A graphic monitoring method for electric power of VVVF hydraulic system

SHI Yu-ping, GU Li-chen,2, ZHAO Song, LIU Chang-chang

(1. School of Construction Machinery, Chang’an University, Xi’an 710064, China；2. School of Mechanical-Electronic Engineering, Xi’an University of Architecture and Technology, Xi’an 710054, China)

Abstract： In order to online monitor the running state of variable voltage and variable frequency(VVVF) hydraulic system, this paper presents a graphic monitoring method that fuses the information of variable frequency electric parameters. This paper first analyzes how the voltage and current of the motor stator change with the operation conditions of VVVF hydraulic system. As a result, we draw the relationship between the electric parameters (voltage and current) and power frequency. Then, the signals of the voltage and current are fused as dynamic figures based on the idea of Lissajous figures, and the values of the electric parameters are related to the features of the dynamic figures. Rigorous theoretical analysis establishes the function between the electric power of the variable frequency motor (VFM) and the features of the plotted dynamic figures including area of diagram, area of bounding rectangle, tilt angle, etc. Finally, the effectiveness of the proposed method is verified by two cases, in which the speed of VFM and the load of VVVF hydraulic system are changed. The results show that the increase of the speed of VFM enhances its three-phase electric power, but reduces the tilt angle of the plotted dynamic figures. In addition, as the load of VVVF hydraulic system is increased, the three-phase electric power of VFM and the tilt angle of the plotted dynamic figures are both increased. This paper provides a new way to online monitor the running state of VVVF hydraulic system.

Key words： variable frequency motor (VFM); hydraulic system; condition monitoring; Lissajous figures; electric power; information fusion

0 Introduction

The variable frequency (VF) technology has attracted much attention in the field of AC speed regulation in recent years. Compared with the traditional methods, the variable frequency speed control has the advantages of higher efficiency, wider speed range, and more excellent dynamic response[1-3]. Thus, it has been widely used in the fields of hydraulic elevators[4], bridge jacking hydraulic system[5], hydraulic pipes jacking machine[6]. The variable voltage and variable frequency (VVVF) hydraulic system is a multi-domain coupling system integrating the characteristics of machinery, electricity, liquid and control. An unexpected failure will stop the machines and even lead to life-threatening dangers. Therefore, it is significant to monitor the running states and evaluate the performance of the VVVF hydraulic system during its long-term operation[7].

The commonly used signals in the hydraulic system are vibration, force, torque, speed, pressure and flow. However, in real cases, it costs much to detect multi-source signals.These signals are limited and easy to be disturbed, which brings difficulty and limitation to engineering applications. The theory and experiment confirm that the information contained in the multi-source signals will be coupled with the three-phase electrical parameters of the motor, such as electric power[8-10]. Moreover, the above electrical parameters have been verified that they have the excellent ability of anti-interference without invasive measurement. The motor power contains feature information reflecting the operation state, load variation and power matching of each system, which provides a way for studying the efficiency and optimizing control strategy of asynchronous motor[11-13]. In order to monitor the operation condition of the hydraulic system with the electrical parameters of the driven motors, Gu, et al.[14]proposed a graphic monitoring method based on the idea of Lissajous figure. This method could make full use of the electrical parameter information of amplitude, frequency, phase and phase sequence to monitor the running state of VVVF hydraulic system. However, this method is suitable for three-phase induction motor, whose speed is constant. Facing the issue of measurement for VF motor, the proposed method may present degraded performance.

In order to overcome the above shortcomings, this paper develops the fusion theory of the VF electric parameter. The relationship between the electric parameters and the power frequency is analyzed first. Then, a graphically monitoring method fuses the information of electric parameters under VF operation condition and establishes the mapping from the electric power of the VFM to the features of the plotted dynamic figures. This method is able to reflect the running state of VVVF hydraulic system intuitively.

1 Fusion theory of VF electrical parameters

1.1 Relationship between three-phase electric parameters and power frequency

In the VF control, the stator voltage varies with the power frequency. The ratio of the stator voltage and the power frequency is constant, i.e.U/f=C.

Suppose that the stator voltage is defined as

U=E+IZ,

(1)

whereEis induction electromotive force in the stator windings of the motor,Iis armature current, andZis the resistance of the stator winding.

If we ignore the voltage drop on the stator resistance, i.e.IZ, the root mean square (RMS) of the stator voltage is[15]

U≈E=4.44fK1N1Φ,

(2)

wherefis the power frequency,K1is the winding factor of stator windings,N1is the turns of stator windings, andΦis the magnetic flux of windings.

The electromagnetic torque of the three-phase asynchronous motor is calculated by

(3)

whereIis the stator phase current,Kiis the proportional coefficient, andPis the pole-pairs.

According to Eqs.(2) and (3), the RMS of the stator phase voltage is proportional to the power frequency, and the RMS of the phase current is constant during the VF process.

1.2 Information fusion of single-phase VF electrical parameters

Given that the phase voltage and phase current signals of the stator are expressed as[11].

(4)

wherej=a,b,crepresents the indexes for the phases of the motor;f(t) is the output frequency of the converter;Ais the amplitude of the phase current; andBis the ratio of phase voltage amplitude and frequency, according to Eq.(2),Bis calculated by

(5)

Supposing thatφ=φu-φiis the phase difference between the phase voltage and the phase current, and cosφis the power factor, ifω(t)t+φi=α, Eq.(4) can be expressed as

(6)

According to Eq.(6), the reactive Lissajous equation is

(7)

When adding 90° to the phase of voltage signal in Eq.(6), we can obtain

(8)

According to Eq.(8), the active Lissajous equation is

(9)

Making the voltage the abscissa and the current the ordinate, the single phase active Lissajous figure (ALF) and reactive power Lissajous figure (RLF) of VFM are drawn by using Eqs.(8) and (9). As shown in Fig.1, the active Lissajous figure and the reactive Lissajous figure of the single-phase electric parameter are all ellipses, which are centered at the origin of a Cartesian coordinate system.

Fig.1 Lissajous figures of single-phase electric parameter

2 Mathematical relationship between Lissajous figure and power of motor

2.1 Relationship between Lissajous figure and electricity parameters

The RLF is an ellipse centered at the origin, whose eigenvalue is

(10)

Then, the solution of the ellipse’s major axisaand minor axisbis

Multiplying Eqs.(11) and (12), we can get

ab=f(t)ABsinφ.

(13)

As we know, the area of an ellipse can be calculated by

Sac=πab.

(14)

The reactive powerQis

(15)

According to Eqs.(14) and (15), the relationship between the area of RLF and the reactive power can be expressed as

(16)

We can get the relationship between the area of ALF and the active powerP, which can be expressed as

(17)

As shown in Eqs.(15) and (16), the area of reactive power Lissajous figure is proportional to the reactive power, and the area of ALF is proportional to the active power. Therefore, changes of ALF and RLF can directly reflect the changes of active power and reactive power.

2.2 Relationship between bounding rectangle and electricity parameters

As shown in Fig.2, when the ellipse is centered at the origin, half of the side length of bounding rectangle is equal to the maximum value ofx-axis andy-axis, respectively.

Fig.2 Lissajous figures of single-phase electric parameter

In Fig.2, the maximum values of thex-axis andy-axis represent the maximum values of the voltage and the current, respectively, and the length ofLxand the width ofLycan be expressed as

(18)

The three-phase apparent power of the VFM is calculated by

(19)

The area of the bounding rectangle is

Sbr=LxLy,

(20)

(21)

From Eq.(21), we can find that the area of the bounding rectangle is proportional to the apparent power.

2.3 Power circle based on Lissajous figure

Combined with Eqs.(16), (17) and (21), we can obtain

(22)

Since

S2=P2+Q2,

(23)

the power circle can be calculated as

(24)

The power circle diagram can be drawn by using Eq.(24). In Fig.3, the area of the outer circle represents the square of apparent power, the area of the inner circle represents the square of active power, and the area of the ring represents the square of reactive power. The power circle diagram can directly reflect the dynamic relationship among the three powers under varying operating conditions of VVVF hydraulic system.

Fig.3 Power circle diagram

2.4 Relationship between tilt angle of Lissajous figure and electricity parameters

Supposing that the standard coordinate system isxoy(the focus of ellipse’s equation is on thex-axis), and the nonstandard coordinate system isx′o′y′, the axis rotation formula is

(25)

Substituting Eq.(25) into Eq.(7), we can obtain

(26)

The third part in the right of the equation is equal to zero because Eq.(26) is a standard ellipse equation. Then we can get

β=θ=

Similarly, the tilt angle of ALF is

α=θ=

3 Online monitoring power state of motor

3.1 Experiment platform

The mechanical electro-hydraulic experiment platform consists of the power source, closed hydraulic system, hydraulic loading system and measurement and control system. The power source includes the distribution system, the inverter and the three-phase asynchronous motor. The hydraulic system includes a variable pump, a variable motor and a relief valve, etc. The loading system includes a gear pump and a proportional relief valve. The measurement and control system include various sensors, a multi-function data acquisition card, a industrial computer and a software platform. The schematic diagram of the experiment platform is shown in Fig.4.

Fig.4 Schematic diagram of the test platform of VVVF hydraulic system

The inverter controls the motor 1 to drive the variable piston pump 3. Changing the speed or displacement of variable pump 3 can adjust the input flow of the variable piston motor 6. Regulating the outlet pressure of gear pump 8 through the proportional relief valve 9 can control the load torque of variable piston motor 6. The safety valve 5 sets the maximum working pressure of the hydraulic system. The slippage pump 4 compensates the leakage flow of the hydraulic system, and the relief valve 12 controls the pressure of the oil filling circuit. The flowmeter 21 measures the flow rate of high-pressure side of the hydraulic system. The pressure sensors 19 and 22 measure the pressure of high pressure chamber of variable pump 3 and variable piston motor 6, respectively, and the pressure sensor 13 is used to measure the pressure of the system. The torque and speed sensors 2 and 7 measure the torque and speed of variable pump and variable motor, respectively. In the experiments, we control the speed of the variable pump by the invertor and control the input signal of proportional relief valve 9 to change the load torque of the motor shaft.

3.2 Acquisition of electrical signals

As shown in Fig.5, the Hall sensors of three-phase voltage and current have access to the three-phase output circuit of the inverter, respectively. The three-phase electric parameter acquisition device can acquire the three-phase voltage and current signals simultaneously. The voltage and current signals processed by the conditioning circuit will be sent to A/D acquisition card so as to obtain the digital signals.

Fig.5 Wiring diagram of three-phase electric parameter acquisition device

3.3 Extraction of base frequency component of electrical signal

3.3.1 Voltage signal extraction

In electric drive of AC frequency conversion, the output voltage signal of the inverter is pulse-width modulation (PWM) wave that changes with the power frequency. The voltage waveform comprises the base frequency component and other high-frequency harmonic components. These harmonic components can cause many harmful effects on speed adjusting performance. Therefore, the wavelet filter method can filter the PWM wave into a sinusoidal wave and eliminate the interference components of phase voltage signal. As a result, the sine voltage signal is calibrated.

Fig.6 shows the waveform comparison of voltage signal before and after filter. The voltage of control loading is 0.8 V, the sampling frequency is 5 000 Hz, and the motor speed is 600 r/min.

Fig.6 Waveform comparison of voltage signals before and after filtering

3.3.2 Current signal extraction

(29)

Fig.7 shows the waveform comparison of current signal before and after processing. The voltage of control loading is 0.8 V, the sampling frequency is 5 000 Hz, and the motor speed is 600 r/min.

3.4 Online monitor the motor power during varying speed condition

The load voltage is 0.4 V, the sampling frequency is 5 000 Hz, and the motor speed is changed from 100 to 600 r/min. In Figs.8 and 9, the area and tilt angles of Lissajous figures changed with frequency.

Fig.8 illustrates the trend of active Lissajous figure, reactive power Lissajous figure and power circle vary with frequency. In Fig.8, The gray ellipse is reactive power Lissajous figure, and the black ellipse is active power Lissajous figure; the solid circle represents the active power, and the broken circle represents the apparent power. Figs.6(a) and (b) illustrate the trend of power and angle variing with frequency.

In Figs.8 and 9, as the speed of VFM is increased, the active power, reactive power and apparent power of VFM are increased, too. The ALF rotates anticlockwise and the RLF rotates clockwise, thus the tilt angles are both decreased. Meanwhile, it can be seen that the current amplitude changes very little during acceleration, and the voltage amplitude changes obviously with frequency.

Fig.9 reflects a change law that the increase of motor speed will enhance its electric power while reduce the tilt angles of Lissajous figures.

Fig.9 Change trend of motor power and tilt angles

3.5 Online monitoring motor power during sinusoidal frequency

The load voltage is 0.4 V, the sampling frequency is 5 000 Hz, and the inverter changes the motor speed between 100 r/min and 600 r/min in a sinusoidal manner by control frequency. The periodic variation of Lissajous figures and power circles is shown in Fig.10.

Fig.10 Change trend of Lissajous figures and power circles

In Figs.10 and 11, the increase of the speed of VFM will enhance its electric power while reduce the tilt angle of Lissajous figures. At the same time, the decrease of the speed of VFM will reduce its electric power while enhances the tilt angles of Lissajous figures.

Fig.11 Changes trend of motor power and tilt angles

3.6 Online monitoring the motor power under variable load

The motor speed is 600 r/min, the sampling frequency is 5 000 Hz and the on-load voltage varies from 0 to 0.8 V. In Figs.12 and 13, the area and tilt angles of Lissajous figures change with load. Fig.12 illustrates the change trends of active Lissajous figure, reactive power Lissajous figure and power circle with load. Fig.13 shows the change trend of power and tilt angles with load. As the load of VVVF hydraulic system increasing, the three-phase electric power of VFM increases. The ALF rotates clockwise and the RLF rotates anticlockwise, so the tilt angles both increase. Meanwhile, it can be seen that the voltage amplitude changes very little under load, but the current amplitude changes obviously with load. The curves of Fig.13 reflect a change law, that is the increase of the load will enhance its electric power and tilt angles of Lissajous figures.

Fig.12 Change trend of Lissajous figures and power circles

Fig.13 Change trend of motor power and tilt angles

4 Conclusions

1) The area of the ALF and the RLF is proportional to frequency and system load. It can intuitively express the active and reactive power of the VFM and reflect the power state of VVVF hydraulic system.

2) The area of the bounding rectangle is proportional to the apparent power, and it represents the load state of the power supply. The apparent power and active power can directly calculate the reactive power and the power factor of the motor. The dynamic power circle drawn by the active power, reactive power and apparent power can directly reflect the power changes of the motor. It is convenient for online monitoring the power matching and the energy reserve of VVVF hydraulic system.

3) We can identify the typical working conditions such as varying speed or varying load of the hydraulic system by observing the features of tilt angles. The tilt angle of the Lissajous figure is sensitive, and it contains many dynamic information about the operation of the equipment and needs further excavation and utilization.

4) The higher harmonic frequency with the multiplier of 5, 7, 11, 13, … in the voltage waveform will lead to higher copper consumption and distortion power of high harmonic current. Some fault information is hidden in the high harmonics of electric parameters. Therefore, the Lissajous fusion method of the harmonic components needs to be further researched in future work.