Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Load flow”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Iterative Linearization for Phasor-Defined Optimal Power Dispatch

Optimal power flow (OPF) problems, which dispatch power targets to controllable generating units across a network, must generally account for non-convex constraints on power flow. Furthermore, adapting those problems so as to make them solvable with convex optimization techniques is an area of much academic and operational interest. In this paper, we present a method for solving OPF as a quadratic program by iteratively refining and re-initializing a linearized model of power flow based on the outputs of an associated nonlinear solver. The linear model on which we demonstrate this method is an adapted version of an approximation designed for use with unbalanced distribution networks. As an important benefit, the model allows for the explicit inclusion of nodal voltage phasor values in both the OPF problem's objective and its constraints, which opens the door to the idea of phasor-based control (PBC) design. We show in simulations on the IEEE 13-node test feeder that our method quickly converges to a set of phasor targets that are sufficiently precise for use in operations at the distribution level.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

AGGREGATE: dAta-driven modelinG preservinG contRollable dEr for outaGe mAnagemenT and rEsiliency (Final Report)

The AGGREGATE project team successfully developed and validated various modules for outage management. Brief summaries of each module are provided to showcase their strength for outage management and restoration for a distribution system with a high penetration of connected distribution energy resources (DERs). In recent years, inverter-based DERs have been widely deployed in distribution system. A most of behind-the-meter (BTM) solar power generation is not visible to the utility. The data-driven DER and load estimation modules are using machine learning (ML) and artificial intelligence (AI) to manage this issue, which provides an opportunity for distribution system operators (DSOs) to operate systems and make decisions in real-time for a distribution system with a high penetration of DERs deployed. Also, the estimated DER and true load can be further leveraged in network aggregation and cold-load pick up estimation for reducing the computing complexity and providing for fast restoration. After load demand and DER power generations have been estimated, the information will support topology and state estimation (SE). The topology estimation module demonstrated the viability of mixed integer linear programming (MILP) formulation to estimate the most likely operational radial topology and outage sections using power flow measurements, historical/estimated load and DERs data and smart meter ping measurements. Formulation includes continuous (power flow, load and DERs data) and binary measurements (smart meter ping measurements) in a single formulation. Errors in continuous data and binary data are modeled as normal distribution and Bernoulli distribution, respectively. In the future distribution grid, the power injection from controllable DERs will be essential for efficient and resilient grid operation. However, determining the optimal DER injections and restoration actions is dependent on knowledge of the system states. State estimation (SE), already the cornerstone of transmission energy management systems, will become commonplace in distribution management systems as more measurements become available from deployment of automated metering infrastructure (AMI). Observability analysis is the first step in SE, as it determines the sufficiency of the available measurements for accurately estimating the current system states. A new type of pseudo-measurement called a Correlational Measurement (CM) is introduced in this module, to enhance the observability of the system to enable more accurate SE. CMs encapsulate knowledge of correlation between demand patterns for similar classes of loads as well as injection patterns for same-technology renewable DERs. During grid contingency scenarios, DERs have been traditionally disconnected, without any fault ride-through capabilities. However, with new regulations and better technology, it is feasible for these resources to contribute to the grid’s restoration after an adverse event and hence enhance resilience. The controllability module proposes a two-step restoration scheme for the power system restoration process by leveraging additional degrees of freedom in power electronics interfaced DERs for mitigating voltage problems. In a resilience mode without the utility system, the distribution grid relies on DERs to serve critical load. In such a severe event with multiple faults on the distribution feeders, actuation of various protective devices (PDs) divides the distribution system into electrical islands. The undetected actuated PDs due to fault current contributions from DERs can delay the restoration process, thereby reducing the system resilience. The Advanced Outage Management (AOM) and the Advanced Feeder Restoration (AFR) modules developed in this project provide improved system resilience with multiple DERs. AOM identifies the faulted sections and actuated PDs in a distribution system with DERs by incorporating smart meter data. The most credible outage scenario including fault locations, PD actuations, and fault indicator (FI) failures is identified by a set of binary integer linear programming incorporating hypotheses. The AFR module serves to restore a distribution system with available energy resources taking into consideration the availability of utility sources and DERs. By partitioning the system into islands, critical load will be served with the available generation resources within islands based on the solution of a MILP. When the utility systems become available, the optimal path will be determined by a spanning tree search algorithm that reconnects these islands back to substations and restores the remaining load. The transmission and distribution (T&D) co-simulation module was used to validate the effect of a control action performed on the distribution side assets as it propagates to the transmission side. This ensures that the control action performed results in a feasible operating point on both the transmission and the distribution system. In addition to validation, the team used the T&D co-simulation module to demonstrate how distribution system assets can be used to mitigate issues on the transmission system. Specifically, the team demonstrated that appropriate switching operations on the distribution side can alleviate the line overload condition on the transmission side without causing new operational constraint violations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Quantifying particle movement in a spout-fluidized bed with irregular feedstock morphology

Here, the spout-bed fluidization behavior of nonspherical, 140 μm SiC feedstock was quantified via particle image velocimetry for varying gas distributor geometries. A bench-scale, room-temperature fluidization setup was assembled to model a 50 mm fluidized bed chemical vapor deposition (FB-CVD) system, and fluidized bed motion was captured using a high-speed camera. Modular tips with varying inlet geometries were 3D printed and tested on the bench-scale rig using identical feedstock and gas flow rates in the range of 3.0–9.0 L/min. Fluidization behavior was quantified by extracting parameters of the bed velocity, frequency, dead time, and other measurements, which were ranked for each inlet geometry configuration tested. The results from this work demonstrate that changing the path of inlet gas flow can significantly change the hydrodynamics within a spout-fluidized bed under identical feedstock, loading, and flow rate conditions, potentially enabling experimental control of particle fluidization behavior for a given condition. Moreover, composite rankings of fluidization behavior for unique distributor geometries hold potential to guide the design of FB-CVD experiments for various engineering and scientific applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Multi-Physics Investigation of a Natural Circulation Molten Salt Micro-Reactor that Utilizes an Experimental In-Pile Device to Improve Core Physics and System Thermal-Hydraulic Performance.

INL employee PhD Dissertation - The Molten Salt Reactor (MSR) concept is a rapidly evolving Generation IV design that has recently attracted favorable attention due to the potential for reducing waste generation, realizing passive safety features, and seizing on the opportunity for cost effective economics. This thesis investigates the performance benefit of a new device invented by the doctoral candidate. The device is referred to as a Wrapped Helix around an Inclined Plane or WHIP. The WHIP is protected under a provisional patent filed with the USA Patent Office on 28 September 2021 under application number 63/261,776, BEA docket number BA-1254. The WHIP device can be located in-core or near-core to promoted enhanced thermal-hydraulics and neutronics performance. While the WHIP can be employed in a variety of solid or liquid fuel designs, this thesis investigates the device’s benefit in the application of a natural-circulation, micro-molten salt nuclear battery concept (MsNB). This thesis will specifically investigate the temperature coefficient of the MsNB fuel (FLiNaK) using novel temperature sensitivity techniques unique to Serpent particle transport code, evaluate the WHIP’s thermal-hydraulic and neutronic performance effects using both established (STAR-CCM+) and novel (Python code developed to estimate the circulation effective delayed neutron fraction, ßef f ) analytical and numerical methods, evaluate the neutron noise behavior of the MsNB and how the WHIP may alter the character of the MsNB’s transfer function, and how the WHIP affects the autonomous, load-following performance under transient power conditions using Python code developed by the candidate. The sum body of this work, in part, has been published in three journal articles as the timing of the provisional patent process has allowed. Results show that creative utilization of WHIP engineering design and function reduces reactor system volume, fuel loading, control/stability in the buoyant regime

buoyant flow↗
DOE OSTI2024

High Frequency Monitoring and Nitrate Sourcing Reveals Baseflow and Stormflow Controls on Total Dissolved Nitrogen and Carbon Export Along a Rural‐Urban Gradient

Abstract Efforts to reduce nitrogen and carbon loading from developed watersheds typically target specific flows or sources, but across gradients in development intensity there is no consensus on the contribution of different flows to total loading or sources of nitrogen export. This information is vital to optimize management strategies leveraging source reductions, stormwater controls, and restorations. We investigate how solute loading and sources vary across flows and land‐use using high frequency monitoring and stable nitrate isotope analysis from five catchments with different sanitary infrastructure, along a gradient in development intensity. High frequency monitoring allowed estimation of annual loading and attribution to storm versus baseflows. Nitrate loads were 16 kg/km 2 /yr. from the forested catchment and ranged from 68 to 119 kg/km 2 /yr., across developed catchments, highest for the septic served site. Across developed catchments, baseflow contributions ranged from 40% of N loading to 75% from the septic served catchment, and the contribution from high stormflows increased with development intensity. Stormflows mobilized and mixed many surface and subsurface nitrate sources while baseflow nitrate was dominated by fewer sources which varied by catchment (soil, wastewater, or fertilizer). To help inform future sampling designs, we demonstrate that grab sampling and targeted storm sampling would likely fail to accurately predict annual loadings within the study period. The dominant baseflow loads and subsurface stormflows are not treated by surface water management practices primarily targeted to surface stormflows. Using a balance of green and gray infrastructure and stream/riparian restoration may target specific flow paths and improve management.

Delesantro, Joseph M.↗
DOE OSTI2021

Impact of particle loading and phase coupling on gas–solid flow dynamics: A case study of a two-phase, gas–solid flow in an annular pipe

The present study is devoted to a two-phase, gas–solid flow in an annular pipe (hollow cylinder) at an elevated pressure of 15 bars and moderate Reynolds number of circa 6000. The influence of the particle loading, the interaction between the phases, and turbulence dispersion on the flow dynamics is systematically studied by means of computational fluid dynamics simulations, employing the Ansys FLUENT commercial package. The cases with a particle volumetric fraction of 1.2% are referred to as “high particle loading,” and those with 0.13% are denoted as “low particle loading.” The following cases are investigated: (1) pure gas flow; (2) low particle loading two-phase flow with one-way coupling and with turbulence dispersion; (3) low particle loading two-phase flow with two-way coupling but without turbulence dispersion; (4) low particle loading two-phase flow with two-way coupling and with turbulence dispersion; (5) high particle loading two-phase flow with one-way coupling and with turbulence dispersion; (6) high particle loading two-phase flow with two-way coupling but without turbulence dispersion; and (7) high particle loading two-phase flow with two-way coupling and with turbulence dispersion. Additionally, the boundary layer is found to grow without fluctuations of the turbulent kinetic energy (TKE) for cases 1, 2, and 5. For case 4, the TKE fluctuations have been identified, although they appear to be less substantial than those in cases 6 and 7. The authors attribute the semi-chaotic nature of the TKE fluctuations to the particle loading and two-way coupling. In addition, the onset and development of the flow instability have been observed at a random axial distance in cases 4, 6, and 7. Such instability is also attributed to the two-way coupling with turbulence dispersion in the flow. It is concluded that the particle loading, one-way, or two-way coupling between the phases, and the turbulence dispersion models significantly influence the development of the flow dynamics with the same inlet and boundary conditions. Consequently, it is not a trivial question, which result a user should trust. The present computational results inspire to perform verification as well as experimental validation of the simulations, so the simulation results can subsequently be used with confidence for design analysis.

42 ENGINEERING↗
DOE OSTI2022

An Information Theoretic Approach to Identify Dominant Voltage Influencers for Unbalanced Distribution Systems

Smart distribution grid with multiple renewable energy sources can experience random voltage fluctuations due to variable generation, which may result in voltage violations. Traditional voltage control algorithms are inadequate to handle fast voltage variations. Therefore, new dynamic control methods are being developed that can significantly benefit from the knowledge of dominant voltage influencer (DVI) nodes. DVI nodes for a particular node of interest refer to nodes that have a relatively high impact on the voltage fluctuations at that node. Conventional power flow-based algorithms to identify DVI nodes are computationally complex, which limits their use in real-time applications. This paper proposes a novel information theoretic voltage influencing score (VIS) that quantifies the voltage influencing capacity of nodes with DERs/active loads in a three phase unbalanced distribution system. VIS is then employed to rank the nodes and identify the DVI set. VIS is derived analytically in a computationally efficient manner and its efficacy to identify DVI nodes is validated using the IEEE 37-node test system. It is shown through experiments that KL divergence and Bhattacharyya distance are effective indicators of DVI nodes with an identifying accuracy of more than 90%. Additionally, the computation burden is also reduced by an order of 5, thus providing the foundation for efficient voltage control.

42 ENGINEERING↗
DOE OSTI2021

AC Power Flow Based DLMP Calculation and Decomposition Method to Smooth Power Fluctuation of Distributed Renewable Energy Sources

As the penetration of renewable energy sources increases, the growing renewable power variability brings ramping issues to power systems. Meanwhile, the development of distributed energy resources (DERs) makes the distribution systems to provide both energy and ancillary services. To incentivise individual resources and customers to alleviate ramping issues on the demand side, a two-stage distribution locational marginal price (DLMP) calculation and decomposition method is developed to formulate the marginal power ramping price for DERs. In the first stage of the proposed method, a distribution system operator market scheduling model based on AC optimal power flow is designed to estimate the optimal operating point of the distribution system. Subsequently, the voltage and power flow constraints are linearised in stage two to calculate DLMP. Finally, based on the Lagrange function and sensitivity factors, DLMP is decomposed to the marginal costs for active/reactive power, voltage management, power loss and power variability. Case studies demonstrate that the proposed model can effectively smooth the power fluctuation and reduce the ramping flexibility requirements of distribution systems.

AC optimal power flow↗
DOE OSTI2023

Electrochemical Behavior of Low Loading Slurry Electrodes for Redox Flow Batteries

The scalability of all-iron redox flow batteries is limited by the plating reaction at the negative electrode on charge. Slurry electrodes have been proposed to allow the plated metal to remain dispersed in the electrolyte and alleviate this limitation. Greater understanding is needed in how faradaic current is distributed between the slurry and the stationary electrode/current collector, especially at relatively low slurry particle loadings. In this work, experiments were conducted using three carbon powders (Kuraray YP-50F, SGL Carbon GFG20HP, and Fisher Scientific GP14736) dispersed in aqueous acidic electrolyte to investigate the effects of slurry particle size, shape, composition, and loading on the behavior of the iron (II/III) reaction. The slurries of YP-50F carbon particles were shown to significantly enhance the faradaic reaction rate due to their high specific surface area but failed to pull the majority of the faradaic current away from the stationary electrode due to the low conductivity of the percolated network. The two graphitic carbons’ slurries did not accelerate the reaction in the same way, but their higher electrical conductivity did succeed in allowing the faradaic reaction to occur primarily on the mobile slurry instead of the stationary current collector.

25 ENERGY STORAGE↗
DOE OSTI2024

Joint Management and Optimization of Residential Natural Gas and Electricity Distribution Networks Coupled via Fuel Cells

The interesting properties of natural gas as well as the growing electric power demand worldwide have led to increasing attention to natural-gas-based distributed generation applications in electric distribution systems. This paper goes over the interdependency between a residential natural gas network and an electric distribution network that are coupled via fuel cells. The modeling of the gas network is introduced first, and then the algorithm for gas flow study is presented. The optimal placement and sizing of fuel cell based distributed generation systems are formulated to minimize the losses in both the gas and electric distribution networks, subject to their model constraints. In addition to this, in order to capture the probabilistic nature of the optimization problem under study, the K-means clustering algorithm is applied to the gas and electricity demands to determine hourly load states and their corresponding probabilities. Furthermore, simulation studies are carried out on an integrated system consisting of the IEEE 69-bus distribution feeder and a radial 27-node natural gas network to verify the developed optimization model and the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Joint Management and Optimization of Residential Natural Gas and Electricity Distribution Networks Coupled via Fuel Cells

The attractive features of natural gas as well as the growing electric power demand worldwide have created increasing interest in natural-gas-based distributed generation applications for electric distribution networks. Here, this paper investigates the interdependency between a residential natural gas network and an electric distribution network that are linked together via fuel cells. The modeling of the natural gas network is introduced first, and then the algorithm for gas flow study is presented. The optimal placement and sizing of fuel cell based distributed generation systems are formulated to minimize the losses in both the natural gas network and the electric distribution grid, subject to the constraints imposed by both networks. In addition, a probabilistic model for both gas and electricity demands is developed based on historical electricity and natural gas demand data. A K-means clustering method is used to determine the hourly load states to solve the joint probabilistic optimization problem. Simulation studies are carried out on an integrated system consisting of the IEEE 69-bus distribution network and a radial 27-node natural gas network to verify the developed optimization model and the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Adaptive Power Flow Approximations With Second-Order Sensitivity Insights

The power flow equations are fundamental to power system planning, analysis, and control. However, the inherent non-linearity and non-convexity of these equations present formidable obstacles in problem-solving processes. To mitigate these challenges, recent research has proposed adaptive power flow linearizations that aim to achieve accuracy over wide operating ranges. The accuracy of these approximations inherently depends on the curvature of the power flow equations within these ranges, which necessitates considering second-order sensitivities. In this paper, we leverage second-order sensitivities to both analyze and improve power flow approximations. We evaluate the curvature across broad operational ranges and subsequently utilize this information to inform the computation of various sample-based power flow approximation techniques. Additionally, we leverage second-order sensitivities to guide the development of rational approximations that yield linear constraints in optimization problems. In conclusion, this approach is extended to enhance accuracy beyond the limitations of linear functions across varied operational scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Top Loading Helium Cryostat Integrated with High-Pressure Cell with Fast Remote Pressure Control (Final Report for SBIR Phase 1)

A large number of physical phenomena, such as superconductivity and quantum critical phenomena, often appear only at very low temperatures below 5 K. There is an immense interest to investigate these phenomena at high pressure as a means of tuning interatomic distances, and thus the interaction parameters controlling these phenomena, in a continuous and controlled fashion. The current P-T condition for neutron scattering experiments are limited to either relatively low pressures of about 2 GPa at temperatures below 5 K, or to relatively high temperatures at pressures or tens of GPa. The purpose of this research is to develop neutron sample environment instrumentation for reaching 10-20 GPa at 1-2K with rapid and reliable online pressure and temperature control (i.e. without having to interrupt the experiment). The ultimate goal of the project is to design an integrated fast-cooling low-temperature sample environment cryogenic system compatible with state of the art neutron diamond anvil cells suitable for single-crystal neutron scattering experiments for temperatures down to 2K and pressures of several tens of GPa. The integrated system will consist of top-loading Helium flow cryostat with in-situ sample alignment mechanisms, large-volume diamond anvil cells (DAC) made from novel superalloy Pascalloy and optimized for fast cooling and heating, and a compact remote pressure control mechanism for the DAC based on a novel concept of inflatable bellows integrated with a lever-arm based force amplifier. In Phase I, we have designed, manufactured, and tested prototypes of the novel compact force-amplified pneumatic pressure control mechanism for Neutron Diamond Anvil Cell (nDAC), which allows to use pneumatic bellows system for smooth remote pressure control in the nDAC inside a top-loading cryostat with bore size of 70 mm or larger. This allows significant minimum temperature decrease in remotely controlled nDAC from 5-10 K down to 2 K. We also studied mechanical properties of a novel non-magnetic superalloy Pascalloy with different heat-treatment conditions and preliminary results indicate that up to date this is probably the strongest and most suitable material for making more compact and lightweight cryogenic nDACs for neuron scattering experiments at extreme conditions, allowing much faster cooling and heating. Potential applications: The new developments will allow to create a wide range of compact Diamond Anvil Cells for neutron diffraction which can reach several tens of GPA pressure at 2-4 K while preserving accurate remote pressure control capabilities. The new concepts can be used for developing sample environment instrumentation outside the neutron scattering field. The new development have very strong potential for expanding experimental capabilities in materials sciences and have high commercialization potential. The proposed new cryogenic high-pressure system or any of its individual components will be in high demand not only in neutron scattering facilities, but also at synchrotron beamlines and other high-pressure research facilities around the world.

36 MATERIALS SCIENCE↗
DOE OSTI2021

VSC-HVDC Interties for Urban Power Grid Enhancement

Urban power grids are facing many operational and expansion challenges to meet further demand growth and increased reliability requirements. Advanced transmission technologies have been considered by the electric utilities to effectively increase the utilization of existing infrastructure and operational flexibility. The focus of this paper is on VSC-HVDC technologies for urban power grid enhancement and modernization. First, a potential technical scheme is proposed for converting an existing AC circuit to DC operation, which could boost the power transfer capability of the critical transmission corridor and increase network operational flexibility. Second, this paper proposes three operation modes for the VSC-HVDC interties in urban power grids corresponding to normal, emergency and island operating conditions, respectively. An integrated, adaptive emergency control strategy (AEC) is proposed that can enable adaptive power flow responses of the VSC-HVDC intertie under varying system operating conditions and critical contingencies. The flexibility and effectiveness of the proposed operational principles of urban VSC-HVDC intertie and the corresponding control strategies are verified in PSCAD/EMTDC using a realistic urban power grid in China.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.

approximation algorithms↗
DOE OSTI2021

DC-Saturated Continuously Variable Series Reactors (CVSRs) for Power Flow Control in Power Transmission Systems

This paper proposes a novel continuously variable series reactor (CVSR) based on a dc current controller (DCC) to manage power flow in transmission systems. There are three major contributions. First, the three-dimensional electromagnetic interaction has been comprehensively analyzed to extend the understanding beyond the conventional 2D relationship. Second, a high-fidelity reluctance model of the CVSR with an improved DCC model is proposed and implemented. To overcome the fundamental concern for the system modeling, the DCC has been modeled as an ideal current source in parallel with an output impedance. Additionally, the induced back-EMF can be precisely projected which provides critical design guidelines for the DCC. Third, inspired by the theoretical analysis and modeling, a reliable high power DCC converter is designed accordingly to interface with kV-level back-EMF and supply kA-level dc current for a 115 kV/1500 A CVSR. Experiments are conducted in a practical transmission demonstration system. When the ac current in the transmission system varies from zero to 1500 A, experimental results show that the proposed CVSR can continuously regulate the reactance from 1.6 Ω to 5 Ω, validating the effectiveness of the proposed system design and modeling methodology.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Estimation of process steady state with autoregressive models and Bayesian inference

To improve efficiency, separations engineers will typically design process circuits containing recirculating streams, which mix one or more of the process outputs with the feed material. Doing so can improve efficiency, but will cause a delay in the system reaching steady state conditions until the recirculating load mass flows stabilize. In testing separation circuits, engineers will often test a variety of factors and complete an analysis from sample results. Knowledge of if a process is at steady state, as well as the steady state conditions of a process, is essential for a valid techno-economic analysis. However, the definition of process steady state is often poorly defined, or does not include uncertainty quantification. If the performance of a process operating under two different sets of conditions are compared, an engineer who does not test for steady state or quantify steady state conditions risks producing a faulty analysis. In this work, a Bayesian statistical method for testing if all streams are at steady state is further motivated and then derived. Then after testing for steady state, the same model is used with a prior distribution that enforces a steady state assumption to estimate steady state conditions. Further, these methods were validated in a solvent extraction pilot plant where steady state conditions for all outflows were inferred with uncertainty quantification. Analysis is completed with functions available to the reader as part of the BayesMassBal (V 1.1.0) software package written in R.

01 COAL, LIGNITE, AND PEAT↗