Ramp Rate Limits Research Articles

Simulation of the ITER-CS coil operation including the effect of the ramp rate limitation

A model to simulate conductor performance of the Central Solenoid (CS) coil of the International Thermo-nuclear Experimental Reactor (ITER) is discussed. The conductor for the ITER-CS coil consists of multistage cables, where a non-uniform current distribution may be expected during operation which affects the stability of the conductor. A probable mechanism for the non-uniform distribution in a pulsed coil is flux loops between the strands or cable substages as the current is ramped up or down. A model for this distribution is presented. Simulations are then performed to quantify the effect of parameters, such as the unbalanced voltage of each strand caused by the flux loops, on the stability limit of the ITER-CS coil.

Voltage spike observation in superconducting cable-in-conduit conductor under ramped magnetic fields: 1. Experiment

A 27-strand hybrid superconducting cable-in-conduit conductor (CICC) was fabricated and tested under quickly-ramped high magnetic fields. When the field increased linearly on the CICC, the voltage signal showed several intermittent spikes before it quenched. This paper describes an observation of peculiar voltage spikes during these ramp-rate limitation experiments. The voltage spikes are interpreted as quench precursors and understood as current redistribution events within the local cable inside the conduit. A quantitative correlation is obtained for the magnetic field at which the first voltage spike occurs during ramping fields. The non-uniform current distribution among the strands and the induced loop current in the cable, which is generated by ramped fields, are found to be responsible for the voltage spikes.

Ramp-rate limitation experiments using a hybrid superconducting cable

Ramp-rate limitation experiments were done in a new facility at the MIT (Massachusetts Institute of Technology) Plasma Fusion Center. The features of this new facility include (1) a superconducting pulse coil that can superimpose high ramp-down rates, up to 25 T s −1, (2 T in 80 ms) at a background field up to 5 T, (2) new power supplies that can supply high rates of dl dt and dB dt to the sample under test and (3) a forced-flow supercritical helium system for cooling CICCs (Cable-In-Conduit Conductors). This paper discusses the results of the ramp-rate limitation experiments on a 27-strand hybrid Nb 3Sn cable. The cable was tested under field ramps of up to 2.5 T s −1 with various operating currents. It did not quench with dB dt , field and average strand currents that were simultaneously above the operating range of TPX-PF (Tokamak Physics Experiment Poloidal Field) coils. Further ramp-rate limitation experiments revealed that the tested 27-strand hybrid cable has very high transient stability at ramped fields, extending out to average strand currents that are nearly triple the TPX-PF operating current.

A possible explanation of the problem of ramp rate limitation in large superconducting magnets

Unexpected ramp rate limitations were found in large superconducting magnets for fusion experiments as well as in accelerator magnets. In this paper it is shown that a variation of the field sweep rate dB/dt along the length of a superconducting cable induces superposed extra coupling currents flowing over long lengths. These lead to a highly nonhomogeneous current distribution in the cable and to additional coupling losses (supercurrent losses), even in magnet sections with dB/dt=0. These both effects may drastically reduce the stability of a magnet during fast ramp up. The solution of the diffusion equation allows us to calculate the space and time dependence of supercurrents as well as of supercurrent losses. The time constants of supercurrents are many orders of magnitude larger than typical coupling time constants of a superconducting cable. The proposed model can explain typical results of ramp rate limitations in large magnets.

The Polo coil, a prototype tokamak poloidal field coil, design features and test results

A prototype tokamak poloidal field coil of 3 m diameter was successfully tested. The coil was designed to withstand typical field transients like fast ramping, plasma controlling and plasma disruptions. In order to achieve these requirements, a low loss conductor was developed. The coil with its components was designed according to rules of high voltage technology. A realistic test of the magnet requires at 23 kV a current of 15 kA, that means a peak power of 345 MW. Therefore, a fast switching circuit was used combined with an additional current lead at the middle of the magnet winding. This allowed the performance of fast field changes with increasing or decreasing field. In one operation mode, the coil was discharged into a dump resistor. In another operation mode, only one coil half is discharged which generated a field increase in the second short circuited half of the coil. Discharging time constants of 1 ms and local field sweep rates of about 240 T/s were obtained without quench. A reproducible and sharp quench boundary was found. The results showed clearly that ramp rate limitations are only given by the expected stability limit or the load line boundary.

Stability of a poloidal field coil in rapidly changing magnetic fields

A poloidal field model coil of 3 m in diameter was designed and built according to the following specifications: stability was required during an exponential field variation of /spl Delta/=0.4 T with a time constant of 5 ms, corresponding to a maximum field change of 80 T/s. The superconducting cable developed for this purpose was tested in a short sample experiment, yielding a stability limit beyond this requirement. The test results of the model coil are in good agreement with the stability limit expected from the cable experiment. They can be explained in terms of a simple stability model which compares the energy input due to coupling losses with the transient heat removal capability of supercritical helium. A more detailed stability calculation was performed with a computer code taking into account the temperature dependence of helium and conductor material properties. The coil reached the stability limit expected from the measured cable parameters and showed no unexpected ramp rate limitations.

Ramp-rate limitation in large superconducting magnets due to ‘supercurrents’

Unexpected ramp-rate limitations were found in large superconducting accelerators magnets as well as in magnets for fusion experiments. We show in this article that the variation of the field sweep rate dB dt along the length of a superconducting cable induces extra coupling currents which flow over long lengths. Their time constants are many orders of magnitude larger than the time constant of ‘ordinary’ coupling currents. These ‘supercurrents’ can lead to a highly inhomogeneous current distribution in the cable. They furthermore create additional coupling losses (‘supercurrent losses’), even in magnet sections where dB dt = 0 . Both of these effects may drastically reduce the stability of magnets during fast ramping up. It is shown that ramp-rate limitations measured in accelerator dipoles can clearly be attributed to the proposed effects. Experimental data that remained unexplained can thus be understood. This article gives the complete solution of time and space dependence of supercurrents and supercurrent losses in the approach of a two-wire model cable, which is obtained by solution of the diffusion equation.

Interruptible load management using optimal power flow analysis

An interruptible load management (ILM) scheme is proposed using dynamic optimal power flow analysis. It enables real-time selection of interruptible loads incorporating power network constraints and dynamic restriction on generation, viz. ramp-rate limits. The model provides an analytical framework for addressing several important issues associated with optimal selection of load curtailment, e.g. advance notification for load curtailment, short-term price discounts and long-term discounts on demand-charges, power factor of the load and customer-cost associated with the load to be curtailed, and power system security. A six-bus example illustrates the proposed methodology.

Investigation of critical parameters for the stability of AC magnets

Abstract Testing the POLO coil ( O = 3 m, U N = 23 kV, I N = 15 kA), a prototype coil for generating the poloidal field in a tokamak, no ramp rate limitation (RRL) was observed. Such a phenomenon can be attributed to a current imbalance amongst the cabled strands or subcables leading to a lower than expected quench current. The achievement of discharge time constants of 2 ms and local field change rates of 240 T/s without quench is mainly attributed to the design of the POLO conductor, a low loss conductor with a central cooling channel. Motivated by the well defined symmetrical structure of the conductor and winding, a model for calculating the current distribution in one half of the coil was developed. In superconducting magnets the current distribution during ramping depends on the electromagnetic system properties. Therefore, the model considers the complete inductance matrix of the cable and the fact that all turns are mutually coupled. Its validity was confirmed by simulating and measuring quench propagation processes during the POLO experiment. By means of that model a detailed analysis of principle causes for RRL phenomena in superconducting magnets was performed. In this paper the results of these investigations are presented. It is shown that unequal contact resistances can not be responsible for RRL in coils with parameters comparable to those of the POLO coil and that already minor geometrical disturbances in the cable structure can lead to major and lasting imbalances in the current distribution of cables with insulated and non-insulated strands. The simulations demonstrate that the electrodynamics of subcable current distribution in short sample cable experiments differ extremely from the ones in a coil, so that such experiments do not seem to be suited for an analysis of the causes for RRL in superconducting magnets.

Co-ordinated economic and advance dispatch procedures

The paper deals with the problem of improving co-ordination between the online economic dispatch (ED) function and the very short-term advance dispatch (AD). Both procedures are formulated as optimal dispatching problems, but while a static model is used for the ED function, a dynamic model is employed in AD. The need to account for ramp-rate limits of thermal power generation even in the ED phase is satisfied by adding suitable penalty terms to the objective function of the classical ED problem. These penalties are proportional to the Lagrange multipliers associated with ramp-rate limits that are active at the AD solution. An efficient updating procedure is used to correct the penalization by taking the load forecast errors into account. The proposed co-ordination procedure can provide the snapshot ED with the long range perspective of AD without resorting to heuristic approaches. The procedure is validated by extensive testing carried out both on a small CIGRE test case and on a medium-large scale network representative of the Italian EHV system. Moreover, test results show that the CPU time requirements of the modified ED procedure are still suited to online applications.

Large-scale economic dispatch by genetic algorithm

This paper presents a new genetic approach for solving the economic dispatch problem in large-scale power systems. A new encoding technique is developed. The chromosome contains only an encoding of the normalized system incremental cost in this encoding technique. Therefore, the total number of bits of chromosome is entirely independent of the number of units. The salient feature makes the proposed genetic approach attractive in large and complex systems which other methodologies may fail to achieve. Moreover, the approach can take network losses, ramp rate limits, and prohibited zone avoidance into account because of genetic algorithm's flexibility. Numerical results on an actual utility system of up to 40 units show that the proposed approach is faster and more robust than the well-known lambda-iteration method in large-scale systems.

Theory of ‘‘supercurrents’’ and their influence on field quality and stability of superconducting magnets

Unexpected periodic variations of the magnetic field were recently found along the axes of superconducting accelerator magnets. This modulation, which reduces the field quality of the magnets, shows a complex space and time dependence containing very long time constants. We show in this article that the variation of the field rate dB/dt along the length of a superconducting cable induces superposed coupling currents which flow over a long length. The space and time dependence of these ‘‘supercurrents’’ for a two-wire cable model is obtained by the solution of the diffusion equation with the diffusivity given by the cable parameters. The existence of supercurrents explains the observed effects in accelerator magnets. It is furthermore shown that supercurrents can lead to a highly inhomogeneous current distribution over the cable cross section and to additional coupling losses, even in sections of the magnet where dB/dt=0. Both these effects can reduce the stability of magnets, which may explain the ramp rate limitation found in accelerator magnets as well as in large magnets for fusion research.

On stability of multistrand cables with insulated or highly resistive matrix strands

The stability of multi-strand superconducting cables or cables-in-conduit is degraded by rapid changes in current or field (ramp rate limitation or current degradation). The maximum achievable AC current is significantly less then the sum of DC critical currents of strands. Measurements of the dependence of quench current on ramp rate were made for one, two, and three strand cables. Samples had different strand types and lengths. It was shown that although the theory of thermomagnetic instability explains single strand performance very well, it does not explain the reduction of quench current observed in multi-strand cables. The influence of joint resistance between cable strands and current leads is shown to be the most probable reason for the reduction. >

Ramp-rate limitation test of cable-in-conduit conductors with supercritical helium

It has been found on the United States Demonstration Poloidal Coil (US-DPC) and in 27 strand subsized cables of pool boiling cable-in-conduit conductor (CICC), that there is critical current degradation due to fast ramping of the magnetic field. The characteristics of this ramp-rate limitation phenomenon are investigated by using a 27 strand Nb/sub 3/Sn cable in supercritical helium at 6 atm. A 3 m long cable-in-conduit conductor is prepared noninductively and tested in a background field up to 9.5 tesla with maximum ramp rate of 1.6 tesla/second. The ramp-rate limitation results are compared with results of the ramp rate test of the US-DPC and previous experiments. The experimental data are analyzed to identify and understand possible sources of ramp-rate limitation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

New method of current distribution studies for ramp rate stability of multistrand superconducting cables

The ramp rate limitation phenomena were studied using local field sensors to observe the intrinsic processes within the cable. Sensitive miniature Hall sensors and small pick-up coils placed around cable-in-conduit superconductor were used to measure local magnetic fields and field derivatives associated with currents in the cable. Using this method, both fast jumps and slow changes in local magnetic fields at different conditions mere observed. First jumps occured during ramping background magnetic field and may indicate a fast current redistribution processes. Slow changing of local fields may be associated with current loops closed through the current lead joints. Such current loops may also indicate the nonuniformity of current distribution in the cable strands. The new method is a promising tool for future investigations of stability of multistrand cables.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

FENIX experimental results of large-scale CICC made of bronze-processed Nb/sub 3/Sn strands

The Fusion Engineering International Experiments (FENIX) Test Facility has successfully completed the testing of a pair of Nb/sub 3/Sn cable-in-conduit conductors developed by the Japan Atomic Energy Research Institute. These conductors, made of bronze-processed strands, were designed to operate stably with 40-kA transport current at a magnetic field of 13 T. In addition to the measurements of major design parameters such as current-sharing temperature, FENIX provided several experiments specifically designed to provide results urgently needed by magnet designers. Performed experiments include measurements of ramp-rate limit, current-distribution, stability, and joint performance. This paper presents the design and results of these special experiments.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Review of stability experiments on cable-in-conduit conductors

The stability of a cable-in-conduit conductor (CICC) cooled with supercritical helium can be very high if it is operated below a certain limiting current. This limiting current can be determined by a Stekly type heat balance equation. However, an effective heat transfer coefficient that depends not only on the conductor and the coolant, but also on the heating condition, should be used in the equation. By reviewing the stability experiments performed on CICCs, it is shown that, depending on the effectiveness of the heating induced flow, the effective heat transfer coefficient can be as low as 400 W m −2 K −1 or as high as 1400 W m −2 K −1. Based on this review, conclusions and comments are made with regard to the permissible current density, ramp rate limitation and dual cooling channel in a CICC.

Ramp-rate limits in unit commitment and economic dispatch incorporating rotor fatigue effect

In this study, a rigorous mathematical method is proposed for dealing with the ramp-rate limits in unit commitment and the rotor fatigue effect in economic dispatch. An iterative procedure is employed to coordinate the unit commitment and the power dispatch for obtaining an economical solution within a reasonable time. The Lagrangian relaxation method is used to generate the unit commitment schedule with relaxed power balance constraints. A network model is adopted to represent the dynamic process of operating a unit over the entire study time span, as the required unit commitment schedule can be achieved by searching for the shortest path in the network. In order to find the global optimal solution for the economic dispatch problem within personal computer resources, a piecewise linear model is used for thermal units. Furthermore, linear programming is used in optimizing the benefits of ramping the units, with low operating cost against the cost of shortening the service life of the turbine rotor. In this regard, linear programming is used to dispatch the power generation among committed units by considering a ramping penalty for the fatigue effect in rotor shafts, while preserving the operational constraints of the system as well as the generating units. >

Price-based ramp-rate model for dynamic dispatch and unit commitment

The ramp-rate limits of generators can significantly impact power system operation. As a result, they need to be properly modeled in power system production simulations. This paper presents a price-based ramp-rate model. This model is particularly suited for application to power system scheduling models that are based on dual formulation (i.e. price-based). In this model, the impact of binding ramp-rate limits is reflected via the hourly marginal ramp-rate values ($/MW-Hr) of generators. In the paper, the proposed ramp-rate model is applied to price-based dynamic dispatch and price-based unit commitment. Simple examples are used throughout the paper to illustrate the concept of the proposed model. >

Measurements of ramp-rate limitation of cable-in-conduit conductors

The ramp-rate limitation found in the US-demonstration poloidal coil (US-DPC) test was studied in a laboratory scale experiment. The ramp-rate sensitivity has been identified on a 27-strand cable-in-conduit conductor at a background ramped field to 9.5 T with various ramp rates of 0.5 T/s to 2 T/s, simulating the US-DPC test conditions. A model assuming the existence of periodic disturbances is proposed in which the disturbance frequency is directly proportional to the ramp rate of the square of field. A semi-empirical formula was developed which fits the ramp-rate limitation data of both the US-DPC large coil and the 27-strand cable. The ramp-rate limitation does not occur for currents below the conventional limiting current. >