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![Figure 2.5: Schematic of a Hydronic Heating System [4]](profile/Vikas-Chandan/publication/43939768/figure/fig3/AS:650765110624256@1532165901095/Schematic-of-a-Hydronic-Heating-System-4_Q320.jpg)
Energy requirements for heating and cooling of residential, commercial and industrial spaces constitute a major fraction of end use energy consumed. Centralized systems such as hydronic networks are becoming increasingly popular to meet those requirements. Energy efficient operation of such systems requires intelligent energy management strategies,...
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Citations
... Such water or steam based heating and cooling systems are also known as hydronic systems. The reader is directed to Chapter 2 of [70] for a detailed discussion of such systems. ...
Energy requirements for heating and cooling of buildings constitute a major fraction of end use energy consumed. Therefore, it is important to provide the occupant comfort requirements in buildings in an energy efficient manner. However, buildings are large scale complex systems, susceptible to sensor, actuator or communication network failures in their thermal control infrastructure, that can affect their performance in terms of occupant comfort and energy efficiency. The degree of decentralization in the control architecture determines a fundamental tradeoff between performance and robustness. This thesis studies the problem of thermal control of buildings from the perspective of partitioning them into clusters for decentralized control, to balance underlying performance and robustness requirements. Measures of deviation in performance and robustness between centralized and decentralized architectures in the Model Predictive Control framework are derived. Appropriate clustering algorithms are then proposed to determine decentralized control architectures which provide a satisfactory trade-off between the underlying performance and robustness objectives. Two different partitioning methodologies the CLF-MCS method and the OLF-FPM method are developed and compared. The problem of decentralized control design based on the architectures obtained using these methodologies is also considered. It entails the use of decentralized extended state observers to address the issue of unavailability of unknown states and disturbances in the system. The potential use of the proposed control architecture selection and decentralized control design methodologies is demonstrated in simulation on a real world multi-zone building.
... The electrical analogy approach to modeling multiple interconnected zones reduces the heat transfer model to an equivalent electrical circuit network. The model can be further modified to include building occupancy, room and heating equipment dynamics [43,45]. In this paper we take this electrical circuit analogy approach, and combine it with occupant discomfort feedback modeling. ...
In this work we propose a framework for incorporating occupant feedback towards temperature control of multi-occupant spaces, and analyze it using singular perturbation theory. Such a system would typically have to accommodate occupants with different temperature preferences, and incorporate that with thermal correlation among multiple zones to obtain optimal control for minimization of occupant discomfort and energy cost. In current practice, an acceptable temperature set point for the occupancy level of the zone is estimated, and the control law is designed to maintain temperature at the corresponding set point irrespective of the changes in occupancy and the preferences of multiple occupants. Proposed algorithm incorporates active occupant feedback to minimize aggregate user discomfort and total energy cost. Occupant binary feedback in the form of hot/cold or thermal comfort preference input is used by the control algorithm. The control algorithm also takes the energy cost into account, trading it off optimally with the aggregate occupant discomfort. For convergence to the optimal, sufficient separation between the occupant feedback frequency and the temperature dynamics of system is necessary; in absence of which, the occupant feedback provided do not correctly reflect the effect of current control input value on occupant discomfort. Under sufficient time scale separation, using singular perturbation theory, we establish the stability condition of the system and show convergence of the proposed solution to the desired temperature that minimizes energy cost plus occupant discomfort. The occupants are only assumed to be rational in that they choose their own comfort range to minimize individual thermal discomfort. Optimization for a multi-zone building also takes into account the thermal correlation among different zones. Simulation study with parameters based on our test facility, and experimental study conducted in the same building demonstrates performance of the algorithm under different occupancy and ambient conditions. © 2017 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd.
... The electrical analogy approach to modeling multiple interconnected zones reduces the heat transfer model to an equivalent electrical circuit network. The model can be further modified to include building occupancy, room and heating equipment dynamics [19], [20]. In this paper we take this electrical circuit analogy approach, and combine it with the distributed consensus algorithm to achieve collaborative temperature control of buildings. ...
... Also, (24) which completes the proof of inequality (20). ...
Buildings with shared spaces such as corporate office buildings, university dorms, etc. involve multiple occupants who are likely to have different temperature preferences. The building temperature control system needs to balance the desire of all users, as well as take the building energy cost into account. Centralized temperature management is challenging as the use comfort function is held privately and not centrally known. This paper proposes a distributed temperature control algorithm which ensures that a consensus is attained among all occupants, irrespective of their temperature preferences. Occupants are only assumed to be rational, in that they choose their own temperature set-points to minimize a combination of their individual energy cost and discomfort. We establish the convergence of the proposed algorithm to the optimal temperature set-point that minimizes the sum of the energy cost and the aggregate discomfort of all occupants. Simulations with realistic parameter settings illustrate the performance of the algorithm and provide insights on the dynamics of the system with a mobile user population.
... This model may also be modified to include the effect of occupancy, load changes and even room dynamics [7]. The model may be further expanded to include the dynamics of heating equipments [18]. ...
... where Γ > 0. Using (17)- (18), the derivative along solution isV ...
A common approach to the modeling of temper-
ature 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 four-
room example with realistic ambient temperature variation is
included to illustrate the performance of the proposed passivity
based control strategy.
... Substitution of the predicted outputs in the objective function (1) results in a restatement (11) of the optimization problem, which is a quadratic program. For details on this procedure, the reader is directed to [25].ū * c = arg min u g c (ū) (11) where, g c (ū) =ū T H cū + f T cū (12) The Hessian matrix H c in (12) is a function of the matrices A w,w , A w,z , A z,w , A z,z , B a , and B z . ...
This paper studies the problem of thermal control of buildings from the perspective of partitioning them into clusters for decentralized control. A measure of deviation in performance between centralized and decentralized control in the model predictive control framework, referred to as the optimality loss factor, is derived. Another quantity called the fault propagation metric is introduced as an indicator of the robustness of any decentralized architecture to sensing or communication faults. A computationally tractable agglomerative clustering approach is then proposed to determine the decentralized control architectures, which provide a satisfactory trade-off between the underlying optimality and robustness objectives. The potential use of the proposed partitioning methodology is demonstrated using simulated examples.
... Phetteplace (1995) studied a large-scale heat distribution system and recommended that such system may lose significantly heat as fluid circulated through the system. Bobenhausen (1994), Castro et al. (2000), Sugarman (2000) and Chandan (2010) all present results from studies of small-scale HVAC systems that use water to transport heat. Other study cases dealing especially with a distributed cooling/ heating system that uses water have been done by To solve these types of problem addressed in this research, we used EPANET, a software program developed by the Environmental Protection Agency, to simulate the pipe network and consider the heat-transfer rates, The EPANET version we used had been modified so that it could calculate heat-transfer rates. ...
Climatic conditions inside the dairy barn do not concern dairy farmers until those
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this work proposes an alternative system for reducing the risk of heat stress. This
innovative conductive cooling system does not depend on current weather conditions, and
it does not require significant modifications when it is installed or during its operation.
Also, the system circulates water that can be reused. Given that a review of the literature
found very few related studies, it is suggested that each freestall be equipped with a
viable prototype in the form of a waterbed able to exchange heat. Such a prototype has
been simulated using Computational Fluid Dynamics (CFD) and later verified by a set of
experiments designed to confirm its cooling capacity. Furthermore, this investigation sets
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waterbeds. EPANET, a software program developed by the Environmental Protection
Agency, simulates the hydraulic model. Its Water Quality Solver has been modified
according to an analogy in the governing equation that compares mass to heat transfer
and serves to simulate water temperature as the water is transported from its source to the point of delivery and then as it returns to the same source.
... Similarly, let the elements of u i (k) be denoted by u j i (k), where j ∈ {1, 2, ..., N zi }. The lifted vectorū i is constructed by the concatenation (18). ...
... Proof : Conversion of J c to the quadratic form (25) is achieved by expressing the outputs, {T z (k + l|k)} l=N l=1 in terms of the inputs {u(k + l|k)} l=N −1 l=0 , initial conditions T z (k), and disturbances {d(k + l)} l=N −1 l=0 and {T a (k + l)} l=N −1 l=0 , using the model given by (6) and (7). For more details, the reader is directed to [18]. Strict convexity of g c (.) follows from strict convexity of (3) and convexity of the constraints ((6) and (7)). ...
This paper considers the problem of partitioning a building or any other complex energy system into clusters for its decentralized thermal control. Using a Model Predictive Control (MPC) framework, a measure of deviation in performance between centralized controland decentralized control, called the Optimality Loss Factor (OLF) is derived. For a given partition size, the computationally intractable problem of determining the partition with the smallest OLF is then considered and an agglomerative clustering approach is proposed to overcome the computational limitation. The potential use of this approach to determine decentralized control architectures which yield the best trade-off between the underlying optimality and robustness objectives is demonstrated using an example.
... J k can be expresssed as a quadratic function of the control sequence {u (k + j|k)} N −1 j=0 , by successive substitution of (1) and (2) in (3) (Chandan, 2010). ...
The problem of partitioning a building into clusters is considered in this paper, with reference to its decentralized thermal control. Optimal control schemes for these systems are often centralized and address both the thermal comfort and energy efficiency requirements. However, due to robustness considerations, a decentralized architecture may be preferred for large scale systems, which is at best sub-optimal. Therefore, the `degree of decentralization' governs the tradeoff between optimality and robustness. This paper proposes a combinatorial optimization based systematic methodology for obtaining an optimal degree of decentralization on the basis of two metrics - one for optimality (defined as Coupling Loss Factor) and one for robustness (defined as Mean Cluster Size). The methodology was evaluated on a detailed building case study to obtain the decentralized control architectures for different values of wall insulation parameters. The results are found to be in agreement with the physics of the underlying thermal interactions.
... J k can be expresssed as a quadratic function of the control sequence {u (k + j|k)} N −1 j=0 , by successive substitution of (1) and (2) in (3) [18]. ...
The problem of partitioning a building into clusters is considered in this paper, with reference to its decentralized thermal control. Optimal control schemes for these systems are often centralized and address both the thermal comfort and energy efficiency requirements. However, due to robustness considerations, a decentralized architecture may be preferred for large scale systems, which is at best sub-optimal. Therefore, the 'degree of decentralization' governs the trade-off between optimality and robustness. This paper proposes a combinatorial optimization based systematic methodology for obtaining an optimal degree of decentralization on the basis of two metrics one for optimality (defined as Coupling Loss Factor) and one for robustness (defined as Mean Cluster Size). The methodology was evaluated on a building model and results were found to be in agreement with the physics of the underlying thermal interactions.
... For details of H k , f k , G k and w k appearing in this formulation, the reader is directed to [16]. Solution to this optimization problem can be obtained online using standard solvers available in applications such as MATLAB which use the active set or barrier function methods. ...
... Here, the role of leader and followers are played by the source and sink elements respectively. [16]. STEPS: ...
The control of hydronic building systems is considered in this paper, using a simulated chilled water system as a case study. In this context, model-based predictive control strategies have been proposed and compared with traditional feedback control schemes. The advantages and limitations associated with these methodologies has been demonstrated. The cornerstone of this work is the development of a novel, distributed predictive scheme which provides the best compromise in the multidimensional evaluation framework of `regulation', `optimality', `reliability' and `computational complexity'.
