Robust randomized model predictive control for energy balance in smart thermal grids

2019

IEEE Trans. Smart Grid

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This paper presents an energy management framework for building climate comfort (BCC) systems interconnected in a grid via aquifer thermal energy storage (ATES) systems in the presence of two types of uncertainty (private and common). ATES can be used either as a heat source (hot well) or sink (cold well) depending on the season. We consider the uncertain thermal energy demand of individual buildings as a private uncertainty source and the uncertain common resource pool (ATES) between neighbors as a common uncertainty source. We develop a large-scale stochastic hybrid dynamical model to predict the thermal energy imbalance in a network of interconnected BCC systems together with mutual interactions between their local ATES. We formulate a finite-horizon mixed-integer quadratic optimization problem with multiple chance constraints at each sampling time, which is in general a non-convex problem and difficult to solve. We then provide a computationally tractable framework by extending the so-called robust randomized approach and offering a less conservative solution for a problem with multiple chance constraints. A simulation study is provided to compare completely decoupled, centralized and move-blocking centralized solutions. We also present a numerical study using a geohydrological simulation environment (MODFLOW) to illustrate the advantages of our proposed framework.

Section: Contributionsmentioning

confidence: 99%

Section: We Next Definementioning

confidence: 99%

Probabilistic Energy Management for Building Climate Comfort in Smart Thermal Grids with Seasonal Storage Systems

2019

IEEE Trans. Smart Grid

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“…Moreover, one can also define the cost function (5a) as a desired quantile of the sum of discounted stage costs ("value-at-risk"), instead of the sum of expected values. Instead of a state feedback law, one can also consider a nonlinear disturbance parametrization feedback policy over the prediction horizon, similar to [22], using the scenario-based approximation. Such a parametrization does not affect the convexity of the resulting optimization [16].…”

Section: Problem Formulationmentioning

confidence: 99%

“…In particular, ε i ∈ (0, 1) the level of constraint violation in each agent i ∈ N will increase, since it is proportional with the inverse of j∈N i (α j ) ∈ (0, 1), and therefore, ε = i∈N ε i ∈ (0, 1) will also increase. After receiving the parametrization ofB j and the level of reliabilityα j , agent i ∈ N should immunize itself against all possible variation of x j ∈B j by taking the worst-case ofB j , similar to the worst-case reformulation proposed in [22,Proposition 1]. It is important to notice that in this way, we decoupled the sample generation of agent j ∈ N i from agent i ∈ N .…”

Section: Information Exchange Schemementioning

confidence: 99%

Distributed Stochastic Model Predictive Control Synthesis for Large-Scale Uncertain Linear Systems

2018 Annual American Control Conference (ACC)

2018

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This paper presents a distributed stochastic model predictive control (SMPC) approach for large-scale linear systems with private and common uncertainties in a plug-and-play framework. Using the so-called scenario approach, the centralized SMPC involves formulating a large-scale finitehorizon scenario optimization problem at each sampling time, which is in general computationally demanding, due to the large number of required scenarios. We present two novel ideas in this paper to address this issue. We first develop a technique to decompose the large-scale scenario program into distributed scenario programs that exchange a certain number of scenarios with each other in order to compute local decisions using the alternating direction method of multipliers (ADMM). We show the exactness of the decomposition with a-priori probabilistic guarantees for the desired level of constraint fulfillment for both uncertainty sources. As our second contribution, we develop an interagent soft communication scheme based on a set parametrization technique together with the notion of probabilistically reliable sets to reduce the required communication between the subproblems. We show how to incorporate the probabilistic reliability notion into existing results and provide new guarantees for the desired level of constraint violations. Two different simulation studies of two types of systems interactions, dynamically coupled and coupling constraints, are presented to illustrate the advantages of the proposed framework. 1 arXiv:1703.06273v3 [math.OC] 8 Jan 2019 2 V. ROSTAMPOUR AND T. KEVICZKY compared to robust model predictive control (MPC) [4], since it directly incorporates the tradeoff between constraint feasibility and control performance.Distributed MPC has been an active research area in the past decades, due to its applicability in different domains such as power networks [5], chemical plants [6], process control [7], and building automation [8]. For such large-scale dynamic systems with state and input constraints, distributed MPC is an attractive control scheme. In distributed MPC one replaces large-scale optimization problems stemming from centralized MPC with several smaller-scale problems that can be solved in parallel. These problems make use of information from other subsystems to formulate finitehorizon optimal control problems. In the presence of uncertainties, however, the main challenge in the formulation of distributed MPC is how the controllers should exchange information through a communication scheme among subsystems (see, e.g., [9], and references therein). This highlights the necessity of developing distributed control strategies to cope with the uncertainties in subsystems while at the same time minimizing information exchange through a communication framework. Related WorksIn order to handle uncertainties in distributed MPC, some approaches are based on robust MPC [10,11]. Assuming that the uncertainty is bounded, a robust optimization problem is solved at each sampling time, leading to a control law that sat...

“…Remark 2. It is important to note that, as in [16], [18], we do not require the sample spaces W, V and the probability measures P W , P V to be known explicitly, as it will be explained in Section IV.…”

Section: A System Dynamicsmentioning

confidence: 99%

A set based probabilistic approach to threshold design for optimal fault detection

Ferrari

2017 American Control Conference (ACC)

2017

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Abstract-Traditional deterministic robust fault detection threshold designs, such as the norm-based or limit-checking method, are plagued by high conservativeness, which leads to poor fault detection performance. On one side they are ill-suited at tightly bounding the healthy residuals of uncertain nonlinear systems, as such residuals can take values in arbitrarily shaped, possibly non-convex regions. On the other hand, they must be robust even to worst-case, rare values of the modeling and measurement uncertainties. In order to maximize performance of detection, we propose two innovative ideas. First, we introduce threshold sets, parametrized in a way to bound arbitrarily well the residuals produced in healthy condition by an observerbased residual generator. Secondly, we formulate a chanceconstrained cascade optimization problem to determine such a set, leading to optimal detection performance of a given class of faults, while guaranteeing robustness in a probabilistic sense. We then provide a computationally tractable framework by using randomization techniques, and a simulation analysis where a well-known three-tank benchmark system is considered.