# Performance improvement of a measurement station for superconducting cable test.

TL;DR: A fully digital system, improving measurements flexibility, integrator drift, and current control of superconducting transformers for cable test, is proposed, based on a high-performance integration of Rogowski coil signal and a flexible direct control of the current into the secondary windings.

Abstract: A fully digital system, improving measurements flexibility, integrator drift, and current control of superconducting transformers for cable test, is proposed. The system is based on a high-performance integration of Rogowski coil signal and a flexible direct control of the current into the secondary windings. This allows state-of-the-art performance to be overcome by means of out-of-the-shelf components: on a full-scale of 32 kA, current measurement resolution of 1 A, stability below 0.25 A min−1, and controller ripple less than ±50 ppm. The system effectiveness has been demonstrated experimentally on the superconducting transformer of the Facility for the Research of Superconducting Cables at the European Organization for Nuclear Research (CERN).

## Summary (3 min read)

### Introduction

- The system effectiveness has been demonstrated experimentally on the superconducting transformer of the Facility for the Research of Superconducting Cables at the European Organization for Nuclear Research (CERN).
- On the other hand, for large-size cables, facilities of appropriate dimensions and functionality are few, mainly owing to the difficulty and cost of providing a large and complex set-up for assessing the device properties as a function of the abovementioned parameters 3-8 .
- The control loop, on the other hand, must account for the physical characteristics of the coupled system formed by the primary winding, and its power supply, the secondary, and the current transducer.
- In 11 , these issues are addressed both by implementing a custom FPGA-based integrator with higher resolution and by minimizing the residual offset via a dedicated procedure.

### II. The Proposed System

- In Fig. 1, the architecture of a measurement station for superconducting cable test, based on a transformer for supply and Rogowski coils for current measurement, is reported.
- The secondary current is then obtained by integrating the differential signal VRC from the Rogowski coils.
- The measured current is finally compared to the reference Iref in order to generate the feedback signal Im compensating for resistive losses.
- 4/21 In this architecture, the fundamental elements are the measurement system and the control strategy.
- The above-mentioned requirements are met by exploiting high-performance numerical integration and digital control algorithms, as described below.

### A. The measurement and control system

- In Fig. 2a, the architecture of the measurement and control system is shown.
- The control reference Vref is generated by a digital waveform generator, with at least 16 bits of resolution in the input range of the voltage-controlled current source (Fig. 2b) in order to accurately control Ip.
- Then, after digital integration, the measured magnetic flux is: ( ) ( ) ( ) (2) where n stands for a discrete time instant, and offset(n) is the undesired flux contribution arising from the voltage offset on the data acquired from the integrator.
- Beyond well-known advantages of a fully digital measurement, the proposed architecture allows off-the-shelf boards, advanced digital signal processing, and software flexibility to be exploited.
- Moreover, a software control algorithm can be implemented if the sampling frequency is less than few hundreds of samples/s.

### B. The system under control

- The first eq. of (3) provides the dependence of the currents on the voltage Vp, and the second eq. of (3) provides the link between primary and secondary currents.
- 6/21 From (3) the transformer transfer function is derived using the Laplace transform: ( ) ( ) ( ) (4) where GT is the transformer gain, i.e. the current amplification factor, without losses (Rs=0) , and τ the decay time constant of Is, .
- The (4) justifies the need for a control strategy to counteract the resistive current decay in the secondary circuit 21 .
- According to 12,13 , the joint resistance and the self-inductance are a function of the current and the field.

### C. Digital control algorithm

- Conversely, in this work, a fully digital measurement system and control algorithm, taking into account only the plant characteristic without further analog signal handling, is proposed.
- This provides an accurate conversion of the reference voltage V * ref into the primary current Ip.
- The transformer is modeled according to (4).
- The transfer function of the Proportional-Integral controller PI(z) can be written for a backward digital integrator as: ( ) (5) where KP and KI are the gains of the proportional and integral actions, respectively.
- (12) The (12) represents a first-order filter with behavior defined by the pole position inside the unit circle.

### III. Experimental Results

- The proposed system was tested at CERN, on FReSCa, the Facility for Research on Superconducting Cables 4 .
- The primary winding of the transformer is wound from insulated NbTi wire, with a diameter of 0.542 mm, a Cu/SC (Copper to Superconducting) ratio of 1.35, a residual resistivity ratio of 82, and a filament diameter of 45 μm.
- The secondary is impregnated with epoxy to support mechanically the coil.
- In the following, (A) the experimental set-up, (B) the controller parameters determination, (C) the measurement system characterization, and (D) the validation results of the proposed system are described.

### A. Experimental Set-Up

- The waveform generator is realized through a data acquisition board NI-PXI 6281 of National Instruments 22 .
- The board drives a fourquadrants power supply Lake Shore Mod 622 24 , supplying the transformer’s primary (voltage-controlled current source in Fig. 1).
- The signal-to-noise and distortion ratio is higher than 100 dB.
- The timing board is a NI PXI-6682 of National Instruments, with 10 MHz of internal clock 26 , used to generate the trigger signal for the FDI and for the data acquisition board.
- The embedded computer is a Single-Board Computer D9-6U by Mikro Elektronik 28 , hosting the software handling the whole system functions, based on the Flexible Framework for Magnetic Measurements 29 , and implementing the controller algorithm.

### B. Controller parameters determination

- Defining the largest required signal bandwidth for the secondary current enables to specify the sample frequency of the closed-loop operation and thereafter the controller parameters.
- In practice, this value can be thought much lower because for testing purposes the current has smooth transition to the maximum ramp-rate.
- The required numeric bandwidth for the control is therefore 0.2 (B/fs).
- Once the sample rate is defined, the controller parameters K, KI, and KP can be calculated 18 .
- In Figs. 6, the bounds of the frequency response of the closed-loop transfer function (12), using ideal GT and τ are illustrated for a typical variation of ±30 % of the transfer function parameters (namely, left, the magnitude, and, right, the phase).

### C. Measurement System Characterization

- Main problems in the secondary current measurement arise from the integration equivalent offset and from the repeatability of Rogowski Coils in typical test conditions.
- For the repeatability tests of the system composed by the Rogowski coils and FDI, the sample was fed directly from the room-temperature 32-kA power supply, through large current leads (Fig. 7a).
- Stability In Fig. 7b, the experimental set up for the stability tests of the measurement system is illustrated.
- In Figs. 11b1 and 11b2, the differences between the measured current and the ideal linear reference at ramp up and its average value at the flattop, respectively, are detailed.
- III, the average values of the measured critical current on the sample under test with the reference 32-kA power supply and the superconducting transformer are compared by reporting also their percentage difference.

### IV. Conclusions

- A fully digital system for the control of transformers for superconducting cable testing is proposed.
- The digital system is based on a low-drift precision integrator and a simple but robust PI control algorithm, achieving brilliant performance and improving test flexibility.
- The set-up has also a definite cost advantage for the use of off-the-shelf components.
- The effectiveness of the architecture was assessed by an experimental implementation aimed at controlling the superconducting transformer available at the Facility for Research on Superconducting Cables of CERN.
- These results were demonstrated in practical working conditions, measuring the critical current of a NbTi Rutherford cable with well known properties.

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##### Citations

40 citations

36 citations

^{1}

3 citations

### Cites background from "Performance improvement of a measur..."

...Widely used current sensors are Rogowski and pick up coils [6], [7], [9], [11]....

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...in addition to the difficulty of operating a superconducting transformer [11], a major metrological issue is the measurement...

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...This classical solution has drawbacks such as intrinsic AC nature and limited measurement time due to the need of low drift integration (to keep accuracy of the measured current within the range of hundreds of ppm [11])....

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##### References

^{1}

57 citations

40 citations

^{1}

39 citations

38 citations

### "Performance improvement of a measur..." refers background in this paper

...The desired current in the transformer secondary I * ref is related to the measured current I * m: ( ) ( ) (7)...

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36 citations