Building temperature control: A passivity-based approach

Mukherjee, Sumit; Mishra, Sandipan; Wen, John T.

doi:10.1109/cdc.2012.6426676

Cited by 47 publications

(30 citation statements)

References 16 publications

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“…This example is taken from [11], with the added heat transfer to the ambient for all the rooms. We have also used this example in our previous work [2]. For the 4 rooms and 8 walls, the number of capacitive elements is N = 4 + 2 * 8 = 20.…”

Section: F Optimization For Energy Efficiencymentioning

confidence: 98%

“…We model a single zone as a single thermal capacitor and use the standard 3R2C model [1] for the wall (i.e., the wall is characterized by three thermal resistors in series shunted by two thermal capacitors at the nodes). As shown in [2], the temperature dynamics of a thermal RC network modeled as a graph consisting of n nodes (capacitors) and links (resistors) is given by…”

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confidence: 99%

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Building temperature control with adaptive feedforward

Wen

Mishra

Mukherjee

et al. 2013

52nd IEEE Conference on Decision and Control

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A common approach to the modeling of temperature evolution in a multi-zone building is to use thermal resistance and capacitance to model zone and wall dynamics. The resulting thermal network may be represented as an undirected graph. The thermal capacitances are the nodes in the graph, connected by thermal resistances as links. The temperature measurements and temperature control elements (heating and cooling) in this lumped model are collocated. As a result, the input/output system is strictly passive and any passive output feedback controller may be used to improve the transient and steady state performance without affecting the closed loop stability. The storage functions associated with passive systems may be used to construct a Lyapunov function, to demonstrate closed loop stability and motivate the construction of an adaptive feedforward control to compensate for the variation of the ambient temperature and zone heat loads (due to changing occupancy). The approach lends itself naturally to an inner-outer loop control architecture where the inner loop is designed for stability, while the outer loop balances between temperature specification and power consumption. Energy efficiency consideration may be added by adjusting the target zone temperature based on user preference and energy usage. The initial analysis uses zone heating/cooling as input, but the approach may be extended to more general model where the zonal mass flow rate is the control variable. A fourroom example with realistic ambient temperature variation is included to illustrate the performance of the proposed passivity based control strategy. I. INTRODUCTIONHeating, ventilation, and air conditioning (HVAC) system is a major energy consumer in buildings. For the analysis of building temperature evolution under HVAC control, a common approach is to model it as an interconnected network of lumped thermal capacitors and resistors. Thermal resistance models the heat flow due to temperature difference: Q = ∆T /R, where Q (in W) is the rate of heat transfer across the resistance, ∆T is the temperature difference (in K), and R is the thermal resistance (K/W). Thermal capacitance (or thermal mass) models the ability of a space (or wall) to store heat: C d∆T dt = Q,where C has the unit J/K. We model a single zone as a single thermal capacitor and use the standard 3R2C model [1] for the wall (i.e., the wall is characterized by three thermal resistors in series shunted by two thermal capacitors at the nodes). As shown in [2], the temperature dynamics of a thermal RC network modeled as a graph consisting of n nodes (capacitors) and links (resistors) is given by where C ∈ R n×n is a diagonal, positive definite matrix consisting of the thermal capacitances, R ∈ R × is a diagonal, positive definite matrix consisting of the link thermal resistances, D ∈ R n× is the incidence matrix of the graph, B 0 = −DR −1 d T 0 ∈ R n is a column vector with non-zero elements as the thermal conductance of nodes connected to the ambient, T ∞ is the ambient temperature, u ∈ R...

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Section: F Optimization For Energy Efficiencymentioning

confidence: 98%

mentioning

confidence: 99%

Building temperature control with adaptive feedforward

Wen

Mishra

Mukherjee

et al. 2013

52nd IEEE Conference on Decision and Control

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“…Using a smiliar line of analysis as in [16], the stability of the system can be established. We present our results with the proposed control law in section IV.…”

Section: Control Law Designmentioning

confidence: 99%

Distributed consensus algorithms for collaborative temperature control in smart buildings

Gupta

Kar

Mishra

et al. 2015

2015 American Control Conference (ACC)

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Abstract-Multi-occupant buildings with shared spaces such as corporate office buildings, university dorms, etc. are occupied by multiple occupants who typically have different temperature preferences. Attaining a common temperature set-point that is agreeable to all users (occupants) in such a multi-occupant space is a challenging problem. Furthermore, the ideal temperature set-point should optimally trade off the building energy cost with the aggregate discomfort of all the occupants. However, the information on the comfort range functions is held privately by each occupant. Using occupant-differentiated dynamicallyadjusted prices as feedback signals, we propose a distributed solution which ensures that a consensus is attained among all occupants upon convergence, irrespective of their temperature preferences being in coherence or conflicting. Occupants are only assumed to be rational, in that they choose their own temperature set-points so as to minimize their individual energy cost plus discomfort. We establish the convergence of the proposed algorithm to the optimal temperature set-point vector that minimizes the sum of the energy cost and the aggregate discomfort of all occupants in a multi-zone building. Simulations with realistic parameter settings illustrate validation of our theoretical claims and provide insights on the dynamics of the system with a mobile user population.

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“…Discretizing the system at the level of the functional elements will result in a large number of capacitors in the RC thermal model which means a large number of nodes in the graph-based thermal model. Therefore, the resulting state space thermal model of an 21 actual power electronics system will have a large number of states which imposes a high computational cost. Also, it will be problematic to implement such a complex system in an online estimator.…”

Section: State Space Modelmentioning

confidence: 99%

“…Graph-based modeling has been used in the literature in different areas. It was found to be a useful tool for modeling of power electronics systems [18], thermal modeling of buildings [19][20] [21], among many other applications. The main advantage of this modeling technique is that it captures the structure of the conservation of mass and energy laws in these systems [22].…”

Section: Network Modeling 221 Thermal Network Representationmentioning

confidence: 99%

Dynamic temperature estimation of power electronics systems

Tannous

Peddada

Allison

et al. 2017

2017 American Control Conference (ACC)

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This thesis proposes a method for accurate temperature estimation of thermally-aware power electronics systems. The duality between electrical systems and thermal systems was considered for thermal modeling. High dimensional thermal models present a challenge for online estimation. RC (resistor-capacitor) circuits that create a tradeoff between accuracy and complexity were used to simulate the dynamic thermal behavior of power electronics. The complexity of the thermal network was further reduced by applying a structure-preserving model order reduction technique. The reduced order thermal model was an RC circuit with fewer capacitors. Preserving the physical correspondence between the reduced order model and the physical system allows the user to use the reduced order thermal model in the sensor placement optimization process. The accuracy of the thermal estimates can be easily increased by increasing the number of sensors in the system. However, a large number of sensors increases the cost and complexity of the system. It might also interfere with the circuit design and create packaging problems. An optimal number and optimal placement of temperature sensors was found. The optimal sensor placement problem was solved by maximizing the trace of observability Gramian. The optimal number of temperature sensors was based on the state estimation error obtained from a Kalman filter. The dynamic thermal behavior of the power electronics systems was represented by a linear state space model by applying the conservation of energy principle. Therefore, assuming Gaussian noise, it is well-known that a Kalman filter is an optimal estimator for such systems. A continuous-discrete Kalman filter was used to estimate the dynamic thermal behavior of power electronics systems using an optimal number of temperature sensors placed at optimal locations. The proposed method was applied on 2-D and 3-D power electronics systems. Theoretical results were validated experimentally using IR thermal imaging and thermocouples. It was shown that the proposed method can accurately iii reconstruct the dynamic temperature profile of power electronics systems using a small number of temperature sensors. for Power Optimization of Electro-Thermal Systems (POETS). I feel so lucky to be part of this multidisciplinary research center that gave me the opportunity to work with extraordinary people from different disciplines and different institutions. Tables Table 2.1 Thermal-electric analogy used to model resistor-capacitor thermal models. ........... 6 Table 5.1 Dimesions for the inverter regions defined in Figure 5

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Building temperature control: A passivity-based approach

Cited by 47 publications

References 16 publications

Building temperature control with adaptive feedforward

Building temperature control with adaptive feedforward

Distributed consensus algorithms for collaborative temperature control in smart buildings

Dynamic temperature estimation of power electronics systems

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