# Integrating Industrial Energy Consumptions as Short – term Demand Response Resources

*Abstract *— Demand response has attracted much attention in recent years. It has been identified as one of the solutions to overcome electricity network equilibrium problems related to peak consumptions and renewables intermittency. From all the different consumption sectors, industrial electricity consumptions are of particular interest due to the magnitude they represent. Thus, industrial consumptions (equipments, workshops, etc.) can be considered as resources for demand response programs to be integrated in balancing the electricity network. In order to be able to integrate these consumptions, it is necessary to standardize the procedures to evaluate their availability as well as forecasting their behavior. The standardization of the procedures shall focus on the program constraints in which the resource is valued, but most importantly, in ensuring the safety of the electricity network. This research paper focuses in three industrial usages with different behaviors. For this purpose, three different forecasting techniques, adapted to the data and operational constraints, are used. Specific performance indicators called “trust” parameters are proposed and calculated for different times of the day for the different usages. The different forecasting techniques show similar performances depending mainly on the data. The estimated trust parameters allow evaluating the probability for a specific consumption of not complying with the operational constraints.

**Keywords: Demand Response, Energy Management, Industry, Short-Term Load Forecasting, Load Curve Clustering, Lasso Regression**

**José Blancarte, Valérie Murin**

EDF R&D

Département Eco-Efficacité et Procédés Industriels

Moret-sur-Loing, France

jose.blancarte@edf.fr / blancarte@emse.fr

**Mireille Batton-Hubert, Xavier Bay, Marie-Agnès Girard**

Ecole Nationale Supérieure des Mines

UMR 6158, EMSE-Fayol

Saint-Etienne, France

**I. INTRODUCTION**

Ensuring the equilibrium between production and consumption of an electricity network is a core issue for utility companies and Transmission System Operators (TSOs). With the deployment of intermittent renewable energies, the growth in electricity consumption due to new appliances, and the ageing of current power production facilities, this equilibrium may become more and more compromised [1]. One of the solutions to overcome these predicaments that has been favored by utility companies and energy policy makers in recent years is demand response.

Demand response can be defined as the change in electricity consumption by end-users according to a “normal” behavior, in response to a specific demand (paid or not) or to changes in the electricity price [2]. Demand response brings flexibility to address peaking and network congestion situations, and has been named as one of the key elements for a better integration of renewables and the deployment of “smart- grid” solutions [1].

With the deployment of industrial energy management systems and individual real-time household electricity consumption monitoring, energy data will be abundant in the years to come. These data will serve to the development of new services and the design of better energy systems, including demand response resources that can be controlled and activated almost in real-time. However, even if energy consumption is monitored at a particular consumption point (household, building or industrial site level) for billing purposes, it is the endpoint equipments or services consumptions’ that can be curtailed.

Among the different electricity consumption sectors, industry presents a particular interest due to the amounts of energy involved in different industrial processes. Previous research has been focused in forecasting electricity consumption to determine an electricity consumption baseline in the short-term at an industrial site level as an ex-ante calculation [3]. The importance of consumption at this level lies in being the controlled data used by demand response operators.

Demand response resources have been proposed to be addressed as an equivalent of virtual power plants, but with different availability factors and taking into account specific considerations [4]. The most important questions to be answered when considering a demand response resource are how to assess the “curtailable” energy at every moment to better integrate these resources, and how to assign a confidence or trust factor through a robust methodology.

The integration of demand response resources lies on the market valuation of the different resources for all types of programs [5]. Since different approaches are followed by the different demand response implementing operators, the constraints of every particular market mechanism shall be integrated for a better use of the available resources in determining the resource availability and its confidence. Within these research works, and in order to include these operational constraints, different forecasting techniques are evaluated according to specific performance indicators. These performance indicators can be adapted to different conditions of the very diverse demand response programs, according to their objectives, goals, and operational constraints.

**II. CONTEXT AND OBJECTIVES**

During recent years, the reliability of the electricity network in France has been compromised during peaking times in very cold winters. France has a particular thermo-sensitive electricity consumption curve, due to a wide penetration of electrical heating across the country. During these peaking times, costly and more polluting power plants are put into operation in order to ensure the equilibrium of the network. Demand response programs have been deployed as one of the solutions to address peaking and congestion problems, especially in the regions where production is scarce compared to the demand. Added to this, with the expected increase in electric vehicles usage and the development of new electric appliances, consumption peaks are expected to increment in the years to come. The French TSO (RTE) has been keen in adopting demand respond solutions and is in charge of the implementation of the different programs across the country in order to maintain the stability of the electrical network [6].

Industrial electricity consumptions are of particular interest for participating in the electricity network equilibrium through demand response due to the order of magnitude of curtailable power consumption. In order to achieve substantial curtailment potentials in the household or tertiary sectors, dozens or hundreds of endpoint consumptions shall be aggregated. On the contrary, for industrial endpoint consumptions, a similar amount of curtailable power can be achieved through single industrial equipments or the aggregation of just a few of them. Added to this, the costs of control, monitoring, and verification may be a burden if special equipments must be installed for every consumption point.

Electric utilities have been aware of this potential since the

80’s, proposing special tariffs to big electricity customers in order to be able to “curtail” their consumption during particular peaking days by extremely high electricity prices during those events (Time Based Rate Programs, TBRP. For a classification of the different programs, see [7]). However, not all of industrial processes or electrical consumptions are “controllable” or easily activated. Only a few of all the industrial equipments available at a particular site or platform may be able to participate to demand response mechanisms. In

order to integrate these consumptions to shorter term programs (such as system services or primary reserve programs), the electricity consumption of the different participating sites and equipments must be forecasted in order to not to include resources that will not be available when needed or which would have been anyways turned off during a demand response event. For every particular site and short-term integration, the participant shall specify which equipments are of no harm to the process if controlled by a third party or remotely turned off.

As previously stated, preceding research works have focused in forecasting electricity consumption at the industrial site level, which is the consumption that is commonly verified by demand response program operators. Establishing baseline energy consumptions for compensation purposes has been at the center of the demand response problematic: how to establish the hypothetical energy consumption that a particular site or usage would have consumed in case the demand response event did not take place? The answer to this question allows compensating the participant accordingly to the magnitude of its effort with an ex-post calculation. Little bibliography exists in how to establish the potential curtailment in an ex-ante manner.

Industrial electricity consumptions are somehow different than other sectors [8]. The behavior of the consumption may be very variable from site to site and from usage to usage, even for sites producing the same products or services. Thus, standardizing a procedure can be a difficult task. In order to address this, different forecasting techniques adapted to a particular process may be proposed, but they shall all respect basic principles (integrity, simplicity, accuracy and alignment, as it has been proposed for ex-post baseline calculations [9]) and compared in the same manner. This is the procedure that shall be standardized.

When participating to a demand response program, a consumer proposes a curtailment block or “an amount of power through a specific period of time” (energy) to balance disequilibria in the network. However, depending on the specific demand response program, different constraints are imposed in order to ensure the network’s safety and to reduce risky situations. These constraints or rules can be used to construct the performance indicators for the different proposed forecasting methodologies for estimating the potential curtailment, as well as to control demand response events. Specific performance indicators are thus proposed in section III which can be adapted to different regulations according to their objectives and constraints.

To sum-up, from a demand response aggregator’s perspective, in order to choose a participating industrial site or equipment, different parameters have to be taken into account. However, some principles need to be respected:

• Not compensating a participant for something it would have done anyways

• Ensuring a “fairer” treatment of the different participants according to their historical behavior

The main objectives of this research work are:

• To compare relevant short-term load forecasting techniques that use only historical electricity consumption as input parameters to address resource availability issues for demand response, through a unified procedure

• To propose and adapt performance indicators to evaluate “ex-ante” a potential failure in the verification process respecting the integrity principle (not maximizing the gains but minimizing the “failing” situations)

If a forecasting procedure is able to predict the electricity consumption and a “trust” parameter can be associated to it, a merit-order decision process can then be implemented for the different available demand response resources, including different operational parameters.

**III. AVAILABLE DATA AND METHODS**

This section presents the different sets of data used as study cases as well as the different forecasting methods and overall methodology.

*A. Materials*

*A. Materials*

Electricity consumption data from industrial sites at the equipment or workshop level is in many cases not available or scarce. In order to achieve substantial results, we recommend a minimum of three months of good quality electricity consumption data for the considered consumption equipment. Most industrial processes and equipments do not present a thermo-dependant behavior and thus, temperature data will not be included in the modeling and forecasting methods.

Data acquisition must be continuously verified in order to avoid communication problems and missing periods. Data shall be standardized to comply with the regulations of demand response program operators. Thereby, timestamps and time- intervals of the available data shall be the same as those used by the program operator.

Industrial electricity consumption data present very different behaviors for the very diverse endpoint consumptions. The available load curves have been standardized and consist of 10-minute interval power consumption points. In order to appreciate these differences, data issued from three different monitored industrial workshops are used, which are briefly presented below. All of these endpoint energy consumption usages have agreed to participate to a demand response experimentation and are thus “curtailable”.

*1) Usage I*

*1) Usage I*

Figure 1 presents a glimpse to the load curve of Usage I corresponding to a four-week period from a Sunday to a Saturday.

Usage I is a single equipment with a two state behavior, “on” or “off”. When the equipment is “on”, it consumes at its nominal power consumption, with a very small variation around 1,500 kW, which, in comparison, is equivalent to the peaking power consumption of several hundred households. Duration periods of the operating times are very variable as it can be seen in Figure 1. The equipment can be running for more than 24 hours continuously, or turned on or off several times during a single day. As well, it can be observed that during certain situations, the equipment is not turned on at all (probably due to maintenance procedures).

For the purpose of this research work, there are 113 full days available (almost four months of data). One of the major advantages of this type of behavior is the possibility to propose an energy block that is rather rectangular, which is comparable to production resources that are available in electricity markets. However, the availability of the resource, even if operating most of the time, shall be assessed in order to ensure the required energy, and to satisfy the previously defined objectives.

*2) Usage II*

*2) Usage II*

Figure 2 presents the plot of four weeks of electricity consumption of Usage II. The format of the graph is similar to the format of the previous figure for Usage I. For the purpose of this research, only 93 full days of electricity consumption are available, with the previously mentioned characteristics.

Usage II has a totally different behavior than Usage I. It corresponds to a workshop instead of a single equipment, for which electricity consumption is permanently monitored. The workshop has a base-load consumption of about 300 kW. Consumption is very variable, attaining peaks of up to 1,500 kW during operating conditions.

During weekends (Saturdays and Sundays), the workshop consumes at its base-load value (the variability is still higher than Usage I), and during the week, electricity consumption is increased, corresponding to operating conditions of the industrial site.

The energy that can be recovered from this particular endpoint electricity consumption is important, especially during normal operational conditions. Some of the equipments can be regulated to lower their consumption and recover up to 800 kW of power during a specific period of time (up to two hours).

*3) Usage III*

*3) Usage III*

As in previous graphs, Figure 3 shows four weeks of electricity consumption of Usage III. For Usage III, as for Usage I, 113 full days of electricity consumption are available for study. Usage III is an industrial workshop that includes several small equipments that can be turned “off” without compromising the operation of the industrial site they belong to. When the usage is not in operation, there is not any remaining base-load consumption and the workshop consumes no electricity.

Usage III has a very different behavior when compared to the two previous usages. It is in operation only during weekdays (from Monday to Friday) but not all the time. When in operation, electricity consumption can be very variably, attaining peaks of up to 600 kW, but rarely at this level. This behavior can be found in different industrial sites which present weekday working schedules.

*B. General Methodology*

*B. General Methodology*

A general approach is proposed in order to provide an answer to the previously stated questions (as presented in Figure 4):

• How to forecast the consumption behavior of different industrial equipments or workshops?

• How to evaluate the relevance of the forecast according to a particular demand response scheme?

Generalizing procedures for establishing baselines for different subjects, including demand response, has been identified as one of the drawbacks for a deeper deployment of energy management related programs [10]. Through this proposed methodology, focus is made on addressing these problems for a better integration of industrial consumption as demand response resources.

To achieve a standardized procedure, simple or easily understandable methods and approaches shall be used to forecast the behavior of electricity consumption, respecting the simplicity principle. The proposed forecasting methods, which correspond to part A of Figure 4 are presented in the following section. Any forecasting technique, as long as it generates power consumption forecasts in the same terms (in power units) may be evaluated following this procedure.

Demand response events usually take place during the day and late afternoon, since it coincides with peaks in electricity demand (and thus, production). Therefore, forecasting simulations will be done at every hour from 9:00 am to 9:00 pm for a forecasting period or “time-horizon” of two hours, which is common demand response event duration. Since electricity consumption forecasts required for demand response are very short term, daily electricity consumptions will be considered independent from each other for practical purposes. The daily load curves are composed of 144 values of electricity consumption, (corresponding to every ten minute interval from 12:00 am to 11:50 pm), which is the common electricity consumption data format in France.

For all of the available usages, 85% of the data will be used as learning datasets and 15% as test datasets. This procedure will be adapted accordingly to the chosen validation procedure, corresponding to part B of Figure 4, explained further. The individuals to be assigned to the different learning and test datasets will be the different available daily consumptions. Thus, only fully available days will be used for the analysis.

Lastly, specific forecast performance indicators are proposed in order to assess the confidence of the demand response resource, corresponding to part C of Figure 4.

*1) Forecasting consumption patterns through load-curve clustering*

*1) Forecasting consumption patterns through load-curve clustering*

Summarizing large amount of time-series data can be done through clustering techniques [11]. Different authors have addressed the possibility of using load-curve clustering techniques as forecasters for electricity consumption [12], [13], but in most of the cases they have dealt with the issue of long term energy forecasting, and are applied to national, regional, or sector energy related topics.

This work focuses on one specific clustering technique used in previous works which has shown a good performance for different energy management related applications at an industrial site or usage scale, in order to forecast its short term energy consumption (two-hour forecasting horizon): Self-organizing Maps (SOM) [14]. This proposed forecasting technique will be identified as CLASS throughout this article for simplification purposes.

The basic principle of the proposed CLASS forecasting technique is to summarize the learning data into different clusters or classes (consumption patterns), then try to assign a corresponding cluster to the current day for which a forecast is needed (or a day belonging to the test dataset in this case), and then propose the cluster coordinates as the forecast for the rest of the day.

Since a cluster is represented by the mean load-curve of all the curves assigned to that cluster during the learning process, an adjustment factor can be used to better reflect the real consumption level of a particular day. As stated previously, no temperature dependence is assumed in industrial electricity uses and thus, temperature related adjustment factors will not be applied (suggested by different authors [9], [15]) in order to better standardize the approach. The chosen adjustment factor will be scalar and based in the previous consumption point and the clustering forecast ratio, as expressed in (1), where **𝐅 _{sc,1}** is the adjustment factor to be applied to every forecasted value,

**t**is the time interval at which a forecasting simulation is launched, 𝐏

_{n}**is the actual consumption value at the time interval immediately before the forecast is provided, and the 𝐏̂**

_{tn-1}**is the forecasted value with the proposed model at that same time interval. This adjustment factor is applicable only when consumption is not very variable (as in Usages I and III) and will not be applied to Usage II.**

_{tn-1}In order to provide a forecast, clustering through a SOM algorithm is performed on centered and non reduced data. The SOM algorithm is initialized through a Principal Component Analysis (PCA) [16], in order to always converge to the same solution and to standardize the learning procedure (for details of the SOM algorithm, different references can be consulted [17], [18]).

A fixed number of clusters, has been chosen as suggested for large electricity customers load curve profiling [19] in order to homogenize the approach, even though data at the endpoint usage level is more disaggregated. The classes will be obtained from the learning dataset, which will correspond to the historical consumption when implemented in real-time demand response platforms. For every data-slitting procedure (85%-15% for learning and test datasets as previously indicated), the SOM algorithm is launched on the learning dataset to obtain the reference vectors composed of 144 variables for each one of the 12 clusters or classes, identified by Cl_{k} , as in (2), where 𝐏** _{k,h}** correspond to the

**h**power consumption value of the

^{th}**k**cluster (1 ≤ k ≤ 12 and 1 ≤ h ≤ 144).

^{th}These reference vectors will be used to provide the forecasts for the different days corresponding to the test dataset and at different times of the days. As stated previously, **t _{n}** correspond to the time of the day at which a forecast is simulated. When an individual (a daily consumption from the test dataset) is used to simulate a forecast at

**t**, the individual will be truncated up to the

_{n}**n**element, and represented by

^{th}**TV**, as in (3), where 𝐏

_{n}**corresponds to the**

_{n,h}**h**power consumption time interval of the truncated vector (

^{th}**h ≤ n ≤ 144**).

The different previously obtained reference vectors will be truncated as well up to the **n ^{th}** element and identified by

**Cl**. In order to find the most similar vector, Euclidean distances have been chosen as the decision factor. Euclidean distances

_{k,n}will be then calculated between

**TV**and all

_{n}**Cl**. The

_{k,n}**Cl**vector with the minimum distance will be then considered the winning vector, and called

_{k,n}**Cl**as in (4).

_{w}

The coordinates corresponding to the winning vector will then serve as the reference vector for the individual issued from the dataset. The different values corresponding to the different consumption time intervals of the day will then be proposed as the forecast for the rest of the day. The forecasted consumptions (represented by 𝐏̂̂_{i} , where **i** is a particular consumption point) will correspond to the consumption points of the winning vector with the same index **i,** **Cl _{w,i}**, as in (5).

*2) Forecasting consumption behaviors through variable selection regression: the Lasso*

*2) Forecasting consumption behaviors through variable selection regression: the Lasso*

Different regression techniques can be used to forecast the behavior using different approaches for using the available parameters. The simplest case would be the Multiple Linear Regression (MLR) over the historical individuals (the daily electricity consumptions). It can be assumed that the daily electricity consumption is a linear combination of different historical daily electricity consumptions. Thus, a typical MLR approach can be contemplated, as expressed in (6) (where **𝐏(i)** is the current day electricity consumption at time-interval **i**, **𝐏 _{j}(i)** is the electricity consumption of the different available historical daily consumptions at time-interval

**i,**and

**𝛃**and

_{o}**𝛃**correspond to the different coefficients obtained through the linear regression, with

_{j}**q**the total amount of individual historical daily consumptions

**1 ≤ j ≤ q**, and

**𝛆̂**the error term).

However, not all of the different available historical days shall be used, since not all of them behave or explain the behavior of the current electricity consumption in a good manner. Added to this, when the number of variables is bigger than the number of observations, different type of regressions shall be implemented.

A different type of regression is proposed, which aims to optimize the choice of the different available electricity consumptions: the Lasso regression (Least Absolute Shrinkage and Selection Operator). For the purpose of this study, this method will be abbreviated HILR (Historical Individuals Lasso Regression).

The Lasso regression (firstly proposed by Tibshirani [20]) is a regularization method for linear models that involves penalizing the absolute size of the regression coefficients. The main advantages of the Lasso regression is that it reduces the variability of the estimates by shrinking the coefficients, providing models that can be understood by estimating some of the coefficients to zero, thus reducing the number of variables used in the model [21].

The Lasso regression penalty for the coefficients can be written as in (7), where the coefficient 𝛌 is the tuning parameter, which controls the strength of the penalty. When the tuning parameter is equal to zero, (7) becomes the ordinary least squares argument. When 𝛌 tends to infinity, all the coefficients are set to zero.

The Lasso regression will select the relevant historical daily consumptions according to the chosen tuning parameter and will exclude daily electricity consumptions that are considered not relevant to explain the forecasted day. Attention shall be paid when forecasting a day with no consumption: the response variable will always be zero and thus the solution algorithm will tend to not to converge to a solution, since λ shall tend to infinity.

When a forecast simulation is launched, the selection of the lambda parameter will be performed through a cross-validation procedure using only the learning dataset. These data (the different **𝐏 _{j}** vectors) will be considered as the historical electricity consumptions. The chosen value of the tuning parameter will correspond to the one that minimizes the cross-validated error. Once the 𝛌 parameter has been fixed, the

**TV**of the forecasted day (defined previously) will be used as the different 𝐏

_{n}**(i)**values, and the different 𝐏

**will also be truncated up to the corresponding**

_{j}(i)**t**time-interval when a forecast is launched, in order to solve for the different 𝛃̂̂

_{n}**parameters. Forecasts for 𝐏̂̂**

^{lasso}_{i}can then be provided for the different future time-intervals by using (8), where the estimated values are issued from the solution to (7).

*3) Forecasting using “dimension reduced” information: Principal Components Lasso Regression*

*3) Forecasting using “dimension reduced” information: Principal Components Lasso Regression*

Summarizing the information contained in the original or the learning dataset can accelerate the solution of the algorithms with little loss of relevant information. From all the different existing dimension reduction techniques, Principal Component Analysis (PCA) has been chosen, since it has a broad range of applications for exploring large sets of data [21]. Previous works have focused in coupling PCA and MLR with mixed results. In order to try to overcome these difficulties and to integrate the previous techniques in a different way, a combination of PCA and the Lasso regression is proposed. For the purpose of this study, this forecasting technique will be called PCLR (Principal Components Lasso Regression) and will be described briefly below.

One of the main advantages of using dimension reduced information is the lower calculation times for model selection. It can be assumed that the electricity consumption changes and variability can be explained by different variables. PCA allows obtaining the eigenvalues (Λ matrix) that explain most of the variability of the data, and the eigenvectors (U matrix) of the principal components which are obtained by the decomposition of covariance matrix in ^{t}UΛU that are uncorrelated to each other.

For the proposed forecasting method, PCA is performed on the training dataset (on centered and non-reduced data). The coordinates of the **k** first eigenvectors explaining 99% of the

variability are preserved. These coordinates have in fact a meaning according to a specific power consumption interval of the day. **U _{s}** correspond to the coordinates of the eigenvectors, where 𝟏 ≤ 𝐬 ≤ 𝐤 as expressed in (9).

The preserved principal components which have the same dimension of 144 values as the daily electricity consumptions are used to build a predictor using a linear combination. The proposed method will use a similar procedure as in the previous method, by using a Lasso regression. At the time **t _{n}** a forecast is simulated for an element of the test dataset, the

**U**vectors are then truncated up to the

_{s}**n**point, and called

^{th}**Un**as in (10).

_{s}The Lasso regression will then be used to fit the best model by the previously detailed procedure. The **TV _{n}** vector is defined as the

**𝐏(i)**function. Using the

**k**truncated

**Un**eigenvectors, a linear model as expressed in (11). The

_{s}**Ĉ**coefficients (to differentiate them from the HILR method) are obtained through the Lasso Regression

_{s}

The coefficients and the eigenvectors coordinates **U _{s}** are used for predicting the power consumption of the site for the rest of the day for every consumption point

**𝐏̂̂**, as in (12).

_{i}

*C. Performance indicators and validation: adding a “trust” parameter to a demand response resource*

*C. Performance indicators and validation: adding a “trust” parameter to a demand response resource*

For comparing different techniques’ performance, a universal performance indicator shall be used. This means, the indicator may be calculated in the same manner for all the different modeling and forecasting techniques, and produce a result in the same terms or units. In other words, the procedure

for estimating it shall be the same.

When participating to a demand response program, a certain amount of energy is “offered” or proposed to the program operator. However, this energy shall respect some operational constraints. When posted, the operator is expecting to recover a specific energy or power amount, allowing some fluctuations, in order to not to compromise the safety of the different systems. Thus, the energy “block” shall not be inferior nor exceed a certain amount of energy, related to what it has been “offered”. This proposed energy will be the result of an ex-ante estimation, issued from a forecasting method adapted to the characteristics of the electricity consumption behavior.

If 20% is fixed as the maximum failing energy volume [22] according to what is has been offered to the program operator, this threshold shall be used to construct a trust parameter, reflecting the respect (or not) of this operational constraint.

A previously defined performance indicator for energy performance purposes [3] has been used: the Gross Energy Difference (GED). This indicator aggregates the losses point by point during a specific forecasting period or time-horizon (identified by 𝛉), as defined in expression (12), where **t _{n}** is the time at which a forecast is launched, 𝐏

**is the real power consumption at time-interval**

_{i}**i**,

**𝐏̂̂**is the forecasted power consumption for that same time interval, and N is the number of 10 minute time intervals corresponding to two hours of forecasting (12 in this case).

_{i}During the demand response event, the “offered” amount of energy to the operator will be based in the forecasted electricity consumption of a particular equipment. Thus, the parameter to be monitored corresponds to the probability that (14) is met, where all the parameters have been previously defined.

Since forecasting simulations will be launched at different times of the day, the performance of the methods according to the defined “trust” parameter can be calculated for each of the

simulated times. When few data are available (𝐌 being the size of the dataset, the number of individuals), a simple data-splitting approach with the characteristics mentioned before (85% of the data as learning dataset to parameter the model and 15% of the data as test dataset) for validating the model is not recommended, since it can be very dependent on the choice of the individuals for each of the datasets. A trust parameter

**( T _{DS,Hr} )** can be calculated by this approach according to expression (15), in which

**DS**indicates the used validation method (data-splitting),

**Hr**is the time of the day at which the simulations are launched,

**p**is the proportion of individuals

from the test dataset that have satisfied the constraint in equation (13),

**k**the number of successes and

**n**the total number of individuals in the test dataset.

In order to give a sufficient robustness to the approach even with few available data, a Monte-Carlo Cross-Validation (MCCV) is performed [23], [24], which is similar to a Jackknife approach for estimating the value of a parameter. For this purpose, the data-splitting procedure will be repeated a big number of times (**B**, which is fixed to 1,000 for this study), as presented in Figure 5. The split will be performed randomly but in a stratified manner at one level, the day of the week (Sunday, Monday, etc.) in order to obtain a good distribution of the different available days in the original dataset.

For each of the **B** samplings (identified by **j**, with 𝟏 ≤ 𝐣 ≤ 𝐁 ), a value **P̂** of the proportion of forecasts respecting the constraints can be calculated as in expression (16), where **k̂** is the number of individuals respecting the constraint for that particular **j** split, and **n** the total number of individuals of the test dataset. This approach will allow estimating the value of the trust parameter **( T _{JK,Hr} )** in a more robust way, less dependent on a simple sampling of the original dataset, as in expression (16), where

**JK**represents the chosen validation method (MCCV),

**Hr**the time of the day at which the simulations take place.

The parameter can be calculated for a specific usage for every simulated hour of the day and for the different proposed forecasting techniques. A “trust” curve of the behavior can be then constructed, with the different obtained values, as it will be shown in the following section. This will allow comparing the different techniques but also the “predictability” and the probability that if a specific endpoint consumption equipment or workshop is called at a particular time of the day, it will respect the imposed constraints.

**IV. RESULTS AND DISCUSSION**

The results for each of the implemented techniques are described below. Focus is made on the evaluation of the performance of the forecasting methods, according to the chosen indicators, as well as in determining the relevance of the studied data for demand response purposes.

*A. Results by Usage*

*A. Results by Usage*

The different obtained trust parameters using the Monte- Carlo Cross-Validation approach for Usage I and for the three different studied forecasting methods throughout the day is shown in Figure 6. The blue dotted lines represent the results obtained with the CLASS method; the red dashed lines represent the results obtained with the HILR method; and the green dotted line the results obtained with the PCLR one.

Usage I trust parameters calculated with the different forecasting methods show similar behaviors. The three different techniques are able to forecast the changes that occur during the day more or less in the same manner. HILR method shows slightly better performances than PCLR method, and both obtain better performances overall than the CLASS method. In this case, when participating to a demand response program with the operational constraints specified previously, it will be better to call Usage I around 12:00 pm and after 7:00 pm, since the probability of respecting the constraints is greater at these periods.

Figure 7 presents the different obtained results for Usage II, with the same plotting characteristics as in Figure 6.

The obtained trust parameters for Usage II are very high when compared to Usage I. This is due to the predictability of the resource, which has a very regular behavior. Even if the electricity consumption signal is noisy, it is easy to forecast the level and the form of this consumption. The three forecasting techniques show similar performances, but PCLR has a better performance overall except for some specific hours of the day, especially at the end of the evaluated period. Usage II is a more “trustable” demand response resource than Usage I.

The different obtained results for Usage III are presented in Figure 8, with the same plotting characteristics as in the previous two figures.

The different obtained trust parameters for Usage III reflect in this case the unpredictability of the resource, assigning very low values throughout the day. The trust parameter becomes zero when no energy can be recovered in any case, since the usage operation stops at around 7:00 pm. The parameter allows evaluating the resource as not available in these hours.

Usage III is a demand response resource that will almost always be at the end of a merit-order list, since it is not a “trustable” resource. It can be considered as a resource that will be only called in extreme situations and less valuable than the previous two resources.

*B. Summary of results*

*B. Summary of results*

HILR has shown better performances overall than the other two forecasting methods. However, for similar results, PCLR shall be preferred since calculation times are greatly reduced (e.g. from 144 dimensions, 99% of the variability is explained with approximately 30 Principal Components). The clarity of the CLASS method is one of its main advantages, since it can be easily presented and implemented (respecting the simplicity principle), and the calculation times are the lowest of the three methods.

The proposed methodology allows obtaining exploitable results even for very different sets of data, which represent very different energy consumption behaviors. The trust parameter allows evaluating the different performances according to the time of the day. Using a probabilistic method such as a Monte- Carlo approach allows establishing in a simple manner the probability of respecting the constraints which are summarized in the trust parameter, even with few available historical data.

**V. CONCLUSIONS AND PERSPECTIVES**

The different forecasting techniques have shown very different results according to the presented data. The proposed methodology for constructing the trust parameter can be a very useful criterion to assess the predictability of the consumption as well as the trust it can be assigned to the resource.

The proposed forecasting techniques have proven to be relevant since they are adapted to the data and the very short- term period for which a forecast is needed. The trust parameter allows judging the performance of these techniques and evaluating them in comparable terms. The chosen indicators validate the procedure, and are as well useful as a decision tools to establish a merit-order of different available resources, dependant on the forecasting method.

The indicators can be constructed in different ways, and in this case a differentiation parameter has been taken into account depending on the time of the day. This difference can also be judged depending on the day of the week or the month of the year (for more seasonal energy consumptions), but since data is not abundant, only the time of the day was chosen.

Depending on the chosen performance indicator, it could be interesting to construct a confidence interval. When two or more forecasting techniques show similar performances according to the chosen indicator (the “trust” parameter in this case), in order to decide which forecasting method converges faster, the size of the confidence interval can be a decision criterion. However, attention shall be paid on how to construct a confidence interval, especially using Monte-Carlo related approaches such as the Bootstrap.

The question about how often an algorithm or the historical data shall be updated in order to improve the algorithm can be studied. This will depend on the specifications of the demand response program and the technical constraints related to real- time participation of the different available resources.

In order to better integrate the different available demand response resources, performance indicators can be constructed according to the objectives and the operational constraints of the program. These indicators can be more adapted to the problematic than traditional forecasting ones.

**REFERENCES**

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