Method for eliminating and compensating DC bias in three-phase AC signal

Abstract

The invention discloses a method for eliminating and compensating direct current bias in three-phase alternating current signals. The method comprises the following steps: S1, selecting modeling objects as (alpha beta) static coordinate system signals i alpha measure and i beta measure; s2, modeling and state expansion; s3, respectively designing independent ESO for the alpha axis and the beta axis; and S4, extracting an unbiased signal: outputting z1 alpha and z1 beta of the ESO, wherein the z1 alpha and z1 beta are results obtained after the estimated direct current biases z2 alpha and z2 beta are removed from the original measurement signals i alpha measurement and i beta measurement. The method does not depend on an accurate disturbance model, various coupling disturbances can be processed at the same time, and the dynamic performance, the steady-state precision and the overall robustness of a control system are remarkably improved; especially in applications (such as high-performance motor driving and precise grid-connected inverters) requiring high-speed and high-precision control, the problem of phase lag introduced by a traditional filter is avoided.

Description

Technical Field

[0001] This invention relates to the field of motor-related technologies, specifically a method for eliminating DC bias in compensated three-phase AC signals. Background Technology

[0002] In digital power supply and motor drive control, estimating and eliminating DC offset by calculating the average value of the AC current over a complete cycle is a widely used and conventional method. Its core principle is based on the property that the average value of a pure AC signal is zero over a complete cycle. Therefore, the average value of the measured current signal over a complete cycle is considered the DC offset for that cycle, and subtracting this estimate from the original signal yields the "bias-free" AC current.

[0003] The drawbacks and limitations of this method are poor latency and dynamic performance. This is because calculating the average value requires waiting for a full AC cycle (or an integer multiple of the cycle) of data acquisition to complete. During rapid changes in system state (such as motor startup, acceleration, deceleration, or sudden load changes), the action to eliminate the DC bias lags by at least one cycle. During this time, the control loop uses a current signal containing the DC bias, which can lead to decreased instantaneous control performance, increased torque ripple, and even transient instability (especially under light loads or at high speeds). In low-frequency applications (such as low-frequency operation of high-power motors), where a cycle is long (e.g., 100ms at 10Hz), this delay becomes very significant, severely impacting the system's dynamic response. Introducing additional latency negatively affects the phase margin of the control loop, potentially becoming a limiting factor for loop bandwidth or causing instability in high-performance or wide-bandwidth control systems.

[0004] The impact of DC bias in three-phase power factor correction (PFC) power supply control is significant and multifaceted, severely undermining the core objectives of PFC—achieving unity power factor (input current and voltage in phase and sinusoidal) and a stable DC bus voltage. When the current loop drives the actual current to track a reference signal containing DC bias, the actual current waveform reaches its limit value prematurely (clipping) in one half-cycle and fails to reach its peak value in the other half-cycle, forming an asymmetrical sine wave. This asymmetrical waveform contains a large number of even harmonics (especially the second harmonic) and DC components. This contradicts PFC's goal of achieving extremely low current harmonic distortion (THDi). The distorted current waveform leads to an increased phase difference between the fundamental component of the input current and the voltage, significantly reducing the power factor (PF). The DC component Idc will generate a constant DC flux offset in the inductor core, which can easily approach or reach the core's saturation flux density. Inductor saturation will cause the inductance to drop sharply and the current to rise sharply (di / dt increases). When the switch is turned on, it will be subjected to excessive current stress, which will increase losses, generate serious noise, and even cause the switch to be damaged by overcurrent.

[0005] Therefore, in three-phase PFC design, effective DC bias elimination or compensation measures must be adopted (such as improved real-time estimation algorithms, adaptive filters, observers with high-pass filters, etc.) to overcome the bias caused by current sensor errors and circuit asymmetry, ensuring high-performance, high-efficiency, stable and reliable system operation. Simple periodic averaging methods are often insufficient in high-performance three-phase PFC due to their delay and waveform sensitivity. Summary of the Invention

[0006] The purpose of this invention is to provide a method for eliminating DC bias in compensated three-phase AC signals, so as to solve the problems in the prior art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for eliminating DC bias in a compensated three-phase AC signal, comprising the following steps:

[0008] S1. Select the modeling objects as the (αβ) stationary coordinate system signals i_α_measured and i_β_measured;

[0009] S2, Modeling and State Expansion:

[0010] For the α-axis, define the state variable x1_α as the AC component of the α-axis without DC bias, and x2_α as the DC bias component of the α-axis, which is the extended state; h_α(t) is the rate of change of the DC bias component. The constructed extended state model is as follows:

[0011]

[0012] y_α=x1_α=i_α_measured

[0013] For the β-axis, define the state variable x1_β as the AC component of the β-axis without DC bias, and x2_β as the DC bias component of the β-axis, which is the extended state; h_β(t) is the rate of change of the DC bias component. The constructed extended state model is as follows:

[0014]

[0015] y_β=x1_β=i_β_measured;

[0016] S3. Design separate ESOs for the α-axis and β-axis:

[0017] For the α axis

[0018] Prediction error: e_α=z1_α-i_α_measured

[0019]

[0020] z1_α: An estimate of the true AC component x1_α;

[0021] z2_α: An estimate of the DC bias component x2_α;

[0022] For the β axis

[0023] Prediction error: e_β=z1_β-i_β_measured

[0024]

[0025] z1_β: An estimate of the true AC component x1_β;

[0026] z2_α: An estimate of the DC bias component x2_α;

[0027] β1 and β2 are the observer gains;

[0028] S4. Extract the unbiased signal:

[0029] The outputs of ESO, z1_α and z1_β, are the results of removing the estimated DC bias z2_α and z2_β from the original measurement signals i_α_measured and i_β_measured.

[0030] i_α_clean=z1_α

[0031] i_β_clean=z1_β.

[0032] Preferably, the three-phase AC signal is a three-phase current signal or a three-phase voltage signal.

[0033] Preferably, the observer gains β1 and β2 are adjustable to balance the disturbance suppression speed with noise sensitivity.

[0034] Preferably, the method also includes obtaining the original three-phase signal through the inverse Clark transform.

[0035] Compared with the prior art, the beneficial effects of the present invention are:

[0036] 1. Model Independence and Strong Robustness: The core idea of ​​ESO (Electronic System Independent Disturbance) is to treat unmodeled system dynamics, external disturbances, parameter variations, and the DC bias itself as a lumped "total disturbance." It does not require precise knowledge of the specific causes of the DC bias (such as sensor zero-point drift, asymmetrical on-state voltage drop of power devices, control integral saturation, etc.) or their precise mathematical models. Regardless of the complexity or time-varying nature of the DC bias source, ESO can effectively estimate and compensate for it. When system parameters (such as resistance and inductance) vary within a certain range, ESO still maintains good compensation performance, improving the system's robustness.

[0037] 2. Elimination of Phase Delay and Fast Dynamic Response: Traditional low-pass filters or notch filters inevitably introduce phase delay when filtering out DC components, especially near the fundamental frequency. This severely affects the dynamic response speed, bandwidth, and stability of the current control loop. ESO, by observing and compensating for the total disturbance (including DC bias) in real time, directly cancels the effect of the disturbance within the control loop, essentially eliminating phase delay. This significantly improves the dynamic response speed and bandwidth of the current loop or other closed-loop controls, enabling the system to track commands and suppress disturbances more quickly.

[0038] 3. Simultaneous estimation and compensation for multiple disturbances: The total disturbance observed by the ESO includes not only DC bias but may also include harmonic distortion, unmodeled dynamics, load abrupt changes, parameter variations, etc. Under a well-designed ESO, these disturbances will be estimated simultaneously and compensated for in the control input. This means that when using ESO to compensate for DC bias, it often provides "free" suppression capabilities for other types of disturbances, improving the overall control performance and harmonic suppression capabilities of the system.

[0039] 4. Simplified Control Design: By accurately estimating and compensating for the total disturbance (including DC bias) through ESO, the original complex nonlinear, strongly coupled, and disturbed system can be "transformed" from the controller's perspective into a simplified model that more closely approximates an ideal linear integrator in series. This decoupling and simplification greatly simplifies the design of subsequent controllers (such as the state feedback controller in ADRC). The controller only needs to be designed for this simplified model, without having to consider the effects of DC bias disturbances and other complex disturbances, thus reducing the complexity of controller design.

[0040] 5. Applicable to rotating coordinate systems (dq coordinate system): In motor vector control and grid-connected converters, three-phase PFC control is typically performed in a synchronous rotating dq coordinate system. DC bias manifests as a DC component in a stationary coordinate system (abc or αβ), but in the dq coordinate system, it manifests as an AC oscillation component at a specific frequency (usually the fundamental frequency). ESO can be easily implemented in the dq coordinate system. By incorporating the ability to observe specific frequency (fundamental frequency) disturbance terms into the dq-axis observer design (a natural extension of standard ESO), the AC oscillation component derived from DC bias can be effectively observed and compensated for, ensuring precise control and zero steady-state error tracking of the dq-axis current.

[0041] 6. The core advantage of the ESO method in eliminating DC bias in three-phase AC signals lies in its model-independent robustness and disturbance compensation capability without phase delay. It does not rely on an accurate disturbance model and can simultaneously handle multiple coupled disturbances, significantly improving the dynamic performance, steady-state accuracy, and overall robustness of the control system. Especially in applications requiring high-speed, high-precision control (such as high-performance motor drives and precision grid-connected inverters), it avoids the phase lag problem introduced by traditional filters, which is its most attractive feature. Although some experience is required in parameter tuning (observer bandwidth), its superior performance and robustness make it an advanced and effective method for solving DC bias problems. Attached Figure Description

[0042] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0043] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention.

[0045] Please see Figure 1 In this embodiment of the invention, a method for eliminating DC bias in a compensated three-phase AC signal includes the following steps:

[0046] S1. Select the modeling objects as the (αβ) stationary coordinate system signals i_α_measured and i_β_measured;

[0047] S2, Modeling and State Expansion:

[0048] For the α-axis, define the state variable x1_α as the AC component of the α-axis without DC bias, and x2_α as the DC bias component of the α-axis, which is the extended state; h_α(t) is the rate of change of the DC bias component. The constructed extended state model is as follows:

[0049]

[0050] y_α=x1_α=i_α_measured

[0051] For the β-axis, define the state variable x1_β as the AC component of the β-axis without DC bias, and x2_β as the DC bias component of the β-axis, which is the extended state; h_β(t) is the rate of change of the DC bias component. The constructed extended state model is as follows:

[0052]

[0053] y_β=x1_β=i_β_measured;

[0054] S3. Design separate ESOs for the α-axis and β-axis:

[0055] For the α axis

[0056] Prediction error: e_α=z1_α-i_α_measured

[0057]

[0058] z1_α: An estimate of the true AC component x1_α;

[0059] z2_α: An estimate of the DC bias component x2_α;

[0060] For the β axis

[0061] Prediction error: e_β=z1_β-i_β_measured

[0062]

[0063]

[0064] z1_β: An estimate of the true AC component x1_β;

[0065] z2_α: An estimate of the DC bias component x2_α;

[0066] β1 and β2 are the observer gains;

[0067] S4. Extract the unbiased signal:

[0068] The outputs of ESO, z1_α and z1_β, are the results of removing the estimated DC bias z2_α and z2_β from the original measurement signals i_α_measured and i_β_measured.

[0069] i_α_clean=z1_α

[0070] i_β_clean=z1_β.

[0071] Preferably, the three-phase AC signal is a three-phase current signal or a three-phase voltage signal.

[0072] Preferably, the observer gains β1 and β2 are adjustable to balance the disturbance suppression speed with noise sensitivity.

[0073] Preferably, the method also includes obtaining the original three-phase signal through the inverse Clark transform.

[0074] In three-phase AC systems (such as motor drives and grid-connected inverters), imperfections in sensors (current transformers, Hall effect sensors), signal conditioning circuits, or the control algorithm itself may introduce DC bias components (Idc_a, Idc_b, Idc_c) into the measured three-phase current or voltage signals ia, ib, ic. These DC components are physically nonexistent (the sum of ideal three-phase currents should be zero, with no DC component), but in the control loop, they can cause dq-axis coupling / oscillation, current waveform distortion, and malfunctioning protection. During Park transformation (abc->dq), the DC bias is converted into a double-frequency oscillation in the dq rotating coordinate system, severely interfering with the control performance of the current loop (especially the q-axis torque current), causing torque pulsation and speed fluctuations. In the stationary coordinate system, the DC bias causes the current waveform to no longer be symmetrical about the zero axis, potentially triggering overcurrent protection.

[0075] Traditional filter methods are simple but introduce phase lag, affecting dynamic response speed and attenuating the low-frequency components at the edge of the fundamental frequency component (the impact is small but not ideal). Calculating the average value over one fundamental frequency cycle as the bias estimate requires precise synchronization, has a slow dynamic response (requiring at least one cycle), and performs poorly under non-stationary operating conditions (variable frequency, variable load).

[0076] The specific implementation plan for ESO in eliminating DC bias in three-phase AC signals is as follows.

[0077] (1) Modeling and State Extension

[0078] The measured three-phase AC signal (e.g., i_a) is considered as the object to be processed; the DC bias component I_{dc_a} is considered as the sum disturbance d(t) to be suppressed. A simple extended state model is constructed. A first-order or second-order integrator model is usually used.

[0079] / / Assume u = 0 (no active control input, pure observation)

[0080] / / x2=I_{dc_a}=d(t) represents the extended state, and h(t) is its rate of change.

[0081] y = x = i_a_measured / / Current measurement value.

[0082] Or, more commonly, the signals i_α and i_β in the two-phase stationary coordinate system (αβ) after Clark transformation are processed directly (because the sum of the three phases is zero, i_α and i_β already contain all the information). The model is similar:

[0083] / / x1_α=i_α

[0084] / / x2_α=I_{dc_α}(extended state)

[0085] y_α=x1_α=i_α_measured

[0086] h_α(t) and h_β(t) represent the rate of change of the DC bias component (usually assumed to be slow or bounded).

[0087] (2) Design ESO

[0088] Design separate ESOs (with identical structures) for the α and β axes. Take the α axis as an example (second-order ESO).

[0089] e_α=z1_α-i_α_measured

[0090]

[0091] z1_α: An estimate of the true AC component i_α (excluding DC bias);

[0092] z2_α: An estimate of the DC bias component I_{dc_α}

[0093] (3) Extracting the unbiased signal

[0094] The outputs z1_α and z1_β of SO are the results of removing the estimated DC bias z2_α and z2_β from the original measured signals i_α_measured and i_β_measured.

[0095] i_α_clean=z1_α

[0096] i_β_clean=z1_β

[0097] If the original three-phase signal is needed, it can be obtained through the inverse Clark transform.

[0098] (4) The role and advantages of ESO in this application

[0099] A) Real-time estimation and compensation: The ESO can estimate the changing DC bias component in real time (the dynamic response speed is determined by the observer gain β1, β2).

[0100] It is then subtracted from the measured signal (achieved through the internal structure of the observer) to output a clean AC signal (i_α_clean, i_β_clean).

[0101] B) No Phase Lag: Unlike filters / notch filters, ESOs do not introduce phase lag into the fundamental AC component (ideally). This is crucial for closed-loop control (such as FOC, PLL) that requires precise phase information.

[0102] C) Amplitude preservation: Theoretically, there is no attenuation of the amplitude of the fundamental component (ideally).

[0103] D) Strong robustness: It has good robustness to the magnitude and slow changes of DC bias (satisfying the bounded assumption of h(t)).

[0104] E) Good dynamic performance: By adjusting the observer bandwidth (determined by β1 and β2), the disturbance suppression speed can be improved ( A trade-off is struck between tracking the speed of d(t) and noise sensitivity. This approach typically achieves a much faster dynamic response than traditional methods based on periodic averaging.

[0105] F) Unified structure: The same ESO framework can not only eliminate DC bias, but also theoretically estimate and compensate for other low-frequency, slowly changing disturbances (such as sensor zero drift).

[0106] No precise synchronization required: Unlike periodic averaging methods, it does not require a precise fundamental period signal.

[0107] ESO models the DC bias in a three-phase AC signal as an extended state that needs to be estimated in the state space, and designs an observer to track and estimate it dynamically in real time. Finally, this estimate is used to directly compensate for (subtract) the DC bias component from the measured signal, thus outputting a clean AC signal (i_α_clean, i_β_clean) without phase lag or amplitude attenuation. This method overcomes the phase lag problem of traditional filters and the shortcomings of periodic averaging methods, such as slow dynamic response and the need for precise synchronization. It has significant advantages in modern motor control, grid-connected inverters, and other applications where high current signal quality is required. Its core value lies in transforming the difficult-to-measure harmful disturbance (DC bias) into an observable state and actively canceling it.

[0108] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for eliminating DC bias in a compensated three-phase AC signal, characterized in that, Includes the following steps: S1. Select the modeling objects as the (αβ) stationary coordinate system signals i_α_measured and i_β_measured; S2, Modeling and State Expansion: For the α-axis, define the state variable x1_α as the AC component of the α-axis without DC bias, and x2_α as the DC bias component of the α-axis, which is the extended state; h_α(t) is the rate of change of the DC bias component. The constructed extended state model is as follows: y_α=x1_α=i_α_measured For the β-axis, define the state variable x1_β as the AC component of the β-axis without DC bias, and x2_β as the DC bias component of the β-axis, which is the extended state; h_β(t) is the rate of change of the DC bias component. The constructed extended state model is as follows: y_β=x1_β=i_β_measured; S3. Design separate ESOs for the α-axis and β-axis: For the α axis Prediction error: e_α=z1_α-i_α_measured z1_α: An estimate of the true AC component x1_α; z2_α: An estimate of the DC bias component x2_α; For the β axis Prediction error: e_β=z1_β-i_β_measured z1_β: An estimate of the true AC component x1_β; z2_α: An estimate of the DC bias component x2_α; β1 and β2 are the observer gains; S4. Extract the unbiased signal: The outputs of ESO, z1_α and z1_β, are the results of removing the estimated DC bias z2_α and z2_β from the original measurement signals i_α_measured and i_β_measured. i_α_clean=z1_α i_β_clean=z1_β.

2. The method for eliminating DC bias in a compensated three-phase AC signal according to claim 1, characterized in that, The three-phase AC signal is either a three-phase current signal or a three-phase voltage signal.

3. The method for eliminating DC bias in a compensated three-phase AC signal according to claim 1, characterized in that, The observer gains β1 and β2 are adjustable to balance the speed of disturbance suppression with noise sensitivity.

4. The method for eliminating DC bias in a compensated three-phase AC signal according to claim 1, characterized in that, It also includes obtaining the original three-phase signal through the inverse Clark transform.

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