A three-phase Vienna rectifier variable clamped interval carrier discontinuous modulation method

Abstract

The application discloses a variable clamping interval carrier discontinuous modulation method of a three-phase Vienna rectifier. ma , u mb , u mc ; a balanced continuous component u bc , a zero-crossing clamping component u oc and a peak clamping component u pc are calculated; a variable interval clamping coefficient k VAC is set according to different modulation ratios, and a variable interval clamping component u VAC is calculated according to a formula u VAC =k VAC (1-m); a zero sequence voltage u z is calculated, and the zero sequence voltage u z is injected into three-phase normalized sinusoidal waves to obtain three-phase Vienna rectifier variable clamping interval modulation waves u ref_a , u ref_b and u ref_c of A phase, B phase and C phase. The variable clamping interval carrier discontinuous modulation method can reduce terminal voltage error, reduce midpoint potential fluctuation, improve input current quality, and has the advantages of simple calculation and convenient implementation.

Description

Technical Field

[0001] This invention relates to the field of power electronics, and more particularly to a carrier discontinuous modulation method for a three-phase Vienna rectifier. Background Technology

[0002] The Vienna rectifier is the simplest circuit structure among three-phase three-level converters and is becoming increasingly popular in many unidirectional active front-end applications. It offers several advantages, such as the ability to operate at unity power factor, thus reducing power supply current distortion. It also boasts high power density, high efficiency, and high reliability. In this topology, only half the DC link voltage is present on the bidirectional switches, thus requiring only lower voltage stress on these switches. These advantages make it an attractive topology for active front-end rectification applications.

[0003] Although the Vienna rectifier is a three-level converter, it only achieves complete control of the neutral point connection through bidirectional switching. However, because the diodes are connected to the positive and negative voltage rails, the current direction determines the voltage of the upper and lower bus capacitors. When the Vienna rectifier operates outside of unity power factor, the reference voltage and current are out of phase near the current zero-crossing point, which will generate a terminal voltage error near the current zero-crossing point, resulting in low-frequency distortion.

[0004] The literature Z. Zhang, OCThomsen, and MAE Andersen, “Discontinuous PWM modulation strategy with circuit-level decoupling concept of three-level neutral-point-clamped (NPC) inverter,” IEEE Trans. Ind. Electron., vol. 60, no. 5, pp. 1897–1906, May 2013, proposes a carrier discontinuous modulation method for traditional three-level inverters. However, this method cannot meet the important condition that the reference voltage and current are in phase near the current zero crossing. When applied to Vienna rectifiers, this method cannot achieve unity power operation and introduces additional low-frequency harmonics into the input current. Therefore, this method is not suitable for Vienna rectifiers. The literature X. Zhang, Q. Wang, R. Burgos and D. Boroyevich, "Discontinuous pulse width modulation methods with neutral point voltage balancing for three-phase Vienna rectifiers," 2015 IEEE Energy Conversion Congress and Exposition (ECCE), 2015, pp. 225-232, doi:10.1109 / ECCE.2015.7309692, proposes a carrier discontinuous modulation method for Vienna rectifiers. This method enables the Vienna rectifier to operate at unity power factor and clamps the reference voltage to zero at the current zero-crossing point, solving the problem of voltage and current out of phase at the current zero-crossing point. However, this method has a large clamping interval at low modulation ratios, which introduces additional low-frequency ripple into the input current.

[0005] Therefore, it is necessary to study a variable clamping interval carrier discontinuous modulation method. Under different modulation ratios, the zero-crossing clamping interval can be kept within a small range, thereby reducing terminal voltage error, reducing midpoint potential fluctuation, and improving the quality of input current. Summary of the Invention

[0006] To overcome the shortcomings of traditional discontinuous carrier modulation methods for Vienna rectifiers, this invention proposes a variable clamping interval discontinuous carrier modulation method for three-phase Vienna rectifiers. This method allows the Vienna rectifier to maintain the zero-crossing clamping interval within a small range under different modulation ratios, thereby reducing terminal voltage error, minimizing midpoint potential fluctuations, and improving input current quality. Furthermore, compared to traditional space vector modulation methods, this invention eliminates the need to calculate the space vector's action time, making engineering implementation very convenient.

[0007] This invention obtains the normalized sine waves of phases A, B, and C as u based on the three-phase normalization formula of the SPWM modulation strategy of a three-phase Vienna rectifier. ma u mb u mc The equilibrium continuous component u is calculated. bc Zero-crossing clamping component u oc and peak clamping component u pc The variable-range clamping coefficient k is set according to different modulation ratios. VAC And according to formula u VAC =k VAC (1-m) is used to calculate the interval clamping component u. VAC ; Calculate the zero-sequence voltage u z and the zero-sequence voltage u z By injecting a three-phase normalized sine wave, the three-phase Vienna rectifier clamping interval modulation wave of phases A, B, and C is obtained. ref_a u ref_b and u ref_c .

[0008] The specific details of the three-phase Vienna rectifier variable clamp interval carrier discontinuous modulation method of the present invention are as follows:

[0009] 1. Based on the three-phase normalization formula of the SPWM modulation strategy for a three-phase Vienna rectifier, the normalized sine waves of phases A, B, and C are obtained as u... ma u mb u mc The method for determining the three-phase normalized sine wave is as follows:

[0010]

[0011] In equation (Ⅰ), f g Let m be the grid frequency, m be the modulation ratio, and m ∈ (0,1). The modulation ratio m can be expressed by the formula... We obtain U, where U m U represents the amplitude of the AC reference phase voltage. dc This indicates the DC-side bus voltage.

[0012] 2. Calculation of balanced continuous components:

[0013] Define the balanced continuous component required for intermittent carrier modulation in the variable clamping interval of a three-phase Vienna rectifier as u. bc This invention relates to u bc The method for determining it is as follows:

[0014]

[0015] In formula (II) u bc The balanced continuous component injected for the variable clamping interval carrier discontinuous modulation of a three-phase Vienna rectifier. for The maximum value, for The minimum value, Calculated by equation (Ⅲ);

[0016]

[0017] In equation (Ⅲ), u mx (x = a, b, c) represents the normalized sine waves u of phases A, B, and C. ma u mb u mc ;

[0018] 3. Calculation of zero-crossing clamping components:

[0019] Define the normalized sine waves u of phases A, B, and C at a certain moment. ma u mb u mc The maximum value is u max The minimum value is u min The intermediate value is the zero-crossing clamping component u. oc .

[0020] 4. Calculation of peak clamping component:

[0021] Define the peak clamping component as u pc This invention relates to u pc The method for determining it is as follows:

[0022]

[0023] In equation (Ⅳ), u max and u min Normalized sine waves u for phases A, B, and C respectively ma u mb u mc The maximum and minimum values;

[0024] 5. Calculation of Variable Interval Clamping Components:

[0025] Define the variable interval clamping component as u VACThis invention relates to u VAC The determination method is as follows:

[0026] u VAC =k VAC (1-m)(V)

[0027] In equation (V), m is the modulation ratio, and k VAC For interval clamping coefficients, 0≤k VAC ≤1;

[0028] 6. Zero-sequence voltage calculation:

[0029] Define the zero-sequence voltage as u z This invention relates to u z The determination method is as follows:

[0030]

[0031] In equation (VI), u max and u min Normalized sine waves u for phases A, B, and C respectively ma u mb u mc The maximum and minimum values; u bc The balanced continuous component injected for the discontinuous carrier modulation of the variable clamping interval of a three-phase Vienna rectifier; u oc The zero-crossing clamping component injected for discontinuous carrier modulation of the variable clamping interval of a three-phase Vienna rectifier; u pc For peak clamping components; u VAC For variable interval clamping components;

[0032] 7. Obtain the modulation wave of the three-phase Vienna rectifier with variable clamping range:

[0033] The modulation waves of the three-phase Vienna rectifier with variable clamping intervals are defined as u ref_a u ref_b and u ref_c This invention relates to u ref_a u ref_b and u ref_c The determination method is as follows:

[0034]

[0035] In the above formula, u ref_a u ref_b and u ref_c The three-phase Vienna rectifier modulation wave with variable clamping range, u ma u mb and u mc This represents the normalized sine wave of phases A, B, and C, u zThis represents the zero-sequence voltage injected by the carrier discontinuous modulation of the variable clamping interval of the three-phase Vienna rectifier.

[0036] The beneficial effects of adopting the above invention are as follows:

[0037] This invention enables Vienna rectifiers to maintain the zero-crossing clamping range within a small range under different modulation ratios, thereby reducing terminal voltage error, minimizing midpoint potential fluctuations, and improving input current quality. Furthermore, this invention is simple to calculate and easy to implement in engineering. Attached Figure Description

[0038] Figure 1 This is a three-phase Vienna rectifier main circuit topology;

[0039] Figure 2 This is a flowchart illustrating the implementation of a three-phase Vienna rectifier variable clamp interval carrier discontinuous modulation method according to the present invention.

[0040] Figure 3 A waveform diagram of a three-phase normalized sinusoidal signal and its sector relationship within one cycle;

[0041] Figure 4 The clamping coefficient k for different intervals in the method of this invention VAC The maximum permissible clamping angle for modulation ratio m∈(0,1);

[0042] Figure 5a , Figure 5b , Figure 5c , Figure 5d The following are simulation results of the modulated wave in the implementation example when the modulation ratio m = 0.7, wherein: Figure 5a For the interval clamping coefficient k VAC Simulation results of the modulation wave when = 0, Figure 5b For the interval clamping coefficient k VAC Simulation results of the modulation wave at 0.5. Figure 5c For the interval clamping coefficient k VAC Simulation results of the modulation wave at 0.7 Figure 5d Variable interval clamping coefficient k VAC Simulation results of the modulation wave when = 1;

[0043] Figure 6 This refers to the clamping region in the first sector of the method of the present invention;

[0044] Figure 7 In this implementation example, the method of the present invention is used when m = 0.7 and k VAC Simulation waveforms of DC-side capacitor voltage and total voltage when = 0.7;

[0045] Figure 8In this implementation example, the method of the present invention is used when m = 0.7 and k VAC Simulation results of the A-phase modulation waveform, A-phase voltage and current, and A-phase bridge arm voltage when the voltage is 0.7.

[0046] Figure 9 In this implementation example, the method of the present invention is used when m = 0.7 and k VAC The THD of phase A current and its spectral characteristics when THD = 0.7. Detailed Implementation

[0047] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0048] Please see Figures 1 to 9 The image shows a method for discontinuous carrier modulation with variable clamping intervals in a three-phase Vienna rectifier according to the present invention.

[0049] like Figure 1 As shown, the main circuit topology diagram of this invention includes a voltage source e for phase A electricity. a The voltage source of phase B electricity e b The voltage source of phase C electricity e c First to third inductors L a L b L c Diodes D from the first to the sixth a+ D a- D b+ D b- D c+ D c- The first to sixth switching transistors Q1, Q2, Q3, Q4, Q5, and Q6; the first capacitor C1 and the second capacitor C2; the first resistor R1 and the second resistor R2; and the voltage source e for phase A. a The voltage source of phase B electricity e b The voltage source of phase C electricity e c One end is connected together, the first inductor L a Voltage source e connected in series with phase A a With the first diode D a+ Between the anodes, the second inductor L b Voltage source e connected in series with phase B b With the third diode D b+ Between the anodes, the third inductor L c Voltage source e connected in series with phase C c With the fifth diode D c+ Between the anodes, the second diode D a- Fourth diode D b- The sixth diode D c- The cathodes are connected together, denoted as point N, and the anodes are connected to the first diode D. a+anode, third diode D b+ anode, fifth diode D c+ The anode connection is made, and one end of the second switch Q2, the fourth switch Q4, and the sixth switch Q6 are connected together, denoted as point O. The first switch Q1 and the second switch Q2 are connected in series and then connected to the first diode D. a+ Between the anode and point O, the third switch Q3 and the fourth switch Q4 are connected in series to the third diode D. b+ Between the anode and point O, the fifth switch Q5 and the sixth switch Q6 are connected in series and then connected to the fifth diode D. c+ Between the anode and point O, the first diode D a+ anode, third diode D b+ Fifth diode D c+ The cathodes are connected together, denoted as point P. The first capacitor C1 and the first resistor R1 are connected in parallel between point P and point O. The second capacitor C2 and the second resistor R2 are connected in parallel between point N and point O.

[0050] This invention obtains the normalized sine waves of phases A, B, and C as u based on the three-phase normalization formula of the SPWM modulation strategy of a three-phase Vienna rectifier. ma u mb u mc The equilibrium continuous component u is calculated. bc Zero-crossing clamping component u oc and peak clamping component u pc The variable-range clamping coefficient k is set according to different modulation ratios. VAC And according to formula u VAC =k VAC (1-m) is used to calculate the interval clamping component u. VAC ; Calculate the zero-sequence voltage u z and the zero-sequence voltage u z By injecting a three-phase normalized sine wave, the three-phase Vienna rectifier clamping interval modulation wave of phases A, B, and C is obtained. ref_a u ref_b and u ref_c .

[0051] like Figure 2 As shown, the specific implementation process of the three-phase Vienna rectifier variable clamp interval carrier discontinuous modulation method of the present invention is as follows:

[0052] 1. Based on the three-phase normalization formula of the SPWM modulation strategy for a three-phase Vienna rectifier, the normalized sine waves of phases A, B, and C are obtained as u... ma u mb u mc The method for determining the three-phase normalized sine wave of this invention is as follows:

[0053]

[0054] In equation (Ⅰ), f g Let m be the grid frequency, m be the modulation ratio, and m ∈ (0,1). The modulation ratio m can be expressed by the formula... We obtain U, where U m U represents the amplitude of the AC reference phase voltage. dc express Figure 1 DC bus voltage.

[0055] 2. Calculation of balanced continuous components:

[0056] Define the balanced continuous component required for intermittent carrier modulation in the variable clamping interval of a three-phase Vienna rectifier as u. bc This invention relates to u bc The method for determining it is as follows:

[0057]

[0058] In formula (II) u bc The balanced continuous component injected for the variable clamping interval carrier discontinuous modulation of a three-phase Vienna rectifier. for The maximum value, for The minimum value, Calculated by equation (Ⅲ);

[0059]

[0060] In equation (Ⅲ), u mx (x = a, b, c) represents the normalized sine waves u of phases A, B, and C. ma u mb u mc ;

[0061] 3. Calculation of zero-crossing clamping components:

[0062] Define the normalized sine waves u of phases A, B, and C at a certain moment. ma u mb u mc The maximum value is u max The minimum value is u min The intermediate value is the zero-crossing clamping component u. oc Combining Figure 3 From the waveform diagram and sector relationship diagram of the three-phase normalized sinusoidal signal within one cycle, the normalized sinusoidal waves u of phases A, B, and C can be obtained. ma u mb u mc The maximum, median, and minimum values, where the maximum, median, and minimum values ​​are respectively umax , u mid , u min . For example, 2πf g When it is between 0 and π / 3, it corresponds to sector I. In sector I, the three-phase normalized sine wave u ma , u mb , u mc Among them, u ma is the maximum value, and u mb is the intermediate value, and u mc is the minimum value.

[0063] 4. Peak clamping component calculation:

[0064] Define the peak clamping component as u pc . In the present invention, the determination method of u pc is as follows:

[0065]

[0066] In formula (IV), u max and u min are the maximum and minimum values of the normalized sine waves u ma , u mb , u mc of phases A, B, and C respectively;

[0067] 5. Variable interval clamping component calculation: <000042�>

[0068] [[ID=5︰]]Define the variable interval clamping component as u VAC . In the present invention, the determination method of u VAC is as follows:

[0069] ?u VAC = k [[ID=6︰]] VAC (1 - m) (V) ?

[0070] In formula (V), m is the modulation ratio, and k VAC is the variable interval clamping coefficient, 0 ≤ k VAC ≤ 1;

[0071] Combined with Figure 4 the critical clamping angles corresponding to different modulation ratios in VAC when m < 0.4, k VAC is set to 0.9; when 0.4 < m < 0.6, k VAC is set to 0.7; when 0.6 < m < 0.8, k VAC is set to 0.5; when 𝟘 < m < 1, k

[0072] The reason for modifying the variable interval clamping coefficient in the present invention is as follows:

[0073] Taking m = 0.7 as an example, in Fig. 5, uma Represents the normalized sine wave of phase A, u z Represents zero-sequence voltage, u ref_a This represents the A-phase modulation wave of a three-phase Vienna rectifier with variable clamping range. Figure 5a In the middle, k VAC The zero-crossing clamp angle is approximately 15°. Figure 5b In the middle, k VAC The value is 0.5, and the zero-crossing clamping angle is approximately 8°. Figure 5c In the middle, k VAC The value is 0.7, and the zero-crossing clamping angle is approximately 4.5°. Figure 5d In the middle, k VAC The value is 1.0, and the zero-crossing clamping angle is 0°, therefore the variable interval clamping coefficient k is 1.0. VAC The larger the value of ∈(0,1), the smaller the zero-crossing clamping angle, and the larger the value of k. VAC When k = 0, the zero-crossing clamping angle is the largest. VAC When =1, the zero-crossing clamping angle is the smallest and is 0°.

[0074] The clamping modes of the variable clamping interval carrier discontinuous modulation in the first sector under different modulation ratios are as follows: Figure 6 As shown, the larger the clamping coefficient in the variable interval, Figure 6 The smaller the zero-crossing clamping region, the larger the equilibrium continuity region; the smaller the interval clamping coefficient, the larger the equilibrium continuity region. Figure 6 The larger the zero-crossing clamping region, the smaller the equilibrium continuity region;

[0075] 6. Zero-sequence voltage calculation:

[0076] Define the zero-sequence voltage as u z This invention relates to u z The determination method is as follows:

[0077]

[0078] In equation (VI), u max and u min These are three-phase normalized sine waves u ma u mb u mc The maximum and minimum values; u bc The balanced continuous component injected for the discontinuous carrier modulation of the variable clamping interval of a three-phase Vienna rectifier; u oc The zero-crossing clamping component injected for discontinuous carrier modulation of the variable clamping interval of a three-phase Vienna rectifier; u pc For peak clamping components; u VAC For variable interval clamping components;

[0079] 7. Obtain the modulation wave of the three-phase Vienna rectifier with variable clamping range:

[0080] The modulation waves of the three-phase Vienna rectifier with variable clamping intervals are defined as u ref_a u ref_b and u ref_c This invention relates to u ref_a u ref_b and u ref_c The determination method is as follows:

[0081]

[0082] In the above formula, u ref_a u ref_b and u ref_c The three-phase Vienna rectifier modulation wave representing the variable clamping intervals of phases A, B, and C, u ma u mb and u mc Represents the normalized sine waves of phases A, B, and C, u z This represents the zero-sequence voltage injected by the carrier discontinuous modulation of the variable clamping interval of the three-phase Vienna rectifier.

[0083] This invention utilizes PLECS software to build a simulation model of a three-phase Vienna rectifier, and verifies the effectiveness of the variable clamping interval carrier discontinuous modulation method of the three-phase Vienna rectifier. The simulation conditions are: simulation step size 3µs, AC voltage RMS value 115V, fundamental frequency 400Hz, and switching frequency 99kHz.

[0084] Figure 7 The invented three-phase Vienna rectifier variable clamp interval carrier discontinuous modulation method is used in m=0.7, k VAC The simulation waveform when U = 0.7 is shown in the figure. dc1 for Figure 1 Upper bus capacitor voltage, U dc2 for Figure 1 The voltage of the lower bus capacitor, U dc This represents the total voltage of the DC-side bus. The results show that the modulation method of this invention has the ability to reduce midpoint potential fluctuations.

[0085] Figure 8 The invented three-phase Vienna rectifier variable clamp interval carrier discontinuous modulation method is used in m=0.7, k VAC Simulation waveform when u = 0.7 z This is the zero-sequence voltage injected in this invention, u ref_a It is a phase A modulated wave, u a It is the AC side A-phase input voltage, i a It is the AC side A-phase input current, u ao This refers to the voltage of phase A bridge arm. AO indicates that the voltage of phase A bridge arm is clamped to 0 at the zero-crossing point of the phase A current, determined by... Figure 8 As can be seen, the variable clamping interval carrier discontinuous modulation method of the present invention can change the clamping angle of the modulation wave near the current zero crossing, and the current waveform quality is good. Figure 9 This indicates that after applying the modulation method of this invention to the three-phase Vienna rectifier, the current harmonic characteristics are good, and the current THD is 1.64%, which is far lower than the 5% requirement in aviation applications. This verifies the effectiveness of the variable clamping interval carrier discontinuous modulation method of this invention.

[0086] The working principle and process of this invention are as follows:

[0087] Based on the three-phase normalization formula of the SPWM modulation strategy for a three-phase Vienna rectifier, the normalized sine waves of phases A, B, and C are obtained as uA, uB, uC, uC, uD, uE ... ma u mb u mc The equilibrium continuous component u is calculated. bc Zero-crossing clamping component u oc and peak clamping component u pc The variable-range clamping coefficient k is set according to different modulation ratios. VAC And according to formula u VAC =k VAC (1-m) is used to calculate the interval clamping component u. VAC ; Calculate the zero-sequence voltage u z and the zero-sequence voltage u z By injecting a three-phase normalized sine wave, the three-phase Vienna rectifier clamping interval modulation wave of phases A, B, and C is obtained. ref_a u ref_b and u ref_c Then, a simulation model of a three-phase Vienna rectifier was built using PLECS software, and the effectiveness of the variable clamping interval carrier discontinuous modulation method of the three-phase Vienna rectifier of this invention was verified by simulation.

Claims

1. A method for discontinuous carrier modulation with variable clamping intervals in a three-phase Vienna rectifier, characterized in that, Based on the three-phase normalization formula of the SPWM modulation strategy of the three-phase Vienna rectifier, the normalized sine waves of phases A, B, and C are respectively obtained. , , ; The equilibrium continuous component was calculated. Zero-crossing clamping component and peak clamping components ; Set the variable-range clamping coefficient according to different modulation ratios And according to the formula The variable interval clamping components were calculated. Calculate the zero-sequence voltage and zero-sequence voltage By injecting a three-phase normalized sine wave, the three-phase Vienna rectifier clamping interval modulation waves of phases A, B, and C are obtained. , and ; Zero-sequence voltage The method for determining it is shown in equation (Ⅰ): （Ⅰ） In formula (Ⅰ), and Normalized sine waves for phases A, B, and C, respectively. , , The maximum and minimum values; The balanced continuous component injected for the carrier discontinuous modulation of the variable clamping interval of the three-phase Vienna rectifier; The zero-crossing clamping component is required for the discontinuous modulation of the carrier in the variable clamping interval of the three-phase Vienna rectifier. For peak clamping components; For variable interval clamping components; The modulation waves of the three-phase Vienna rectifier with variable clamping intervals are defined as follows: , and , , and The determination method is as follows: （Ⅱ） In formula (II), , and This represents the modulation wave of a three-phase Vienna rectifier with a variable clamping range. , and This represents the normalized sine waves of phases A, B, and C. This represents the zero-sequence voltage injected by the carrier discontinuous modulation of the variable clamping interval of the three-phase Vienna rectifier.

2. The three-phase Vienna rectifier variable clamp interval carrier discontinuous modulation method according to claim 1, characterized in that, (1). Based on the three-phase normalization formula of the SPWM modulation strategy of the three-phase Vienna rectifier, the normalized sine waves of phase A, phase B, and phase C are respectively obtained. , , The method for determining the three-phase normalized sine wave is as follows: （Ⅲ） In formula (Ⅲ), For the power grid frequency, The modulation ratio, The modulation ratio It can be derived from the formula We obtain, among which Indicates the amplitude of the AC reference phase voltage. Indicates the DC-side bus voltage; (2) Calculation of balanced continuous components: The balanced continuous components required for the carrier discontinuous modulation of the clamped interval of the three-phase Vienna rectifier. Calculate according to formula (Ⅳ): （Ⅳ） In formula (Ⅳ) The balanced continuous component injected for the variable clamping interval carrier discontinuous modulation of a three-phase Vienna rectifier. for The maximum value, for The minimum value, Calculated using equation (V); （Ⅴ） In formula (V), Normalized sine waves for phases A, B, and C , , ; (3) Calculation of zero-crossing clamping components: Define the normalized sine waves of phase A, phase B, and phase C at a certain moment. , , The maximum value is The minimum value is The intermediate value is the zero-crossing clamping component. ; (4) Calculation of peak clamping component: The peak clamping component is defined as... , The method for determining it is as follows: （Ⅵ） In formula (VI), and Normalized sine waves for phases A, B, and C, respectively. , , The maximum and minimum values.

3. The three-phase Vienna rectifier variable clamp interval carrier discontinuous modulation method according to claim 1, characterized in that, Variable interval clamping components As shown in equation (VII): （Ⅶ） In formula (VII), The modulation ratio, For the variable interval clamping coefficient, .

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