Single Phase inverter / Simulink model of single phase spwm inverter

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Email Address. Sign In. Access provided by: anon Sign Out. Power control of single-phase voltage source inverter for grid-connected photovoltaic systems Abstract: This paper presents the design and analysis of both the active and reactive power control of a single-phase voltage source inverter VSI for grid-connected photovoltaic PV system.

The proposed method is based on vector control of power by decoupling control of the active and reactive current components to feed the active and reactive power to the grid. The aim of this research is to control power factor at grid, to improve overall efficiency of transferring power of PV to alternate current power conversion into the grid, and to decrease phase current distortion of VSI.

In this work, mathematical model of system has presented in details. Article :. DOI: Need Help?Compared with L-type filter, LCL-type filter is more suitable for high-power low-switching frequency applications with reducing the inductance, improving dynamic performance.

However, the parameter design for the LCL filter is more complex due to the influence of the controller response performance of the converter. If the harmonic current around switching frequency can be fully suppressed, it is possible for inverter to decrease the total inductance as well as the size and the cost.

In this paper, the model of the LCL filter is analyzed and numerical algorithms are adopted to analyze the stability of the closed-loop control system and stable regions are deduced with different parameters of LCL filter. Then, the minimum sampling frequencies are deduced with different conditions.

Simulation and experimental results are provided to validate the research on the generating mechanism for the unstable region of sampling frequency.

Due to the limit of switching frequency, the filter inductance of L-type grid-connected inverter cannot effectively suppress the harmonic voltage of PWM switching frequency, resulting in grid current with large harmonic current around switching frequency, which should be suppressed by larger filter inductance [ 1 — 4 ].

However, larger filter inductance will cause too large equipment volume and high cost and affect dynamic performance of grid-connected control [ 5 ]. Therefore, the inductance-capacitance-inductance LCL filter is designed to replace the conventional filter [ 67 ]. In order to improve the attenuation rate of harmonic current around switching frequency, LCL filter is adopted to suppress harmonic voltage around switching frequency as well [ 8 ].

In order to research the stability of inverter with LCL filter, it is important to use simulation models which are sufficiently detailed to realistically represent their real world physical system behaviors. A new modeling approach for inverter-dominated microgrids using dynamic phasor is presented. The proposed dynamic phasor model is able to predict accurately the stability margins of the system, while the conventional reduced-order small-signal model fails [ 10 ].

In order to predict the dynamic behaviors of inverter, new small-signal -domain models are deduced for digitally controlled grid-connected inverters with converter current control scheme and converter current plus grid current control scheme [ 11 ]. The proposed methods allow direct design for controllers in -domain. The simulation results show that the proposed -domain models are more effective in predicting instabilities.

mathematical model of single phase inverter

As to control method, a PI controller with self-tuning parameter based on fuzzy inferring is proposed [ 12 ]. This controller is capable of automatically adjusting two parameters P and I of PI controller. For an LCL filter based single-phase grid-connected full-bridge inverter system, it is possible to decrease the total inductance as well as the size and the cost, if the harmonic current around switching frequency can be fully suppressed. LCL filters resonance may lead to the instability of the control system.

In order to address this issue, passive damping and active damping have been presented to improve system stability [ 13 — 15 ]. In order to cope with the grid inductance variations, a simple tuning procedure for the notch filter is proposed to estimate the resonance frequency by means of Fourier analysis.

The Goertzel algorithm, instead of the FFT, is used to reduce the calculation and memory requirements. Thus, the proposed self-commissioning notch filter increases and consumes little computational resources [ 16 ]. Improved passive damping which includes double loop control and makes the system less loss and more stable is proposed [ 17 ]. An active damping strategy with harmonics compensation which can alleviate the harmonics around the resonance frequency caused by the LCL filters is proposed in [ 18 ].

However, whether LCL filter can effectively suppress the harmonic current with different switching frequencies is not deeply analyzed [ 19 ].

Since stability margin of grid current feedback control is small, double closed-loop control, capacitor current feedback inner loop, and grid current feedback outer loop are adopted to increase the stability margin of the system [ 20 ].

The inverter side inductance current feedback, which is inner inductance current feedback, is proposed in [ 8 ], and they found that the stability margin using this current feedback is larger than current closed-loop control. Besides, the inner inductance current feedback with advantages of simple control algorithm and less feedback parameters has already been applied in [ 21 — 23 ].

In order to enhance the tracking characteristics of grid current, reference current feed forward control is presented. However, whether inner inductor current feedback control can meet grid current tracking features alone is not discussed [ 8 ].

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This paper will analyze mathematical model of the LCL filter and deeply analyze the stability of inner inductance current control system. The PWM inverter can be equivalent to proportion enlargement link which is generally normalized to 1 [ 25 ].

And the voltage between the two bridges can be substituted by reference wave voltage Figure 2. The electrical relationship of the schematic can be described as follows: where The transfer function of LCL filter which can be derived from formula 1 and Figure 1 is shown in Figure 2.

The dead zone effect can be equal to dead zone equivalent voltage source ; the transfer function block diagram and state equation are shown in Figure 3 and formula 3respectively.Updated 17 Dec This model demonstrates a DC-AC converter. Can be used to demonstrate the relationship of input DC, output voltage, modulation indexfilter selection and switching frequency.

Rashmil Dahanayake Retrieved April 13, When starting the simulation, the following error pops up: Struct contents reference from a non-struct array object. Component:Simulink Category:Model error. I did not do this example.

But I guess that Ts would be the switching period of the inverter therefore it would be defined in the PWM block. Hello Rashmil, I have a question. Where do you define the sampling time Ts that is being load by the digital clock for the sinus reference signal for the PWM switching blocks? I would be very glad, if you would give me any advise soon. Thanks in advance. Updated the PWM generation block. Automated post simulation plots.

mathematical model of single phase inverter

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Toggle Main Navigation.Documentation Help Center. The drive configuration consists of a half-bridge rectifier, a divided DC bus with two filter capacitors, and a two-leg inverter that supplies the motor windings. The single-phase induction machine SPIMwithout its startup and running capacitors, is treated as an asymmetric two-phase machine. The auxiliary and main windings are accessible and are in quadrature.

This configuration provides good performances and operation in regenerating mode. The single-phase induction motor is asymmetrical due to the unequal resistances and inductances of the main and auxiliary windings. To obtain the mathematical model of the motor with constant parameters voltage, current, and fluxit is necessary to transform all the variables to the stationary reference frame d - q fixed to the stator.

N a and N m represent the number of auxiliary and main stator windings, respectively. The equations that define the voltage for the model in the stationary reference frame d - q are:.

V qs is the q -axis stator voltage. R s is the main stator resistance. V ds is the d -axis stator voltage. R a is the auxiliary stator resistance. R' r is the rotor winding resistance referred to the main stator winding. N a is the number of auxiliary stator windings. N m is the number of main stator windings. The equations that define the flux for the model in the stationary reference frame d - q are:. L ls is the leakage inductance of the main stator winding.

L la is the leakage inductance of the auxiliary stator winding. L ms is the magnetizing inductance of the main stator winding. L' lr is the leakage inductance of the rotor winding referred to the main stator winding.

The electromagnetic torque expressed as a function of the rotor flux linkages and currents is. T e is the electromagnetic torque. Using the stator currents and rotor flux linkages as state-space variables for the SPIM model, the electromagnetic torque equation is.

This type of control selects the voltage vector from a switching table to control the power switches in the inverter to obtain the required stator flux and corresponding motor torque.

mathematical model of single phase inverter

From the motor equations in the stationary reference frame d - qestimate the stator flux and the torque:. If the voltage drop on the stator resistance is omitted, the stator flux linkage directly depends on the inverter output voltage. The next diagram shows the available voltage vectors, which correspond to possible inverter states, and the four distinct sectors in the d - q plane for a two-leg inverter.

The estimated flux and torque are compared with the references using hysteresis control. The digitalized output variables and the stator flux position sector are used to select the appropriated voltage vector from the switching table. Speed set point, in rpm. The speed set point can be a step function, but the speed change rate follows the acceleration and deceleration ramps.

To enable this port, set the Mechanical input parameter to Torque Tm. The motor measurement bus.Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions.

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Email Address. Sign In. Access provided by: anon Sign Out. Mathematical model of grid-connected inverter system in weak grid Abstract: Impedance-based analysis is widely used to study the grid-connected inverter system in a weak grid.

The advantage of the analysis is that without knowing the accurate parameters of an inverter, its equivalent output impedance can be obtained by specific methods e.

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A more complete mathematical model of the grid-connected inverter system in a weak grid is proposed, which contains the grid impedance and the load at the point of common coupling being neglected in the traditional model. Then, the error of the Pm from the impedance-based analysis is proved in detail in theory which indicates that the Pm of the analysis can hardly reflect the real state of the grid-connected system.

Simulations validate the theoretical analysis. Published in: Electronics Letters Volume: 51Issue: 2311 5 Article :. Date of Publication: 12 November DOI: Sponsored by: Institution of Engineering and Technology.

mathematical model of single phase inverter

Need Help?This paper presents a mathematical small-signal model of an electronically interfaced distributed generator DG by considering the effect of voltage and frequency variations of the prime source. Dynamic equations are found by linearization about an operating point. In this study, the dynamic of DC part of the interface is included in the model. The stability analysis shows with proper selection of system parameters; the system is stable during steady-state and dynamic situations, and oscillatory modes are well damped.

The proposed model is useful to study stability analysis of a standalone DG or a Microgrid. Distributed generation DG systems have been expected to be an important electric power supply system for next generation. DGs are able to be installed near the loads, so they can increase the power quality and reliability of electricity delivered to sensitive loads. Some of the DG technologies require a power electronics interface in order to convert the energy into the grid compatible AC power.

These interface devices make the sources more flexible in their operation and control compared to the conventional electrical machines. However, due to their negligible physical inertia, they also make the system potentially susceptible to oscillation resulting from network disturbances [ 1 ].

The coordinated operation and control of DGs together with loads and storage devices are central to the concept of microgrid [ 2 ]. The analysis of the dynamic stability of conventional power systems is well established, but for microgrid there is a need to investigate how circuit and control features give rise to particular oscillatory modes, and which of these have poor damping. Finding an exact mathematical model by considering DGs and their control is needed to investigate dynamic stability of the microgrid under transient events such as islanding from main grid and small-signal deviation like slow changing in load.

Reference [ 3 ] presented a small-signal model for inverter in stand-alone AC supply system by using only the droop controller's variables as state variables of the DG model. An averaged current source model has been suggested for the converter in [ 4 ].

In this investigation, the high frequency converter current dynamics have been neglected in order to focus exclusively on the dynamics and control of the islanded microgrid. Regardless of the type of the DG, an equivalent RLC circuit including output filter and transformers impedances has been modeled as a power circuit of DG in most of the literatures [ 15 — 8 ]. In these cases, output currents and voltages are considered as state variables.

References [ 167 ] by adding controller equations to the DG system made an accurate model for small signal stability analysis of a microgrid. In the reference [ 8 ], the input DC voltage variation of the inverter has been represented as the external perturbation in the open-loop model of the DG, but it has been set as a constant during control loop design and frequency-domain analysis.

The DC voltage has been related to the input and output equations of electronically interface of the DG by using switching function of rectifier and inverter in [ 5 ]. Moreover, two types of models have been presented in this paper for the prime source of the DG. While the proposed models have been used in steady-state and load flow analysis, but their linear forms can be used also in dynamic studies.

The objective of this paper is to find a comprehensive dynamic model of DG, including the prime source, power electronically interfaces, output filter, and controller. The proposed model represents all components of the DG in a dq0 reference frame, thus it ensures any application such as steady-state and dynamic analysis that meets requirements and constraints of both AC and DC parts of the system. The dynamic stability of the DG is investigated by the small signal and step response analysis.Skip to Main Content.

A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Personal Sign In. For IEEE to continue sending you helpful information on our products and services, please consent to our updated Privacy Policy. Email Address. Sign In. Access provided by: anon Sign Out. Model predictive control of single phase grid-connected inverter with LC filter Abstract: Model Predictive Control MPC method is proposed in this paper applied to a single phase grid-connected inverter.

This method uses a state-space equation of the system to predict the next time value of current from the grid side by adjusting the duty ratio of inverter in each sampling period. The duty ratio which minimizes a cost function is selected. Then, taking advantage of the duty ratio to control the output current of single phase inverter. This scheme is easy to realize and its mathematical model is simple. This method is convenient compared with traditional control method of single phase inverter.

There is no need to adjust PI parameters. The Simulation results show that the model predictive control can effectively predict the output current and the system performs very well.

Article :. DOI: Need Help?