This paper presents a distributed computational framework for stochastic convex optimization problems using the so-called scenario approach. Such a problem arises, for example, in a large-scale network of interconnected linear systems with local and common uncertainties. Due to the large number of required scenarios to approximate the stochasticity of these problems, the stochastic optimization involves formulating a large-scale scenario program, which is in general computationally demanding. 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 to compute local decisions using the alternating direction method of multipliers (ADMM). We show the exactness of the de-composition with a-priori probabilistic guarantees for the desired level of constraint fulfillment for both local and common uncertainty sources. As our second contribution, we develop a so-called 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 interconnected network, namely dynamically coupled and coupling constraints, are presented to illustrate advantages of the proposed distributed framework.

In this article two limitations in current distributed model based approaches for anomaly detection in large-scale uncertain nonlinear systems are addressed. The first limitation regards the high conservativeness of deterministic detection thresholds, against which a novel family of set-based thresholds is proposed. Such set-based thresholds are defined in a way to guarantee robustness in a user-defined probabilistic sense, rather than a deterministic sense. They are obtained by solving a chance-constrained optimization problem, thanks to a randomization technique based on the Scenario Approach. The second limitation regards the requirement, in distributed anomaly detection architectures, for different parties to regularly communicate local measurements. In settings where these parties want to preserve their privacy, communication may be undesirable. In order to preserve privacy and still allow for distributed detection to be implemented, a novel privacy-preserving mechanism is proposed and a so-called privatized communication protocol is introduced. Theoretical guarantees on the achievable level of privacy, along with a characterization of the robustness properties of the proposed distributed threshold set design, taking into account the privatized communication scheme, are provided. Finally, simulation studies are included to illustrate our theoretical developments.

This paper presents a framework to carry out multi-area stochastic reserve scheduling (RS) based on an AC optimal power flow (OPF) model with high penetration of wind power using distributed consensus and the alternating direction method of multipliers (ADMM). We first formulate the OPF-RS problem using semidefinite programming (SDP) in infinite dimensional spaces that are in general computationally intractable. Using a novel affine policy, we develop an approximation of the infinite dimensional SDP as a tractable finite dimensional SDP, and explicitly quantify the performance of the approximation. To this end, we adopt the recent developments in randomized optimization that allow a priori probabilistic feasibility guarantees to optimally schedule generating units while simultaneously determining the required reserve. We then use the geographical pattern of the power system to decompose the large-scale system into a multi-area power network, and provide a consensus ADMM algorithm to find a feasible solution for both local and overall multi-area network. Using our distributed stochastic framework, each area can use its own wind information to achieve local feasibility certificates, while ensuring overall feasibility of the multi-area power network under mild conditions. We provide numerical comparisons with a new benchmark formulation, the so-called converted DC (CDC) power flow model, using Monte Carlo simulations for two different IEEE case studies.

This paper presents an approach to distributed stochastic model predictive control (SMPC) of large-scale uncertain linear systems with additive disturbances. Typical SMPC approaches for such problems involve formulating a large-scale finite-horizon chance-constrained optimization problem at each sampling time, which is in general non-convex and difficult to solve. Using an approximation, the so-called scenario approach, we formulate a large-scale scenario program and provide a theoretical guarantee to quantify the robustness of the obtained solution. However, such a reformulation leads to a computational tractability issue, due to the large number of required scenarios. To this end, we present two novel ideas in this paper to address this issue. We first provide 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. We show the exactness of the decomposition with a-priori probabilistic guarantees for the desired level of constraint fulfillment. As our second contribution, we develop an inter-agent soft communication scheme based on a set parametrization technique together with the notion of probabilistically reliable sets to reduce the required communication between each subproblem. We show how to incorporate the probabilistic reliability notion into existing results and provide new guarantees for the desired level of constraint violations. A simulation study is presented to illustrate the advantages of our proposed framework.

Distributed fault diagnosis has been proposed as an effective technique for monitoring large scale, nonlinear and uncertain systems. It is based on the decomposition of the large scale system into a number of interconnected subsystems, each one monitored by a dedicated Local Fault Detector (LFD). Neighboring LFDs, in order to successfully account for subsystems interconnection, are thus required to communicate with each other some of the measurements from their subsystems. Anyway, such communication may expose private information of a given subsystem, such as its local input. To avoid this problem, we propose here to use differential privacy to pre-process data before transmission.

In this paper, we present an implementation of a model predictive controller (MPC) for wind farm power tracking problem. The controller is evaluated in the high-fidelity PAral-lelized Large-eddy simulation Model (PALM). By taking measurements from PALM, we show that the closed-loop MPC can provide power reference tracking while reducing force variations on a farm level by solving a constrained optimization problem at each time step. A six turbine wind farm case study is presented in which the controller operates with yawed turbines that increases the potential power that can be harvested with the wind farm, and we show that it is possible to track a reference power signal that temporarily exceeds the power harvested when operating under the so-called greedy control settings.

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 private uncertainty source and the uncertain common resource pool (ATES) between neighbors as 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 hard 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.

The objective of active power control in wind farms is to provide ancillary grid services. Improving this is vital for a smooth wind energy penetration in the energy market. One of these services is to track a power reference signal with a wind farm by dynamically de- and uprating the turbines. In this paper we present a computationally efficient model predictive controller (MPC) for computing optimal control signals for each time step. It is applied in the PArallelized Large-eddy simulation Model (PALM), which is considered as the real wind farm in this paper. By taking measurements from the PALM, we show that the closed-loop controller can provide power reference tracking while minimizing variations in the axial forces by solving a constrained optimization problem at each time step. A six turbine simulation case study is presented in which the controller operates with optimised turbine yaw settings. We show that with these optimized yaw settings, it is possible to track a power signal that temporarily exceeds the power harvested when operating under averaged greedy control turbine settings. Additionally, variations in the turbine's force signals are studied under different controller settings.

This paper 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 paper 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 RS-OPF 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 RS-OPF problem from the partial solution which is guaranteed to be rank-one. The IEEE 30 bus system is used to verify theoretical developments together with a comparison with DC counterpart using Monte Carlo simulations.

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.

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).