Data Driven PMV-Comfort and Energy Consumption Control in Common Buildings

HVAC systems are essential in the energy management of commercial buildings. The main goal for HVAC system is to improve productivity of the inhabitants by providing comfortable indoor environment. The most common tool for evaluating comfort is PMV index, non-linear combination of indoor environment state variables. The Paper considers optimization of energy consumption of the building by combining state space expansion and microgrid approach.


Introduction
The Trapeznikov Institute of Control Sciences 1 of the Russian Academy of Sciences organizes research in the area of energy consumption prediction, control, and optimization for common buildings; the work is coordinated by the Centre of Digital Solutions for Smart Grid 2 .The Center's staff combines fundamental research and infrastructure development for modernization and digitization of building operation processes, visualization, and publication of the obtained results.The technological basis of the research is a data collection system that covers the entire Institute's building campus.Energy consumption data is collected in real-time and is available to researchers on our visualization platform.Two local weather stations and several experimental microclimate sites operating by LoRaWAN wireless protocol complement the measurements.The system is currently functioning in the data acquisition mode, and the next stage of its development is the introduction of automatic control devices into operating systems, which requires the development of feedback control, algorithms for generating dynamic models, parametric identification, and optimization of various modes of operation.The Paper describes approaches to control synthesis in indoor environmental comfort problems for the common type of buildings.Our approaches are based on stability theory, analysis of controllability and observability properties, sliding mode methods, and optimization methods for linear problems.In problem formulation, we apply the "grey box" approach, combining a mathematical description of the dynamics of the processes under study with the analysis of collected data for the parametric identification of models.The rest of the Paper is organized as follows.In section 2 we describe our data acquisition system,

Problem Statement
Recently, increased attention has been paid to the problems of providing a high level of comfort for people inside buildings, the focus shifts from saving energy costs [4] to providing an optimal level of human comfort.It is worth noting that such an evolution of the target functional still requires minimizing resource consumption, which leads to two competing optimization formulations.The final optimization problem becomes minimax at different weights of the two conflicting functionals [5].In the Paper, we consider the problem of room preparation for some events without any occupancy.
Let's consider indoor temperature dynamics described by equations where C P is the heat capacity of the room, m is the air mass in the room, U is the heat transfer coefficient between the air in the room and outside, U i is the same coefficient for the i-th adjacent room, T is the air temperature inside the room, T out is the outside air temperature.Q hum N hum is the heat amount produced by occupants, Q h is the heat from control actuators, C r α(T vent −T ) is the heat removed by ventillation.The variable T * involves the inner temperature inertia of the room and aggregate inertia coefficient U * [4].
According to current building management practices, climate control is divided into two stages: preparing the room for a scheduled event at a time when it is unoccupied, and further maintaining comfortable conditions in real-time.The first stage will be discussed in Section 7, while approaches to the second task are discussed in Sections 4 and 5.The PMV criterion is used to specify the comfortable conditions.Microclimate variables are measured with LoRaWAN complex sensors.This wireless protocol has strong limitations on data transmission time period.Measurements are transmitted every 15 minutes.That is the reason we propose the MPC prediction period to be similar to this limit.These sensors don't provide the mean radiant temperature.So we propose to use an asymptotic observer to estimate unmeasured variables.

Predicted Mean Vote
The first works devoted to comfort level appeared in the 1970s and the main results obtained by Fanger [?] have not lost their relevance.The improvement of this criterion continues.The calculation methodology is detailed in the standard [6].The basic idea is to consider the thermal balance of the body with the environment.Adjustment of the functional coefficients is based on the surveys.

Basic Feedback Synthesis
In this section, we consider synthesizing the control feedback law for the comfort control problem.In the first step, we should get the reference feedback law that is made under the assumption that all variables and dynamic parameters are known, measured, etc.In the Paper, we consider the problem of indoor regulation.In building maintenance, this problem appears when you need to prepare a room for some scheduled event.
In our case, there is no control action in the second equation of the system (1), but it can appear with underfloor heating.So we can say that the dynamics of the system is described by the first equation and the second equation appeared from an expansion of the state space for more accurate approximation.In conditions of our experiment system (1) can be reduced to To provide desired air temperature let's choose the proportional control law where k is the gain coefficient and T d is the goal temperature.Outside air temperature can be considered as external disturbances, which leads to finite accuracy ∆(T − T d ) < ϵ.In terms of our problem weather conditions can be approximately described by constants or very slowly changing variables.That is why we can use the PI-regulator technique to improve control accuracy.For synthesizing appropriate control law we introduce extended state space for the room where I is the integral of regulation mismatch.For system (4) feedback law can be obtained by back-stepping approach [7].In the first step, we set the virtual control T = −k 1 I.The second step is providing this ratio by setting real control action: where k 1 and k 2 are the backstepping gain coefficients, in terms of PI-regulation we get

State-Space Observer for Mean Radiant Temperature
One of the important problems in providing comfort is an estimation of unmeasured variables.Sometimes variables are hard to measure continuously, sometimes sensors are expensive.That is why we considered using the theory of observers [8] to estimate mean radiant temperature.This state variable is essential for comfort prediction and it can be measured by thermovision sensors or by black globe sensors.
Let's consider the situation when the mean radiant temperature can't be measured directly.In the system (1) T * can be considered as mean radiant temperature.In the case it is unmeasured, we can use the observer technique in order to get estimates for the synthesis of feedback control.Let's consider a more common view where x = col(T, T * ), A is the (2 × 2) -matrix of coefficients from 1, B = col(1, 0) -coefficients for control, C = (1, 0) -matrix of output coefficients.The observability matrix for this system is of full rank: which means the system is observable and there is a possibility to get very accurate estimates for unmeasured variables.The synthesis of correction matrix V should make closed-loop system 6 stable, which leads to convergence of observer vector |z − x| → 0 to current values of the state vector.To get this we need all real parts of eigenvalues of matrix (A − V C) to be negative: There is also another way to get estimates of the state vector, by sliding mode observers [9].
where v 1 and v 2 are chosen as signum functions with sufficiently big negative gain coefficients.In the first step, we can choose v 1 = −M 1 sign(x 1 − z 1 ).After the sliding mode occurrence, we can use the filtering procedure to get the equivalent of the switching correction variable v 1,eq = e 2 .
The output of this filter can be used to set second correction input v 2 = −M 2 sign(e 2 ).In both ways after convergence of the observation procedure, we obtain an estimated value for the mean radiant temperature in the current room.

Optimization with MPC
The main approach to solving the in-door microclimate control problem is model predictive control(MPC).In [4] MPC is used to provide energy-efficient solutions to the problem of occupants' comfort.
In our energy center, the problem of preparing the space before people come to the coworking is urgent.In that case, the temperature in space has to lie in the comfort interval of values only at the end of the planning horizon.
For solving such a problem in terms of energy efficiency we consider the problem statement as linear programming problem.Let's set the time at which the meeting begins in the coworking.Then the time from the current moment to the time of the meeting is divided into periods 15 minutes long and the planning horizon is a certain N period.At the end of planning, the air temperature in the coworking should be T opt , which is derived from the equality P M V (T ) = 0 for a given planned number of visitors.
For each time period define temperature dynamics 1 in the linear form via a first-order explicit method for the period i: The temperature values at the beginning of the horizon are taken from the observed values.Add special variable D, which is the absolute value of the gap between optimal temperature and realized temperature at the end of the planning horizon: So, the objective function consists of sum of W h and a penalty on gap D: where A is a penalty size.The formulation is obtained in the form of a linear programming problem, which can be solved with the help of a huge number of LP packages.At the output of the solution to the problem, we get a vector of the window's blackout degrees and a vector of the heater/air conditioner energy.With the appearance of new data on the state of the system, we can restart the solution of the problem taking into account new information, which will improve the quality of the solution.

Conclusion
As the Paper step-by-step procedures for the implementation of control devices in the sites of the Centre can be composed.On their basis, control algorithms can be proposed, the effectiveness of which will be tested on the real data collected in the future from the objects under our proposed control.Studies on verification of the proposed dynamic models for complex distributed objects, such as the indoor environment of buildings, can also be carried out.The approach to the feedback algorithms data coverage in the conditions of incomplete measurements, as well as to the analysis of collected data for parametric identification of dynamic models of the object was considered.On the basis of linear problem optimization methods, a primary approach to improving the energy efficiency of buildings was proposed.