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

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.


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 1 3 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.

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 fieldoriented [15] is as follows: where u * * sd , u * * sq are coupling voltages (V). i * sd , i * sq are motor stator reference current components in the d − q rotating reference frame (A). * r , are motor rotor reference flux linkage amplitude, rotor flux phase angle, 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: (1) Stator model (reference model) where r , r are motor rotor flux linkage components in the − stationary reference frame (Wb). u s , u s are motor stator voltage components in the − stationary reference frame (V). i s , i s are motor stator current components in the − stationary reference frame (A).
(2) Rotor model (adjusted model) where r r , r r are motor rotor flux linkage components in the − stationary reference frame (generated from a rotor model based on the estimated speed)(Wb). , R r are estimate motor angular speed (r/min), motor rotor resistance (Ω), respectively.
(3) Error equation where K p_est , K i_est are motor speed PI controller constants, respectively. Figure 1 shows the control block diagram of feed-forward decoupling and motor stator voltages generated unit [15], where the coupling voltages u * * sd and u * * sq are generated according to the given motor stator d-axis current , q-axis current component i * sq , and rotor flux linkage * r . Figure 2 shows the block diagram for MRASbased speed estimation and flux calculation, where the estimated rotor angular speed ω , rotor flux linkage amplitude r and the rotor phase angle θ are calculated from the measured the motor voltage/current signals. The estimated motor speed, flux linkage amplitude and rotor phase angle are used in the ISSVCA as shown in the following sections. Figure 3 shows the conventional speed sensor-less vector control algorithm (CSSVCA) [17,18] of IM based on long cable. This algorithm is a speed closed-loop control system. The aims are to achieve speed estimation, torque and flux decoupling through coordinate transformation, flux and speed observers. These give independent control of the flux and torque during both the steady state and dynamic condition.

Long Cable Modeling and Calculation of Motor Stator Voltage and Phase Current
The analysis of the problems associated with long motor cable drives needs reliable modeling of the complete drive system, especially the long subsea cable. Where frequencydomain analysis is a powerful tool in long cable modeling [19]. Lumped R, L and C elements can represent the long cable effectively, even for transient analysis. Applying this modeling technique is simple and does not reduce the accuracy [20][21][22], this model is sufficient to give accurate results on long motor cable terminations [5]. Therefore, in this paper, a π-network with lumped elements R, L and C was used to model the long motor cable and output filter. Figure 4 shows the long cable and filter π-network model of inverter IM drive system. The simulated long motor cable was a subsea umbilical, which was also a PWM special insulation. Table 1 lists the parameters of this long cable.
The two-port network model can be used to represent each phase model of the sinewave filter and long cable. Figure 5a shows the sinewave filter two-port impedance network model. Figure 6a shows the long cable two-port impedance π-network model. As a balanced three-phase network [23,24], the each phase parameters of the sinewave filter model and long cable model shown in Fig. 4   Filter model  where L f _ , L f _ are filter inductances per phase in the − stationary reference frame (H). L f _u , L f _v , L f _w are filter inductances per phase (H). C f _ , C f _ are filter capacitances per phase in the − stationary reference frame (F). C f _u , C f _v , C f _w are filter capacitances per phase (F). R c_ , R c_ are cable resistances per phase in the − stationary reference frame (Ω). R c_u , R c_v , R c_w are cable resistances per phase (Ω). L c_ , L c_ are cable inductances per phase in the − stationary reference frame (H). L c_u , L c_v , L c_w are cable inductances per phase (H). C c_ , C c_ are cable

Fig. 4 Long cable and filter network model of inverter induction motor drive system
capacitances per phase in the − stationary reference frame (F).
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 1 , it is solved as the linear equations, without the derivative process, which simplified the calculation. Calculation equation can be expressed by (1) Sinewave filter parameters function equations at both ends (16) Sinewave filter α-axis network model in the where where u f _uvw , i f _uvw , u VFD_uvw , i VFD_uvw are filter output threephase voltage, filter output three-phase current, inverter output three-phase voltage, and inverter output three-phase current, respectively.
(2) Long cable parameters function equations at both ends where (17) where u m_uvw , i m_uvw , l c are motor three-phase voltage, motor three-phase current, and cable length (km), respectively. 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.    (16) into (19), the functional relationship between voltage/current of the motor terminal and output voltage/current of the inverter can be derived as The equations in the − stationary reference frame are expressed as where u s_ , u s_ are calculated motor voltage components from the inverter output voltage/current using a − model for the long cable in the stationary reference frame (V). i s_ , i s_ are calculated motor current components from the inverter output voltage/current using a − model for the long cable in the stationary reference frame (A). u VFD_ , u VFD_ are inverter voltage components in the − stationary reference frame (V). i VFD_ , i VFD_ are inverter current components in the − stationary reference frame (A).
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
The proposed ISSVCA was designed for a motor drive with long cable connection, which was commonly utilized for ESP drives, and the block diagram of algorithm is shown in Fig. 7. The proposed technique was capable of calculating the motor terminal voltage and current from the inverter output voltage/ current signals using a − model for the long cable in the stationary reference frame. The exact motor terminal voltage/ current were calculated to estimate rotor angular speed, rotor flux amplitude and rotor flux phase angle, instead of directly using the measured inverter output voltage/current signals. So that the accurate rotor flux linkage model was constructed to realize the observation of the rotor flux, accurate velocity identification, and closed-loop control of the torque, flux and current.

Simulation and Experimental Results
Computer simulation and experiments were performed with the proposed ISSVCA for IM based on long cable. The experimental setup shown in Fig. 8 was used to emulate an long cable drive system, which typically has an inverter, motor unit, sinewave filer and cable model. The parameters of the three-phase IM and sinewave filter used in simulation and experiments are shown in Tables 2 and 3, and the cable model length is 1 km. Figure 9 shows simulation and experimental no-load response results for motor speed and current with a 1-km cable. Figure 9a, c show simulation and experimental noload start waveforms for motor speed and current with the  Figure 9b, d show simulation and experimental no-load start waveforms for motor speed and current with the ISSVCA. The motor reaches the rated speed from zero speed in 3 s. The simulation and experimental results in Fig. 9 show that the ISSVCA improves the starting electromagnetic torque and increases the dynamic response. Figure 10 shows experimental sudden load response results for motor speed and current with a 1-km cable. Figure 10b shows that the ISSVCA enables the motor to restore the speed to 1460 rpm in less than 500 ms, when a sudden rated load is applied. Figure 10a shows that the CSSVCA increases the time to restore the reference speed and causes the speed dip, when the rated load is applied. Figure 11 shows that the long cable introduces harmonics into the DC-link current as the first element experienced by the inverter is the stray capacitance of the long cable model. This capacitance acts as a short circuit to each inverter voltage pulse. Figure 11 shows that use of the ISSVCA can decrease the harmonics in DC-link current, avoid harmonics in DC-link current which caused problems such as radiated EMI, inaccurate current measurement and false protection system operation, and increase the DC-link capacitor lifetime.

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.