This section presents the methodology applied to quantify the compressed air leakage used in this work. It is divided in three subsections. The first subsection presents how an energy audit usually unfolds. Afterwards, the state-of-art of compressed air leaks detection and which one of the several existent techniques is presented. Then, the NILM technique used in this work, the FHMM, is briefly introduced. Finally, the link between the energy audits, the quantification of compressed air leakage and the use of NILM methods is presented.
2.1. Energy Audits
Energy audits are one way to obtain accurate and objective assessments of how to achieve savings. An energy audit is a process by which a building is inspected and analyzed by an experienced technician to determine how energy is used in it, with the goal of identifying opportunities for reducing the amount needed to operate the building while maintaining comfort levels [
14].
There are several types of energy audits, classified by the level of complexity and detail of the analysis performed. The first and less complex type of energy audit is the Benchmarking Audit. It performs a detailed preliminary analysis of the energy consumption and its cost, relying on utility bills, determining benchmark indices, like the ratio between the energy consumption and the surface area in a determined period, usually a year [
14].
The second type is the Walk-through Audit. It consists of a quick tour of the facility to visually inspect the target systems. This may include the analysis of energy consumption patterns and provide comparisons to average benchmarks for similar facilities. When the inspection of the target systems shows promising savings potential, this audit can lead to a more complex audit later [
14].
The Standard Audit seeks to quantify energy consumption and losses by performing a detailed analysis of the performances of several energy systems. This analysis usually includes on-site measurements, historical data collection, and testing to determine the efficiency of the analyzed systems. Specific energy engineering calculations are applied to determine efficiencies and calculate energy and financial savings based on improvements and changes to each system. As the name suggests and because of its cost-benefit, it is the most common type of energy audit performed. However, when historical data is not available, and the audit relies on on-site measurements, a photo of the operating conditions and the extrapolation for other operating points of the systems may be laborious to obtain [
14].
To address this problem, there is a more complex type of energy audit. It relies on computer simulations to predict the consumption that was not contemplated in the on-site measurements phase. The goal is to build a base for a more consistent comparison with the actual energy consumption of the analyzed facility. This baseline is then used to compare the performances achieved with improvements and changes tested in the simulation environment. Due to the time involved in collecting data and setting up an accurate simulation model, this is the most expensive level of energy audit [
14].
As the Standard Energy Audit is the most common type, the work developed in this paper has been based on it. This procedure can be divided into three phases. The first phase concerns the collection of all necessary data for the efficiency analysis of the evaluated systems. Visual inspections, technical data from catalogs, historical data from the supervisory system, when available, and field measurements are examples of the collected data. This fieldwork consists of taking measurements of various quantities (electrical, thermal, luminous, physical, etc.) necessary to determine the efficiency of the evaluated systems. These measurements should be made following standard technical procedures for each type of system evaluated, using reliable meters adapted to each type of installation and system.
One way to perform this data collection is by incorporating the team into the environment to be evaluated. In this manner, the team can experience the daily operation of the facility. However, besides the fact that the auditors’ time to perform this task is limited, usually a few days or weeks, the ideal is that their activities have as little impact as possible on the normal operation of the systems being evaluated. Due to this, some operating modes of certain equipment may not be measured during the auditors’ data collection period.
The second phase consists of analyzing the collected data and determining the consumption and efficiency of the evaluated systems. To perform this task, the data collected in the preceding phase is applied to procedures specific to each system. In this stage, possible opportunities to promote energy sobriety can also be identified.
The last phase consists of proposing improvements for the reduction of energy consumption, or even the replacement of specific equipment with a more efficient or cheaper one. Replacement by more efficient equipment, changes in operating procedures, or the installation of new components that promote more rational energy are among the most common solutions. All this information is then made available to the customer in the form of a report, in such a way that he can appreciate the alternatives presented and choose whether to make these improvements.
Figure 1 illustrates the flowchart process of a standard energy audit.
Usually, large energy consuming systems are the main targets of an energy audit, because even a small absolute reduction in the consumption of these systems can represent large absolute savings. In buildings, lighting systems, HVAC (Heating Ventilation and Air Conditioning), and the envelope are usually emphasized. In industrial environments, besides those mentioned for buildings, analyses in water pumping systems, motors, boilers, and compressed air systems are common.
2.2. Estimating Compressed Leakage
As stated in
Section 1, compressed air systems are usually among the major energy consumers in a facility in which these systems are present, whether in a building or an industrial environment. Substitution of a modulating air compressor to a variable speed one, the recovery of the wasted heat, and the quantification and repair of leaks are among the most common and effective solutions to improve efficiency and achieve savings in a compressed air system [
6].
Among the energy efficiency measures cited earlier, the repair of compressed air leaks is probably the most impactful energy efficiency measure, applicable to almost all systems. However, the awareness of the importance of a regular leak detection program is usually low, in part because air leaks are invisible, and generally cause no damage [
6]. Due to the similar physical characteristics to other gases, the compressed air leakage quantification and detection can be dealt with in an analogous way to other gases. Several methods have been developed to detect and quantify fluid leaks in pipelines. They can be classified into biological, hardware, and software techniques [
15].
The biological ones rely on empirical methods using sensorial perceptions, such as the hearing, smell, and sight of specially trained staff. The hardware techniques use numerous equipment to enhance the sensorial perception of the staff. In the case of compressed air systems, the most used are ultrasound [
8,
9] devices and infrared cameras [
7]. Although it is considered the industry standard and best practice, ultrasonic leak detection is limited to the application in short distances [
10] and requires highly trained operators. Moreover, due to the compressed air expansion process in the location of the leak, a temperature gradient is created, making it possible to observe it from infrared images. However, these techniques also require the measurement of the openings through which the compressed air escapes from the pipeline to quantify the leaks and thus the potential savings from their repair. The measurement of those openings may be impractical for the auditors. Software-based methods use flow, pressure, temperature, and other data to estimate the leaks. These methods are usually based on the analysis, performed by an automatic algorithm, of both pressure and flow rate data, when available [
16,
17].
An alternative to quantify the compressed air leakage is to estimate the air compressors flow rate during a no compressed air consumption period. Depending on the facility, a period like that could be weekends, vacations or holidays [
11]. During these periods, all the compressed air end use equipment should be turned off. In this scenario all the compressed air is directed to feed only the leaks. This estimation may be done by measuring the input power of the air compressor and correlating it to its flow rate.
This estimation may be done by measuring the input power of the air compressor and correlating it to its Free Air Delivery. There are tables (fixed-speed), and curves (variable-speed) provided by the manufacturers make this correlation possible. When this information is not available, it is possible to measure the flow rate by measuring the air velocity at various points on the intake pipe cross-section and integrate these measurements in the pipe cross-section area, with an anemometer, for example. For the variable-speed compressor, numerous measurements should be done at several operating points, to determine a correlation curve between power and flow rate. The flow rate estimated by correlating the input power of the air compressors, and their free air delivery also enables the determination of the load curve of compressed air in a facility, in the absence of a flow meter.
The most common type of air compressor, used in most installations is the rotary screw fixed-speed air compressor. This type of equipment operates at full capacity, the load state, delivering rated flow, until the pressure set point is reached [
18]. At this point, the compressor unloads, operating at minimum power, only to maintain internal pressure, delivering no air to the system. Due to this behavior, this type of compressor is also called modulating compressor. These two states, the load and the unload one, typically have very distinguishable input power associated in a way that is not difficult to identify them.
Therefore, to estimate the flow of a rotary screw fixed-speed air compressor it is enough to identify its load state well and correlate it with the compressor’s flow rate capacity, either measured, or obtained from manufacturer tables. For the unload state, zero flow is assigned. Hence, the average flow of a rotary screw fixed-speed air compressor depends directly on how long the equipment remains in its load state. An example of a performance table of a rotary-screw fixed speed air compressor operating at rated pressure provided by the manufacturer is presented in
Table 1.
As mentioned earlier, one way to quantify compressed air leaks is to estimate the air compressor’s flow rate during a period of no compressed air consumption. However, this technique implies that the auditors must be on-site during a no compressed air consumption period for the monitoring of the air compressors. In an industrial environment, for instance, a no compressed air consumption period is rare, and it may not coincide with the energy audit planning. An alternative route around this problem would be collecting logged data from the compressed air system. However, it is unlikely that the input power of the air compressor, or even the flow rate, is monitored individually. Although it is improbable to have the air compressor’s data logged individually, logged data from the global consumption is often available.
As the correlation between the input power and the flow rate of an air compressor is an intrinsic characteristic of the equipment, it remains the same regardless of the system’s operation mode. Thus, if one could extract the air compressor’s input power from the global consumption, the leakage estimation could be performed even without the presence of the auditors on-site during a no compressed air consumption period. This would enhance the quality of the analysis performed during the energy audit with a smaller cost where the other options for this analysis are impractical.
The load curve extraction of equipment from the global consumption can be done using NILM (Non-Intrusive Load Monitoring) techniques [
12] under certain circumstances. Thus, this work aims at investigating the possibility of using NILM methods to estimate the compressed air leakage in a tertiary building environment and to calculate the potential savings with the leaks repair in the context of an energy audit.
NILM techniques have already been used to detect leaks in compressed air systems. In his master thesis [
20], Piber used a stationary device to measure the global consumption of a warship. With embedded NILM algorithms, this device was also capable of extracting the consumption of some loads, such as the vacuum-assisted sewage collection system, low pressure compressed air system. Analyzing the operating schedule, he was able to detect the presence of leaks in the compressed air system. However, he did not mention the sampling rate nor the training period used to train the NILM algorithms. In addition, as a stationary device was installed, a permanent change in the facility must be made. So, it is important to highlight that the proposed technique is non-intrusive and does not imply any permanent changes in the system, such as installing flow meters in the pipeline, or stationary power meters.
In summarizing, the idea is to use input power measurements that can be retrieved using portable power analyzers, for instance, to train the algorithm, and logged data from the global consumption to extract the air compressor’s power consumption.
The NILM technique to enhance energy audits was already discussed by Berges et al. [
21], but it was limited to application in a residential environment. So, to this date, the authors have not found other methods that relate to the quantification of compressed air leaks through the application of NILM techniques to enhance energy audits in tertiary buildings or in an industrial environment in the literature.
2.3. NILM Techniques
As already mentioned before, in the context of an energy audit, the measurement campaign on-site lasts, usually, a few days or weeks. This phase may not include a no compressed air consumption period, in which the air compressors would operate only to feed the leaks present in the grid. In addition, air compressors are not always monitored individually by a supervisory system, which would make it possible to use historical operating data to estimate the energy consumption, and, consequently, the air leakage during this period. However, it is common to have historical data of the global load curve of the facility, or even of some transformers in substations internal to the facility. In this way, the use of NILM techniques could come as an aid for estimating leakage from this available historical data.
The initial NILM approach was proposed by Hart in the early 1990s in his work entitled “Nonintrusive appliance load monitoring” [
12], regarding the residential sector especially. In earlier works, the disaggregation problem was addressed mainly in the residential environment. In these cases, there are fewer appliances and the switch between the on and off states is rare and the power of the equipment in each state is, normally, constant. Therefore, in the disaggregation context, to estimate the consumption profile of an appliance, it is sufficient to know when every piece of equipment works in each state of operation. In his incipient work, Hart [
12] proposed a method, nowadays called the Combinatorial Optimization, which consists of finding the combination of the consumption of all appliances in a given instant that minimizes the difference between this combination and the overall ground truth consumption. This method was idealized considering that the appliances operate with finite states, with constant consumption in each one of them. Another commonly applied algorithm is the Factorial Hidden Markov Model [
13], which is used in this work.
Several other algorithms try to address the NILM problem, based on different techniques. Some of them are based on Artificial Neural Networks, using recurrent networks [
22,
23] or convolutional ones [
24] or even incorporating the Fourier transform into neural networks to perform the energy disaggregation task [
25]. These algorithms have the limitation of performing the energy disaggregation task either with the delay of a few minutes or only for past events. Due to that, the real-time application of NILM models is a recent direction taken by several researchers. For example, Athanasiadis et al. [
26] developed a framework combining an event detector, to detect the moment when an appliance changes its state, a convolutional neural network classifier, determining if this state change was caused by a target appliance and a power estimation algorithm to calculate the appliance power and consequently its energy consumption. Later on, a similar framework can be embedded into simple microprocessors to perform on-site energy disaggregation [
27].
Although the real-time application is promising, even in the context of an energy audit, a period of no compressed air consumption is needed to quantify leaks. If a period like that is too far in the future, it could delay the deadline of the energy audit report. That is the reason why it was decided to use logged data and the FHMM to perform the estimation.
The Factorial Hidden Markov Model is based on Markov chains. A Markov chain is a stochastic process with discrete or continuous state space that presents the Markovian property. This property states that in regular and discrete time intervals, this stochastic process evolves from one state to another depending only on its last condition, independently of the others.
The Hidden Markov model comes as an extension of the Markov chain. This model includes the case in which the observation is a probability function of the state, i.e., the resulting model is a double-layer stochastic process, in which one stochastic process is underlying and unobservable (hidden) that can only be observed by the other stochastic process that produces the sequences of observations. Due to its flexibility and the simplicity and efficiency of its parameter estimation algorithm, the hidden Markov model (HMM) has emerged as one of the basic statistical tools for modeling discrete time series, finding widespread application in the areas of speech recognition [
28] and computational molecular [
29].
The disaggregation problem tackled by the FHMM in this work is to infer:
as the power load of each of the M appliances,
Such that
Given
as the aggregated power for
T time periods [
30] as the sequence of observations.
An HMM is essentially a mixture model, encoding information about the history of a time series in the value of a single multinomial variable—the hidden state—which can take on one of K discrete values. The system is characterized by this internal discrete state variable, which evolves as a Markov chain between time points. Formally, an HMM can be defined by:
The finite set of hidden states ,
The matrix representing the probability of transitioning from one state to another , being with and ,
The initial state probability distribution , being
An extension of the HMM is the Factorial Hidden Markov Model (FHMM) [
13]. The FHMM extends the HMM by representing the hidden state in a factored form, as
represents the set of underlying state sequences, where
. This way, the information from the past is propagated in a distributed manner through a set of parallel Markov chains. The parallel chains can be viewed as latent features, which evolve over time, according to Markov dynamics. Then, an optimization approach minimizing the difference between the observable variable (global power) and a combination of the hidden states is applied; the complete formulation was developed by Kolter and Jaakkola and it is available in [
13].
The FHMM applied to solve the NILM problem has been proven to have a good effect on the disaggregation of residential load with a low sampling rate such as 1/60 Hz. It does not directly output the observations of each hidden Markov chain, but outputs the sum of the observations. For the NILM problem, the total active power or reactive power is the observation sequence and the state and power consumption of each piece of equipment is unknown, but the power associated with each state is known. Therefore, each piece of equipment can be described as an HMM, and the working state of the appliance is a Markov chain. The total power is the sum of the power of each appliance, hence, it can be described as an FHMM composed of multiple HMMs, and the observation sequence of the FHMM is the power consumption. In other words, the FHMM tries to predict the combination of active appliances’ energy usage that contributes to global consumption.
Figure 2 illustrates how the FHMM is used in the NILM context.
The FHMM was elected to be used in this work because of its simple implementation, fast calculating time, and good performance when dealing with simple and moderate complex loads, such as a rotary screw air compressor addressed in this work. However, the FHMM is not the most suitable algorithm to tackle the NILM task in the presence of more complex loads, such as multi state appliances, or continuously variable loads [
32].
2.4. Estimating Compressed Air Leakage in the Context of an Energy Audit
As already stated in previous sections, compressed air systems are usually among the major energy consumers in a facility, and because of the capillarity of their grid, several leaks may appear because of worn out piping and connections. In poorly maintained systems, the leakage can rise to more than half of the total compressed air generated by the air compressors, representing a great opportunity for energy efficiency measures.
In the absence of monitoring by some management system, which is the typical condition in a facility, the compressed air flow rate can be estimated from the measurement of the air compressor power, and the later determination of its load curve, by the application of the procedure presented in
Section 2.2. This estimation, if performed in a period with no compressed air consumption (weekends, vacations, holidays…), represents the leakage present in the grid. If the amount of the leakage is known, the estimation of the savings achieved with the repair of the leaks is feasible. Thus, with input power data, during both normal operation and no compressed air consumption periods, along with the datasheets of the equipment, it is possible to estimate the potential saving by repairing the leaks present in the compressed air system.
However, during a standard energy audit, the auditors normally have only a few days, or a week, to find potential savings and to collect the data needed to perform the calculations, and no compressed air consumption periods may not be included in the auditors’ schedule. Besides that, monitoring and logging data from air compressors individually is unusual. Thus, without the data from a period like that, it would be impossible to satisfactorily estimate the number of compressed air leaks in the grid.
Even if it is unusual to log individual data from air compressors, the load curve of the global consumption is often available. Hence, one way to go around this limitation is to extract, through the application of NILM techniques, air compressor’s load curves from the global consumption.
Figure 3 presents the procedure to estimate compressed air leakage and energy savings with its repair. It shows that would be possible to use the NILM output as power data input during a no compressed air consumption period.