Steady-state Power Distribution Research Articles

Sequential power flow algorithm and post-event steady-state power distribution analysis in hybrid AC/MT-MVDC systems

In hybrid ac/multi-terminal medium-voltage dc (AC/MT-MVDC) systems with multiple voltage source converters (VSCs) and dc/dc converters, it is essential to attain accurate initial power flow (PF) and post-event power distribution solutions efficiently. This paper proposes: (i) a novel sequential PF algorithm for hybrid AC/MT-MVDC systems by a Fibonacci search-based Newton–Raphson (FSNR) approach with uniform MVDC bus type definition, while considering power losses and varied control schemes of different converters; (ii) a zero error steady-state post-event power distribution calculation method under droop control by the introduction of dynamic I/V droop coefficients based on the FS algorithm. The FSNR approach simplifies the MVDC PF derivation by only requiring the definition of the dc current bus type, effectively eliminating the need to solve multiple sub-Jacobian matrices. Furthermore, the post-event power distribution analysis offers precise power redistribution calculation approach following disturbances by considering both open- and closed-loop operation in an MT-MVDC distribution system. The computational efficiency and validity of the proposed PF algorithm, along with the accuracy of presented post-event power distribution calculation method are verified through Python and RTDS real-time simulators in an extended MT-MVDC distribution network incorporated with the IEEE 14/33/69 bus transmission/distribution systems.

Theoretical and experimental investigation of the steady-state power distribution in multimode step-index plastic optical fibers

In this work we have examined theoretically and experimentally the influence of mode coupling on steady-state distribution (SSD) in step-index plastic optical fiber (SI POF). Numerical and analytical solution of the PFE under steady-state conditions are compared to our experimental results. A numerical solution of the power flow equation (PFE) has been obtained by the explicit finite difference method (EFDM). We demonstrated that SSD in the SI POF is achieved at length of 140 m, which is much shorter length compared to the case with silica fibers. The reported results appear to be particularly important since none of the main optical properties of an optical fiber (attenuation, bandwidth) can be accurately determined until the transmitted optical power reaches its SSD, due to strong influence of mode coupling phenomena that occur during the transmission process. These results are important for employment of the SI POFs as a part of communication or sensory systems.

Steady-state power distribution in VSC-based MTDC systems and dc grids under mixed P/V and I/V droop control

This paper proposes a steady-state power distribution derivation method for voltage source converter (VSC)-based multi-terminal HVDC (MTDC) systems and dc grids under mixed power/voltage (P/V) and current/voltage (I/V) droop control. P/V and I/V droop control are two commonly used control schemes, which can be combined to achieve co-regulation of powers & currents in MTDC systems and dc grids. The proposed method can be used to estimate the power distributions under different scenarios for MTDC systems and dc grids based on VSCs with mixed P/V and I/V droop control. After determining the initial operating point based on an estimation-correction algorithm, redistributed power due to power disturbances, current changes or converter outages is analyzed in detail considering converter overload. An excess power reduction strategy is further proposed to avoid violation of power limits after converter outage. The accuracy of the proposed method is validated through multiple scenarios in a modular multilevel converter (MMC)-based four-terminal dc grid. The comparison between the proposed method and other approaches in the current literature further demonstrates the advantages of proposed power distribution derivation method. • Determination of initial operating point for mixed P/V and I/V droop control by proposed estimation-correction algorithm. • Derivation of power redistribution after dc power/ current reference changes and converter outages. • Consideration of possible converter overloads caused by different system disturbances.

Optimal Load Distribution in DG Sources Using Model Predictive Control and the State Feedback Controller for Switching Control

The distributed energy management of interconnected microgrids, which is based on model predictive control (MPC), relies on the cooperation of all the agents (i.e., microgrids). Model predictive control or MPC is widely used in industrial applications as an effective tool for dealing with multivariable limited control problems. MPC uses an explicit system model to predict the future horizon of the system and its outputs. This predictability allows calculating the optimal order of inputs to minimize output errors over a limited horizon, which is effected by the limitations of the system. This study presents a distributed economic model predictive control method using the new state feedback controller to control the switching of interface converters and compensate for the unbalanced and nonlinear loads. In this model, the islanding mode and the reconnection of the grid are considered to improve the transient behavior of the system to achieve steady-state power distribution. It has been proposed that it could obtain better results in predictive control, utilizing similarity transform in the state matrix and its modification. First, this model is simulated on distributed generation sources with power-sharing and local loads using the state feedback controller in MATLAB Simpower. Then, the performance of the proposed method is evaluated, confirming that it is more reliable than the FS-MPC and DSVM-MPC methods.

Benchmark Analysis on Loss-of-Flow-without-Scram Test of FFTF Using Refined SAC-3D Models

The Fast Flux Test Facility (FFTF) is a liquid sodium-cooled nuclear reactor designed by the Westinghouse Electric Corporation for the U.S. Department of Energy. In July 1986, a series of unprotected transients were performed to demonstrate the passive safety of FFTF. Among these, a total of 13 loss-of-flow-without scram (LOFWOS) tests were conducted to confirm the liquid metal reactor safety margins, provide data for computer code validation, and demonstrate the inherent and passive safety benefits of specific design features. In our preliminary work, we have performed relatively coarse modeling of the FFTF. To better predict the transient behavior of FFTF LOFWOS test #13, we modeled it using a more refined thermal-hydraulics model. In this paper, we simulate FFTF LOFWOS test #13 with the system safety analysis code SAC-3D according to the benchmark specifications provided by Argonne National Laboratory (ANL). The simulation range includes the primary and secondary circuits. The reactor core was modeled by the built-in 3D neutronics calculation module and the parallel-channel thermal-hydraulics calculation module. To better predict the reactivity feedback introduced by coolant level variations within the GEMs, a real-time macro cross-section homogenization processing module was developed. The steady-state power distribution was calculated as the transient simulation initial boundary conditions. In general, both the steady-state calculation results and the whole-plant transient behavior predictions are in good agreement with the measured data. The relatively large deviations in transient simulation occur in the outlet temperature predictions of the PIOTA in row 6. It can be preliminarily explained by the reason for neglecting the heat transfer between channels in this model.

Transient analysis of the Brazilian Multipurpose Reactor by the coupled neutronics and thermal hydraulics code NTHC1

Dynamical behavior of the Brazilian Multipurpose Reactor (RMB) is investigated by using the coupled neutronics and thermal hydraulics code NTHC1, which consists of the neutron point kinetics (NPK) equations with six groups of delayed neutrons, the heat conduction equations in a fuel plate, and the energy transport equation in a coolant subchannel. The Serpent 2 Monte Carlo code is employed to calculate the RMB kinetic parameters of the NPK equations and steady state power distribution. Improved lumped formulations are adopted for heat conduction in the transversal direction of the fuel and cladding, while the fluid energy equation is discretized along the subchannel by finite difference method. The resulting system of ordinary differential equations is solved by numerical method. The NTHC1 code was verified against the IAEA 10 MW MTR benchmark problems, showing good agreement with literature data. The simulation results demonstrated that RMB operates safely under the postulated initiating events (PIE) of loss of flow and reactivity insertion.

Capacitor Bank Sizing for Squirrel Cage Induction Generators Operating in Distributed Systems

The design of the capacitor bank to be placed with the squirrel cage induction generator, when operating with a direct connection to the distribution system, is performed from the value of the magnetization reactance of the machine. Based on the experimental procedures, the necessary reactive power is simulated according to the induction generator loading. Therefore, with the increase in generated active power, a larger portion of reactive is required. The simulation indicates the values of ideal capacitors. Thus, an analysis is made of which magnetization reactance factor is ideal for the capacitor bank design designated for the generator. The characteristic curve for capacitor bank sizing is related to the load torque loading depending on the active power generated. Thus, this work contributes to the analysis of the self-excitation curve of the three-phase induction generator that operates in parallel with the steady-state power distribution network. Obtaining the active power generated as a function of the absorbed reactive power required for induction generator magnetization can be found.

Research on steady-state power distribution calculation technology of electrothermal coupled regional energy system

When large-scale power grids are connected to the power grid, it is conceivable that adverse effects on the operation and planning of power grids can be imagined. Therefore, wind power has characteristics such as intermittency, volatility, anti-peaking characteristics, and large prediction errors. At the same time, the ability to absorb wind power is also weakened by the contradiction between the peak load and the heating load. In addition, due to the thermo-electric coupling characteristics of the cogeneration unit, ie, “heating with electricity,” this characteristic directly determines that its heat output severely limits the regulation of the electric output. The results of the study indicate that the co-production unit’s electric power and thermal power are coupled. Strong nature, the peak load capacity of the unit is greatly affected by the heat load, and the electric power and thermal power distribution lacks a unified calculation and analysis method, which restricts the means of improving the peaking capacity of the unit by controlling the thermal power output of the unit, and through implementation, establishes the main power equipment, The steady-state power model of the thermal equipment, the steady-state power analysis and calculation method of the regional energy system of the power thermocouple, and the realization of adjusting the thermal load related parameters to improve the peak capacity of the thermal power unit.

Model Averaging and Feedforward Temperature Control in an Oscillating Annealing Furnace

The impact of an oscillating motion on the temperature uniformity of a specimen in an experimental annealing furnace is analyzed. For the specimen temperature, three feedforward control strategies using dynamic optimization are developed and compared. The controllers provide reference signals to electrically powered infrared lamps to ensure optimal temperature trajectories. In the first controller design, no specimen oscillation is considered. This design uses an amplified adjustment of the steady-state power distribution obtained from static optimization. The second and the third controller are developed for an oscillating specimen. Both these controllers are designed on the basis of a dynamic optimization problem, where in addition to the amplification factor the constant power distribution serves as additional degree of freedom. While the second controller takes into account the oscillating motion directly, the last approach utilizes time averaging of the model equations. An evaluation of all controllers is carried out with an experimentally validated model. This analysis shows that the temperature uniformity can be significantly improved when the specimen oscillates.

Feedforward Control of the Temperature Field in an Experimental Annealing Furnace

Two feedforward control strategies for an experimental annealing furnace equipped with electrically powered infrared (IR) lamps are developed and compared. For the first controller, the optimal time evolution of the electric power supplied to IR-lamps is computed from a dynamic optimization problem. This ensures optimal temperature trajectories and temperature uniformity in the specimen fillet. The second controller is based on an amplified adjustment of the steady-state power distribution obtained from static optimization at an operating point. Here, the temperature uniformity during transients is traded-off against the computing time while still ensuring the best temperature uniformity at the final temperature level. For both strategies, a tailored control-oriented reduced-order model of the 2D spatial-temporal temperature evolution is used. The evaluation of the feedforward controllers is carried out with an experimentally validated simulation model. The temperature non-uniformity during transients is less than 0.9 % and reduces to 0.3 % of the setpoint value at the steady state.

Advances in H-mode physics for long-pulse operation on EAST

Since the 2012 International Atomic Energy Agency Fusion Energy Conference (IAEA-FEC), significant advances in both physics and technology has been made on the Experimental Advanced Superconducting Tomakak (EAST) toward a long-pulse stable high-confinement (H-mode) plasma regime. The experimental capabilities of EAST have been technically upgraded with the power enhancement (source power up to 26 MW) of the continuous-wave heating and current drive system, replacement of the upper graphite divertor with an ITER-like W monoblock divertor, and installation of a new internal cryopump in the upper divertor and a set of 16 in-vessel resonant magnetic perturbation (RMP) coils. This new upgrade enables EAST to be a unique operating device capable of investigating ITER-relevant long-pulse high-performance operations with dominant electron heating and low torque input within the next 5 years. Remarkable physics progress in controlling transient and steady-state divertor heat fluxes has been achieved on EAST, e.g. (i) edge-localized mode (ELM) mitigation/suppression with a number of attractive methods including lower hybrid wave (LHW), supersonic molecular beam injection (SMBI), RMPs, and real-time Li aerosol injection; and (ii) active control of steady-state power distribution by the synergy of LHW and SMBI. In the 2014 experimental campaign, a long-pulse high-performance H-mode plasma with H98 ∼ 1.2 has been obtained with a duration over 28 s (∼200 times the energy confinement time). In addition, several new experimental advances have been achieved in the last EAST campaign, including: (i) high-performance H-mode with βN ∼ 2 and stored plasma energy ∼220 kJ; (ii) H-mode plasma sustained by neutral beam injection (NBI) alone or modulated NBI with lower hybrid current drive (LHCD), for the first time in EAST; (iii) high current drive efficiency and nearly full noninductive plasmas maintained by the new 4.6 GHz LHCD system; (iv) demonstration of a quasi-snowflake divertor configuration; and (v) observation of a new edge-coherent mode and its effects on edge transport in H-mode plasmas.

A Study on Boiling Water Reactor Regional Stability from the Viewpoint of Higher Harmonics

A quantitative study on a mechanism for boiling water reactor regional stability has been carried out from the viewpoint of higher harmonics. In the mechanism, the gain decrease in the void-to-power transfer function can be explained by the higher harmonics mode subcriticality. It is shown that the thermal-hydraulic feedback effect can compensate for the gain decrease, and regional oscillation can be sustained that way. For quantitative evaluations, a three-dimensional higher harmonics analysis model has been developed. The results show that the first azimuthal harmonics subcriticality has a relatively small value under a regionally unstable condition. Comparing the subcriticality and the steady-state power distribution, it is shown that the distribution exists whose first azimuthal harmonics subcriticality takes a small value. A method of decomposition for the oscillated power responses into the harmonics modes is presented. The results show that the corewide oscillation power response consists almost entirely of the fundamental mode, and the regional oscillation power response consists almost entirely of the first azimuthal harmonics mode. This indicates that regional oscillation is a phenomenon in which the first azimuthal harmonics mode oscillates on the basis of the fundamental mode.

Measuring fiber connection loss using steady-state power distribution: a method

This paper describes conditions for the reproducible measurement of optical fiber connection losses. The steady-state power distribution is characterized by the width of the far-field pattern (FFP). A method is proposed to determine the power distribution in the fiber from the measured FFP. Using this method, connection losses of graded-index fibers are calculated for various widths of the FFP. Calculated results are verified experimentally. The width of the FFP must be controlled to within an accuracy of 3% for a 0.05-dB reproducibility of the connection loss. Connection loss dependence on mismatch of fiber parameters is also calculated. Calculation shows that variations in core radius, numerical aperture, and index gradient have to be controlled to within 3%, 6%, and 0.3, respectively, for the same reproducibility.

A ray approach to scattering in optical fibres

The problem of scattering in optical fibres is approached by means of a ray theory and by considering both the parameters that characterize each ray congruence. Starting from a general transport equation a two-variable diffusion equation is derived and its field of validity is discussed. Preliminary results (steadystate power distribution among ray congruences; steady-state attenuation and steady-state length) are given in some simple but common cases. These results permit interesting comparisons with other theories.

Excitation of steady-state power distribution in parabolic-index fibres by Gaussian TEM00-beam

At z = 0 a power distribution may be excited by a Gaussian TEM00 beam in a parabolic-index fibre in which each group of modes with a given propagation constant carries the same power as prescribed by Olshansky's steady-state distribution. This power distribution, however, still depends on both mode numbers ν, μ. Such an excitation may be advantageous for measuring losses in fibres and coupling elements.

Pulse Propagation in a Two-Mode Waveguide

The results of an earlier paper, describing pulse propagation in multimode dielectric waveguides with random coupling, are specialized to the two-mode case. Because of their greater simplicity, the results for this special case provide more insight into the mechanism of pulse shortening due to mode coupling. The two-mode theory yields a formula for the width of a pulse carried by coupled guided modes that is found to hold also for four modes, so that it may be true for an arbitrary number of modes. This formula [eq. (23)] contains only the measurable distance required to establish the steady-state power distribution and the length of uncoupled pulses. The pulse length formula is identical with Personick's important result. Our treatment suggests that the characteristic length appearing in this formula may be accessible to measurement.