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Hydrogen-electrical microgrids are increasingly assuming an important role on the pathway toward decarbonization of energy and transportation systems. This paper studies networked hydrogen-electrical microgrids planning (NHEMP), considering a critical but often-overlooked issue, i.e., the demand-inducing effect (DIE) associated with infrastructure development decisions. Specifically, higher refueling capacities will attract more refueling demand of hydrogen-powered vehicles (HVs). To capture such interactions between investment decisions and induced refueling demand, we introduce a decision-dependent uncertainty (DDU) set and build a trilevel stochastic-robust formulation. The upper-level determines optimal investment strategies for hydrogen-electrical microgrids, the lower-level optimizes the risk-aware operation schedules across a series of stochastic scenarios, and, for each scenario, the middle-level identifies the "worst" situation of refueling demand within an individual DDU set to ensure economic feasibility. Then, an adaptive and exact decomposition algorithm, based on Parametric Column-and-Constraint Generation (PC&CG), is customized and developed to address the computational challenge and to quantitatively analyze the impact of DIE. Case studies on an IEEE exemplary system validate the effectiveness of the proposed NHEMP model and the PC&CG algorithm. It is worth highlighting that DIE can make an important contribution to the economic benefits of NHEMP, yet its significance will gradually decrease when the main bottleneck transits to other system restrictions.

The multistage robust unit commitment (UC) is of paramount importance for achieving reliable operations considering the uncertainty of renewable realizations. The typical affine decision rule method and the robust feasible region method may achieve uneconomic dispatches as the dispatch decisions just rely on the current-stage information. Through approximating the future cost-to-go functions, the dual dynamic programming based methods have been shown adaptive to the multistage robust optimization problems, while suffering from high computational complexity. Thus, we propose the robust approximate dynamic programming (RADP) method to promote the computational speed and the economic performance for large-scale robust UC problems. RADP initializes the candidate points for guaranteeing the feasibility of upper bounding the value functions, solves the linear McCormick relaxation based bilinear programming to obtain the worst cases, and combines the primal and dual updates for this hybrid binary and continuous decision-making problem to achieve fast convergence. We can verify that the RADP method enjoys a finite termination guarantee for the multistage robust optimization problems with achieving suboptimal solutions. Numerical tests on 118-bus and 2383-bus transmission systems have demonstrated that RADP can approach the suboptimal economic performance at significantly improved computational efficiency., Comment: 9 pages, 3 figures, 4 tables

The unit commitment problem (UC) is crucial for the operation and market mechanism of power systems. With the development of modern electricity, the scale of power systems is expanding, and solving the UC problem is also becoming more and more difficult. To this end, this paper proposes a new fast solution method based on Lagrangian relaxation and dynamic program-ming. Firstly, the UC solution is estimated to be an initial trial UC solution by a fast method based on Lagrangian relaxation. This initial trial UC solution fully considers the system-wide con-straints. Secondly, a dynamic programming module is introduced to adjust the trial UC solution to make it satisfy the unit-wise constraints. Thirdly, a method for constructing a feasible UC solution is proposed based on the adjusted trial UC solution. Specifically, a feasibility-testing model and an updating strategy for the trial UC solution are established in this part. Numerical tests are implemented on IEEE 24-bus, IEEE 118-bus, Polish 2383-bus, and French 6468-bus systems, which verify the effec-tiveness and efficiency of the proposed method., Comment: 10 pages, journal paper, transactions

Linear power flow (LPF) models are essential in power system analysis. Various LPF models are proposed, but some crucial questions are still remained: what is the performance bound (e.g., the error bound) of LPF models, how to know a branch is applicable for LPF models or not, and what is the best LPF model. In this paper, these crucial questions are answered and a general formulation (GF) for evaluating the performance of LPF models is proposed. The GF actually figure out two core difficulties, the one is how to define the definition range of the LPF models, and the second is how to analytically obtain the best LPF model and evaluate the performance of a given LPF model. Besides, the key factors that affect the performance of LPF models are also analyzed through the proposed framework. The case studies compare the proposed LPF model with the DC power flow model, the physical-model-driven LPF model, and the data-driven LPF model, and the results show the effectiveness as well as the superiority of the proposed method., Comment: 9 pages

Linearization of power flow is an important topic in power system analysis. The computational burden can be greatly reduced under the linear power flow model while the model error is the main concern. Therefore, various linear power flow models have been proposed in literature and dedicated to seek the optimal approximation. Most linear power flow models are based on some kind of transformation/simplification/Taylor expansion of AC power flow equations and fail to be accurate under cold-start mode. It is surprising that data-based linearization methods have not yet been fully investigated. In this paper, the performance of a data-based least-squares approximation method is investigated. The resulted cold-start sensitive factors are named as least-squares distribution factors (LSDF). Compared with the traditional power transfer distribution factors (PTDF), it is found that the LSDF can work very well for systems with large load variation, and the average error of LSDF is only about 1% of the average error of PTDF. Comprehensive numerical testing is performed and the results show that LSDF has attractive performance in all studied cases and has great application potential in occasions requiring only cold-start linear power flow models.

Estimating set similarity and detecting highly similar sets are fundamental problems in areas such as databases, machine learning, and information retrieval. MinHash is a well-known technique for approximating Jaccard similarity of sets and has been successfully used for many applications such as similarity search and large scale learning. Its two compressed versions, b-bit MinHash and Odd Sketch, can significantly reduce the memory usage of the original MinHash method, especially for estimating high similarities (i.e., similarities around 1). Although MinHash can be applied to static sets as well as streaming sets, of which elements are given in a streaming fashion and cardinality is unknown or even infinite, unfortunately, b-bit MinHash and Odd Sketch fail to deal with streaming data. To solve this problem, we design a memory efficient sketch method, MaxLogHash, to accurately estimate Jaccard similarities in streaming sets. Compared to MinHash, our method uses smaller sized registers (each register consists of less than 7 bits) to build a compact sketch for each set. We also provide a simple yet accurate estimator for inferring Jaccard similarity from MaxLogHash sketches. In addition, we derive formulas for bounding the estimation error and determine the smallest necessary memory usage (i.e., the number of registers used for a MaxLogHash sketch) for the desired accuracy. We conduct experiments on a variety of datasets, and experimental results show that our method MaxLogHash is about 5 times more memory efficient than MinHash with the same accuracy and computational cost for estimating high similarities.

Efficient methods for large-scale security constrained unit commitment (SCUC) problems have long been an important research topic and a challenge especially in market clearing computation. For large-scale SCUC, the Lagrangian relaxation methods (LR) and the mixed integer programming methods (MIP) are most widely adopted. However, LR usually suffers from slow convergence; and the computational burden of MIP is heavy when the binary variable number is large. In this paper, a variable reduction method is proposed: First, the time-coupled constraints in the original SCUC problem are relaxed and many single-period SCUC problems (s-UC) are obtained. Second, LR is used to solve the s-UCs. Different from traditional LR with iterative subgradient method, it is found that the optimal multipliers and the approximate UC solutions of s-UCs can be obtained by solving linear programs. Third, a criterion for choosing and fixing the UC variables in the SCUC problem is established, hence the number of binary variables is reduced. Last, the SCUC with reduced binary variables is solved by MIP solver to obtain the final UC solution. The proposed method is tested on the IEEE 118-bus system and a 6484-bus system. The results show the method is very efficient and effective.

With the integration of large-scale renewable energy sources to power systems, many optimization methods have been applied to solve the stochastic/uncertain transmission-constrained unit commitment (TCUC) problem. Among all methods, two-stage and multi-stage robust optimization-based methods are the most widely adopted ones. In the two-stage methods, nonanticipativity of economic dispatch (ED) decisions are not considered. While in multi-stage methods, explicit decision rules (for example, affine decision rules) are usually adopted to guarantee nonanticipativity of ED decisions. With explicit decision rules, the computational burden can be heavy and the optimality of the solution is affected. In this paper, a multi-stage robust TCUC formulation with implicit decision rules is proposed, as well as a decomposition framework to solve it. The solutions are proved to be multi-stage robust and nonanticipativity of ED decisions is guaranteed. Meanwhile, a computationally efficient time-decoupled solution method for the feasibility check subproblems is also proposed such that the method is suitable for large-scale TCUC problems with uncertain loads/renewable injections. Numerical tests are conducted on the IEEE 118-bus system and Polish 2383-bus system. Performances of several state-of-the-art methods are compared.

With rapid integration of power sources with uncertainty, robustness must be carefully considered in the transmission constrained unit commitment (TCUC) problem. The overall computational complexity of the robust TCUC methods is closely related to the vertex number of the uncertainty set. The vertex number is further associated with 1) the period number in the scheduling horizon as well as 2) the number of nodes with uncertain injections. In this paper, a column merging method (CMM) is proposed to reduce the computation burden by merging the uncertain nodes, while still guar-anteeing the robustness of the solution. By the CMM, the transmission constraints are modified, with the parameters obtained based on an analytical solution of a uniform approximation problem, so that the computational time is negligi-ble. The CMM is applied under a greedy-algorithm based framework, where the number of merged nodes and the ap-proximation error can be well balanced. The CMM is designed as a preprocessing tool to improve the solution efficiency for robust TCUC problems and is compatible with many solution methods (like two-stage and multi-stage robust optimi-zation methods). Numerical tests show the method is effective.