7)
trn=52.3742, chk=54.5250
trn=41.1807, chk=42.0272
Tp(t-8)
trn=52.1233, chk=54.1242
Q(t-9)
T(t-9)
trn=41.5470, chk=43.1625
Tp(t-9)
trn=52.6300, chk=54.6249
Q(t-10)
T(t-10)
trn=42.3937, chk=45.0065
Tp(t-10)
trn=53.7382, chk=55.8719
cr
ip t
T(t-4)
trn=54.6882, chk=56.7346
us
T(t-8)
Ac ce p
Q(t-8)
trn=55.3658, chk=57.6018
an
Q(t-6)
Tp(t-3)
M
Q(t–5)
trn=41.1861, chk=42.6920
d
Q(t-4)
T(t-3)
te
Q(t-3)
0 trn=53.3291 , chk=55.392 6 trn=54.5148 , chk=56.554 1 trn=54.5403 , chk=56.087 9 trn=53.3924 , chk=55.379 3 trn=51.9017 , chk=54.269 4 trn=50.7877 , chk=53.473 8 trn=50.5160 , chk=53.001 5 trn=51.0514 , chk=53.801 0
trn=53.4096, chk=55.5093
Table 6: ANFIS regression errors for heat load prediction for 4 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE Q(t)
trn=47.6960 , chk=50.726 4
T(t)
trn=39.8829, chk=42.7250
Tp(t)
trn=52.3018, chk=54.7999
16 Page 16 of 28
Q(t–5)
Q(t-6)
T(t-2)
trn=41.1805, chk=42.6434
Tp(t-2)
trn=55.3929, chk=57.5883
T(t-3)
trn=41.3897, chk=42.2864
Tp(t-3)
T(t-4)
trn=41.3521, chk=41.8553
T(t–5)
trn=41.1842, chk=41.5760
Tp(t–5)
trn=53.4410, chk=55.4581
trn=41.0975, chk=41.5200
Tp(t-6)
trn=52.4095, chk=54.4561
T(t-7)
trn=41.1695, chk=41.9314
Tp(t-7)
trn=52.1618, chk=54.0499
Q(t-8)
T(t-8)
trn=41.5375, chk=43.0616
Tp(t-8)
trn=52.6693, chk=54.5482
Q(t-9)
T(t-9)
trn=42.3835, chk=44.8832
Tp(t-9)
trn=53.7731, chk=55.8063
Q(t-10)
T(t-10)
trn=43.6668, chk=47.1534
Tp(t-10)
trn=54.9893, chk=57.2846
ip t
trn=54.3666, chk=56.6729
cr
trn=55.4872, chk=57.4205
us
T(t-6)
Ac ce p
Q(t-7)
Tp(t-1)
Tp(t-4)
an
Q(t-4)
trn=40.6430, chk=42.8077
M
Q(t-3)
T(t-1)
d
Q(t-2)
trn=51.0699 , chk=53.377 6 trn=53.3278 , chk=55.408 4 trn=54.5416 , chk=56.538 2 trn=54.5638 , chk=56.049 5 trn=53.4137 , chk=55.354 4 trn=51.9208 , chk=54.190 9 trn=50.8185 , chk=53.377 5 trn=50.5508 , chk=52.918 9 trn=51.0851 , chk=53.663 1 trn=52.4701 , chk=55.100 0
te
Q(t-1)
trn=54.7172, chk=56.6951
17 Page 17 of 28
Table 7: ANFIS regression errors for heat load prediction for 5 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE
Q(t-4)
Tp(t-1)
T(t-2)
trn=41.3864, chk=42.2510
T(t-3)
trn=41.3484, chk=41.8427
Q(t-6)
Q(t-7)
Q(t-8)
Q(t-9)
ip t
trn=41.1779, chk=42.5763
trn=54.3626, chk=56.6739
trn=55.3952, chk=57.6094
us
cr
T(t-1)
Tp(t-2)
trn=55.5022, chk=57.4272
Tp(t-3)
trn=54.7342, chk=56.6758
trn=41.1819, chk=41.5718
Tp(t-4)
trn=53.4571, chk=55.4286
trn=41.0962, chk=41.5172
Tp(t–5)
trn=52.4278, chk=54.4145
T(t-6)
trn=41.1673, chk=41.8856
Tp(t-6)
trn=52.1822, chk=53.9932
T(t-7)
trn=41.5342, chk=42.9848
Tp(t-7)
trn=52.6910, chk=54.4904
T(t-8)
trn=42.3787, chk=44.8038
Tp(t-8)
trn=53.7959, chk=55.7512
T(t-9)
trn=43.6612,
Tp(t-9)
trn=55.0097,
T(t-4)
T(t–5)
Ac ce p
Q(t–5)
Tp(t)
an
Q(t-3)
trn=40.6404, chk=42.7364
M
Q(t-2)
T(t)
d
Q(t-1)
trn=51.0621 , chk=53.351 9 trn=53.3217 , chk=55.421 3 trn=54.5409 , chk=56.573 3 trn=54.5780 , chk=56.060 8 trn=53.4252 , chk=55.329 5 trn=51.9306 , chk=54.176 1 trn=50.8276 , chk=53.313 9 trn=50.5664 , chk=52.838 4 trn=51.1036 , chk=53.600 6 trn=52.4891
te
Q(t)
18 Page 18 of 28
chk=47.0595
T(t-10)
trn=45.0621, chk=49.1532
chk=57.2385
Tp(t-10)
trn=55.7488, chk=58.3628
ip t
Q(t-10)
, chk=55.002 5 trn=54.3674 , chk=56.864 6
trn=41.1809, chk=41.6122
Q(t-4)
Q(t–5)
Q(t-6)
Q(t-7)
Tp(t)
trn=54.7618, chk=56.8747
an
us
T(t-1)
Tp(t-1)
trn=53.5019, chk=55.5668
Tp(t-2)
trn=52.4866, chk=54.4673
trn=41.1675, chk=41.9999
Tp(t-3)
trn=52.2487, chk=53.9740
T(t-4)
trn=41.5356, chk=43.0744
Tp(t-4)
trn=52.7591, chk=54.4410
T(t–5)
trn=42.3796, chk=44.8432
Tp(t–5)
trn=53.8669, chk=55.7041
T(t-6)
trn=43.6602, chk=47.0546
Tp(t-6)
trn=55.0841, chk=57.1981
T(t-7)
trn=45.0591, chk=49.1230
Tp(t-7)
trn=55.8249, chk=58.3323
T(t-2)
T(t-3)
Ac ce p
Q(t-3)
trn=41.3484, chk=41.8337
M
Q(t-2)
T(t)
trn=41.0950, chk=41.6095
d
Q(t-1)
trn=54.5813 , chk=56.289 6 trn=53.4481 , chk=55.564 8 trn=51.9682 , chk=54.351 5 trn=50.8745 , chk=53.394 1 trn=50.6123 , chk=52.815 9 trn=51.1507 , chk=53.545 6 trn=52.5436 , chk=54.943 1 trn=54.4289 ,
te
Q(t)
cr
Table 8: ANFIS regression errors for heat load prediction for 8 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE
19 Page 19 of 28
Tp(t-8)
trn=55.6216, chk=58.0292
T(t-9)
trn=47.2279, chk=51.6329
Tp(t-9)
ip t
T(t-10)
trn=47.8853, chk=52.0691
Tp(t-10)
trn=54.5531, chk=56.1642
trn=52.7642, chk=53.3312
an
Q(t-10)
trn=46.2934, chk=50.6651
cr
Q(t-9)
T(t-8)
us
Q(t-8)
chk=56.801 4 trn=55.7351 , chk=58.318 1 trn=55.8477 , chk=58.270 7 trn=55.0368 , chk=56.726 1
Q(t-2)
Q(t-3)
Q(t-4)
Q(t–5)
trn=41.0936, chk=41.5411
Tp(t)
trn=52.4887, chk=54.5494
trn=41.1673, chk=41.9727
Tp(t-1)
trn=52.2691, chk=54.0241
T(t-2)
trn=41.5370, chk=43.0909
Tp(t-2)
trn=52.8052, chk=54.4347
T(t-3)
trn=42.3795, chk=44.8749
Tp(t-3)
trn=53.9237, chk=55.6714
T(t-4)
trn=43.6595, chk=47.0878
Tp(t-4)
trn=55.1427, chk=57.1587
T(t–5)
trn=45.0566, chk=49.1317
Tp(t–5)
trn=55.8887, chk=58.2842
d
T(t)
T(t-1)
Ac ce p
Q(t-1)
trn=51.9598 , chk=54.439 6 trn=50.8692 , chk=53.504 0 trn=50.6320 , chk=52.896 3 trn=51.1906 , chk=53.545 1 trn=52.5829 , chk=54.921 2 trn=54.4724 , chk=56.761
te
Q(t)
M
Table 9: ANFIS regression errors for heat load prediction for 10 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE
20 Page 20 of 28
Q(t-10)
T(t-7)
trn=47.2243, chk=51.6215
Tp(t-7)
trn=54.6266, chk=56.0926
T(t-8)
trn=47.8843, chk=52.0503
Tp(t-8)
T(t-9)
trn=48.2574, chk=51.9141
Tp(t-9)
T(t-10)
trn=48.2828, chk=51.3018
Tp(t-10)
cr
ip t
trn=55.6901, chk=57.9717
trn=52.8385, chk=53.2475
us
Q(t-9)
Tp(t-6)
an
Q(t-8)
trn=46.2895, chk=50.6554
M
Q(t-7)
T(t-6)
trn=50.2114, chk=49.8828
trn=46.7029, chk=45.7276
d
Q(t-6)
2 trn=55.7853 , chk=58.267 5 trn=55.9075 , chk=58.226 4 trn=55.1044 , chk=56.660 5 trn=53.6388 , chk=54.404 5 trn=51.3695 , chk=51.738 8
trn=50.6168 , chk=52.906 0 trn=51.1892 , chk=53.504 9 trn=52.6170 , chk=54.835 4 trn=54.5287 , chk=56.654 4
T(t)
trn=41.5339, chk=43.1127
Tp(t)
trn=52.8112, chk=54.3996
T(t-1)
trn=42.3797, chk=44.8693
Tp(t-1)
trn=53.9579, chk=55.5887
T(t-2)
trn=43.6584, chk=47.0260
Tp(t-2)
trn=55.2082, chk=57.0428
T(t-3)
trn=45.0522, chk=49.0262
Tp(t-3)
trn=55.9656, chk=58.1641
Ac ce p
Q(t)
te
Table 10: ANFIS regression errors for heat load prediction for 12 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE
Q(t-1)
Q(t-2)
Q(t-3)
21 Page 21 of 28
Q(t-8)
Q(t-9)
T(t–5)
trn=47.2187, chk=51.5485
Tp(t–5)
trn=54.7142, chk=56.0300
T(t-6)
trn=47.8796, chk=52.0315
Tp(t-6)
T(t-7)
trn=48.2565, chk=51.9076
T(t-8)
trn=48.2848, chk=51.2993
Tp(t-8)
trn=46.8089, chk=45.7143
trn=47.8538, chk=50.2476
Tp(t-9)
trn=42.5001, chk=40.3925
trn=47.0542, chk=48.7725
Tp(t-10)
trn=38.1975, chk=34.5664
cr
trn=52.9339, chk=53.2032
us
T(t-9)
T(t-10)
ip t
trn=55.7712, chk=57.8739
Ac ce p
Q(t-10)
Tp(t-4)
Tp(t-7)
an
Q(t-7)
trn=46.2842, chk=50.5394
M
Q(t-6)
T(t-4)
d
Q(t–5)
trn=55.8445 , chk=58.121 5 trn=55.9717 , chk=58.114 5 trn=55.1768 , chk=56.599 7 trn=53.7236 , chk=54.352 6 trn=51.4630 , chk=51.711 9 trn=48.2193 , chk=48.099 5 trn=43.8235 , chk=42.764 1
te
Q(t-4)
trn=50.3153, chk=49.8525
Table 11: ANFIS regression errors for heat load prediction for 24 hours ahead Predictor RMSE Predictor RMSE Predictor RMSE Q(t)
Q(t-1)
Q(t-2)
trn=35.5636 , chk=31.995 1 trn=39.0603 , chk=36.400 6 trn=44.7021
T(t)
trn=45.7837, chk=46.0671
Tp(t)
trn=39.3249, chk=34.5699
T(t-1)
trn=45.6952, chk=45.5254
Tp(t-1)
trn=45.1348, chk=42.0252
T(t-2)
trn=45.9545,
Tp(t-2)
trn=50.1689,
22 Page 22 of 28
Q(t-7)
trn=46.9863, chk=45.7115
Tp(t-4)
T(t–5)
trn=47.4259, chk=45.7907
Tp(t–5)
T(t-6)
trn=47.7263, chk=45.7960
Q(t-9)
Q(t-10)
ip t
T(t-4)
trn=53.7760, chk=52.8384
trn=56.2092, chk=55.8128
cr
Tp(t-3)
us
trn=57.7812, chk=57.4859
Tp(t-6)
trn=58.6343, chk=58.2266
trn=47.8672, chk=45.6251
Tp(t-7)
trn=58.8414, chk=58.0522
trn=48.0004, chk=45.2993
Tp(t-8)
trn=58.3689, chk=57.2833
T(t-9)
trn=48.0852, chk=45.2001
Tp(t-9)
trn=57.3964, chk=56.2021
T(t-10)
trn=48.2015, chk=45.3173
Tp(t-10)
trn=56.4651, chk=55.2410
T(t-7)
T(t-8)
Ac ce p
Q(t-8)
trn=46.4530, chk=45.5456
an
Q(t-6)
T(t-3)
M
Q(t–5)
chk=48.3488
d
Q(t-4)
chk=45.4167
te
Q(t-3)
, chk=43.138 9 trn=49.4617 , chk=48.302 2 trn=52.9598 , chk=52.206 5 trn=55.4112 , chk=54.701 7 trn=57.0660 , chk=56.384 0 trn=57.9623 , chk=57.089 3 trn=58.0841 , chk=56.853 9 trn=57.3238 , chk=56.005 6 trn=56.1756 , chk=55.040 7
Table 12: ANFIS regression errors for heat load prediction for two and three input parameter combinations Predictor RMSE
23 Page 23 of 28
Q(t), T(t), Tp(t) Q(t), T(t)
2 hours ahead
Q(t-6), Q(t), T(t)
3 hours ahead
cr
Q(t-7), T(t) Q(t-5), Q(t), T(t) Q(t-7), T(t) Q(t-4), T(t), Tp(t-10)
an
4 hours ahead
M
Q(t-6), T(t) 5 hours ahead
Q(t-3), T(t), Tp(t-10)
d
Q(t), T(t-2)
Q(t-8), Q(t), T(t)
te
8 hours ahead
Ac ce p
T(t-2), Tp(t-10)
10 hours ahead
12 hours ahead
Q(t-10), T(t-1), Tp(t10) T(t), Tp(t-10) T(t-6), T(t), Tp(t-10) Q(t), Tp(t-1)
24 hours ahead
4.
us
1 hour ahead
trn=22.2632, chk=26.9841 trn=20.3209, chk=25.9834 trn=31.7865, chk=36.5678 trn=28.4119, chk=32.2106 trn=35.8337, chk=38.0809 trn=31.9307, chk=36.1877 trn=36.7978, chk=39.4246 trn=32.7425, chk=34.8671 trn=37.7118, chk=39.9263 trn=33.0647, chk=33.8502 trn=38.3282, chk=38.0467 trn=34.4196, chk=35.4864 trn=38.6445, chk=39.2871 trn=35.3245, chk=36.4954 trn=33.8509, chk=32.5914 trn=32.0151, chk=32.8701 trn=34.7263, chk=31.0598 trn=33.0816, chk=32.2453
ip t
Q(t), Tp(t)
Q(t), T(t), Tp(t-5)
Conclusion
24 Page 24 of 28
M
an
us
cr
ip t
There can be problems with the inclusion of multiple input variables in predictive models. Excessive number of input variables will negatively affect interpretability as well as predictive power of constructed models. Additionally, this will reduce the generalization capability of the model. In that respect, methods for selecting the most influential variables from a huge set of potential variables are necessary. In this study, a systematic approach was used to select the most dominant input variables for prediction of heat load in DHS using the ANFIS methodology. The simulations also employed MATLAB, and outcomes were checked on the corresponding output blocks. Wrapper approach was used to select the subset of most influential variables (in the sense of minimal RMSE) from a set of potential input variables. The ANFIS network was used to perform a variable search and then to determine how 33 selected input variables (11 time lagged heat load, 11 time lagged outdoor temperature, 11 time lagged outdoor primary return temperatures) influence prediction of heat load in DHS for different prediction horizons. The results demonstrated that the proposed method has potential, although further refinements are needed in order to practically apply the method. One direction would be to accelerate the process of testing different predictive models. This will open up the possibility of starting the testing process with a greater number of potential input variables and including more lags, which will certainly improve the predictive power of created models.
[3]
[4] [5] [6] [7]
[8]
te
[2]
Gadd, H., Werner, S. (2015). Thermal energy storage systems for district heating and cooling in Advances in Thermal Energy Storage Systems. (pp. 467–478), Elsevier. Rezaie, B., & Rosen, M. A. (2012). District heating and cooling: Review of technology and potential enhancements. Applied Energy, 93, 2-10. Lund, H., Werner, S., Wiltshire, R., Svendsen, S., Thorsen, J. E., Hvelplund, F., & Mathiesen, B. V. (2014). 4th Generation District Heating (4GDH). Energy, 68, 1–11. doi:10.1016/j.energy.2014.02.089 Dyrelund A, Lund H. Heat plan Denmark 2010: a road map for implementing the EU directive on renewable energy (Varmeplan Danmark); 2010. Lund H, Möller B, Mathiesen BV, Dyrelund A. The role of district heating in future renewable energy systems. Energy 2010;35:1381-90. Münster M, Morthorst PE, Larsen HV, Bregnbæk L, Werling J, Lindboe HH, et al. The role of district heating in the future Danish energy system. Energy 2012;48:47-55. Connolly D, Lund H, Mathiesen BV, Werner S, Möller B, Persson U, et al. Heat roadmap Europe: combining district heating with heat savings to decarbonise the EU energy system. Energy Policy 2014;65:475-89. Brand M, Svendsen S. Renewable-based low-temperature district heating for existing buildings in various stages of refurbishment. Energy 2013;62:311-319.
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[1]
d
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Highlights •
District heating systems for increase in fuel efficiency.
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Control and prediction future improvement of district heating systems operation.
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To predict the heat load for individual consumers in district heating systems.
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A process which simulates the head load conditions.
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