Resonance overvoltage control algorithms in long cable frequency conversion drive based on discrete mathematics

Yonghong Deng; Quanzhu Zhang

doi:10.1515/phys-2020-0120

Article Open Access

Resonance overvoltage control algorithms in long cable frequency conversion drive based on discrete mathematics

Yonghong Deng and Quanzhu Zhang

Published/Copyright: August 3, 2020

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From the journal Open Physics Volume 18 Issue 1

Abstract

In order to solve the problem that the long cable variable voltage and variable frequency (VVVF) system does not adopt an effective capacitor voltage sharing control method, resulting in a poor effect of resonance overvoltage control, the resonance overvoltage control algorithm of the long cable VVVF system based on discrete mathematics is studied. First, the long cable frequency conversion drive system is established. In order to ensure voltage loss in the range of motor requirements, a frequency converter–cable–motor (ICM) system connection mode is used to maintain the system operation. Based on the research of the capacitor voltage balance control strategy of a long cable frequency conversion drive system, the discrete mathematical model of the AC side of the ICM system is established by using this control strategy. The improved constant active power controller is obtained by establishing the mathematical model, and the resonant overvoltage in a long cable frequency conversion drive is realized by using the constant active power controller. The experimental results show that the algorithm can effectively control the resonance overvoltage phenomenon in the long cable frequency control system, and the control accuracy is over 97%. It has good performance and can be applied in practice.

Keywords: discrete mathematics; long cable; frequency conversion drive; resonance; overvoltage; control algorithm

1 Introduction

In the electric drive system of metallurgy, petrochemical, papermaking, textile, and other industries, in some application fields, the distance between frequency converter and induction motor can reach hundreds of meters or even thousands of meters, at this time, it must be connected with a long cable [1]. The insulation failure of long wires and cables will bring a great threat to the reliable operation of the system, which not only affects the production, but also increases the maintenance funds, resulting in undue economic losses [2]. Due to the distributed inductance and capacitance of the cable itself, the impedance of the cable does not match the impedance of the motor, resulting in a large du/dt of the motor, damaging the winding and cable of the insulating material of the motor, shortening the service life of the motor, and enhancing the electromagnetic interference [3]. In order to suppress the effect of overvoltage at the motor end, an output reactor with a voltage drop of 5% of the output phase voltage is often added at the output end of the converter. This method is simple in design and high in reliability, especially at high power. The system is widely used, but the cost of the reactor method is high and the ability of restraining overvoltage is limited. Therefore, in view of the problem of overvoltage suppression, a lot of research has been carried out in the literature at home and abroad. In reference [4], an LC output filter, which is suitable for the converter system with a high switching frequency, is proposed; in reference [5], an RC filter is proposed to be added at the motor end; in reference [6], the RLC filter has high requirements for parameter impedance matching, which is difficult to be applied in practice. According to the voltage level, power level, cable length, and application situation of the converter, different optimal overvoltage suppression methods are selected. Modeling and simulation is the most effective and cheap method.

Under the action of a sinusoidal AC power supply, when the natural frequency of a system is equal to or close to the resonant frequency of the system, the system would have resonance [7]. As the resonance is caused by a higher harmonic of the system, as long as the harmonic of the system is eliminated, the resonance of the system can be avoided. The first method is to filter out the harmonic vibration of the system by installing a filter [8]. This method can not only filter out the harmonics, but also restrain the reflection of the waves. However, the installation of a filter will bring cost, installation, and maintenance problems. An improper setting of filter parameters will lead to new resonance between the long cable and the filter, which will aggravate the resonance effect of the system [9]. The second method is to use a high-performance inverter to reduce the harmonic content of the system. The research shows that the system can reduce the harmonic of the system to a great extent without installing a filter. However, high-performance converters are expensive and account for a large part of the whole system investment. Once the wiring mode of the system is determined, the electrical parameters in the system can be determined, and the resonant frequency can be obtained through calculation and analysis [10]. Therefore, a new method to suppress the resonance overvoltage of the variable frequency long cable drive system is necessary.

2 Algorithmic definitions

2.1 Frequency conversion driving system for a long cable

Due to the long distance of a long cable, the influence of distribution parameters cannot be ignored. Assuming that the voltage at the receiver ( x = 0 ) is V m and the current is I m , the boundary conditions are determined. For the voltage and current at the distance x from the receiving end, the general solution of the above equation is as follows:

(1) V x = V m + Z b I m 2 e γ x + V m − Z b I m 2 e − γ x

(2) I x = V m / Z b + I m 2 e γ x + V m / Z b − I m 2 e − γ x

In equations (1) and (2), when x = l is used, the voltage and current at the end of the cable are calculated.

(3) V C = V m cosh ( γ l ) + Z b I m sinh ( γ l )

(4) I C = I m cosh ( γ l ) + V m Z b sinh ( γ l )

However, in order to analyze the connection between the cable and other components of the system, the equivalent circuit [11], which can represent the performance of the transmission line, is selected only from the end.

According to equations (3) and (4), a π -shaped equivalent circuit with lumped parameters can be obtained. The π -shaped equivalent circuit of long cable is shown in Figure 1.

$Figure 1 π \pi -shaped equivalent circuit of a long cable.$

Figure 1

π -shaped equivalent circuit of a long cable.

Among them:

(5) Z 1 ( j w ) = Z b sinh ( γ l )

(6) Z 2 ( j w ) = Z b sinh ( γ l ) cosh ( γ l ) − 1

In the above equations, z = r + j ω L denotes the series impedance/phase per unit length; y = g + j ω C denotes the parallel admittance/phase per unit length; Z b denotes the characteristic impedance of the cable; Z b = z / y denotes the transmission coefficient of the cable; and γ = z × y , l denotes the length of the cable.

For the long-distance variable frequency drive system, because of the different power supply distances, the connection mode of the system is also different. The research shows that the power supply system from several kilometers to more than ten kilometers can guarantee the voltage loss within the range required by the motor because of the short distance. Therefore, the connection mode of the converter–cable–motor (ICM) system is adopted, that is, the connection mode of the ICM system. It can meet the requirements.

Because the system resonance is mainly caused by the high-order harmonics of the system, and relative to the high-frequency components of the system, the impedance of the motor is very large, which is equivalent to the open circuit at the end of the cable [12]. The analysis shows that the influence of end-to-end open circuit on the whole analysis results is not obvious. According to Figure 1, the equivalent impedance Z C equation of the cable is as follows:

(7) Z C = Z b 1 tanh ( γ l )

Then the ratio G v of the cable end voltage U m to the cable end voltage U c is:

(8) G v = 1 cosh ( λ l )

However, for long cables, especially at high frequencies, skin effect must be considered. Skin effect is due to the current gathering on the surface of the cable conductor, “reducing” the cross-section of the conductor, and increasing the AC resistance of the conductor. Therefore, skin effect has a certain inhibition effect on the motor terminal overvoltage [13]. Usually, skin effect intensity can be calculated by the Bessel function, but considering the complexity of a Bessel function calculation, we adopt hyperbolic approximation method for the calculation. The parameters of a cable conductor considering skin effect are as follows:

(9) R hyp = 1 2 π r σ δ sinh 2 r δ + sin 2 r δ cosh 2 r δ − cos 2 r δ Ω m

(10) L hyp = 3 μ δ 32 π r sinh 2 r δ − sin 2 r δ cosh 2 r δ − cos 2 r δ H m

(11) Z b ′ = R hyp + j w [ L hyp + ( L e − L hyp ( f 0 ) ) ] G + j w C

(12) r ′ = { R hyp + j w [ L hyp + ( L e − L hyp ( f 0 ) ) ] } ( G + j w C )

Z b ′ and γ ′ are the characteristic impedance and propagation coefficient of the cable considering skin effect. Among them, ω is the angular frequency of the system, L e is the mutual inductance between conductors, and f 0 is the oscillation frequency of the cable. σ is the conductivity of a conductor (for copper σ = 5.75 × 10 7 Ω m − 1 ). μ is the permeability of the medium. The δ equation of skin depth is as follows:

(13) δ = 2 σ μ ω [ m ]

By substituting equation (11) and equation (12) into equations (7) and (8), we can obtain:

(14) Z C = Z b ′ 1 tanh ( γ ′ l )

(15) G V = 1 cosh ( γ ′ l )

From the above deduction, it can be found that G V is a function of the frequency. According to equation (15), the overvoltage of motor terminals at different frequencies can be obtained. Due to the skin effect, the motor terminal overvoltage is consistent to a certain extent. Moreover, with the increase in frequency, skin effect becomes more and more obvious, and the amplitude of an electric extreme overvoltage decreases gradually [14]. Therefore, we only consider the resonant frequency of the nearest fundamental frequency, that is, the resonant frequency that has the greatest impact on the system.

2.2 Resonant overvoltage control

2.2.1 Modulation strategy for an ICM system

In ICM systems, carrier phase shifted–PWM (CPS–PWM), space vector PWM, and nearest level modulation are commonly used as modulation strategies. When the number of levels is too large, the number of voltage vectors is too large and the control is complex. Therefore, for ICM systems with more levels, carrier phase shift modulation and near-level approximation modulation have advantages [15]. In this paper, carrier phase shift modulation is used, and the modulation wave is the output voltage of the upper and lower arms of each phase. Because of the symmetry of ICM three-phase units, it is known that the output voltage of upper and lower leg of ICM system is as follows:

(16) u p j = − u j O + U dc / 2 u n j = u j O + U dc / 2

The carrier is a triangular carrier with a frequency of f c , maximum amplitude of U dc , minimum amplitude of 0, and phase angle of 360 / n in turn ( n is the number of sub-modules of each bridge arm). The trigger signals of each sub-module are generated by comparing the modulated wave with the triangular carrier with the phase-shifted one.

When the traditional sequencing method is used in the capacitance voltage balance control of an ICM system, only according to the direction of bridge arm current and the result of capacitance voltage sequencing of sub-modules, the corresponding sub-modules are selected to be put in or removed [16,17,18], without considering the original switching status of sub-modules, which results in frequent switching of sub-modules and high loss of switching devices. Therefore, this paper adopts the improved capacitor voltage balance control, that is, on the basis of the traditional sequencing method, according to the change in bridge arm current direction, SM capacitor voltage is multiplied by different retention coefficients, and then sequenced [19]. The capacitor voltage equalization control flow is as follows:

Input the capacitance voltage U c i , current i arm of upper (lower) arm module, and the number of modules n that should be put into one arm obtained by the CPS method.
Detect whether the arm current i arm is greater than 0.
When the bridge arm current i arm is greater than 0, the capacitance voltage of the input sub-module is multiplied by a retention factor slightly less than 1. Then, according to n , n modules with smaller capacitance voltage are selected by the traditional sequencing method.
When the bridge arm current is not more than 0, the capacitance voltage of the input sub-module is multiplied by a retention factor slightly less than 1, and then the n modules with larger capacitance voltage are selected, according to the traditional sequencing method.
The trigger signal amplitude of n selected modules is 1.
Output trigger pulse signal.

Whether the bridge arm current is charged or discharged, the SM which is in the cut-off state and whose capacitor voltage deviates from the rated value is multiplied by a holding factor slightly greater than 1 when capacitor voltage balance control is adopted. Combining the charging and discharging conditions of the bridge arm current, this paper multiplies the SM capacitor voltage to be put into operation by different holding coefficients, and then sequences [20], so that the SM to be put into operation can keep its original working state, effectively improve the frequent switching of the sub-modules in the ICM system, and reduce the switching frequency and switching of the switching devices.

2.2.2 Discrete mathematical model of the AC side

Through the control strategy of capacitance voltage balance, it can be seen that the two connecting points J and J ′ of upper and lower bridge arm reactances connected with an equivalent controlled voltage source of upper and lower bridge arms in ICM system are equipotential points, so J and J ′ points can be virtually short-connected. From the AC side of the ICM system, the reactance of upper and lower bridge arms of each phase is equivalent to a parallel connection, and the equivalent reactance of the parallel connection is L / 2 . Thus, the mathematical model of the AC side of the ICM system can be obtained as follows:

(17) u s j − i s j R S − L S + L 2 d i s j d t = u j O

In the equation, u j o ( j = a , b , c ) is the ground voltage of J point, which is the output voltage of the AC side of the ICM system.

Equal Park transformation is used in pair (17). The transformation matrix is:

(18) P = 2 3 cos ω t cos ( ω t − 120 ° ) cos ( ω t + 120 ° ) − sin ω t − sin ( ω t − 120 ° ) − sin ( ω t + 120 ° ) 1 / 2 1 / 2 1 / 2

ω is the fundamental frequency of the system. In the d–q synchronous rotating coordinate system, the AC side mathematical model of the ICM system is as follows:

(19) u s d + ω L e i q − R S i d − L e d i d d t = u d u s q − ω L e i d − R S i q − L e d i q d t = u q

In equation (19), L e = L S + L / 2 ; u s d , u s q , i d , i q , d, and q axis components of u s j and i s j , respectively; u d and u q are d and q axis components of u J O .

Assuming that the sampling period of the control system is T S , within the sampling time t t = k T S to t + T S , the current differential term in equation (19) can be obtained from the Euler approximation equation.

(20) d i d d t ≈ i d ( t + T S ) − i d ( t ) T S d i q d t ≈ i q ( t + T S ) − i q ( t ) T S

Equation (20) is used to discretize equation (19). The mathematical model of AC side discretization of the ICM system is obtained as follows:

(21) u s d ( t + T S ) + ω L e i q ( t + T S ) − R S i d ( t + T S ) − L e [ i d ( t + T S ) − i d ( t ) ] / T S = u d ( t + T S ) u s d ( t + T S ) − ω L e i d ( t + T S ) − R S i q ( t + T S ) − L e [ i q ( t + T S ) − i q ( t ) ] / T S = u q ( t + T S )

Considering that the sampling frequency of an ICM control system is much higher than the fundamental frequency of an AC system, and the variation of power supply voltage in a sampling period is very small [21], it is assumed that the sampling period T S does not change.

(22) u s d ( t + T S ) = u s d ( t ) u s q ( t + T S ) = u s q ( t )

In addition, in practical control systems, because of the computational time of control instructions, the current inner loop controller usually has a period delay, so the instantaneous values of voltage and current at t + T S time can be approximately equal to the reference values at t time, that is:

(23) u d ( t + T S ) = u d ref ( t ) u q ( t + T S ) = u q ref ( t ) i d ( t + T S ) = i d ref ( t ) i q ( t + T S ) = i q ref ( t )

In equation (23), u d ref ( t ) , u q ref ( t ) , i d ref ( t ) , and i q ref ( t ) are, respectively, the reference values of u d , u q , i d , and i q at t time, i.e., the expected output voltage and current injected into an ICM system at t + T S time in d and q synchronous rotating coordinates.

By substituting equations (22) and (23) into equation (21), it can be obtained that:

(24) u s d ( t ) + ω L e i q ( t ) − R S i d ref ( t ) − L e [ i d ref ( t ) − i d ( t ) ] / T S = u d ref ( t ) u s d ( t ) − ω L e i d ( t ) − R S i q ref ( t ) − L e [ i q ref ( t ) − i q ( t ) ] / T S = u q ref ( t )

According to equation (24), the internal current loop discrete controller of the AC side of the ICM system can be obtained, as shown in Figure 2.

Figure 2

Discrete inner current controller of the ICM system.

In order to balance the power transmitted in the DC system, the external loop control of the ICM system must adopt a constant DC voltage control at one end and a constant active power control at the other end.

The structure of the constant power controller in the outer loop of the inverter side and the constant DC voltage and AC voltage controller in the rectifier side are shown in Figure 3. The K p and K i in the figure are, respectively, the proportional gain and integral gain of the PI controller.

Figure 3

Outer loop controller. (a) Fixed active power controller; (b) fixed reactive power controller; (c) constant DC voltage controller. (d) fixed AC voltage controller.

In Figure 3, P 2ref and Q 2ref are the active power and reactive power instruction values of the inverting side, respectively; P 2 and Q 2 are the active power and reactive power measurement values of the inverting side; the outputs i d 2 ref and i q 2 ref of the power controller are the reference values of the d and q components of the current of the AC system on the inverting side; U dcref and U s 1 ref are the voltage instruction values of the DC bus and the AC bus on the rectifying side, respectively. U s 1 ref and U s 1 are the measured values of the DC bus voltage and AC bus voltage on the rectifier side; outputs i d 1 ref and i q 1 ref of the voltage controller are the reference values of current d and q components of the AC system on the rectifier side. When the voltage of the AC side of the ICM system is unbalanced or the AC system is asymmetrical, the DC voltage outer loop controller shown in Figure 3 is not enough to maintain the stable operation of the DC voltage due to the existence of negative sequence components. Especially when the asymmetrical fault occurs at the fixed DC voltage side, the active power transmission on both sides is uneven. Hence, it is difficult to maintain the control of DC voltage. The active power controller in Figure 3 is improved by adding a DC voltage control link on the basis of the originally active power control, which can maintain the stable control of the DC voltage when an AC system fails and improve the anti-disturbance ability of an ICM system [22]. The improved constant active power controller includes two parts: DC voltage command correction and control. The correction of DC voltage instruction is the correction of the deviation between the active power instruction value Pref and the actual measurement value P of active power. The correction of the reference value U of DC voltage is obtained by the PI regulation.

(25) Δ U dcref = K p + K i S ( P ref − P )

The revised DC voltage instruction value is:

(26) U ′ dcref = U dcref + Δ U dcref

The control link is the deviation between the revised DC voltage instruction value U dcref ′ and the DC voltage measurement value U dc . The reference value of the d-axis current i d ref is obtained by the PI adjustment.

(27) i d ref = [ K P + ( K i / S ) ] ( U dcref ′ − U dc )

The structure of the fixed active power controller that can be improved is shown in Figure 4.

Figure 4

Improved active power controller.

The improved fixed active power controller based on Figure 4 can effectively control the overvoltage phenomenon in the long cable frequency conversion drive system.

3 Results

In order to verify that the algorithm in this paper is to control the resonant overvoltage of a long cable drive by frequency conversion, the long cable drive system controlled by the algorithm is simulated based on the simulation software of MATLAB. The power supply voltage of the system is 4,160 V and the rated power is 60 Hz [23]. The rated voltage of the medium voltage converter is 41,160 V, the rated current is 140 A, and the rated capacity is 1,000 K. VA; cable 15 km in diameter 150 mm²; motor rated voltage 3,848 V, rated current 130 A, rated power 840 HP, and rated torque 1,400 N m.

The starting frequency of the motor in the long cable variable frequency drive system controlled by this algorithm is shown in Figure 5.

Figure 5

Starting frequency rise curve.

According to the motor starting frequency of the long cable variable frequency drive system in Figure 5, it can be seen that the starting frequency of the long cable variable frequency drive system controlled by the algorithm in this paper is gradually increased, turning to constant speed in about 15 s, and finally reaching 65 Hz. It can be seen that the algorithm can effectively control the resonance overvoltage phenomenon in the long cable frequency control system, with high control accuracy and good performance, which can be widely used.

Load torque is a function of the motor speed in a long cable variable frequency drive system. The load torque characteristics of motor in long cable variable frequency drive system are shown in Figure 6.

Figure 6

Motor load torque.

The variation of electromagnetic torque of the motor is obtained from the load torque characteristics of the long cable variable frequency drive motor in Figure 6, as shown in Figure 7.

Figure 7

Motor electromagnetic torque changes.

According to the results of electromagnetic torque of the long cable variable frequency drive motor in Figure 7, it can be seen that with the change of starting frequency of the motor, the electromagnetic torque also changes, and the fluctuation is large. The whole change in trend of electromagnetic torque of long cable variable frequency drive motor varies with the change of load torque until the rated torque is reached [24]. The large torque fluctuation of the motor in the long cable variable frequency drive system is mainly due to the distortion of the sinusoidal control signal and speed on the boundary of the frequency change. This is because the time of frequency change does not necessarily occur at the end of a complete cycle of the adjustment signal. Before the end of one cycle of the control signal, the first half cycle of the signal in the next cycle may be widened or narrowed.

The control signal of the long cable frequency conversion drive system is controlled by the algorithm presented in this paper, as shown in Figure 8.

Figure 8

Control signal change.

After using this algorithm to control the long cable frequency conversion drive system, the stator current variation of the motor in the long cable frequency conversion drive system is shown in Figure 9.

Figure 9

Motor stator current changes.

From Figure 9, it can be seen that the starting current of the motor is about 1.5 times of the rated current of the frequency converter, and the duration is very short, within the required range of the frequency converter [25]. With the change of load torque, the stator current has the same trend, and finally runs in the rated current state.

The stator voltage variation of the motor of the long cable frequency conversion drive system is shown in Figure 10, after the algorithm is used to control the long cable frequency conversion drive system.

Figure 10

Motor stator voltage changes.

Through the simulation results of Figure 10, it can be seen that the stator voltage of the motor increases gradually with the increase of the system frequency and finally stabilizes near the rated voltage after using the algorithm to control the long cable variable frequency drive system. Through the above experimental results, it can be seen that the proposed algorithm can control the long cable frequency conversion drive system, which can meet the normal starting requirements of the motor and prevent the occurrence of overvoltage phenomenon.

In order to further verify the control effect of the proposed algorithm, three algorithms are used to control the resonant overvoltage in the long cable frequency conversion drive by comparing the proposed algorithm with the pulse width modulation algorithm and the MultiMedia Card (MMC) algorithm. The comparison results of the three algorithms are shown in Table 1.

Table 1

Comparison of three algorithm control results

Number of experiments	This algorithm			Pulse width modulation algorithm			MMC algorithm
Number of experiments	Control precision/%	Control time/s	Robustness/%	Control precision/%	Control time/s	Robustness/%	Control precision/%	Control time/s	Robustness/%
1	98.51	10.52	99.05	91.52	18.62	87.18	89.62	22.61	86.51
2	98.47	11.52	98.12	92.64	19.64	86.54	93.64	18.64	85.46
3	98.62	12.64	97.18	91.36	20.18	88.19	91.54	23.61	84.71
4	97.58	11.85	97.48	93.64	18.64	87.49	92.07	17.42	91.62
5	99.05	12.47	98.15	93.05	18.61	83.36	95.17	16.84	92.67
6	97.65	12.96	97.05	92.14	19.62	91.58	91.26	21.54	88.64
7	98.05	9.64	98.17	93.64	19.89	94.36	92.64	23.64	87.49
8	97.58	10.11	98.47	91.47	19.99	87.62	88.47	22.08	89.65
9	97.36	10.63	98.05	92.61	20.47	81.62	87.64	19.64	88.29
10	99.15	11.47	98.34	90.74	19.68	84.62	89.05	21.47	90.54

From the experimental results in Table 1, it can be seen that the control accuracy of the proposed algorithm is above 97%, while the control accuracy of the pulse width modulation algorithm and the MMC algorithm is below 96%, and the proposed algorithm is used to control the resonance overvoltage in the long cable frequency conversion drive. The control time of the resonance overvoltage phenomenon is about 10 s, and the control time of pulse width modulation algorithm and MMC algorithm is about 20 s [26]. The control precision and control time of this algorithm are obviously better than those of the other two algorithms, and the robustness of this algorithm to control resonance overvoltage phenomenon in variable frequency drive of long cable is better. Third, the robustness of this algorithm to control resonance overvoltage phenomenon in variable frequency drive of long cable is better. The control performance of the proposed algorithm is verified. It can be seen that the resonance overvoltage control algorithm based on discrete mathematics has high control accuracy, short control time, and good robustness, which can effectively control the resonance overvoltage phenomenon in the long cable frequency control system, and can be applied to real life.

4 Discussions

Resonance refers to a periodic or quasi-periodic operating state in an oscillating system, which is characterized by a sharp rise in the amplitude of one or more harmonics. In general, series resonance will produce overvoltage in a part of the power grid, endangering the insulation of electrical equipment. It can also generate electricity and burn equipment. It may also affect the working conditions of overvoltage protection devices, such as the arc extinguishing conditions of valve arresters. Resonance is a kind of steady-state phenomenon. Resonance overvoltage in a power system will not only occur in the transition process of an operation or accident, but also exist stably for a long time after the transition process, until a new operation occurs and the resonance condition is destroyed. Therefore, the duration of resonance overvoltage is longer than action. The longer voltage time, the greater harm to the insulation of electrical equipment. Once overvoltage occurs, it usually has serious consequences [27]. The operation experience shows that resonance overvoltage will be produced in all voltage levels of power grid, especially at 35 kV and below, which causes more accidents.

In a normal synchronous operation, the reactance of hydrogenerator will change two cycles after each cycle. In addition, the reactance of hydrogenerator or turbogenerator changes periodically with the change of stator flux during an asynchronous or synchronous operation. In all these cases, if the reactance of the external circuit of the motor meets certain conditions and the loss resistance is small enough, it is possible to excite a special parametric resonance phenomenon in the oscillating circuit with periodic changes of inductance parameters. During the periodic change of inductance parameters, the resonance between inductance and capacitance will pass continuously. The oscillation point leads to a sharp rise in voltage and current amplitude at the end of a synchronous motor, and the self-excitation overvoltage multiple is high. It not only threatens the insulation of electrical equipment and damages the arrester, but also prevents the motor from running in parallel with other power sources.

Electrical equipment in the operation of power grid, for some reasons, such as neutral point voltage displacement, circuit breaker non-full-phase or different operations, electromagnetic voltage transformer saturation, and so on, easily produce resonance overvoltage. Overvoltage first causes equipment aging, and electrical equipment with a low insulation level is damaged, eventually causing accidents. In order to avoid such accidents as far as possible, it is necessary to prevent resonance overvoltage as far as possible. The following measures are usually taken:

Necessary calculations must be made in design and necessary arrangements must be made in operation to avoid unfavorable resonance circuits. Additional measures should be taken to prevent resonance and reduce the amplitude of resonance overvoltage and shorten its existence time.
Make sure that the three-phase synchronous operation of the circuit breaker does not occur in all-phase operation, avoiding the generation of neutral point displacement voltage. Avoid the occurrence of circuit breaker rejection, do not use fuse equipment.
Strengthen line inspection and maintenance to avoid line breakage.
Select voltage transformers with better excitation characteristics and capacitive voltage transformers.
A certain ground capacitance is added to the bus.
Keep electrical equipment clean regularly.

Of course, there are many reasons for overvoltage, such as lightning overvoltage, switching overvoltage, and so on. It is not only resonance that causes overvoltage. However, resonance overvoltage is one of the most common and harmful causes of power system equipment accidents, which cannot be solved carefully.

5 Conclusions

Resonance overvoltage phenomenon can easily cause damage to power devices or even large-scale power outages. In order to effectively control the resonance overvoltage phenomenon in a long cable frequency conversion drive, the long cable frequency conversion drive system with connection mode of the ICM system is studied, and the AC side discretization number of a long cable frequency conversion drive system is established. Based on the discrete mathematical model, an improved constantly active power controller is designed to effectively control the resonance overvoltage in the variable frequency drive of a long cable. The experimental results show that the proposed algorithm has high control efficiency and good robustness in controlling the resonance overvoltage phenomenon in a long cable frequency conversion drive, and can effectively ensure the operation safety of a long cable frequency conversion drive.

In future research, in order to better control the resonant overvoltage phenomenon in the long cable variable frequency drive, the more precise control effect will be the goal, and the long cable variable frequency speed regulation overvoltage control algorithm based on discrete mathematics will be further optimized.

Acknowledgments

This work is supported by “The Fundamental Research Funds for the Central Universities” (No. 3142018049).

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Received: 2020-04-01

Revised: 2020-05-28

Accepted: 2020-06-07

Published Online: 2020-08-03

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/phys-2020-0120

Keywords for this article

discrete mathematics; long cable; frequency conversion drive; resonance; overvoltage; control algorithm

Creative Commons

BY 4.0