1.1 Home Energy Management System

A methodological HEMSA proposition was obtained from reviewing papers about what is a demand system [²], which are its components, and what are the variables that are necessary to consider in the development. In the review, there are two main topics: demand system architecture (components, data kind, and characteristics) and conscious systems (it is about data flow in projects) [³].

From an architectural perspective, a demand system consists of five parts: sensors array, three modules (programming, monitor, and prediction), and one logical control unit [⁴]. In conscious system dataflows passes through five layers: sensor, physic, conscious of behavior, digital, and meta; between physics and conscious of behavior layers there is a fusion of information module. So, the data flow itself determines how the data is acquired, its processing, and how the results are displayed.

From architectural demand system and the conscious system has conceptualized a methodology that embeds three main parts: sensor layer (SL), intelligent ambient (IA), and prediction module (PM).

To design SL which considers the occupant behavior (action when the occupant turns on/off household appliances and time-consumption of household appliances). How the devices are used affects the consumption that is being generated and allows us to predict how this consumption is carried out. SL is made by implementing a simulator that generates consumption and uses profiles of household appliances. These profiles allow emulating household appliances (room air conditioner, heater, washing clothes and furnace fan) On/Off behavior.

IA is the user interface through which the user feeds the system with de context features and gets feedback with graphical information about data consumption.

PM is the part where data consumption is analyzed and is obtained an optimal consumption, in this module is implemented a bioinspired metaheuristic (Particle Swarm Optimization (PSO)).

This paper is organized as follows. Section 2 presents the related work. Section 3 the topics that conform to the parts of the home energy system architecture methodology. In section 4 is presented the case study. The experimental results and validations are presented in section 5. Finally, conclusions and further work are presented in section 6.

3.1 Energy Consumption Model

A mathematical representation of electric consumption in a house is made by a mathematical model. The sort of devices and their characterization are used to model them. The device's description is done by every kind of household appliance, the minimum, and maximum consumption, and they frequently use time. The on/off household appliances´ states are represented by 1 and 0 respectively.

3.2 Household Appliances

According to the way which the household appliances work, they can be sorted into flexible (𝐹), not flexible (𝑁𝐹), interruptible (𝐼), and uninterruptible (𝑁𝐼) devices. The flexible devices are the devices of electric consumption whose function can be interrupted and continue at another moment [¹⁸]. Flexible devices can be put on standby. The not-flexible appliances are devices of electric consumption that cannot be turned off, this type of appliance has a constant operation [¹⁷]. Interruptible appliances are electrical consumption devices that can be used at any time, the time of use varies according to the user´s needs [¹⁷]. Uninterruptible appliances are electrical devices that stop to function has finished; the electric consumption can be constant or variable [¹⁸].

3.3 Household Appliances Consumption

The set of devices in a context is represented by 𝐴, and 𝑖 −device is represented by 𝑎_𝑖. Set 𝐴 have four subsets 𝐴𝐼, 𝐴𝑁𝐼, 𝐴𝐹, and 𝐴𝑁𝐹. Set 𝐴 = 𝐴𝐼 ∪ 𝐴𝑁𝐼 ∪ 𝐴𝐹 ∪ 𝐴𝑁𝐹, every subset represents a kind of device, 𝑎_𝐼 ∈ 𝐴𝐼, 𝑎_𝑁𝐼 ∈ 𝐴𝑁𝐼, 𝑎_𝐹 ∈ 𝐴𝐹, 𝑎_𝑁𝐹 ∈ 𝐴𝑁𝐹.

The on/off devices state in the 𝜏 moment is represented by 𝜏(𝑡) ∈ {0,1}, 1 represents 𝑂𝑁 and 0 represents 𝑂𝐹𝐹. There are considered 24 moments in the modeling, 𝜏 ∈ 𝑇, 𝑇 = {𝜏₁, 𝜏₂, … , 𝜏₂₄}.

The cardinality of set 𝐴 and its subsets are represented as |𝐴| = 𝑚, |𝐴𝐼| = 𝑛, |𝐴𝑁| = 𝑝, |𝐴𝐹| = 𝑞, |𝐴𝑁𝐹| = 𝑟. So, 𝑛 + 𝑝 + 𝑞 + 𝑟 = 𝑚, and 𝐴 = {𝑎₁, 𝑎₂, … , 𝑎_𝑚}.

Set 𝐴 can have devices belonging to the same type of device with different identifiers. The household appliances consumption function takes the elements of the set 𝐴 in every moment in set 𝑇 and generates the consumption measured in watts. The kind of values is ε: A × T → R⁺, the hourly consumption of a device at a specific time is:

The total consumption of the set is represented as the sum of daily devices consumption (where ε_𝐼 represents the daily total consumption of interruptible devices group and is the same for the others ε_𝑖), it is represented as:

The hourly consumption is the sum of the consumption that is carried out at a specific moment by every device group (here ϒIτ represents the total hour-consumption interruptible group in 𝜏 moment, it is the same for the other groups), it is:

The minimum consumptions per day is:

And per hour consumption is:

The maximum consumptions per day is:

And per hour, are represented as:

For the model, it is identified that ε_𝑚í𝑛 < ε_𝑜𝑝𝑡 < ε_𝑚𝑎𝑥, where ε_𝑜𝑝𝑡^t it meets the needs of the user minimizes consumption and reduces the peak average ratio.

𝐴𝐼 = {𝑎_𝐼1, 𝑎_𝐼2, … , 𝑎_𝐼𝑛}, |𝐴𝐼| = 𝑛 < 𝑚, and ∃ 𝑎_𝐼𝑖, 𝑎_𝐼𝑗 ∈ 𝐴_𝐼, 𝑖 ≠ 𝑗 → 𝑎_𝐼𝑖 = 𝑎_𝐼𝑗.

The total consumption of the subset AI is obtained from (8) and represents the sum of the total consumption of every device belonging to this subset and whose consideration depends on the state of the device (on / off) for each moment. The partial consumption is obtained in (9) (consumption per hour), which is the sum of the consumption made by all the devices that are on in the moment 𝑇.

To define the subsets 𝐴𝑁𝐼, 𝐴𝐹, and 𝐴𝑁𝐹 are used similar expressions to those exposed for the subset 𝐴𝐼. For 𝐴𝑁𝐹, 𝛼(𝜏) =1, because they are turned on all time.

A window represents the range of hours between which a device can operate, [σaI,ψaI], To define the window device, are identified four parameters: the device on time σaIi, the time for which the device will no longer turn on ψaIi, the frequent operating time ξaIi, and the time ζaIi at which the device 𝑎_𝐼𝑖 has been turned on.

These four parameters fulfill the following constraints: σaIi≤ψaIi,ζaI≥σaI   y   ζaI≤ψaI−ξaI,ζaI≥σaI   y   ζaI≤ψaI−ξaI,ζaI∈[σaI,ψaI−ξaI].

The objective function is defined to minimize the daily consumption, it is:

3.4 Monte Carlo Method

A strategy to approximate an unknown quantity μ is using random sampling, referred to as Monte Carlo Methods. This method is based on finding a sequence 𝑋₁, 𝑋₂, … ,  𝑋_𝑛 of mutually independent, identically distributed random variables, such that the expectation E𝑋_𝑖 = 𝜇 exits for i = 1,2, … , n. Let be 𝑆_𝑛 = 𝑋₁ + 𝑋₂ + ⋯ + 𝑋_𝑛, the Weak Law of Large Numbers states that, for every ε>0,limn→∞pr(|Snn−μ|>ε)=0.

Besides, when the expectation 𝜎² = 𝐸(𝑋_𝑖 − 𝜇)² exits the Central Limit theorem asserts that pr(|Snn−μ|<3σn)≈0.997.

Then the mean of 𝑆_𝑛/𝑛 will be approximately equal to 𝜇.

3.5 Methodology to Implement a Simulator

The simulator was programmed in MATLAB R2018a following the Monte Carlo method with the Acceptance-Rejection technique to generate the fins. This technique supposes that there is a method for simulating a random variable from the probability mass function. First is simulated a random variable “𝑌” from the mass function “𝑞_𝑗” and then accepting this simulated value with a probability of 𝑝_𝑗/𝑞_𝑗. The constant 𝑐 is defined as getting the maximum of 𝑝_𝑗/𝑞_𝑗, where 𝑝_𝑗 > 0. So, the simulated value 𝑌 with the probability mass function 𝑞_𝑗 generates a random number 𝑈, if 𝑈 > 𝑝_𝑗/𝑐𝑞_𝑗 set 𝑋 = 𝑌 and stop, otherwise generating a new 𝑌.

The diagram of the Acceptance-Rejection technique is shown in Figure 1.

Fig. 1 Acceptance-Rejection technique diagram 

3.6 Model-Driven

The benefit of developing software with a rational ser of principles includes reproducibility. The task model describes each task in a system workflow like enable access, user functions, device functions, scenario functions, report functions. Enable access refers to validation when a user is in the system. The user´s needs include CRUDs for the user, devices, scenarios, reports, and special comments on data visualization. Scenario specification refers to creating scenarios tasks (see Figure 2) and adding devices to them. Report functions convey data to the user.

Fig. 2 Task Model of the definition of demanding Home Energy Management System 

To get a class model, first, the scenarios to be characterized are identified. Second, the frequent devices. Third, the list of devices and devices’ characteristics. Fourth, for every device the most common data of minimum, maximum and standby power, and the frequently daily time use. Fifth, the devices are categorized into the group to which they belong.

The user interface design was introducing sources of data and introducing an aspect of social computing to reinforce the current perspective of the framework and gamification strategies. Finally, the prototyping is created by considering User Interface (UI) design patterns. To exemplify the challenges that the potential users may face is using storytelling with which is possible to see different situations from a general point of view as designers of the project.

3.7 Particle Swarm Optimization Algorithm

Particle Swarm Optimization (PSO) is a social behavior metaphor of birds and fishes. PSO is a stochastic search that uses swarm particles, everyone particle moves through the cluster adjusting its trajectories to find the best solution using the objective function. The position of every particle, x_i, is determined by the velocity v_i, the acceleration coefficient, inertia, and the size of the cluster of particles. The velocity and position equations [¹⁹] are:

Table 1 describes the components of (11) and (12).

To warranty the PSO algorithm convergence is needed to satisfy that 0 < 𝑐₁, 𝑐₂ < 1, and aleatory 𝑟₁, 𝑟₂ evenly distributed in (0,1) [²⁰]. The particle velocity is defined by the components which are described in Table 2.

4.1 Simulation phases

Problem definition: the implementation objective of a demand system is defined accordingly with the context, geographical area, and variables that define the electricity consumption. The devices, the moments in which each of the devices is on, and their consumptions features are identified in Table 3, the features were obtained from their datasheet’s device.

System´s conceptualization: identify devices that characterize the context of use, and then classify them according to the type of device to which they belong see Table 3. Once the devices are identified, the associations and correlations that exist between the devices concern the moments of use.

Model representation: the relationships between devices are formalized by equations that identify the states of devices at specific and daily moments and consumption.

Behavior model: behavior representation and devices consumption over time are represented in the behavior matrix and consumption matrix.

Model´s evaluation: it is observed the behavior of devices’ probability distribution function (PDF) [²¹], the devices are furnace fan, space heater, room air conditioner, and clothes washer. For every device PDF, the (𝑥, 𝑦) coordinates obtained from their graphs [²¹] are shown in Table 4, the coordinates were obtained by manual and visual graph analysis.

4.2 Validating Simulator

The simulator is validated generating almost 1000 data. The data were graphed in a histogram, the waves between the histogram and Probability Distribution Function’s (PDF) furnace fan histogram [²¹] are similar (Figure 3). The same procedure is followed with room air conditioner, heater, and washing clothes in [²¹].

Fig. 3 Furnace fan histogram 

The simulation of the trial was carried out for furnace fan, space heater, air conditions, and clothes washer. Four arrays were made per device, every array has #number_of_experiments rows by 24 columns, each array corresponds to schedules, turn on device, usage profile, and consumption profile. From the arrays were generated two more, in the first one is storage the total consumption and in the second one the total use time per experiment per device.

The number of experiments by each simulation is defined:

The margin of error of the system is calculated using the standard deviation, and considering that the experiment is non-sensitive, it was established at 5%. When the standard deviation is no longer significant then the simulation is stopped, the number of experiments necessary per device is almost 189 for a furnace fan, 388 for a space heater, 419 for a room air conditioner, and 100 for a clothes washer.

4.3 Model-Driven Map

To build and share customer knowledge across the organization about what they need at each point in their day and how these requirements are being met and provide insight into customer paint points were used Card Sorting technique and Journey Map. An empathy map (see Figure 7) is used too to model the user´s care about his electricity consumption and environment.

Fig. 7 Empathy maps of the user of a demanding HEMS 

Finally, the codesign Framework focuses on Social Computing to achieve a perfect balance between social behavior and computational systems. it seeks to create new practices that allow socialization through technology. The demand home management system includes certain actions that family members or acquaintances, in the case of shared floors, can perform, since the application will be used by any member of a community using the same devices. For instance, share a limit of energy expenditure, an alert will be sent to each of the participants warning the current consumption and to know a little more in-depth the electrical activity, can be complemented with smart connected devices to the current in which through Siri or Alexa, you can identify the devices that consume more energy, and in this way the different members can see the consumption of other participants and send messages warning of excessive consumption in some area of the house or even emojis, allowing interaction between participants of the same family, plus if the monthly goal of maximum energy consumption is achieved, it can be shared on social networks like Facebook. User stories are written once the co-design is finished.

4.4 PSO Constraints

The space research is formed by consumption arrays of ten devices and swarm with 1000 particles. For the experiments, the inertia is 0.8, cognitive weight is 1, social weight is 1.

To stop criteria is 50 cycles or when the minimum value is repeated five times. The code was written in Python using Jupyter in a Dell laptop with an Intel Core i7 processor, 8.0 Gb ram, Windows 10, the PSO program uses the objective function (11).

5.1 Intelligent Ambient Evaluation

At the beginning design of the interface, the participants were required to design a user interface in which they could define the electrical devices they have at home. The interface used architectural plans of their houses to represent the physical spaces. In this work, we compared preferences vs performance during the experiment. To this work were compared preferences vs performance during the experiment, a vignette study was conducted. Collecting prospective users was a problem due to the pandemic, so a sample for convenience around the family and acquaintances is used. Ten Participants were presented our graphical mock-ups for the scenario specification, In Figure 13, the two alternatives are shown, the rationale behind each option is described as follows:

Fig. 13 User interface alternatives to create scenarios 

To control the presentation of multiple pairs, we employed the A/B testing method, apart from being popular it is well accepted in research to elicit preferences. Although preference and performance are sometimes indirectly related, not as expected, it frequently happens that you might prefer the tool that is not necessarily the one in which you are performant. On the contrary, it could happen exactly the opposite. In the end, you learn to use the tool even if you have poor performance. In our case, we can confirm this scenario. Our user performs better in the blueprint scenario but prefers the solution that is similar to existing solutions in the A/B testing and IBM CSUQ as usability measurements. A web page was used for collecting preferences of A/B testing. Figure 13 shows two alternatives to create scenarios, in A) the preferred solution, a list of scenarios is listed to the right and the object in each scenario are listed in the middle with representative icons. In B) a blueprint of a house.

The application design and its process are carried out with the co-design technique, supported by known techniques of analysis and user experience design. The prototype proposal was evaluated with a convenience sample and the final decision gives us a clue of what the interactive system should look like that helps people make decisions regarding their electricity consumption, how they can design spaces or scenarios of houses room. The application design uses icons that allow the user to interact intuitively, the characterization of the rooms (Figure 14) choosing the device

Fig. 14 Selection and identify the type of room 

The consumption of all devices is plotted and showed it through application to the user (Figure 15).

Fig. 15 Graph of the month- consumption 

5.2 PSO Implemented

PSO was implemented in a database with 24 by 365 records. Each record is used to make a comparison with the vector found by PSO. 100 repetitions for the experiment were made for each record. The Analysis was made with the data obtaining the average for the 100 experiments for every device. The device-experiment average and standard deviation are calculated. The results are shown in Table 6.

The PSO implementation lets to propose consumption that each device should have to lower the total consumption without having to turn off any device that is in an inactive state. The proposal generated is displayed in the application transposing the real consumption graph (graph above) with the proposed by PSO (graph below) (Figure 16).

Fig. 16 Real consumption – proposed PSO consumption