The problem at hand is to develop the code for the mictrocontroller of an autonomous thermostat for a building with multiple rooms. The goal is to minimize power usage while ensuring that the temperature in each room is maintained at a comfortable level. The system must take into account various factors such as the current day of the week, time of the day, external temperature, and motion prediction in each room. Based on this data the system has to determine the radiator schedule for a number of time intervals.

The goal of this example is of demonstrating how SOLVER-AI can be used to optimize energy usage in smart home systems. It showcases the use of predictive modeling in anticipating room occupancy and temperature changes, leading to more efficient energy usage. The system forecasts future states enabling it to make proactive decisions and optimize performance.

The example also showcases how the system can intelligently adapt to changes in habits by uploading updated historical data.

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The clients with its examples can be downloaded from https://github.com/SOLVER-AI-LTD/client. The code can be found in:

• C++: cpp/example_thermostat.cpp
• python: /python/example_thermostat.py
• JavaScript: js/example_thermostat.js

Let's consider a building with numRooms number of rooms. We'll refer to i as the room number, with i being an integer in range [0, numRooms-1]. The building is fitted with an autonomous thermostat which:

• Is connected to motion sensors in every room and gathers data stored in a motionSensorData.csv file at time intervals Dth (1/6 hour in the example). The file has as columns:
  • weekday: Day of the week, integer in range [0, 6] where 0 is Monday and 6 is Sunday.
  • th: Time of the day in hours, with range [0, 23.99].
  • motion_i: Motion in room i, which has value 1 if motion was detected in the interval Dth and 0 if no motion was detected.
• Is connected to temperature sensors in every room and also has a sensor to measure the external temperature. It collects data at time intervals Dth and stores it in a temperatureSensorData.csv, which has columns:
  • C_i: State of the radiator in room i, which has values 0 if off and 1 if on.
  • T_i: Temperature in room i.
  • Te: External temperature.
  • DTh_i: Temperature variation in room i in the time interval Dth.
  • power: Power consumption during interval Dth.

Objectives and Constraints

Considering numForecastIntervals times, spaced by Dth, our objective is to determine the radiator states C_i_j for each of the times th_j and weekday_j, so that:

• The total power consumption is minimized.
• If motion is detected in room i the temperature is greater than a required temperature requiredT_j.
• If no motion is detected in room i the temperature is greater than a required Tmin_j.

The implementation that can be found in the code is as depicted in the image below, with N = numForecastIntervals - 1.

Autonomous Thermostat Implementation (for room i).

The columns correspond to the different times j, with each subsequent column at Dth time difference from the previous one.

at j = 0

1. The thermostat knows for each room i: temperature T_i_0, the current state of the radiators C_i_0 and the external temperature.
2. temperatureSensorData.csv can be used for predicting DTh_i_0 and power_0.

at j = 1

1. We determine the time th_1 and weekday_1 by adding Dth to the previous time and weekday.
2. We determine the temperature T_i_1 from DTh_i_0 from the prediction at the previous step.
3. We consider the external temperature to still be Te.
4. Given unknown C_i_1 temperatureSensorData.csv can be used for predicting DTh_i_1 and power_1.

at j, where j is greater or equal to 2 and smaller than N

1. We determine the time th_j and weekday_j by adding Dth to the previous time and weekday.
2. We determine the temperature T_i_j from DTh_i_1 from the prediction at the previous step.
3. We consider the external temperature to still be Te.
4. Given unknown C_i_j temperatureSensorData.csv can be used for predicting DTh_i_j and power_j.
5. motionSensorData.csv can be used for predicting motion_i_j.
6. Given motion_i_j and the required temperature requiredT_i relative to room i :
   • If motion_i_j is greater than 0.4 (the probability of having movement is greater than 40%) then Tconstraint_i_j is the difference between the current temperature T_i_j and the requiredT_i temperature for room i.
   • Otherwise, T_i_j is a large positive number.
7. Given the minimum temperature Tmin_i, TconstraintMin_i_j is the difference between the current temperature T_i_j and the minimum temperature.

at j = N = numForecastIntervals - 1

1. We determine the time th_N and weekday_N by adding Dth to the previous time and weekday.
2. We determine the temperature T_i_N from DTh_i_1 from the prediction at the previous step.
3. We consider the external temperature to still be Te.
4. motionSensorData.csv can be used for predicting motion_i_N.
5. Given motion_i_N and the required temperature requiredT_i relative to room i :
   • If motion_i_N is greater than 0.4 (the probability of having movement is greater than 40%) then Tconstraint_i_N is the difference between the current temperature T_i_N and the requiredT_i temperature for room i.
   • Otherwise, T_i_N is a large positive number.
6. Given the minimum temperature Tmin_i, TconstraintMin_i_N is the difference between the current temperature T_i_N and the minimum temperature.

Therefore, in order to perform this implementation, we need to set up:

• Equation modules for th_j and weekday_j
• Equation modules for Te_j, where in this case we consider all of them equal to Te.
• A SoftData for the temperatureSensorData.csv with VectorizationIndices: 0 to numForecastIntervals - 2.
• A SoftData for the motionSensorData.csv with VectorizationIndices: 2 to numForecastIntervals - 1.
• Equation modules for computing T_i_j for j from 1 to numForecastIntervals - 1.
• Equation modules for computing Tconstr_i_j for j from 2 to numForecastIntervals - 1.
• Equation modules for computing TconstrMin_i_j for j from 2 to numForecastIntervals - 1.
• An Equation module for computing power as the sum of the power_j for j from 1 to numForecastIntervals - 2.

We'll then have to set:

• As constants:
  • The time at which the calculation is performed (th_0, weekday_0) and the the state values for j = 0, T_i_0 for each room.
  • The required temperatures for each room requiredT_i.
  • The minimum temperatures for each room Tmin_i.
  • The interval Dth.
• As ranges:
  • The radiators controllers C_i_j for all rooms and i and j from 1 to numForecastIntervals - 2 to vary between 0 and 1 and be an integer.
• As constraints:
  • Require that Tconstr_i_j is greater than 0 for j from 0 to numForecastIntervals - 1.
  • Require that TconstrMin_i_j is greater than 0 for j from 0 to numForecastIntervals - 1.
• As objective:
  • power to be minimized.

In the code we:

1. Create a SolverAiClientSetup object solverAiClientSetup.
2. Use the solverAiClientSetup object for creating all required modules and Problem.
3. Create a SolverAiComputeInput object input.
4. Use the input object to set up the solverSetup, constants, inputs, objectives and constraints.
5. Create a SolverAiClientCompute object solverAiClientCompute.
6. Run the computation with the runSolver function of the solverAiClientCompute object.

Notes:

• The data provided for the example was generated so that:
  • The temperatureSensorData.csv file was created by specific heat transfer coefficients between rooms and definition of the positioning of the rooms.
  • The motionSensorData.csv file was created by specifying ranges of times within the week where motion was expected for each room on different days. A random number generator was then used so to produce I higher likelihood of motion during those periods.

The code provided in example_thermostat perform all of the operations, from createion of the modules and Problem, to execution, to deletion. This would obviously not be the case if this was implemented in reality. We could imagine that:

1. The thermostat could provide a server with the number of available sensors. The server would then call SOLVER-AI to setup modules and Problem. This would have to be performed only once at installation of the thermostat, or if additinal sensors were added to the system.
2. In operation, the thermostat would upload (update) the motion and temperature data on a daily / weekly basis to avoid performing the machine learning training, which is time-consuming.
3. A intermediary server should be interposed between the thermostat and SOLVER-AI to ensure the token is kept safe.