# Improved Speed Sensorless Vector Control Algorithm of Induction Motor Based on Long Cable

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## Abstract

In many applications, especially electrical submersible pump required remote operation of inverter via a long motor cable. The conventional control algorithm of induction motor (IM) didn’t operate effectively, which ignored the influence of the cable length, and didn’t consider the effect of long cable distribution parameters. A speed sensor technique was also difficult to achieve. In this paper, an improved speed sensorless vector control algorithm (ISSVCA) for IM based on long cable was proposed. Based on the analysis of long cable motor drive system of the inverter, the two-port *π* network model of the long cable was established. The functional relationship between the voltage/current parameters of the two ports of the long cable and the cable distribution parameters was deduced. The function expression was transformed to the *α* − β stationary reference frame, the accurate motor terminal voltage/current was calculated, so that the flux model was constructed to realize the observation of the flux, accurate velocity identification, and closed-loop control of the torque, flux and current. Simulation and experimental results showed that the proposed ISSVCA based on long cable increased the starting electromagnetic torque, decreased speed dip and speed recovery time caused by sudden loads, reduced the DC current harmonics, and had good dynamic and static characteristics.

## Keywords

Speed sensor-less vector control Long cable Electrical submersible pump (ESP) Inverter Induction motor (IM)## Introduction

The electric submersible pump (ESP) is an important production device for oil exploitation in deep-sea oil fields, particularly applicated for the fluids that contain minimal amounts of gas [1]. In the actual production of deep-sea oil fields, this device is installed at the bottom of subsea wells up to 7000 m deep for oil extraction, and is driven by the inverter via long transmission cable of ranging from several kilometers to tens of kilometers [2]. The inverter can control the ESP to a speed well that better producing the well and keeping the ESP within its best efficiency range, it also offers soft motor starting for ESP systems and reduces impact to power grid during the ESP systems start-up [3]. Hence, the inverter is widely used in oil field facilities, some of latest facilities could have up to 80% loads supplied power by Inverter.

The connection between inverter and the ESP through the long submarine cable incurs some problems [4, 5], mainly long cable distribution parameters [2] which caused changes in the inverter output voltage, current and phase, introduce harmonics into the DC-link current. Moreover, the long cable impedance voltage drop which decreased the starting electromagnetic torque, increases the rise time and causes starting problems, especially in case with high-inertia motor loads [6]. The voltage drop across the long cable impedance increases speed dip and speed recovery time, when sudden load was applied. The voltage regulation needs to be increased and the inverter modulation index is apt to be saturated with the increase of the cable length [7]. These problems limit the application of the inverter, which making the various control algorithms of the inverter, especially the vector control algorithm, unable to operate effectively. For speed sensor-less vector control algorithm, the flux and velocity estimation technique are prerequisite [8, 9]. The observers which are used for IM flux and velocity estimation require the exact motor terminal voltage**/**current [10]. That direct measuring motor terminal voltage**/**current signals may be too costly or too difficult to achieve for long motor subsea cable drives due to subsea cable length or safety/environmental precautions. Hence, the motor terminal voltage**/**current must be calculated from the inverter side.

There are some control algorithms used for remote operation of inverter via a long motor subsea cable, such as the stability controller for open-loop operation which can be used for motor derived with an output filter and transformer in oil pump applications [11], the open loop current regulated sensor-less control scheme for an induction and permanent magnetic motor derived with output sinewave filter and transformer which provides sufficient starting torque with controlled drive/motor current [12], the robust voltage vector control strategy for a PMSM driving a high-power ESP [13]. These methods are to improve the conventional scalar control algorithm to control the motor drives. However, there is no literature on the research of the speed sensor-less vector control algorithm for IM based on long cable.

In this paper, the ISSVCA, needed for long motor cable, was proposed. The presented ISSVCA was based on the exact long cable model, which was the motor stator voltage and current could be calculated from the inverter output voltage/current using *α* − β model for the long cable in the stationary reference frame, and the correct command voltage could be given in current control cycle which was based on the state equation of the IM in the synchronous rotating reference frame. An experimental setup was implemented with a 1-km cable model. Practical aspects, such as cable selection and inverter limitations, were considered in the experimental setup to match a scaled-down actual inverter. Simulation in addition to experimental results verified the correctness and effectiveness of the proposed ISSVCA.

This paper is organized into six sections. Following the introduction in Sect. 1, speed sensor-less vector control technique is discussed in Sect. 2. In Sect. 3, the long motor subsea cable model and remote motor voltage/current calculator are illustrated. The proposed ISSVCA for IM is presented in Sect. 4. Simulation and experimental results are illustrated in Sect. 5. Finally, the conclusion forms Sect. 6.

## Speed Sensorless Vector Control Technique

### IM Model

The fundamental operation principle of the rotor field-oriented vector control (FOC) [14] is to obtain equivalent DC motor model in a synchronous rotating reference frame through an appropriate coordinate transformation. The torque *T*_{e} and rotor flux *ψ*_{r} are controlled independently of each other following the control method of the DC motor, and then the control amounts in the synchronous rotating reference frame are inversely transformed to obtain the corresponding amounts of the three-phase coordinate system to implement the control. The motor model after rotor field-oriented [15] is as follows:

*u*

_{sd}, \(u_{sq}\) are motor stator voltage components in the

*d*−

*q*rotating reference frame (V).

*i*

_{sd}, \(i_{sq}\) are motor stator current components in the

*d*−

*q*rotating reference frame (A).

*R*

_{s},

*p*,

*σ*,

*L*

_{s},

*ω*

_{1},

*L*

_{r},

*L*

_{m},

*ψ*

_{r}are motor stator resistance (Ω), differential operator, leakage coefficient, motor stator inductance (H), synchronous angular velocity (r/min), motor rotor inductance (H), motor mutual inductance (H), motor rotor flux linkage amplitude, respectively.

*n*

_{p}, \(T_{e}\) are motor number of pole pairs, motor developed torque (N m), respectively.

### The Model Reference Adaptive System Based on Rotor Flux

The model reference adaptive system (MRAS) [16] based on rotor flux, which is using the voltage model as a reference model and using the current model as an adjustable model. The error from cross multiplication of the voltage and current model outputs is used to generate the estimated speed using a PI controller. The system equations are as follows:

## Long Cable Modeling and Calculation of Motor Stator Voltage and Phase Current

Cable parameters

Quantity | Value | Unit |
---|---|---|

Cable | 2XS(FL)2YRAA 6/10(12) kV | – |

Resistance | 0.34 | \(\Omega /{\text{km}}\) |

Inductance | 0.38 | \({\text{mH}}/{\text{km}}\) |

Capacitance | 0.29 | \(\upmu {\text{F}}/{\text{km}}\) |

\(C_{c\_u} , C_{c\_v} ,C_{c\_w}\) are cable capacitances per phase (F).

Thanks to the inverter with filter is nearly sinusoidal output, the voltage/current are as well nearly sinusoidal. Figures 5 and 6 show the functional relationship between the voltage/current of the two-port π-network model and the model distribution parameters. It is not necessary to perform derivative calculation at the fundamental operating frequency, and by replacing the Laplace transform variable s with \(j\omega_{1}\), it is solved as the linear equations, without the derivative process, which simplified the calculation. Calculation equation can be expressed by

The inductive reactance and capacitive reactance of the unit length (km) of the cable are given by (20) and (21). For different cable lengths (\(l_{c}\)), by putting \(l_{c}\) into (19), the functional relationship values between the parameters at both ends of this cable length can be calculate.

The actual motor terminal voltage and current can be calculated from the inverter side by (23) and (24).

## ISSVCA of IM Based on Long Cable

## Simulation and Experimental Results

IM parameters

Parameter | Value | Unit |
---|---|---|

Rated power | 2.2 | \({\text{kW}}\) |

Poles | 4 | |

Rated voltage | AC380 | \({\text{V}}\) |

Rated current | 5.1 | \({\text{A}}\) |

Rated frequency | 50 | \({\text{Hz}}\) |

Rated speed | 1460 | \({\text{rpm}}\) |

Stator resistance | 2.706 | \(\Omega\) |

Rotor resistance | 1.543 | \(\Omega\) |

Mutual inductance | 245 | \({\text{mH}}\) |

Rotor inductance | 10.11 | \({\text{mH}}\) |

Stator inductance | 10.11 | \({\text{mH}}\) |

Sinewave filter parameters

Parameter | Value | Unit |
---|---|---|

Inductance | 4.5 | \({\text{mH}}\) |

Capacitance | 2 | \(\upmu {\text{F}}\) |

## Conclusion

In this paper, the proposed ISSVCA of IM based on long cable that could be effectively applied to long cable-connected motor loads. This algorithm was fast and accurate in flux and velocity identification, simple in algorithm, less in computation, easy to implement online.

Simulation and experimental results showed that the ISSVCA could control the reliable and stable operation of the motor, provided sufficient starting electromagnetic torque, and starting current of the motor, made the motor start smoothly, reduced the harmonics in DC-link current, increased the DC-link capacitor lifetime. And it has good dynamic and static characteristics, strong engineering practicality and application promotion value.

## Notes

### Acknowledgements

This work are supported by Beijing Natural Science Foundation (no. 3162025), the National Key Research and Development Plan (no. 2016YFC0800103) and “the Fundamental Research Funds for the Central Universities” (no. 3142018049).

## References

- 1.Chien CH, Bucknall RWG (2007) Analysis of harmonics in subsea power transmission cables used in VSC–HVDC transmission systems operating under steady-state conditions. IEEE Trans Power Deliv 22(4):2489–2497CrossRefGoogle Scholar
- 2.Smochek M, Pollice AF, Rastogi M, Harshman M (2016) Long cable applications from a medium-voltage drives perspective. IEEE Trans Ind Appl 52(1):645–652CrossRefGoogle Scholar
- 3.Liang X, Kar NC, Liu J (2015) Load filter design method for medium-voltage drive applications in electrical submersible pump systems. IEEE Trans Ind Appl 51(3):2017–2029CrossRefGoogle Scholar
- 4.Abu-Rub H, Holtz J, Rodriguez J, Baoming G (2010) Medium-voltage multilevel converters—state of the art, challenges, and requirements in industrial applications. IEEE Trans Ind Electron 57(8):2581–2596CrossRefGoogle Scholar
- 5.Abdelsalam AK, Masoud MI, Finney SJ, Williams BW (2011) Vector control PWM-VSI induction motor drive with a long motor feeder: performance analysis of line filter networks. IET Electr Power 5(5):443–456CrossRefGoogle Scholar
- 6.Raad RO, Henriksen T, Raphael HB, Hadler-Jacobsen A (1996) Converter-fed subsea motor drives. IEEE Trans 32(5):1069–1079Google Scholar
- 7.Matheson E, von Jouanne A, Wallace A (1999) Evaluation of inverter and cable losses in adjustable speed drive applications with long motor leads. In: International conference on electric machines and drives, IEMD’99, Seattle, WA, USA, pp 159–161Google Scholar
- 8.Harnefors L (2001) Design and analysis of general rotor-flux-oriented vector control systems. IEEE Trans Ind Electron 48(2):383–390CrossRefGoogle Scholar
- 9.Rehman H, Derdiyok A, Guven MK, Xu L (2002) A new current model flux observer for wide speed range sensorless control of an induction machine. IEEE Trans Power Electron 17(6):1041–1048CrossRefGoogle Scholar
- 10.Verghese GC, Sanders SR (1988) Observers for flux estimation in induction machines. IEEE Trans Ind Electron 35(1):85–94CrossRefGoogle Scholar
- 11.Liu J, Nondahl TA, Royak S, Rowan TM (2017) Generalized stability control for open-loop operation of motor drives. IEEE Trans Ind Appl 53(3):2517–2525CrossRefGoogle Scholar
- 12.Liu J, Dai J, Royak S, Schmidt P, Alnabi E (2017) Design and implementation of position sensorless starting control in industrial drives with output filter and transformer for oil/pump applications. In: Proceedings of the 32nd IEEE annual applied power electronics specialists conference and exposition (APEC), pp 578–584Google Scholar
- 13.da Cunha G, Rossa AJ, Alves JA, Cardoso E (2018) Control of permanent magnet synchronous machines for subsea applications. IEEE Trans Ind Appl 54(2):1899–1905CrossRefGoogle Scholar
- 14.Santisteban JA, Stephan RM (2001) Vector control methods for induction machines: an overview. IEEE Trans Educ 44(2):170–175CrossRefGoogle Scholar
- 15.Kawabata Y, Kawakami T, Sasakura Y, Ejiogu EC, Kawabata T (2004) New design method of decoupling control system for vector controlled induction motor. IEEE Trans Power Electron 19(1):1–9CrossRefGoogle Scholar
- 16.Kumar R, Das S, Syam P (2015) Review on model reference adaptive system for sensorless vector control of induction motor drives. IET Electr Power Appl 9(7):496–511CrossRefGoogle Scholar
- 17.Santisteban JA, Stephan RM (2001) Vector control methods for induction machines: an overview. IEEE Trans Educ 44(2):170–175CrossRefGoogle Scholar
- 18.Cheng Q, Cheng Y, Wang Y, Wang M (2011) Overview of control strategies for AC motor. Power Syst Prot Control 39(9):145–153Google Scholar
- 19.Amarir S, Al-Haddad K (2008) A modeling technique to analyze the impact of inverter supply voltage and cable length on industrial motor-drives. IEEE Trans Power Electron 23(2):753–762CrossRefGoogle Scholar
- 20.Pomilio JA, de Souza CR, Matias L, Peres PLD, Bonatti IS (1999) Driving AC motors through a long cable: the inverter switching strategy. IEEE Trans Energy Convers 14(4):1441–1447CrossRefGoogle Scholar
- 21.Aoki N, Satoh K, Nabae A (1999) Damping circuit to suppress motor terminal overvoltage and ringing in PWM inverter-fed AC motor drive systems with long motor leads. IEEE Trans Ind Appl 35(5):1014–1020CrossRefGoogle Scholar
- 22.Khodaparast J, Khederzadeh M (2017) Least square and Kalman based methods for dynamic phasor estimation: a review. Prot Control Mod Power Syst 2(2):1–18CrossRefGoogle Scholar
- 23.Hancock NN (1975) Matrix analysis of electrical machinery. Elsevier, AmsterdamGoogle Scholar
- 24.Roostaee S, Thomas MS, Mehfuz S (2017) Experimental studies on impedance based fault location for long transmission lines. Prot Control Mod Power Syst 2(1):16. https://doi.org/10.1186/s41601-017-0048-y CrossRefGoogle Scholar

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