No-load field characterisation of a sine-wave-filtered variable-frequency drive feeding an electrical submersible induction motor through a 6000 m cable

Technical Summary: No-load Field Characterisation of a Sine-wave-filtered Variable-frequency Drive Feeding an Electrical Submersible Induction Motor through a 6000 m Cable

Problem Statement
Electrical submersible pumps (ESPs) in deep wells rely on surface variable-frequency drives (VFDs) connected to downhole motors via multi-kilometre power cables. The fast-switching pulse-width-modulated (PWM) output of standard VFDs creates severe power-quality stresses, including reflected-wave overvoltage, steep voltage rise times ($dv/dt$), and harmonic heating, which can lead to premature insulation and bearing failures. While sine-wave (LC) output filters are the standard remedy to reshape PWM into sinusoidal waveforms, existing literature on long-cable ESP systems is predominantly model-based or validated through reduced-scale laboratory tests. There is a scarcity of full-scale field data that isolates the performance of the sine filter from the effects of the long cable itself. Specifically, it is unclear how much fundamental voltage is lost across a real multi-kilometre cable after filtering, and how the motor's no-load current behaves under these specific conditions.

Methodology
The authors conducted a controlled, three-state field test on a 45 kW, 946 V Zhongcheng submersible induction motor driven at no load through a 6000 m armoured cable. The test was performed at 20, 30, and 40 Hz under V/f control. The three measurement states were:

1. State 1: VFD output directly (raw PWM).
2. State 2: VFD output through a sine-wave filter (measured at the filter output).
3. State 3: VFD output through the filter and the 6000 m cable (measured at the motor terminal).

Measurements were captured using a VITREK PA910VT power-quality analyser. Cable parameters, including DC resistance and frequency-dependent inductance, were measured directly using a multimeter and an LCR bridge. A frequency-dependent distributed-parameter transmission line model was constructed using these measured parameters to simulate and validate the observed voltage drops. Additionally, an LC sine-wave filter was designed from first principles to compare its simulated response against the field-measured filter performance.

Key Results

• Filter Performance: The sine filter successfully transformed the raw PWM voltage (Total Harmonic Distortion [THD] of 250–470% and crest factors up to 2.72) into a clean sinusoid (THD reduced to 2.4%, crest factor reduced to 1.49).
• Cable Voltage Drop: The 6000 m cable caused a significant fundamental voltage drop at the motor terminal, ranging from 8.3% to 15.0% depending on frequency. A lumped series-impedance model using measured resistance and inductance reproduced these drops within 3% error at 30 and 40 Hz.
• No-Load Current Reduction: A distinct and disproportionate reduction in motor current was observed. While voltage dropped by 8–15%, the no-load current fell by 29–36%. Analysis of reactive power revealed that the effective magnetising inductance increased by approximately 30% (e.g., from 93.7 mH to 121.7 mH at 20 Hz).
• Magnetic De-saturation Mechanism: The authors attribute the current reduction to magnetic de-saturation. The V/f ratio at the filter output placed the near-saturated motor slightly above its rated flux. The cable voltage drop lowered the air-gap flux, moving the operating point to a less-saturated region of the magnetisation curve where inductance is higher. Since magnetising current is inversely proportional to inductance, the current decreased more sharply than the voltage.
• High-Frequency Effects: The cable introduced a small high-frequency ripple, raising the terminal THD slightly from ~2.4% to 3.3–3.6%. Distributed-parameter modelling identified a quarter-wave resonance band between 2.4 and 5.4 kHz, which overlaps with the switching frequency but is well-damped by the cable's high-frequency resistance.

Key Contributions

1. Full-Scale Field Dataset: The paper provides rare, full-scale field measurements of a sine filter and a 6000 m cable operating together, separating the filter's waveform shaping capabilities from the cable's voltage drop and resonance effects.
2. Validated Voltage Drop Model: It offers a field-validated, frequency-dependent circuit model for the cable voltage drop, confirming that series impedance (resistance and inductance) is the dominant factor, rather than capacitive charging currents, at fundamental frequencies.
3. Identification of De-saturation Effect: The study identifies and quantifies a magnetic de-saturation mechanism as the cause of the pronounced no-load current reduction in long-cable ESP systems, an effect not previously reported in this configuration.
4. Filter Design Validation: An LC sine filter designed from first principles was simulated and compared against field data, validating the design methodology and confirming the filter's ability to suppress switching-band harmonics by approximately 29 dB.

Significance and Claims
The paper claims that while the sine filter is essential for protecting motor insulation by eliminating high $dv/dt$ and harmonic distortion, it does not mitigate the fundamental voltage drop or the associated magnetic de-saturation effects caused by long cables. The authors assert that for long-cable ESP design, engineers must address the voltage drop (e.g., via V/f boost or tap changes) and account for the cable's impact on motor magnetisation. The findings complement existing model-based literature by providing empirical evidence from a real-world installation, suggesting that the magnetic de-saturation effect should be considered in future ESP system models. The authors note that these results are specific to no-load conditions and that loaded behaviour, while projected, requires further field validation.