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DOE OSTI2020

In situ , in vivo , and in operando imaging and spectroscopy of liquids using microfluidics in vacuum

This review offers a succinct overview of the development of a vacuum-compatible microfluidic reactor system for analysis at the liquid vacuum interface (SALVI), and its diverse applications in in situ, in vivo, and in operando imaging of liquid surfaces as well as the air-liquid (a-l), liquid-liquid (l-l), and solid-liquid (s-l) interfaces in the past decade. SALVI is one of the first microfluidics-based reactors that has enabled direct analysis of volatile liquids in vacuum surface tools such as scanning electron microscopy (SEM) and time-of-flight secondary ion mass spectrometry (ToF-SIMS). Its integration into ambient and vacuum spectroscopy and microscopy is illustrated. Several applications are highlighted including (1) imaging nanoparticles in liquid using in situ SEM; (2) mapping the evolving l-l interface using in situ x-ray absorption spectroscopy and ToF-SIMS; (3) following complex a-l interfacial oxidation reaction products using in situ ToF-SIMS; (4) capturing biological interfaces of cells and microbes via in vivo multimodal and correlative imaging; and (5) monitoring the dynamic solid electrode and liquid electrolyte interface using in operando molecular imaging. Finally, outlook and recommendations are presented. Besides showing the holistic information volume obtained by real-time multiplexed imaging, this review intends to convey the importance of tool development in revolutionizing surface and interface analysis using vacuum platforms previously limited to solid surfaces. Microfluidics is manifested to be not limited to ambient conditions in many examples in this review. Moreover, fundamental interfacial phenomena underpinning mass and charge transfer can now be pursued in real time via innovated chemical imaging and spectroscopy.

42 ENGINEERING↗

DOE OSTI2025

Rapid monitoring of fermentations: a feasibility study on biological 2,3-butanediol production

2,3-butanediol (2,3-BDO) is an economically important platform chemical that can be produced by the fermentation of sugars using an engineered strain of Zymomonas mobilis . These fermentations require continuous monitoring and modification of fermentation conditions to maximize 2,3-BDO yields and minimize the production of the undesired coproducts glycerol and acetoin. Because of the time required for sampling and off-line chromatographic measurement of fermentation samples, the ability of fermentation scientists to modify fermentation conditions in a timely manner is limited. The goal of this study was to test if near-infrared spectroscopy (NIRS) along with multivariate statistics could reduce the time needed for this analysis and enable real-time monitoring and control of the fermentation. In this work we developed partial least squares (PLS) calibration models to predict the concentrations of glucose, xylose, 2,3-BDO, acetoin, and glycerol in fermentations via NIRS using two different spectrometers and two different spectroscopy modalities. We first evaluated the feasibility of rapid NIRS monitoring through experiments where we measured the signals from each analyte of interest and built NIRS-based PLS models using spectra from synthetic samples containing uncorrelated concentrations of these analytes. All analytes showed unique spectral signatures, and this initial modeling showed that all analytes could be detected simultaneously. We then began work with samples from laboratory fermentation experiments and tested the feasibility of regression model development across two spectral collection modalities (at-line and on-line) and two instruments: a laboratory-grade instrument and a low-cost instrument with a more limited spectral range. All modalities showed promise in the ability to monitor Z. mobilis fermentations of glucose and xylose to 2,3-BDO. The low-cost instrument displayed a lower signal-to-noise ratio than the laboratory-grade instrument, which led to comparatively lower performance overall, but still provided sufficient accuracy to monitor fermentation trends. While the ease of use of on-line monitoring systems was favored as compared to at-line systems due to the lack of sampling required and potential for automated process control, we observed some decrease in performance due to the additional complexity of the sample matrix. We have demonstrated that NIRS combined with multivariate analysis can be used for at-line and on-line monitoring of the concentrations of glucose, xylose, 2,3-BDO, acetoin, and glycerol during Z. mobilis fermentations. The decrease in signal-to-noise ratio when using a low-cost spectrometer led to greater prediction error than the laboratory-grade spectrometer for at-line monitoring. The on-line monitoring modality showed great promise for real time process control via NIRS.

09 BIOMASS FUELS↗

DOE OSTI2025

Real-Time Detection of Hydrogen and Ammonia Isotopologues for Impurity Removal and Recovery of Tritium

To accommodate gas measurements for impurity removal and recovery of tritium, a silver-coated optical or waveguide is employed for collecting Raman scattered signals to determine relative hydrogen and ammonia isotopologue populations in real time. The data and results presented here demonstrate an analytical methodology for the analysis of four ammonia and three hydrogen isotopologues in a hydrogen–deuterium exchange reaction by gas phase Raman spectroscopy. Standard chemometric modeling techniques effectively unravel the signatures of the isotopologues involved observed here; however, a sophisticated quantum chemical approach supports the spectral assignments. An interpretation of the data presented here can emphasize the practicality and reliability of the gaseous monitoring system in complex chemical environments for the hydrogen fuel economy as well as the more distant energy source from a facility that handles tritium. There are still considerable concerns about the measurement of tritium in isotope separation and radiological impurities from gas processing. A common impurity in gas processing is ammonia, which can form readily in the presence of nitrogen and tritium. Substituted ammonia (NQ 3 ), where Q = H, D, or T, is traditionally removed through getters or diffusers along with other non-hydrogen contaminants. A preferable analytical approach is noninvasive and can be deployed for real-time process evaluation in radiological environments.

Ammonia↗

DOE OSTI2024

Markov Decision Processes for Intelligent, Risk-Informed Asset-Management Decision-Making

Advanced nuclear reactors are a promising option for aiding the world in achieving its net-zero carbon emission goals, however, there are significant challenges to attaining and maintaining economic competitiveness with other sources of electricity. To improve the economic competitiveness of advanced reactor designs, a project was initiated to explore the use of Markov Decision Processes (MDPs) to guide asset-management decision-making during advanced reactor operation. MDPs are a powerful tool for optimizing decision-making in complex environments and their application to advanced reactors can aid in planning maintenance and repair activities to minimize downtime and maximize generation. The described approach expands on previous work regarding the use of MDPs for operational decision-making through the direct incorporation of real-time plant information. The integral MDP analysis includes information from online component diagnostic tools and the plant’s real-time generation risk assessment (GRA) and probabilistic risk assessment (PRA), which evaluate plant risk from both an economic and safety perspective. The result is an asset-management optimization framework that is based on real-time data regarding plant component status and the current best-estimate of plant risk. The paper presents an overview of the theoretical framework to incorporate the different information pathways into an integral MDP analysis, along with example analyses.

Grabaskas, David↗

DOE OSTI2025

Cost-Benefit Analysis of Electricity Resilience Projects: State of the Art and Gap Analysis

Utilities and regulators must weigh the benefits of electricity resilience projects against their costs, which would be passed on to customers. Cost-benefit analysis (CBA) is an appropriate method for assessing this tradeoff. Here, in this paper we review the literature on CBA of electricity resilience projects and analyze gaps in the available methods and tools. The costs of resilience projects are typically straightforward to estimate but their benefits — particularly the avoided costs of power interruptions — are complex to quantify and monetize. A common perception among practitioners is that current CBA tools are not sufficiently mature to be adopted into real-world practice. We propose an electricity resilience CBA framework consisting of several elements: risks, physical impacts, power interruptions, economic impacts, and resilience projects. While methods for some elements are well-developed, there is a need for novel approaches to value avoided power interruptions, integrate multiple risks and benefit streams, and incorporate uncertainty.

Cost-benefit analysis↗

DOE OSTI2024

OC6 Phase IV: Validation of CFD Models for Stiesdal TetraSpar Floating Offshore Wind Platform

ABSTRACT With only a few floating offshore wind turbine (FOWT) farms deployed anywhere in the world, FOWT technology is still in its infancy, building on a modicum of real‐world experience to advance the nascent industry. To support further development, engineers rely heavily on modeling tools to accurately portray the behavior of these complex systems under realistic environmental conditions. This reliance creates a need for verification and validation of such tools to improve reliability of load and dynamic response prediction and analysis capabilities of FOWT systems. The Offshore Code Comparison Collaboration, Continued with Correlation and unCertainty (OC6) project was created under the framework of the International Energy Agency to address this need and considers a three‐sided verification and validation between engineering level models, computational fluid dynamics (CFD), and experimental results. In this paper, a novel floating offshore wind platform, the Stiesdal TetraSpar, is simulated using CFD under the load conditions defined by Phase IV of the OC6 project. The comparison of these CFD results against the experimental results demonstrated the ability to predict the platform response to waves when imposing the measured wave signals as input. Although validation versus experiment was largely successful, the damping behavior was impacted by uncertainties likely originating from the mooring system and sensor umbilical cable. This extensive comparison effort with multiple CFD practitioners offers insight into best practices to achieve reliable results.

17 WIND ENERGY↗

DOE OSTI2025

Non-Hermitian quantum mechanics approach for extracting and emulating continuum physics based on bound-state-like calculations: Detailed description

Here, this work applies a reduced basis method to study the continuum physics of a finite quantum system—either few or many-body. Specifically, I develop reduced-order models, or emulators, for the underlying inhomogeneous Schrödinger equation and train the emulators against the equation's bound-state-like solutions at complex energies. The emulators rapidly and accurately interpolate and extrapolate the matrix elements of the Hamiltonian resolvent operator (Green's function) across a parameter space that includes both complex energy and other real-valued physical inputs in the Schrödinger equation. The spectra, discretized and compressed as the result of emulation, and the associated resolvent matrix elements (or amplitudes), have the defining characteristics of non-Hermitian quantum mechanics calculations, featuring complex eigenenergies with negative imaginary parts and branch cuts moved below the real axis in the complex energy plane. Therefore, one now has a method that extracts continuum physics from bound-state-like calculations and emulates those extractions in the input parameter space. Building on a prior Letter [Zhang, Phys. Rev. Lett. 135, 242501 (2025)], this article provides the full theoretical details, a comprehensive analysis of the method's performance, and a brief discussion of how it can be coupled with existing continuum approaches to perform emulations in their input parameter spaces.

ab initio calculations↗

DOE OSTI2022

Data reduction through optimized scalar quantization for more compact neural networks

Raw data generation for several existing and planned large physics experiments now exceeds TB/s rates, generating untenable data sets in very little time. Those data often demonstrate high dimensionality while containing limited information. Meanwhile, Machine Learning algorithms are now becoming an essential part of data processing and data analysis. Those algorithms can be used offline for post processing and post data analysis, or they can be used online for real time processing providing ultra low latency experiment monitoring. Both use cases would benefit from data throughput reduction while preserving relevant information: one by reducing the offline storage requirements by several orders of magnitude and the other by allowing ultra fast online inferencing with low complexity Machine Learning models. Moreover, reducing the data source throughput also reduces material cost, power and data management requirements. In this work we demonstrate optimized nonuniform scalar quantization for data source reduction. This data reduction allows lower dimensional representations while preserving the relevant information of the data, thus enabling high accuracy Tiny Machine Learning classifier models for online fast inferences. We demonstrate this approach with an initial proof of concept targeting the CookieBox, an array of electron spectrometers used for angular streaking, that was developed for LCLS-II as an online beam diagnostic tool. We used the Lloyd-Max algorithm with the CookieBox dataset to design an optimized nonuniform scalar quantizer. Optimized quantization lets us reduce input data volume by 69% with no significant impact on inference accuracy. When we tolerate a 2% loss on inference accuracy, we achieved 81% of input data reduction. Finally, the change from a 7-bit to a 3-bit input data quantization reduces our neural network size by 38%.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Model-Based Investigation of Multi-Fault Interactions and Performance Degradation in Residential Heat Pump Systems

Faults in heat pump systems can significantly degrade performance, reduce efficiency, and accelerate component wear, leading to higher operating costs and maintenance demands. While numerous studies have investigated the impact of individual faults, the interactions between multiple concurrent faults remain insufficiently understood, despite their common occurrence in real-world operation. This study conducts a comprehensive simulation analysis of multiple simultaneous faults in a vapor compression heat pump using a validated heat pump design model (HPDM) tool. Detailed component-level modeling methods are implemented to examine performance sensitivity under combinations of refrigerant flow and heat exchanger faults. The results reveal complex fault interactions that can mask or amplify system deviations, challenging conventional diagnostic approaches. Findings from this work provide meaningful insights for the development of more robust fault detection and diagnosis algorithms, supporting improved reliability and energy efficiency in next-generation heat pump technologies.

Hu, Yifeng [ORNL] (ORCID:0000000242875185)↗

DOE OSTI2025

HOLISTIC ENERGY EFFICIENCY ANALYSIS OF ELECTRIFIED OFF-HIGHWAY MATERIAL HANDLER: FROM DRIVE CYCLE CHARACTERIZATION TO POWERTRAIN, HYDRAULIC, AND THERMAL SYSTEM PERFORMANCE

Three complexities surrounding the operation and testing of hybrid electric, heavy-duty nonroad machines have been addressed experimentally and using 1D simulation. Their resolutions have been intertwined with the development of a prototype machine that was proven to reduce fuel consumption in excess of 20%. A real-world drive cycle that leveraged hydraulic cylinder position was developed and utilized to ensure accurate reproduction of hydraulic work between the baseline and hybrid machines, while simultaneously maintaining less than 5% RMS error in position for main load handling functions. The newly developed, machine-specific drive cycle also contributed towards making equivalent comparisons in energy consumption between machine types through composite performance metrics that were extrapolated over a typical shift duration. Lastly, this work addressed thermal management energy consumption, a topic of increasing popularity when discussing electrified vehicles, by proposing a 1.4% energy savings through special mechanization and control of cooling system components.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

Phagosomal chloride dynamics in the alveolar macrophage

Acidification in intracellular organelles is tightly linked to the influx of Cl – counteracting proton translocation by the electrogenic V-ATPase. We quantified the dynamics of Cl – transfer accompanying cargo incorporation into single phagosomes in alveolar macrophages (AMs). Phagosomal Cl – concentration and acidification magnitude were followed in real time with maximal acidification achieved at levels of approximately 200 mM. Live cell confocal microscopy verified that phagosomal Cl – influx utilized predominantly the Cl – channel CFTR. Relative levels of elemental chlorine (Cl) in hard X-ray fluorescence microprobe (XFM) analysis within single phagosomes validated the increase in Cl – content. XFM revealed the complex interplay between elemental K content inside the phagosome and changes in Cl – during phagosomal particle uptake. Cl – -dependent changes in phagosomal membrane potential were obtained using second harmonic generation (SHG) microscopy. These studies provide a mechanistic insight for screening studies in drug development targeting pulmonary inflammatory disease.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Distinct Gas-Particle Partitioning and Viscosity Characteristics of Secondary Organic Aerosols Derived from α-Pinene versus Ocimene

Secondary organic aerosols (SOA) have complex, multicomponent composition that controls particle viscosity and gas-particle partitioning, key factors to their atmospheric evolution. This study investigates the chemical composition, volatility and viscosity of SOA formed by ozonolysis of cyclic α-pinene (PSOA) and acyclic ocimene (OSOA) monoterpenes. Using Temperature-Programmed Desorption combined with Direct Analysis in Real-Time ionization and High-Resolution Mass Spectrometry, we determined the molecular composition and saturation mass concentration of individual SOA constituents. These data enabled gas-particle partitioning and viscosity estimates under varied atmospheric conditions. PSOA, composed of higher molecular weight and less oxidized species, shows higher condensability and viscosity under high total organic mass (tOM) loadings. Here, in contrast, OSOA, consisting of more oxidized, lower molecular weight species, exhibits greater sensitivity to tOM, with viscosity increasing significantly upon dilution. Poke-flow experiments support this trend, indicating that OSOA undergoes more dynamic compositional and phase changes during atmospheric aging. These observations reveal distinct dynamic trends in the atmospheric transformations and reactivity of SOA from cyclic and acyclic monoterpenes, with the latter showing greater compositional changes during aging that alter viscosity and diffusion. This highlights the importance of incorporating such dynamic transformations into atmospheric models to improve predictions of SOA atmospheric loadings, lifetimes, and impacts.

cyclic and acyclic monoterpenes↗

DOE OSTI2025

Spontaneous magnon decays from nonrelativistic time-reversal symmetry breaking in altermagnets

Quasiparticles are central to condensed matter physics, but their stability can be undermined by quantum many-body interactions. Magnons, i.e., quasiparticles in quantum magnets, are particularly intriguing because their properties are governed by both real and spin space. While crystal symmetries may be low, spin interactions often remain approximately isotropic, limiting spontaneous magnon decay. Textbook wisdom holds that collinear Heisenberg magnets follow a dichotomy: ferromagnets host stable magnons, while antiferromagnetic magnons may decay depending on dispersion curvature. Up to now, relativistic spin-orbit coupling and noncollinear order that connect spin space to real space were shown to introduce more complex magnon instability mechanisms. Here, we show that even in nonrelativistic isotropic collinear systems, this conventional dichotomy is disrupted in altermagnets. Altermagnets, a newly identified class of collinear magnets, exhibit compensated spin order with nonrelativistic time-reversal symmetry breaking and even-parity band splitting. Using kinematic analysis, nonlinear spin-wave theory, and quantum simulations, we reveal that even weak band splitting opens a decay phase space, driving quasiparticle breakdown. Additionally, 𝑑-wave altermagnets form a rare “island of stability” at the Brillouin-zone center. Furthermore, our findings establish a quasiparticle stability trichotomy in collinear Heisenberg magnets and position altermagnets as a promising platform for unconventional spin dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Virtual Power Plant Architecture and Resilient Design

Virtual Power Plants (VPPs) represent a fundamental shift in electric grid operations, aggregating distributed energy resources (DERs) such as solar panels and battery storage to deliver utility-scale grid services traditionally provided by centralized power plants. This report examines the unique architectural, operational, and digital assurance considerations that distinguish VPPs from conventional utility infrastructure as they scale from pilot projects to mainstream deployment across the United States. While VPPs offer significant opportunities for grid modernization and enhanced flexibility, their distributed, multi-stakeholder architecture introduces distinct security challenges that differ fundamentally from traditional generation facilities. The analysis identifies risks in VPP operations, including device-level security gaps, platform vulnerabilities, and communication protocol weaknesses that create expanded attack surfaces compared to centralized power plants. Through examination of real-world incidents and emerging threat patterns, the report demonstrates how some VPPs' reliance on consumer-owned devices, public internet infrastructure, and complex vendor ecosystems require new approaches to digital assurance and operational security. The findings provide practical guidance for utilities, regulators, and aggregators to implement robust security frameworks and operational best practices essential for maintaining grid reliability as VPP deployment accelerates under the Federal Energy Regulatory Commission (FERC) Order 2222 and related regulatory initiatives.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

3D ion gyro-orbit heat load predictions for NSTX-U

Abstract High power tokamaks operate with divertor heat loads capable of destroying the plasma facing components (PFCs). High fidelity heat load predictions are necessary to ascertain the PFC state for design and during operation. Typical heat flux calculations are 2D, time invariant, and assume that power flows directly along the magnetic field lines (the optical approximation). These assumptions neglect the complex 3D geometries employed to protect the PFCs, the time varying nature of the plasma and PFC thermal state, and the helical trajectories of ions with finite Larmor radii (the gyro-orbit approximation). An integrated software framework, the heat flux engineering analysis toolkit (HEAT), was developed to generate time varying optical heat loads applied to real engineering computer aided design (CAD) (Looby et al 2022 Fusion Sci. Technol. 78 10–27). Recently, an ion-gyro orbit module has been added to HEAT. This module calculates the helical trajectories of ions as they gyrate about the magnetic field lines using kinetic theory macro-particles to accelerate the calculation. First, the new gyro-orbit module will be presented. Next, a comparison to existing research is performed. Finally, an analysis of the gyro-orbit heat loads for NSTX-U is presented for diverted discharges using the engineering CAD models utilized for PFC fabrication. Including these gyro-orbit effects can enhance the PFC performance by ‘smearing’ out the magnetic shadows associated with the castellated fish-scaled geometry. Simultaneously, the helical trajectories can degrade performance when they load narrow regions on edges and corners with high heat fluxes. Analysis of the trade-offs between these competing effects is included, and regions for further investigation are identified.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Tensor Text-Mining Methods for Malware Identification and Detection, Malware Dynamics Characterization, and Hosts Ranking

Malware is one of the most persistent and costly cyber threats endangering reputation, confidentiality, integrity, and availability for organizations and national security. Consequently, many of the incident detection and prevention systems, and incident responders have begun to utilize machine learning as a helper in the fight against malware and other cyber threats. However, cyber defenders rely on interpretability and generalizability, yet the popular machine learning methods are black-box and often use traditional supervised solutions that do not generalize to novel malware. Therefore, there is a need to improve the existing solutions. At the same time, the majority of the prior research ignored essential evaluation criteria when reporting the results of their methods, which disables the safe reproducibility of the methods in a production environment. Tensor decomposition, on the other hand, enables interpretable unsupervised analysis of the large-scale data for the discovery of hidden patterns. Our findings, performed on real-world and large-scale experiments, show that tensor factorization-based methods yield performance results that surpasses or competes with existing supervised solutions with the added benefit of interpretability and generalizability. With the ability to analyze complex and large-scale data using tensors, we report results that reflect real-world production environments. We propose to develop new game- changing tools for malware identification and characterization that can trace malware evolution, rank the infected or malicious hosts, and streamline the work of incident response teams, malware analysts, and incident detection and prevention systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A new form of the Saint-Venant equations for variable topography

The solution stability of river models using the one-dimensional (1D) Saint-Venant equations can be easily undermined when source terms in the discrete equations do not satisfy the Lipschitz smoothness condition for partial differential equations. Although instability issues have been previously noted, they are typically treated as model implementation issues rather than as underlying problems associated with the form of the governing equations. This study proposes a new reference slope form of the Saint-Venant equations to ensure smooth slope source terms and eliminate one source of potential numerical oscillations. It is shown that a simple algebraic transformation of channel geometry provides a smooth reference slope while preserving the correct cross-section flow area and the total Piezometric pressure gradient that drives the flow. The reference slope method ensures the slope source term in the governing equations is Lipschitz continuous while maintaining all the underlying complexity of the real-world geometry. The validity of the mathematical concept is demonstrated with the open-source Simulation Program for River Networks (SPRNT) model in a series of artificial test cases and a simulation of a small urban creek. Validation comparisons are made with analytical solutions and the Hydrologic Engineering Center's River Analysis System (HEC-RAS) model. The new method reduces numerical oscillations and instabilities without requiring ad hoc smoothing algorithms.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Spacetime pq theory for AC and DC electric power systems

The 50/60 Hz alternating current (AC) electric power has been the standard and most flexible energy source powering our modern societies for one and a half centuries since the war of the currents: AC versus direct current (DC). A reactive power concept that was introduced at the beginning of the AC power was very useful for circuit/system analysis, design, control, optimization, and ultimately for more efficient and stable generation, transmission, distribution, and consumption. The initial reactive power theory was based on single-phase sinusoidal AC power to capture inductive and capacitive power that yields to net-zero average power over one fundamental cycle. Soon it was expanded to non-sinusoidal AC power and finally to instantaneous three-phase AC power. However, these reactive power theories remain separate and limited to special cases and have never been consolidated and made valid to all cases. Today, more widespread adoption of power electronics and renewable energy is bringing back DC power into the electric grids. The reactive power concept has never been applied to DC power systems. There is no reactive power in DC power systems according to the existing reactive power theories. Do DC power systems really have no reactive power? Capacitors and inductors are widely used in DC just like in AC power systems. Are they not reactive power components? Why are they different from their AC counterparts? Furthermore, are batteries active or reactive power components? What about active devices like power converters (or inverters) with AC (or DC) on one side and DC (or AC) on the other? Do they generate or consume reactive power? Finally, what about AC and DC hybrid power systems? How to define reactive power in such a complex power system that has a multitude of loads, buses, and sources? Is there reactive power between any two loads, any two buses, or any two sources in a power system and what is the total reactive power in such a complex power system as a whole? As the motivation and goal of this paper to answer the above basic questions, to unify the existing AC reactive power theories and to ultimately provide theoretical and insightful guidance for system analysis, design, control, efficiency, optimization, and operation of complex power systems, a concept of spacetime (both spatial and temporal) active and reactive power (pq) theory—the spatiotemporal aspect of active and reactive power—is developed for both AC and DC power systems. The theoretical definitions and physical meanings of the spacetime reactive power will be developed, and real applications and thought experiments/cases/exercises will be explored and discussed. The developed mathematics to define the active (or real) and reactive (or imaginary) power— p and q respectively by dot (scalar) and cross (vector) products of multi-dimension spacetime vectors and time-space mapping principle/law can have some fundamental implications as well.

24 POWER TRANSMISSION AND DISTRIBUTION↗