The heating, ventilation and air condition (HVAC) system consumes the most energy in commercial buildings, consisting over 60% of total energy usage in the U.S. Flexible HVAC system setpoint scheduling could potentially save building energy costs. This paper first studies deterministic optimization, robust optimization, and stochastic optimization to minimize the daily operation cost with constraints of indoor air temperature comfort and mechanic operating requirement. Considering the uncertainties from ambient temperature, a Wasserstein metric-based distributionally robust optimization (DRO) method is proposed to enhance the robustness of the optimal schedule against the uncertainty of probabilistic prediction errors. The schedule is optimized under the worst-case distribution within an ambiguity set defined by the Wasserstein metric. The proposed DRO method is initially formulated as a two-stage problem and then reformulated into a tractable mixed-integer linear programming (MILP) form. The paper evaluates the feasibility and optimality of the optimized schedules for a real commercial building. The numerical results indicate that the costs of the proposed DRO method are up to 6.6% lower compared with conventional techniques of optimization under uncertainties. They also provide granular risk-benefit options for decision making in demand response programs.
The integration of distributed renewable generation (DRG) in distribution networks can be effectively promoted by scheduling flexible resources such as heating, ventilation, and air conditioning (HVAC) loads. However, finding the optimal scheduling for them is nontrivial because DRG outputs are highly uncertain. To address this issue, this paper proposes a learning-based joint chance-constrained approach to coordinate HVAC loads with DRG. Unlike cutting-edge works adopting individual chance constraints to manage uncertainties, this paper controls the violation probability of all critical const…
Power systems are shifted from conventional bulk generation toward renewable generation. This trend leads to the frequency security problem due to the decline of system inertia. On the other hand, natural gas-fired units are frequently scheduled to provide operational flexibility due to their fast adjustment ability. The interdependence between power and natural gas systems is thus intensified. In this paper, we study the frequency constrained scheduling problem from the perspective of an integrated electricity-gas system under variable wind power. We propose a distributionally robust (DR) cha…
Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. In this paper, we decide HVAC control schedules under uncertain PV generation, using a distributionally robust chance-constrained (DRCC) building load control model under two typical ambiguity sets: the moment-based and Wasserstein ambiguity sets. We derive mixed-integer linear programming (MILP) reformulations for DRCC problems under both sets. Especially, for the Wasserstein ambiguity set, we utilize the right-hand si…
A high number of electric vehicles (EVs) in the transportation sector necessitates an advanced scheduling framework for e-mobility ecosystem operation as a whole in order to overcome range anxiety and create a viable business model for charging stations (CSs). The framework must account for the stochastic nature of all stakeholders' operations, including EV drivers, CSs, and retailers and their mutual interactions. In this paper, a three-layer joint distributionally robust chance-constrained (DRCC) model is proposed to plan grid-to-vehicle (G2V) and vehicle-to-grid (V2G) operation in day-ahead…
To ensure a successful bid while maximizing of profits, generation companies (GENCOs) need a self-scheduling strategy that can cope with a variety of scenarios. So distributionally robust opti-mization (DRO) is a good choice because that it can provide an adjustable self-scheduling strategy for GENCOs in the uncertain environment, which can well balance robustness and economics compared to strategies derived from robust optimization (RO) and stochastic programming (SO). In this paper, a novel mo-ment-based DRO model with conditional value-at-risk (CVaR) is proposed to solve the self-scheduling…
We study a single-server appointment scheduling problem with a fixed sequence of appointments, for which we must determine the arrival time for each appointment. We specifically examine two stochastic models. In the first model, we assume that all appointees show up at the scheduled arrival times yet their service durations are random. In the second model, we assume that appointees have random no-show behaviors and their service durations are random given that they show up at the appointments. In both models, we assume that the probability distribution of the uncertain parameters is unknown bu…
We propose two distributionally robust optimization (DRO) models for a mobile facility (MF) fleet sizing, routing, and scheduling problem (MFRSP) with time-dependent and random demand, as well as methodologies for solving these models. Specifically, given a set of MFs, a planning horizon, and a service region, our models aim to find the number of MFs to use (i.e., fleet size) within the planning horizon and a route and schedule for each MF in the fleet. The objective is to minimize the fixed cost of establishing the MF fleet plus a risk measure (expectation or mean conditional value-at-risk) o…
In this paper, we identify partial correlation information structures that allow for simpler reformulations in evaluating the maximum expected value of mixed integer linear programs with random objective coefficients. To this end, assuming only the knowledge of the mean and the covariance matrix entries restricted to block-diagonal patterns, we develop a reduced semidefinite programming formulation, the complexity of solving which is related to characterizing a suitable projection of the convex hull of the set $\{(\bold{x}, \bold{x}\bold{x}'): \bold{x} \in \mathcal{X}\}$ where $\mathcal{X}$ is…
Distributionally robust optimization (DRO) is a powerful tool for decision making under uncertainty. It is particularly appealing because of its ability to leverage existing data. However, many practical problems call for decision-making with some auxiliary information, and DRO in the context of conditional distribution is not straightforward. We propose a conditional kernel distributionally robust optimization (CKDRO) method that enables robust decision making under conditional distributions through kernel DRO and the conditional mean operator in the reproducing kernel Hilbert space (RKHS). I…
HVAC Energy Cost Optimization for a Multi-zone Building via a Decentralized Approach
Berkeley Education Alliance for Research in Singapore（新加坡伯克利教育联盟）；Nanyang Technological University（南洋理工大学）；University of California, Berkeley（加州大学伯克利分校）
We study elective surgery planning in flexible operating rooms (ORs) where emergency patients are accommodated in the existing elective surgery schedule. Specifically, elective surgeries can be scheduled weeks or months in advance. In contrast, an emergency surgery arrives randomly and must be performed on the day of arrival. Probability distributions of the actual durations of elective and emergency surgeries are unknown, and only a possibly small set of historical realizations may be available. To address distributional uncertainty, we first construct an ambiguity set that encompasses all po…
In this paper, we focus on a data-driven risk-averse multistage stochastic programming (RMSP) model considering distributional robustness. We optimize the RMSP over the worst-case distribution within an ambiguity set of probability distributions constructed directly from historical data samples. The proposed RMSP is intractable due to the multistage nested minimax structure in its objective function, so we reformulate it into a deterministic equivalent that contains a series of convex combination of expectation and conditional value at risk (CVaR), which can be solved by a customized stochasti…
Specifying a proper input distribution is often a challenging task in simulation modeling. In practice, there may be multiple plausible distributions that can fit the input data reasonably well, especially when the data volume is not large. In this paper, we consider the problem of selecting the best from a finite set of simulated alternatives, in the presence of such input uncertainty. We model such uncertainty by an ambiguity set consisting of a finite number of plausible input distributions, and aim to select the alternative with the best worst-case mean performance over the ambiguity set. …
We study a routing and appointment scheduling problem with uncertain service and travel times arising from home service practice. Specifically, given a set of customers within a service region that an operator needs to serve, we seek to find the operator's route and time schedule. The quality of routing and scheduling decisions is a function of the total operational cost, consisting of customers' waiting time, and the operator's travel time, idle time, and overtime. We propose and rigorously analyze a stochastic programming model and two distributionally robust optimization (DRO) models to sol…
University of Sydney（悉尼大学）；University of Queensland（昆士兰大学）
This paper focuses on energy management in buildings with phase change material (PCM), which is primarily used to improve thermal performance, but can also serve as an energy storage system. In this setting, optimal scheduling of an HVAC system is challenging because of the nonlinear and non-convex characteristics of the PCM, which makes solving the corresponding optimization problem using conventional optimization techniques impractical. Instead, we use dynamic programming (DP) to deal with the nonlinear nature of the PCM. To overcome DP's curse of dimensionality, this paper proposes a novel …
