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This paper presents a fully risk-aware model predictive control (MPC) framework for chance-constrained discrete-time linear control systems with process noise. Conditional value-at-risk (CVaR) as a popular coherent risk measure is incorporated in both the constraints and the cost function of the MPC framework. This allows the system to navigate the entire spectrum of risk assessments, from worst-case to risk-neutral scenarios, ensuring both constraint satisfaction and performance optimization in stochastic environments. The recursive feasibility and risk-aware exponential stability of the resulting risk-aware MPC are demonstrated through rigorous theoretical analysis by considering the disturbance feedback policy parameterization. In the end, two numerical examples are given to elucidate the efficacy of the proposed method.

The existing distribution system planning methods do not fully consider improving power supply capacity and reliability through the coordination of multiple planning factors, and they are not comprehensive enough in quantifying planning risks. Therefore, this paper proposes a collaborative planning method for sources and networks that considers risk measurement. A multi-layer planning model is first constructed that includes a grid planning layer, a power planning layer, a switch planning layer, and an operation optimization layer. In the model, a risk measurement method combining opportunity constraints and conditional value-at-risk objectives is used to comprehensively assess the risk of the node voltage and branch current exceeding the limit caused by load uncertainty. Then, a solution strategy based on a genetic algorithm and a sparrow search algorithm is proposed to coordinate the contradiction between the solution time and the accuracy of the multi-layer model. Finally, taking a planned area to be expanded as an example, the results show that compared to the existing collaborative planning methods for sources and networks, the proposed method in this paper reduces the planning risks caused by load uncertainty by more than 50% and increases the annual net income of the power distribution company and the DG operators by RMB 1.5 million and RMB 1.1 million, respectively.

To avoid the problem of insufficient flexibility of the power grid along the cz railway due to source-load fluctuations, a distributionally robust optimization method considering flexibility is proposed in this paper. Firstly, Wasserstein distance is used to establish the uncertainty set of flexibility demand caused by source-load fluctuation, and a risk-cost model of insufficient flexibility is constructed to couple to the objective function. Combined with the flexibility chance constraint, the flexibility over-limit probability is limited to a certain confidence level in the fuzzy set, and a distributionally robust chance constraint optimization model based on Wasserstein distance is established. Then, the proposed model is transformed into a linear programming problem to be solved by dual theory and inner approximation transformation. Finally, a simulation study of the power grid along the CZ railway is carried out to verify the correctness and effectiveness of the model. The experimental results show that the proposed method can improve the flexibility capacity of the system without sacrificing economy.

Recently there has been a considerable increase in the penetration level of distributed energy resources (DERs) due to various factors, such as the increasing affordability of these resources, the global movement towards sustainable energy, and the energy democracy movement. However, the uncertainty and variability of DERs introduce new challenges for power system operations. Advanced techniques that account for the characteristics of DERs, i.e., their intermittency and human-in-the-loop factors, are essential to improving distribution system operations. This paper proposes a behavior-aware approach to analyze and aggregate prosumers’ participation in demand response (DR) programs. A convexified AC optimal power flow (ACOPF) via a second-order cone programming (SOCP) technique is used for system scheduling with DERs. A chance-constrained framework for the system operation is constructed as an iterative two-stage algorithm that can integrate loads, DERs’ uncertainty, and SOCP-based ACOPF into one framework to manage the violation probability of the distribution system’s security limits. The benefits of the analyzed prosumers’ behaviors are shown in this paper by comparing the optimal system scheduling with socially aware and non-socially aware approaches. The case study illustrates that the socially aware approach within the chance-constrained framework can utilize up to 43% more PV generation and improve the reliability and operation of distribution systems.

The required time for surgical interventions in operating rooms (OR) may vary significantly from the predicted values depending on the type of operations being performed, the surgical team, and the patient. These deviations diminish the efficient utilization of OR resources and result in the disruption of projected surgery start times. This paper proposes a two-stage chance-constrained model to solve the OR scheduling problem under uncertainty. The goal is to minimize the costs associated with OR opening and overtime as well as reduce patient waiting times. The risk of OR overtime is controlled using chance constraints. Numerical experiments show that the proposed model provides a better trade-off between minimizing costs and reducing solution variability when compared to two existing models in the literature. It is also shown that the three models converge as the overtime probability threshold approaches one. Moreover, it is observed that the individual chance constraints result in the opening of fewer rooms, lower waiting times, and shorter solution times when compared to that of joint chance constraints. A decomposition algorithm is applied that solves large test instances of the OR scheduling problem, that of which is known to be NP-hard. Strong valid inequalities are derived in order to accelerate the convergence speed. The proposed approach outperformed both a commercial solver and a basic decomposition algorithm after solving all test instances with up to 89 surgeries and 20 ORs in less than 48 minutes.

An unmanned surface vehicles (USV) set point tracking problem is investigated in this paper. The stochastic model predictive control (SMPC) scheme is utilized to design the controller in order to reject the environment disturbances and meet the physical constraints. The design problem is formulated as a chance-constrained stochastic optimization problem, which is non-convex. Thus, the problem is computationally prohibitive. For this, the convex conditional value at risk (CVaR) approximation is introduced to convert the chance constraints into deterministic convex constraints. The converted constraints are then further transformed into the second order cone (SOC) constraints. Therefore, the proposed method is computationally tractable and hence can be implemented online. A numerical example is provided to illustrate the effectiveness of the proposed method.

An industrial microgrid (IMG) consists in a microgrid involving manufacturer plants that are usually equipped with distributed generation facilities, industrial electric vehicles, energy storage systems, and so on. In this paper, the problem of IMG-efficient operation in the presence of plug-in electric vehicles is addressed. To this purpose, the schedule of the different device operations of IMGs has to be optimally computed, minimizing the operation cost while guaranteeing the electrical network stability and the production constraints. Such a problem is formulated in a receding horizon framework involving dynamic optimal power flow equations. Uncertainty affecting plug-in electric vehicles is handled by means of a chance constraint approach. The obtained nonconvex problem is then approximately solved by exploiting suitable convex relaxation techniques. The numerical simulations have been performed showing computational feasibility and robustness of the proposed approach against increased penetration of the electric vehicles.

In this paper, we propose the distributionally robust secure transmit schemes in multi-input single-output (MISO) downlink wireless networks which consist of a transmitter, a desired receiver, multiple eavesdroppers and an assisting jammer. The imperfect channel state information (CSI) is considered and the CSI errors are only captured by the mean and covariance. We first study the transmit power minimization by jointly designing the beamforming vector at transmitter and artificial noise(AN) covariance at jammer, while the lower bound of connection probability at desired receiver and lower bound of outage probability at eavesdroppers are guaranteed simultaneously. Since the chance-constrained problem is non-convex, we derive two safe convex approximations by exploiting the Conditional Value-at-risk (CVaR) based method and Bernstein-type inequality (BTiE) based method, respectively. Specifically, we extend the application of BTiE originally proposed with the Gaussianity assumption to other possible distributions which satisfy the proposed sufficient condition. Furthermore, the secrecy rate maximization is exploited under the constraint of total transmit power. The original problem is non-convex and fractional, hence we design the Bilevel Quick Search (BQS) method to make it tractable. Finally, the simulation results verify the effectiveness and the robustness of the proposed transmit schemes.

This paper proposes a reliability-based economic model predictive control (MPC) strategy for the management of generalised flow-based networks, integrating some ideas on network service reliability, dynamic safety stock planning, and degradation of equipment health. The proposed strategy is based on a single-layer economic optimisation problem with dynamic constraints, which includes two enhancements with respect to existing approaches. The first enhancement considers chance-constraint programming to compute an optimal inventory replenishment policy based on a desired risk acceptability level, leading to dynamical allocation of safety stocks in flow-based networks to satisfy non-stationary flow demands. The second enhancement computes a smart distribution of the control effort and maximises actuators’ availability by estimating their degradation and reliability. The proposed approach is illustrated with an application of water transport networks using the Barcelona network as the case study considered.

In this paper, an adaptively constrained stochastic model predictive control (MPC) is proposed to achieve less-conservative coordination between energy storage units and uncertain renewable energy sources (RESs) in a microgrid (MG). Besides the economic objective of MG operation, the limits of state-of-charge (SOC) and discharging/charging power of the energy storage unit are formulated as chance constraints when accommodating uncertainties of RESs, considering mild violations of these constraints are allowed during long-term operation, and a closed-loop online update strategy is performed to adaptively tighten or relax constraints according to the actual deviation probability of violation level from the desired one as well as the current change rate of deviation probability. Numerical studies show that the proposed adaptively constrained stochastic MPC for MG optimal operation is much less conservative compared with the scenario optimization based robust MPC, and also presents a better convergence performance to the desired constraint violation level than other online update strategies.

The definition of the electric energy procurement plan represents a fundamental problem that any consumer has to deal with. Bilateral contracts, electricity market and self-production are the main supply sources that should be properly combined to satisfy the energy demand over a given time horizon at the minimum cost. The problem is made more complex by the presence of uncertainty, mainly related to the energy requirements and electricity market prices. Ignoring the uncertain nature of these elements can lead to the definition of procurement plans which are infeasible or overly expensive in a real setting. In this paper, we deal with the procurement problem under uncertainty by adopting the paradigm of joint chance constraints to define reliable plans that are feasible with a high probability level. Moreover, the proposed model includes in the objective function a risk measure to control undesirable effects caused by the random variations of the electricity market prices. The proposed model is applied to a real test case. The results show the benefit deriving from the stochastic optimization approach and the effect of considering different levels of risk aversion.