Cascade inverter-oriented complex power factor angle droop control method

Abstract

The invention relates to the technical field of power electronic control, in particular to a cascade inverter-oriented complex power factor angle droop control method, which comprises the following steps of: 1) acquiring a signal; 2) calculating a complex power factor angle; 3) performing complex power factor angle droop control operation; 4) generating a voltage reference; 5) inner double-closed-loop control; and 6) carrying out PWM modulation and power output. The idea of complex frequency and the concept of expanding a power factor angle are used for reference, a complex power factor angle (phi = phi r + j phi i) is introduced, a real part (phi r) of the complex power factor angle represents amplitude correlation information of voltage and current, an imaginary part (phi i) of the complex power factor angle corresponds to phase information of a traditional power factor angle, and meanwhile the amplitude and phase characteristics of the voltage and the current are captured. A decentralized droop control strategy is designed based on the complex power factor angle, self-synchronization, accurate power distribution and stable operation under diversified working conditions of a cascade inverter module are achieved by constructing a complex power factor angle droop control equation and combining inner double closed-loop control and PWM modulation, real-time communication does not need to be depended on, and the robustness and reliability of the system are improved.

Description

Technical Field

[0001] This invention relates to the field of power electronics control technology, and in particular to a complex power factor angle droop control method for cascaded inverters. It is applicable to the stability control and power quality optimization of cascaded power electronic equipment (such as cascaded inverters in high-voltage energy storage power stations and solar photovoltaic systems), and can improve the operational stability, robustness and control flexibility of cascaded inverter systems under islanded / grid-connected dual-mode, diversified load and grid disturbance conditions. Background Technology

[0002] With the global energy structure transformation and the rapid development of distributed generation technology, microgrid systems are widely used in various engineering projects. Based on the connection structure of the interface converter, microgrids are generally divided into two types: parallel and cascaded. Compared with the parallel structure, the cascaded system connects inverter modules in series on the AC side to form a modular output structure. It can achieve high output voltage levels without the need for bulky transformers and has advantages such as high power density, small size, and flexible module expansion. It also avoids circulating current problems, improving system efficiency and reliability, making it particularly suitable for high-voltage energy storage power stations, solar photovoltaic systems, and other scenarios.

[0003] In the field of cascaded inverter control technology, early control schemes focused on basic power conversion and output, without fully considering the collaborative control requirements under complex operating conditions. With the expansion of application scenarios, cascaded inverter systems need to adapt to complex conditions such as islanded / grid-connected dual-mode operation, diverse load power supply, and grid disturbances, which places stringent demands on distributed control strategies. While existing self-synchronization control methods are the preferred solution for high-reliability applications of cascaded systems and do not rely on real-time communication, traditional droop control technology has significant shortcomings in terms of grid voltage fluctuation adaptability, load type compatibility, and dual-mode operation support, making it difficult to meet the high-performance control requirements of new power systems for cascaded inverters.

[0004] Existing publicly available related technologies include: Inverse Power Factor Droop Control: This can achieve frequency synchronization and power distribution, but it is only applicable to resistive-inductive (RL) loads and cannot adapt to complex load conditions in actual engineering (J. He, Y. Li, B. Liang, and C. Wang, “Inverse Power Factor Droop Control for Decentralized Power Sharing in Series-Connected-Microconverters Based IslandingMicrogrids,” IEEE Transactions on Industrial Electronics, vol. 64, no. 9, pp.7444-7454, Sep. 2017.2); fP / Q Droop Control: This extends support for resistive-capacitive (RC) loads, but the control logic is complex, and its stability under grid disturbances needs to be improved (Y. Sun, G. Shi, X. Li, W. Yuan, M. Su, H. Han and X. Hou, “An fP / Q Droop Control in Cascaded-Type Microgrid,” IEEE Transactions on Power Systems, vol. 33, no. 1, pp.). 1136-1138, Jan. 2018.); ω-P droop control can achieve system synchronization, but it has low robustness to grid voltage fluctuations and is susceptible to grid disturbances (N. Rigogiannis, N. Delianidis, I. Mandourarakis, N. Papanikolaou, and E. Koutroulis, “Feasibility Study of a Fully Decentralized Control Scheme for PVCell-Level Cascaded H-Bridge Inverters,” IEEE Access, vol. 11, pp. 69826-69840, 2023.); ω-Q droop control: achieves effective decoupling of active and reactive power in islanded mode, but cannot support grid-connected operation, limiting its application in distributed generation systems requiring dual-mode switching (M. Qiu, M. Wei, S. Yang, X. Liu and D.).Cao, “Fully Decoupled Active and Reactive Power Distribution Control for Single Phase Cascaded Connected Microinverter UnderIsland Mode,” IEEE Transactions on Industry Applications, vol. 60, no. 4, pp.6393-6408, July-Aug. 2024.; Traditional power factor droop control integrates islanded and grid-connected modes, but it carries the risk of instability during grid faults and is sensitive to grid voltage fluctuations (Y. Sun, L. Li, G. Shi, X. Hou and M. Su, “Power Factor Angle Droop Control-A General Decentralized Control of Cascaded Inverters,” IEEE Transactions on Power Delivery, vol. 36, no. 1, pp.465-468, Feb. 2021.), etc.

[0005] The prior art patent CN119651782A provides a converter power factor feedforward compensation control method and device, belonging to the field of wind power generation technology. The method includes: acquiring feedforward compensation control parameters, including filter parameters, grid-side parameters, and input-side parameters; calculating the input-side target power factor angle based on the feedforward compensation control parameters; and compensating the input-side actual power factor angle based on the input-side target power factor angle. This method distinguishes between the input-side power factor and the grid-side power factor. When the grid-side power factor reaches 1, the target power factor angle on the input side is calculated based on the filter parameters, grid-side parameters, and input-side parameters. The actual power factor angle on the input side is then compensated based on the target power factor angle to compensate for the filter's influence on the grid-side power factor angle.

[0006] The differences between this patent application and the prior art CN119651782A are as follows:

[0007] 1. Different technical positioning: The patent application focuses on the stable control of cascaded inverters under multiple operating conditions (dual mode, multiple loads); the comparison patent only optimizes the grid-side power factor of wind power converters.

[0008] 2. The core innovations are different: the patented application introduces a "complex power factor angle" to integrate amplitude and phase; the comparison patent relies on "feedforward compensation" to cancel the interference of the filter on the power factor.

[0009] 3. Different control architectures: The patented design is "distributed droop control + inner closed loop", which does not require communication; the comparative patent is a feedforward architecture of "parameter acquisition - target angle calculation - actual angle compensation".

[0010] 4. Different scope of problems solved: The patent application covers multiple dimensions of problems such as voltage fluctuation and load compatibility; the comparison patent only solves the single problem of power factor deviation caused by the filter.

[0011] 5. Different application scenarios: The patent application is applicable to multiple fields such as energy storage, photovoltaics, and microgrids; the comparison patent is limited to wind power generation scenarios.

[0012] The existing technology, compared with patent CN108039812A, provides a single-cycle control strategy for the power factor lead-lag control of a power electronic converter. Specifically, it includes the following steps: first, determining the relevant input and output parameters of the power electronic converter; then, calculating the relevant control parameters according to the phase shift requirements; finally, introducing a proportional phase-shifting element into the current feedback loop based on the control parameters, and superimposing the output signal onto the original current feedback loop. Based on the characteristics of single-cycle direct current control, this invention adds a proportional phase-shifting element to the current feedback, enabling the system to meet active power control requirements while generating the required inductive or capacitive reactive power by controlling the phase of the current. Furthermore, this invention eliminates the need for additional voltage sensors, filters, and phase-locked loops, making it simple to implement and robust, providing an effective power factor lead-lag control method for single-cycle control.

[0013] The differences between this patent application and the prior art CN119651782A are as follows:

[0014] 1. Different core innovation directions: The patent application uses a complex power factor angle (integrating amplitude and phase); the comparative patent adjusts the power factor angle by adding a proportional phase shift stage in single-cycle control.

[0015] 2. The control architecture and logic are different: the patent application uses a distributed architecture of "complex power factor angle + droop + dual closed loop"; the comparison patent uses a simplified logic of "parameter calculation + proportional phase shift".

[0016] 3. The core problems they solve are different: patented solutions address multi-dimensional issues such as voltage fluctuations and load compatibility; comparative patents only address the active and reactive power coordination problem under single-cycle control.

[0017] 4. Different application scenarios and adaptability: The patented application is adapted to multiple loads, dual modes and voltage fluctuations; the comparison patent does not limit the scenarios and is only adapted to active and reactive power regulation.

[0018] 5. Different system expansion and operation mode support: The patent application supports module expansion and dual-mode switching; the comparison patent has no expansion capability and does not involve dual-mode design.

[0019] In general, the existing technical solutions have the following drawbacks or shortcomings:

[0020] 1) Poor adaptability to grid voltage fluctuations: Existing control methods mostly rely on fixed amplitude references. When the grid voltage drops or rises, the system stability decreases and the robustness is insufficient.

[0021] 2) Limited load compatibility: Some solutions are only applicable to specific types of loads and cannot be adapted to diverse load scenarios such as resistors (R), resistor-inductor (RL), and resistor-capacitor (RC).

[0022] 3) Single operating mode support: Some solutions can only achieve islanded or grid-connected single mode operation, which cannot meet the dual-mode switching requirements of distributed generation systems.

[0023] 4) Lack of four-quadrant operation capability: It is difficult to flexibly adjust active and reactive power and cannot adapt to the diverse power regulation needs of the power grid.

[0024] 5) Insufficient stability under power grid faults: Under fault scenarios such as power grid frequency fluctuations and voltage disturbances, problems such as oscillation and instability are prone to occur, threatening the reliable operation of the system. Summary of the Invention

[0025] The purpose of this invention is to solve the following technical problems existing in the prior art, including: 1) Insufficient robustness to grid voltage fluctuations: Existing technologies are prone to instability when grid voltage drops or rises, and cannot adapt to dynamic changes in grid voltage; 2) Limited load type adaptability: It is difficult to be compatible with diverse loads such as R, RL, and RC, and the control accuracy decreases and the dynamic response is poor when switching loads; 3) Incomplete support for dual-mode operation: Some technologies cannot achieve seamless switching between islanded and grid-connected modes, or there are voltage / current surges during the switching process; 4) Lack of four-quadrant operation capability: It is impossible to flexibly adjust active and reactive power, and it is difficult to meet the diverse power support requirements of the grid; 5) Poor adaptability to grid faults: Under fault scenarios such as grid frequency fluctuations and voltage disturbances, the system dynamic response has large overshoot, slow convergence, and insufficient stability.

[0026] The overall design concept of this invention is as follows: drawing on the idea of ​​complex frequency, extending the concept of power factor angle, and introducing a complex power factor angle (φ=φ). r +jφ i ), actually part (φ r The imaginary part (φ) represents the magnitude correlation between voltage and current. iThis corresponds to the phase information of the traditional power factor angle, while simultaneously capturing the amplitude and phase characteristics of voltage and current. Based on this complex power factor angle, a distributed droop control strategy is designed. By constructing the complex power factor angle droop control equation and combining inner double closed-loop control with PWM modulation, the self-synchronization, precise power distribution, and stable operation of the cascaded inverter modules under various operating conditions are achieved without relying on real-time communication, thus improving the system's robustness and reliability.

[0027] The specific technical solution of the present invention provides a method for controlling the complex power factor droop angle of cascaded inverters, comprising the following steps:

[0028] 1) Signal Acquisition: The k-th inverter module acquires its own output voltage V through a local sensor. k Output current i Lk and the voltage signal i at the point of common coupling (PCC) pcc .

[0029] 2) Complex power factor angle calculation: Based on the collected voltage and current signals, the complex power factor angle φ of the k-th inverter module is calculated. k = φ rkf + jφ ik .

[0030] 3) Complex power factor droop control calculation: φ k , λ k Substituting into the complex power factor droop control equation, the complex angle θ of the inverter output voltage is calculated. k .

[0031] 4) Voltage reference generation: based on θ k Obtain the voltage reference control signal V k,ref And then according to V k,ref Generate voltage reference signal v in the αβ coordinate system αref v βref .

[0032] 5) Inner dual closed-loop control: The voltage reference signal is input to the inner dual closed-loop controller to precisely adjust the current and voltage and output a PWM modulation signal.

[0033] 6) PWM modulation and power output: The inverter switching transistors are driven by PWM modulation signals to achieve stable power output and inter-module coordinated control.

[0034] As a further improvement of the present invention, the complex power factor angle in step 2) is defined as follows:

[0035] Based on complex frequency theory, the complex power factor angle φ is defined as:

[0036] ;

[0037] Wherein, the superscript "*" indicates conjugate operation; v and i represent the inverter output voltage and current, respectively; θ u and θ i These are the complex angles of voltage and current, respectively; φ r The real part of the complex power factor angle is defined as the logarithm of the apparent power magnitude, φ. i This is the imaginary part of the complex power factor angle, consistent with the traditional power factor angle.

[0038] φ r and φ i The expression is:

[0039] ;

[0040] Where ℜ and ℑ represent the real and imaginary part extraction operations, respectively; V and I are the magnitudes of voltage and current, respectively; θ u θ i These are the scalar phase angles for voltage and current, respectively.

[0041] As a further improvement of the present invention, the control equation for the complex power factor angle droop in step 3) is as follows:

[0042] ;

[0043] Where the subscript "k" indicates the k-th inverter; ○ is the Hadamard product (multiplying the real and imaginary parts of the complex signal point by point); ω0 is the complex angular frequency reference value; φ k,ref = φ rk,ref + jφ ik,ref λ is the reference value for the complex power factor angle. k,ref λ is a reference value for the supporting item. k This represents the actual sampled value of the supporting item; the supporting item can be freely selected according to requirements (such as inverter output voltage, frequency, etc.). Г = K S + jK φ K is the complex gain of the complex power factor term. S For the real part of the gain, K φ For the imaginary part of the gain; K λ For the gain of the supporting term; θ k This is the complex angle of the inverter output voltage.

[0044] The application scenarios of the technical solution of this invention include:

[0045] 1) High-voltage energy storage power station: Suitable for high-voltage energy storage systems composed of multiple inverter modules cascaded together. It can realize stable power supply in islanded mode and flexible power interaction in grid-connected mode, cope with load changes and grid disturbances during the charging and discharging process of the energy storage system, and ensure power quality.

[0046] 2) Solar photovoltaic system: Adapts to the cascaded inverter topology after photovoltaic modules are connected in series and parallel, which can maintain stable system operation in scenarios where power fluctuations are caused by changes in light intensity. It also supports local load power supply in islanded mode and grid-connected power supply in grid-connected mode, improving the grid compatibility and operational reliability of the photovoltaic system.

[0047] 3) Industrial / Commercial Microgrids: Suitable for microgrids with cascaded inverters built in factories, parks, etc., which can handle the switching of diverse loads (such as motor RL loads and capacitor-compensated RC loads), achieve seamless switching between islanded and grid-connected modes, and ensure continuous and reliable power supply for industrial production and commercial operation.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] 1) Strong robustness to grid voltage fluctuations: By dynamically adjusting the voltage amplitude changes through the real part of the complex power factor angle, the system can adapt to ±10% grid voltage fluctuations. The characteristic value of the grid-connected system is always located in the left half-plane, and the stability margin is significantly improved.

[0050] 2) Wide load compatibility: It can adapt to various load types such as R, RL, RC, etc. It has fast dynamic response, small overshoot, and high steady-state accuracy when switching loads, without the need for additional adjustment of control parameters.

[0051] 3) Seamless switching between dual modes: It can achieve smooth switching between islanded and grid-connected modes without the need for pre-synchronization logic. The voltage and current surges during the switching process are small, ensuring continuous power supply to the load.

[0052] 4) Flexible four-quadrant operation: By configuring different complex power factor angle reference values, active and reactive power can be flexibly adjusted to achieve stable four-quadrant operation and meet the diverse power support needs of the power grid.

[0053] 5) Distributed and easily expandable: No need to rely on real-time communication, each module achieves collaborative control only through local measurement signals, reducing the complexity of system design and debugging, and facilitating the expansion of the number of modules.

[0054] 6) Excellent dynamic response performance: voltage synchronization time ≤ 0.7 s, load switching and mode switching stabilization time ≤ 4.5 s, power factor angle convergence time ≤ 5 s, and fast and stable dynamic response. Attached Figure Description

[0055] Figure 1 This is a block diagram for controlling the droop angle of the complex power factor.

[0056] Figure 2 It is a cascaded inverter system.

[0057] Figure 3This is for the voltage synchronization process during mode switching.

[0058] Figure 4 To synchronize and switch modes, the PCC voltage and grid current are adjusted.

[0059] Figure 5 To synchronize and switch the output voltage of each inverter.

[0060] Figure 6 Verify PCC voltage and grid current for adapting to diverse loads.

[0061] Figure 7 Verify the power factor angle for adapting to diverse loads.

[0062] Figure 8 Verify the PCC power waveform for adapting to diverse loads.

[0063] Figure 9 To verify the power factor angle for four-quadrant operation.

[0064] Figure 10 To verify the PCC power waveform for four-quadrant operation.

[0065] Figure 11 PCC voltage and grid current are related to grid frequency fluctuations.

[0066] Figure 12 The power factor angle represents the power factor fluctuation of the power grid frequency.

[0067] Figure 13 The PCC power waveform represents the fluctuation of the power grid frequency.

[0068] Figure 14 The grid voltage disturbance affects the PCC voltage and grid current.

[0069] Figure 15 The angle represents the power factor angle of the grid voltage disturbance.

[0070] Figure 16 The PCC power waveform is a result of grid voltage disturbance. Detailed Implementation

[0071] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0072] Example 1

[0073] like Figure 1 The diagram shown is a block diagram for complex power factor droop control; a cascaded inverter system is built on a hardware-in-the-loop (HIL) platform, such as... Figure 2 As shown, the specific configuration is as follows:

[0074] 1. Experimental platform setup:

[0075] 1) Real-time simulator: OPAL-RT OP4510, step size 50 μs, used to simulate the main circuit of a cascaded inverter.

[0076] 2) Controller: DSP-TMS320F28335, sampling frequency 10 kHz, used to implement the control algorithm; the supported item is selected as the inverter output voltage amplitude V. k .

[0077] 3) Cascaded structure: 4 inverter modules are connected in series, and the total output voltage is adapted to the grid requirements.

[0078] 2. Parameter Settings

[0079] The parameter settings are shown in Table 1.

[0080] 3. Experimental verification scenario and results

[0081] 1) Synchronization and Mode Switching Verification

[0082] Initial state: island mode, the initial phases of the 4 inverters are [0, π / 2, π, 3π / 2], and they are connected to load R.

[0083] Experimental results: Voltage synchronization was achieved within 0.7 seconds, and the output voltage of each module stabilized at 77.5 V; when switching from islanded mode to grid-connected mode, the system stabilized within 1.6 seconds, with the PCC voltage at 304.8 V and the grid current at 525 A; when switching back from grid-connected mode to islanded mode, there was no significant voltage fluctuation, achieving seamless switching. Figures 3-5 As shown. Figure 3 For the synchronization of voltage during mode switching; Figure 4 To synchronize and switch modes, the PCC voltage and grid current are adjusted. Figure 5 To synchronize and switch the output voltage of each inverter.

[0084] 2) Verification of adaptability to diverse loads

[0085] Experimental procedure: Switch loads R, RL, RC, and R in sequence, and record the changes in PCC voltage, grid current, and power.

[0086] Experimental results: The PCC voltage maintained a stable sinusoidal waveform throughout, with an amplitude deviation of less than ±2 V; the grid current dynamically adjusted with the load (R load 30.8 A, RL load 28.8 A, RC load 26.5 A); active and reactive power accurately tracked load demand with no steady-state error. Figures 6-8 As shown. Figure 6 Verify PCC voltage and grid current for adapting to diverse loads; Figure 7 Verify the power factor angle for adapting to diverse loads; Figure 8 Verify the PCC power waveform for adapting to diverse loads.

[0087] 3) Four-quadrant operation verification

[0088] Experimental setup: grid-connected mode, complex power factor angle reference value φ i,ref Set them to [1.7, 0.5, -0.5, -1.7] in sequence.

[0089] Experimental results: The power factor angle of each inverter converged to the reference value within 5 seconds, with no steady-state error; four-quadrant stable operation was achieved, and active and reactive power were flexibly adjustable to meet the operational needs of different power grids. Figures 9-10 As shown. Figure 9 Verify the power factor angle for four-quadrant operation; Figure 10 To verify the PCC power waveform for four-quadrant operation.

[0090] 4) Verification of robustness to power grid faults

[0091] Grid frequency fluctuations: When the frequency drops from 50 Hz to 49.5 Hz and then rises again to 50.5 Hz, the PCC voltage and grid current quickly track the new frequency, and the power factor angle is dynamically adjusted to provide reactive power support, maintaining system stability. For example... Figures 11-13 As shown. Figure 11 PCC voltage and grid current are related to grid frequency fluctuations. Figure 12 The power factor angle for grid frequency fluctuations; Figure 13 The PCC power waveform represents the fluctuation of the power grid frequency.

[0092] Grid voltage disturbance: The voltage drops from 311 V to 279.9 V (-10%) and then rises to 342.1 V (+10%). The PCC voltage tracks the grid voltage change, with a steady-state deviation of less than ±1.1 V and a transient transition time ≤4.5 s. The system exhibits no oscillations or instability. Figures 14-16 As shown. Figure 14 The grid voltage disturbance affects the PCC voltage and grid current; Figure 15 The power factor angle for grid voltage disturbance; Figure 16 The PCC power waveform is a result of grid voltage disturbance.

[0093] Table 1 Hardware-in-the-Loop Experiment Configuration Parameters

[0094]

[0095] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for controlling the droop of the complex power factor angle in cascaded inverters, characterized in that: Includes the following steps: 1) Signal Acquisition: The k-th inverter module acquires its own output voltage V through a local sensor. k Output current i Lk and the voltage signal i at the common connection point PCC pcc ; 2) Complex power factor angle calculation: Based on the collected voltage and current signals, the complex power factor angle φ of the k-th inverter module is calculated. k = φ rkf + jφ ik ; 3) Complex power factor droop control calculation: φ k Substituting into the complex power factor droop control equation, the complex angle θ of the inverter output voltage is calculated. k ; 4) Voltage reference generation: based on θ k Obtain the voltage reference control signal V k,ref And then according to V k,ref Generate voltage reference signal v in the αβ coordinate system αref v βref ; 5) Dual closed-loop control: The voltage reference signal is input to the dual closed-loop controller to precisely regulate the current and voltage, and output a PWM modulation signal; 6) PWM modulation and power output: The inverter switching transistors are driven by PWM modulation signals to achieve stable power output and inter-module coordinated control.

2. The complex power factor droop control method for cascaded inverters according to claim 1, characterized in that: The complex power factor angle in step 2) is defined as follows: Based on complex frequency theory, the complex power factor angle φ is defined as: ； Wherein, the superscript "*" indicates conjugate operation; v and i represent the inverter output voltage and current, respectively; θ u and θ i These are the complex angles of voltage and current, respectively; φ r The real part of the complex power factor angle is defined as the logarithm of the apparent power magnitude, φ. i This is the imaginary part of the complex power factor angle, consistent with the traditional power factor angle; φ r and φ i The expression is: ； Where ℜ and ℑ represent the real and imaginary part extraction operations, respectively; V and I are the magnitudes of voltage and current, respectively; θ u θ i These are the scalar phase angles for voltage and current, respectively.

3. The complex power factor droop control method for cascaded inverters according to claim 1, characterized in that: The control equation for the droop of the complex power factor angle in step 3) is as follows: ； Where the subscript "k" indicates the k-th inverter; ○ is the Hadamard product (multiplying the real and imaginary parts of the complex signal point by point); ω0 is the complex angular frequency reference value; φ k,ref = φ rk,ref + jφ ik,ref λ is the reference value for the complex power factor angle. k,ref λ is a reference value for the supporting item. k These are the actual sampled values ​​of the supporting items; the supporting items can be freely selected according to requirements; Г = K S + jK φ K is the complex gain of the complex power factor term. S For the real part of the gain, K φ For the imaginary part of the gain; K λ For the gain of the supporting term; θ k This is the complex angle of the inverter output voltage.

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