Vahab Rostampour

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

This paper presents a stochastic model predictive control approach for a thermal grid with uncertainties in the consumer demand profiles. This approach leads to a finite-horizon chance-constrained mixed-integer linear optimization problem at each sampling time, which is in general non-convex and hard to solve. Earlier approaches for such problems are either suboptimal ad-hoc methodologies, or computationally intractable formulations. We provide a unified framework to deal with production planning problems for uncertain systems, while providing a-priori probabilistic certificates for the robustness properties of the resulting solutions. Our methodology is based on solving a random convex optimization problem to compute the uncertainty bounds using the so-called scenario approach and then, solving a robust mixed-integer optimization problem with the computed randomized uncertainty bounds at each sampling time. Using a tractable approximation of uncertainty bounds, the proposed problem formulation retains the complexity of the problem without chance constraints. In the presented thermal grid application this implies that a robust mixed-integer program is solved to provide a day-ahead prediction for the thermal energy production plan in the grid. The performance of the proposed methodology is illustrated using Monte Carlo simulations and employing two different problem formulations: optimization over input sequences (open-loop MPC) and optimization over affine feedback policies (closed-loop MPC).

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

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 observer-based residual generator. Secondly, we formulate a chance-constrained 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.

Computationally Tractable Reserve Scheduling for AC Power Systems with Wind Power Generation

This work presents a solution method for a day-ahead stochastic reserve scheduling (RS) problem using an AC optimal power flow (OPF) formulation. Such a problem is known to be non-convex and in general hard to solve. Existing approaches follow either linearized (DC) power flow or iterative approximation of nonlinearities, which may lead to either infeasibility or computational intractability. In this work we present two new ideas to address this problem. We first develop an algorithm to determine the level of reserve requirements using vertex enumeration (VE) on the deviation of wind power scenarios from its forecasted value. We provide a theoretical result on the level of reliability of a solution obtained using VE. Such a solution is then incorporated in OPF-RS problem to determine up- and down-spinning reserves by distributing among generators, and relying on the structure of constraint functions with respect to the uncertain parameters. As a second contribution, we use the sparsity pattern of the power system to reduce computational time complexity. We then provide a novel recovery algorithm to find a feasible solution for the OPF-RS problem from the partial solution which is guaranteed to be rank-one. The IEEE 30 bus system is used to verify our theoretical developments together with a comparison with the DC counterpart using Monte Carlo simulations.

Distributed Stochastic Thermal Energy Management in Smart Thermal Grids

This work presents a distributed stochastic energy management framework for a thermal grid with uncertainties in the consumer demand profiles. Using the model predictive control (MPC) paradigm, we formulate a finite-horizon chance-constrained mixed-integer linear optimization problem at each sampling time, which is in general non-convex and hard to solve. We then provide a unified framework to deal with production planning problems for uncertain systems, while providing a-priori probabilistic certificates for the robustness properties of the resulting solutions. Our methodology is based on solving a random convex program to compute the uncertainty bounds using the so-called scenario approach and then, solving a robust mixed-integer optimization problem with the computed randomized uncertainty bounds at each sampling time. Using a tractable approximation of uncertainty bounds, the proposed formulation retains the complexity of the problem without chance constraints. We also present two distributed approaches that are based on the alternating direction method of multipliers (ADMM) to solve the robust mixed-integer problem. The performance of the proposed methodology is illustrated using Monte Carlo simulations and employing two different problem formulations: optimization over input sequences (open-loop MPC) and optimization over affine feedback policies (closed-loop MPC).

Integrated building energy management using aquifer thermal energy storage (ATES) in smart thermal grids

Aquifer Thermal Energy Storage (ATES) is an innovative building technology that can be used to store thermal energy in natural subsurface formations [1, 4, 10]. In combination with a heat pump, ATES can reduce the energy demand of larger buildings by more than half, which has made the technology increasingly popular in northern Europe (see Figure 1). Furthermore, the climate and subsurface conditions required for ATES use can be found in areas across Europe, Asia and North America. By the middle of the century, roughly half of the worlds urban population is therefore expected to live in areas technically suitable for ATES [2].

Energy Management for Building Climate Comfort in Uncertain Smart Thermal Grids with Aquifer Thermal Energy Storage

In this paper, we present an energy management framework for building climate comfort systems that are interconnected in a grid via aquifer thermal energy storage (ATES) systems in the presence of two types of uncertainty namely private and common uncertainty sources. The ATES system is considered as a large-scale storage system that can be a heat source or sink, or a storage for thermal energy While the private uncertainty source refers to uncertain thermal energy demand of individual buildings, the common uncertainty source describes the uncertain common resource pool (ATES) between neighbors. To this end, we develop a large-scale uncertain coupled dynamical model to predict the thermal energy imbalance in a network of interconnected building climate comfort systems together with mutual interactions between the local ATES systems. A finite-horizon mixed-integer quadratic optimization problem with multiple chance constraints is formulated at each sampling time, which is in general a non-convex problem and hard to solve. We then provide a computationally tractable framework based on an extension to the so-called robust randomized approach which offers a less conservative solution for a problem with multiple chance constraints. A simulation study is provided to compare two different configurations, namely: completely decoupled, and centralized solutions.

Chance-constrained model predictive controller synthesis for stochastic max-plus linear systems

This paper presents a stochastic model predictive control problem for a class of discrete event systems, namely stochastic max-plus linear systems, which are of wide practical interest as they appear in many application domains for timing and synchronization studies. The objective of the control problem is to minimize a cost function under constraints on states, inputs and outputs of such a system in a receding horizon fashion. In contrast to the pessimistic view of the robust approach on uncertainty, the stochastic approach interprets the constraints probabilistically, allowing for a sufficiently small violation probability level. In order to address the resulting nonconvex chance-constrained optimization problem, we present two ideas in this paper. First, we employ a scenario-based approach to approximate the problem solution, which optimizes the control inputs over a receding horizon, subject to the constraint satisfaction under a finite number of scenarios of the uncertain parameters. Second, we show that this approximate optimization problem is convex with respect to the decision variables and we provide a-priori probabilistic guarantees for the desired level of constraint fulfillment. The proposed scheme improves the results in the literature in two distinct directions: we do not require any assumption on the underlying probability distribution of the system parameters; and the scheme is applicable to high dimensional problems, which makes it suitable for real industrial applications. The proposed framework is demonstrated on a two-dimensional production system and it is also applied to a subset of the Dutch railway network in order to show its scalability and study its limitations.