Stochastic Optimal Power Flow Based on Data-Driven Distributionally Robust Optimization

We propose a data-driven method to solve a stochastic optimal power flow (OPF) problem based on limited information about forecast error distributions. The objective is to determine power schedules for controllable devices in a power network to balance operation cost and conditional value-at-risk (CVaR) of device and network constraint violations. These decisions include scheduled power output adjustments and reserve policies, which specify planned reactions to forecast errors in order to accommodate fluctuating renewable energy sources. Instead of assuming the uncertainties across the networks follow prescribed probability distributions, we assume the distributions are only observable through a finite training dataset. By utilizing the Wasserstein metric to quantify differences between the empirical data-based distribution and the real data-generating distribution, we formulate a distributionally robust optimization OPF problem to search for power schedules and reserve policies that are robust to sampling errors inherent in the dataset. A simple numerical example illustrates inherent tradeoffs between operation cost and risk of constraint violation, and we show how our proposed method offers a data-driven framework to balance these objectives

Convex Relaxations and Approximations of Chance-Constrained AC-OPF Problems

This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained AC optimal power flow problems. Such approximations are required for the formulation of tractable chance constraints. In this context, we introduce the first formulation of a chance-constrained second-order cone (SOC) OPF. The proposed formulation provides convergence guarantees due to its convexity, while it demonstrates high computational efficiency. Combined with an AC feasibility recovery, it is able to identify better solutions than chance-constrained nonconvex AC-OPF formulations. To the best of our knowledge, this paper is the first to perform a rigorous analysis of the AC feasibility recovery procedures for robust SOC-OPF problems. We identify the issues that arise from the linear approximations, and by using a reformulation of the quadratic chance constraints, we introduce new parameters able to reshape the approximation of the confidence region. We demonstrate our method on the IEEE 118-bus system

Data-Driven Dynamic Robust Resource Allocation: Application to Efficient Transportation

The transformation to smarter cities brings an array of emerging urbanization challenges. With the development of technologies such as sensor networks, storage devices, and cloud computing, we are able to collect, store, and analyze a large amount of data in real time. Modern cities have brought to life unprecedented opportunities and challenges for allocating limited resources in a data-driven way. Intelligent transportation system is one emerging research area, in which sensing data provides us opportunities for understanding spatial-temporal patterns of demand human and mobility. However, greedy or matching algorithms that only deal with known requests are far from efficient in the long run without considering demand information predicted based on data. In this dissertation, we develop a data-driven robust resource allocation framework to consider spatial-temporally correlated demand and demand uncertainties, motivated by the problem of efficient dispatching of taxi or autonomous vehicles. We first present a receding horizon control (RHC) framework to dispatch taxis towards predicted demand; this framework incorporates both information from historical record data and real-time GPS location and occupancy status data. It also allows us to allocate resource from a globally optimal perspective in a longer time period, besides the local level greedy or matching algorithm for assigning a passenger pick-up location of each vacant vehicle. The objectives include reducing both current and anticipated future total idle driving distance and matching spatial-temporal ratio between demand and supply for service quality. We then present a robust optimization method to consider spatial-temporally correlated demand model uncertainties that can be expressed in closed convex sets. Uncertainty sets of demand vectors are constructed from data based on theories in hypothesis testing, and the sets provide a desired probabilistic guarantee level for the performance of dispatch solutions. To minimize the average resource allocation cost under demand uncertainties, we develop a general data-driven dynamic distributionally robust resource allocation model. An efficient algorithm for building demand uncertainty sets that compatible with various demand prediction methods is developed. We prove equivalent computationally tractable forms of the robust and distributionally robust resource allocation problems using strong duality. The resource allocation problem aims to balance the demand-supply ratio at different nodes of the network with minimum balancing and re-balancing cost, with decision variables on the denominator that has not been covered by previous work. Trace-driven analysis with real taxi operational record data of San Francisco shows that the RHC framework reduces the average total idle distance of taxis by 52%, and evaluations with over 100GB of New York City taxi trip data show that robust and distributionally robust dispatch methods reduce the average total idle distance by 10% more compared with non-robust solutions. Besides increasing the service efficiency by reducing total idle driving distance, the resource allocation methods in this dissertation also reduce the demand-supply ratio mismatch error across the city

Probabilistic Optimization Techniques in Smart Power System

Uncertainties are the most significant challenges in the smart power system, necessitating the use of precise techniques to deal with them properly. Such problems could be effectively solved using a probabilistic optimization strategy. It is further divided into stochastic, robust, distributionally robust, and chance-constrained optimizations. The topics of probabilistic optimization in smart power systems are covered in this review paper. In order to account for uncertainty in optimization processes, stochastic optimization is essential. Robust optimization is the most advanced approach to optimize a system under uncertainty, in which a deterministic, set-based uncertainty model is used instead of a stochastic one. The computational complexity of stochastic programming and the conservativeness of robust optimization are both reduced by distributionally robust optimization.Chance constrained algorithms help in solving the constraints optimization problems, where finite probability get violated. This review paper discusses microgrid and home energy management, demand-side management, unit commitment, microgrid integration, and economic dispatch as examples of applications of these techniques in smart power systems. Probabilistic mathematical models of different scenarios, for which deterministic approaches have been used in the literature, are also presented. Future research directions in a variety of smart power system domains are also presented.publishedVersio