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A bottom-up customizable Markov model for household
appliance electric consumption
Chuanyong Shao, Eric Chauveau
To cite this version:
Chuanyong Shao, Eric Chauveau. A bottom-up customizable Markov model for household appliance
electric consumption. sifwict, Jun 2019, Nantes, France. �hal-02495241�
A bottom-up customizable Markov model for household appliance
electric consumption
Chuanyong SHAO
1and Eric CHAUVEAU
2Abstract— Residence load is an important part of the total power consumption. This paper develops a bottom-up non-intrusive method to build a predictive model for the residence load using a Markov model. Taking the fridge as the experi-mental subject, the total load is decomposed into three sub-systems. The applicability of this Markov model is proved by the simulation in the MatlabTM platform. To do this, a pair of Markov chain is then created to predict the load power consumption for historical days. Then the average power of simulation and measurement are compared, as well as the state transitions along time. The results clearly shows that Markov chains can simulate the behavior of the residence load in a good way, but considering the influencing factors of the environment, this Markov model should be improved to obtain a better accuracy.
Key words: residence load, household appliance consump-tion, Markov model, Markov chain, influencing factors
I. INTRODUCTION
One of the main problem in the power system is to keep the balance in the power providing and consuming. Load prediction plays an important part of this problem. Modelling home energy consumption is necessary for studying demand side response, transformer sizing, and distribution network simulation [1].
Household appliances, generally the energy intensive of the load in the power system, lack of the Human-Machine Interaction process. This increases challenges to the system scheduling. Nowadays, several revolutions in electric field leads to fast power system development, thus facing new problems with the renewable sources, smart grid, and etc. Because of advanced technique in information field, smart electric meter has been put into use widely, to help managers and consumers to keep power balance in hand. On the other hand, the grid can achieve to get the real-time feedback from the demand side.
Plenty of works concentrate on load prediction. Most of these researches focuses on the load curve itself, using ma-chine learning ways to build forecasts. Usually, those works put an approach directly to modeling without illustrating the reason. In this paper, a bottom-up method is developed to simulate the behavior of household appliances. Paper [2]-[5] show Markov model have a good effect on load prediction correctly displaying dynamic transition regularity. Instead of static probability distribution, this paper tends to use a Markov model to forecast the possible transition direction.
1C. SHAO is student in master degree, University of Nantes, 44000
Nantes, Francechuanyong.shao at eseo.fr
2E. CHAUVEAU is with ESEO Tech, ESEO engeeniring school, 49000
Angers, France and reseacher at IREENA, University of Nantes, 44600 Saint-Nazaire, Franceeric.chauveau at eseo.fr
Fig. 1. Refrigerator construction scheme, with major power consuming parts. Rectangle up left represent the cold enclosure of the refrigerator.
Paper [6] and [7] introduce a method to decompose the state of an household appliance. Considering the protection to the clients’ privacy, the idea is to find a common model for ap-pliances in a non-intrusive way. Fist of all, the decomposition of the appliance create sub power consumption units. Then a Markovmodel is applied to convenient sub-system analysis. This model involves in the variation of the states of sub-systems along the time, then simulate the possible average power consumption within a certain time period.
II. METHOD
According to former studies [8] and [9], major part of household power consumption comes form freezing or heat-ing devices. Under this circumstances, the refrigerator has a quite complicated operations states, and is usually top-ranked in high energy consuming household appliances. As a result, the chosen experiment subject in this article is the refrigerator.
Three main power consumption units are considered inside the refrigerator: The electrical Board, the light bulb and the compressor as presented in figure 2. Inspired by paper [7], these three parts can be analyzed using two states Markov model respectively. For each part, there are only two complementary states: On or Off. As long as we get the transition probability between the two states as well as the initial states, we can infer following states over time step after step.
All of these three units are supposed to consume constant power during running time. If the prediction of the behavior of these units is obtained, the power consumption can then be determined.
Fig. 2. The assumed total power consumption of a refrigerator relevant to description in figure 1. Any power value is relevant to considered refrigerator model.
For Markov like sub-parts, the analysis based on Markov probable model starts from the inner construction of the time sequence. It was proposed by a russian mathematician Andrey Andreyevich Markov. Markov model is applied to solve questions such as:
• If the system is under the state i, then from now on, what is the probability of the state being j, after transited by n steps.
• In a market demand prediction problem, if there is a company occupy part of the sale route currently, then after n steps, how much property of the market occupied by this company?
Thus, Markov model can be used to show the variation of a process. Then it comes to the problem of Markov process: In case of the state at time t0is give, the state at time t where
t > t0 only depends on the state t0 and has no relationship
with the states before this moment.
Definition 1: Assuming that {X (t) , t ∈ T } is a random process, if for any n numbers of time t, t1 < t2 < ... <
tn−1 < tn, (n > 3) , with the condition that X(ti) = Xi,
i = 1, 2, ..., n − 1 , the distribution function of X(t) is one of the same as the one of Xn when X(tn−1) = Xn−1, i =
1, 2, ..., n−1 happens. Then {X (t) , t ∈ T } is called Markov process. That is:
p {X (tn) ≤ Xn| X(t1) = X1, ..., X(tn−1) = Xn−1} (1)
Markov chain is the simplest Markov process. The time t and state X of a Markov chain are both discrete.
Definition 2: For a random sequence {Xn, n = 0, 1, 2...}
in the discrete space I, at anytime n, and any state i0, i1, ..., in−1, given i, j:
p {X − n + 1 = j | Xn= i, ..., X0= i0} =
p {Xn+1= j | Xn= i} (2)
Then random sequence {Xn, n = 0, 1, 2, ...} is called
Markovchain.
Definition 3 (Single-step Transition Probability):
We suppose that {Xn, n = 0, 1, 2, ...} is a Markov chain.
We denote the single-step transition probability at time n as the following conditional probability:
pij = {Xn+1= j | Xn= i} (3)
where: pij(n) ≥ 0, i, j ∈ I andPj∈Ipi,j(n) = 1, i ∈ I.
In this paper, all of the power consumption units can be represented by two-states circumstances like in figure 3, with A and B representing the states, and ti→jthe transition from
state i to state j. Each state is associated with a given value 1 and 0 representing the states respectively.
Fig. 3. A two discrete states process (A and B) with any possible transition between each of them ti→j.
III. RESULTS A. Refrigerator example
The research is based on historical data of a refrigerator placed in ESEO engineering school in Angers, France. This device can only be accessed by the staff in ESEO (excluding the students). The recorded data contains the date, the real-time power consumption of the whole refrigerator, the states of the door, and the ambient temperature at every sampling time. The sampling time step is 1 second. The research’s models of each convenient sub-part consider user influence as randomness. Figure 4 shows the total load of the fridge under a period of running time demonstrating the assumption of the power consuming is right.
Fig. 4. The measured total power consumption [W] (top) and door opening [binary] (bottom) of an operating fridge. Recording sample is about 30 minutes long.
1) The Controller Board: The controller board is the easiest to analyze inside the refrigerator. It always works to control the operation units in the fridge. So there is only one On states for the controller board.
2) The Light Bulb: The light bulb doesn’t work all the time. It’s switched on when the door of the fridge is open, and off when the door is close. Considering the light bulb by its own, its state working state is driven by randomness. It is more dependent on the behavior of the users. So it can be seen as a probable event. In this paper the states of the bulb are only On or Off.
3) The compressor: The operation principle of the com-pressor involves the process of thermal exchange. The con-densing system of a fridge is composed of (see figure 1) a compressor, and a refrigerant pipe (internal and external of the refrigerator). Under order of a temperature sensor inside the fridge, if the temperature inside the fridge is higher than the set level, then the compressor starts to work. The essential of the compressor is a pump driven by a motor. Due to a particular refrigerant gas saved inside the pipe, when the compressor is working, the pump constricts and enhance the pressure initiating the condensing cycle. Then the gas which is becoming hot because of the pressure will be sent to the external heat exchanger meeting the cooler air. This results in changing of the gas to liquid phase. The compressor goes on working and then the liquid is pushed into the internal coil through a capillary. At this time, the temperature inside the fridge is higher than the liquid, which will lead the liquid absorbing the heat inside the fridge to convert back to gas. That is the principle of the condensing cycle system.
Considering the compressor by its own, its working state is due to:
• measured temperature inside the refrigerator;
• ambient temperature of the room;
• and refrigerator users habits.
So, as the same as the light bulb, there are only two possible states (On or Off ) for the compressor.
B. Recording
A specific equipment show in figure 5 is use to log data during a given period, from seconds to many months, with 1 second sample time.
Recorded data are (see example in table III):
• current date and time stamp;
• real power consumption of the whole refrigerator; • door state (open or close);
• ambient temperature. C. Analyzing
Measurements in figure 4 clearly shows:
• a power profile due to light bulb relevant to door
opening and closing;
• a power profile due to compressor;
• a constant power due to electronic controller board. Using recorded power variations from in figure 4 and sub-system decomposition, power profile of each sub-part of the refrigerator are built independently step by step:
Fig. 5. Data recording equipment containing a power analyzer (bottom center) with two adapted current clamps (top right), a processor board (bottom right) with door Hall effect sensor connection, and a USB memory stick. Door Hall effect sensor and ambient temperature sensor are not represented.
1) Light bulb power consumption refers to door open-ing/closing and power consumption is relevant to bulb specifications.
2) Extract supposed bulb power consumption profile, then subtract to total power profile.
3) Remaining power profile shows two complementary power states. Lower one for standby mode only due to controller board, higher one due to cold compressor power adding.
4) Power variation is supposed to be due only to compres-sor. Power variation value is quite constant over hours, days, and weeks, and quantity is relevant to induction motor compressor specification.
5) Subtract this last power power profile to remaining power to find controller board power.
Controller board power consumption is very small, less than 1W in our case, compared to compressor and light bulb so that it can be ignored. Finally, the total power consumption is supposed to be composed of only two main parts: the light bulb and the compressor.
D. Modeling
As shown in figure 4, door state is a two state random variable, and so it is for the compressor power profile. So, for each light bulb and compressor, a simple 2 states Markov chain is considered.
Power consumption profiles from previous analysis for each sub-part of the refrigerator can be computed to calculate transition matrix over a given recording period. This can be done by simply counting any transition over the given considered time period.
E. Simulate
The simulation presented is developed with Matlab TM.
Chosen data range is between 19.11.2018 and 25.11.2018 within a full working week. For the whole simulation
process, every day’s prediction is completed by the same transition matrix created by the first day of the week, here on Monday.
According to previously described method and modeling, the algorithm is:
1) Extract the sub-profile of the bulb and its power 2) Obtain the states of the bulb directly from door state 3) Separate out the states of the compressor according to
the sub-profile of the total power consumption which is higher than 75W .
4) Compute the transition matrix for each sub-system. 5) Ensure the initial states of each sub-system in the
simulation keep in path with the reality. 6) Calculate the total simulated power.
According to the simulation, the transition matrix over the considered week is:
0.9995 0.0005 0.1340 0.8660
Let’s consider detailed simulated results within the first day as an example to show the transition of the states of sub-systems.
Fig. 6. State of the bulb from measurement (Top) and Simulation (bottom) over a day.
Fig. 7. State of the compressor from measurement (Top) and Simulation (bottom) over a day
Fig. 8. Total power comparison between measurement (Top) and simulation (bottom) over a day.
IV. DISCUSSION
For each considered sub-part of the refrigerator:
• Bulb: Referring to the measurement it is obvious that in a real case, the door is opened between 8:00 and 9:00 in the morning, 11:00 and 13:00 in the mid-day. However, the simulator presents a sequence distributing randomly along the time during a day.
• Compressor: In theory, the compressor operates quite regularly, but the simulation presents a more irregular profile.
• Controller board: The power consumption of the
elec-trical board is smaller than 0.02W and can be ignored compared to the bulb and compressor consumptions. Simulation results shows good global representativeness of the model refer to measurements as shown in tables IV and III. However, because influence of the environment is neglected here, the simulated results does not always meet reality. This specifically embodied in the following aspects:
• The detailed simulation of the states is not convenient with the real distribution of the states for each sub-system.
• The accuracy of the simulation is not good enough compared to the measurement. If there is a large amount of devices gathering together, the simulated load may not be good to put into use.
• This model doesn’t fit to each day within one week, due to the effect of important events. The operation status of the working days is different from that in weekends. This is because nobody works during weekends or holidays.
Sub-system decomposition gives a custozimable model that can be derived to any similar appliance with known specifications (light bulb power, cold compressor power) or deduced by simple analysis of non intrusive measurements. The primary simulation demonstrates that it is impossible to use one unchangeable transition matrix to predict all of the daily power consumption (see table I. Then another simulation is taken to observe the average power using the transition matrix of each day respectively (see IV.
TABLE I
AVERAGEPOWER OF THEREFRIGERATOR DURINGONEWEEK
Meas. [W] 16.16 15.64 18.34 18.93 15.57 14.47 15.03 Simu. [W] 14.77 12.33 15.64 16.74 14.56 15.93 15.93
TABLE II
SIMULATEDAVERAGEPOWER OFEACHDAYRESPECTIVELY
Meas.[W] 16.16 15.64 18.34 18.93 15.57 14.47 15.06 Simu.[W] 14.77 14.91 18.86 20.33 15.20 13.93 10.22
Table I shows that in weekends, the simulated results of the mean power of the device is higher that the reality. In fact, on Saturday and Sunday, because the institution is not accessible, the door is never opened. Theoretically, the simulated power should be similar to the real power. There is no possibility for the fridge to consume more power in the simulation. Conversely, table IV gives the average power simulated through the transition matrix of each day respectively. This model is more accurate than the former one. This indicates that the transition matrix changes from day to day. Although the difference among working days is not so obvious, but it will still contribute to the difference of the results. More significantly, there is a big importance between working days and week-ends. It illustrates that people’s activity do effect the behavior of the appliances. Besides, the ambient temperature will influence the working state of the heating system too. These factors must be taken into account to get a more accurate model.
V. CONCLUSION
According to the analysis and discussion we can draw the following conclusions.
1) Markov chains can be used to predict the behavior of the power consumption of the household devices with a good accuracy on average power.
2) Sub-system decomposition is relevant to reach a good accuracy, and can be put into practice using non-intrusive measurements.
3) Because there are a lot of objectively influencing factors, so the Markov model in this paper is not accurate enough to put into use. Especially if there is a load profile consisted of a large number of household sub-profile.
4) Even if the average power is similar between mea-surements and simulation, the modeled transition state process differs a lot from the measurement. To get a better simulator, a different Markov model should be created for different time sections.
5) Taking the environmental factors into account, work can be developed to make this model more adaptable. Environment factors such as the number of the users, or the ambient temperature can be then considered.
6) Besides, important events influence a lot the results too. The Markov models built for working days and for holidays or weekends should be separated.
APPENDIX
TABLE III RECORDINGS SAMPLE
Date Time Power Bulb Amb. temp. YYYYMMDD HH:MM:SS W Binary oC ... 20181119 08:07:33 0.0185 0 22.8 20181119 08:07:34 0.0171 0 22.8 20181119 08:07:35 0.0177 0 22.8 20181119 08:07:36 0.0176 1 22.8 20181119 08:07:37 0.0175 1 22.8 20181119 08:07:38 31.0700 1 22.8 20181119 08:07:39 31.0400 1 22.8 20181119 08:07:40 31.0100 1 22.8 20181119 08:07:41 31.0200 1 22.8 20181119 08:07:42 31.0100 1 22.8 20181119 08:07:45 31 0 22.8 20181119 08:07:46 31.0100 0 22.8 20181119 08:07:47 0.0172 0 22.8 20181119 08:07:48 0.0167 0 22.8 20181119 08:07:49 0.0173 0 22.8 20181119 08:07:50 0.0169 0 22.8 20181119 08:07:51 0,0175 0 22.7 20181119 08:07:52 0.0171 0 22.8 20181119 08:07:55 0.0184 0 22.8 20181119 08:07:56 0.0184 0 22.8 20181119 08:07:57 0.0168 0 22.7 20181119 08:07:58 0.0181 0 22.8 ... ACKNOWLEDGMENT
The authors wishes to express their appreciation to Thierry Pommeau (ESEO Tech), who helped them by developing the measurement setup, and then make this research work feasible.
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![Fig. 4. The measured total power consumption [W] (top) and door opening [binary] (bottom) of an operating fridge](https://thumb-eu.123doks.com/thumbv2/123doknet/7957454.266593/3.892.505.807.851.1014/measured-total-power-consumption-opening-binary-operating-fridge.webp)
