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This paper presents the Synchronous Reference Frame Theory (SRF) based Phase Locked Loop (PLL) to enhance the performance of Dynamic Voltage Controller (DVR). In a grid connected power conversion system, a critical component is the Phase-Locked Loop (PLL) that generates the grid voltage’s frequency and phase angle for the grid synchronization. For grid voltage control, accurate and fast responding PLLs are required to provide phase angle and frequency measurements of the grid voltage. Therefore, SRF based PLL is presented in this work and it calculates the phase angle accurately and effectively. This paper also presents a novel feedback mechanism for SRF-PLL which uses the estimated frequency and phase to achieve grid control. The fundamental signal of the grid voltage is extracted by low pass filter and a unit value controller to generate a unity sine reference signal for the feedback network. In particular, the performance of the SRF-PLL in the three-phase PV fed grid connected system is analyzed under the different power quality issues such as voltage sag and swell. In addition, a detailed study on synchronous reference frame theory is presented. An appropriate control algorithm for DVR is developed and the validity of the proposed configuration is verified through MATLAB simulation results as well as experimental results under different operating conditions.

The increasing energy demands of today’s world have increased the usage of renewable energy resources, such as photovoltaic (PV) and wind for electricity power generation [

Power factor control is an important task in grid-connected systems [

For grid synchronization, tracking of phase angle is necessary. The process of phase tracking can be divided into two groups [

An earlier version of PLL is Zero Crossing Detector (ZCD), where the zero-crossings are detected by capturing the rising or falling edges of the square-wave signals [

To achieve grid synchronization, the information about instantaneous phase angle and frequency is obtained by time basis PLL technique. To obtain the maximum performance, quality of PLL has to be improved. Grid synchronization is done by locking the phase angle of the grid voltage measured at the Point of Common Coupling (PCC), which is highly distorted due to voltage imbalance, harmonic, and phase or frequency variations with the inverter voltage. In PLL, it is very essential to design and develop a controller very accurately. Because this controller provides fast time response, zero error in the steady state and validity under any input signal for the PLL. The simplest controller used to achieve these parameters is Proportional Integral (PI) controller. The PI controller can be designed in continuous time or discrete-time domain [

The paper is structured as follows. In the first section, introduction about the proposed work is given. Section 2 discusses about the structure of proposed system with SRF-PLL. In section 3, Synchronous Reference Frame theory is explained with its equations and also design of PI controller used in the SRF-PLL system is explained very well. Finally the simulation results of overall PV fed grid connected system with SRF-PLL is shown and explained clearly in section 4. And also, grid synchronization of the PV fed grid connected system under amplitude variation and frequency variations is explained. This section also shows the performance analysis of multi- level inverter and different types of PLL. Section 5 illustrates the experimental setup and results of DVR system for voltage sag and swell compensation.

In this paper, an effort has been made to implement the PLL for grid synchronization under voltage sag and swell condition. And also, various multi-level inverters are designed and simulated. These are used to interface the power generated by PV array to utility grid. Different power quality issues (voltage sag and voltages well) are generated and compensated using DVR. A novel contribution of this work is to introduce SRF-PLL for DVR control circuit to achieve grid synchronization. In order to achieve the grid synchronization, output current of inverter used in DVR operation is considered as one set of input signal and grid voltages are considered as another set of input signals and PLL circuit is implemented.

The proposed PV fed power conversion system with SRF-PLL is shown in

In this working model, DVR control action is done by SRF-theory based PLL. The basic principle of this theory is transformation of current variables in synchronously rotating d-q frame. To generate the unit vectors,

voltage signals are processed by the PLL [_{a}, i_{b}, i_{c}) are carefully detected and then transformed into two-phase stationary frame (α-β-0) from the three-phase stationary frame (a-b-c). This transformation equation is given in Equation (1).

To obtain the dq current components, the two phase current variables i_{α} and i_{β} of stationary αβ axes are transformed into two-phase synchronous (or rotating) frame (d-q axes) and it is given in Equation (2).

In the above equation, the quantities cosθ and sinθ represents the synchronous unit vectors. It can be generated using the PLL block. In the above equation, the d-q current components are generated and it consists of AC and DC quantities. The fundamental component of current is mentioned by the fixed DC part and the harmonic component is represented by AC part [_{d} is a combination of active fundamental current component (i_{d} DC) and the load harmonic current (i_{h}).

Synchronous reference frame theory states that, the fundamental component of current rotates in synchronism with the rotating frame and therefore it can be considered as DC. By filtering i_{d} current variable, the fundamental component of the load current in the synchronous frame can be obtained. By subtracting i_{d} dc part from the total d-axis current (i_{d}), the AC component i_{d} can be produced and it leaves behind the harmonic component of load current. To transform the d-q current variables into α-β variables, inverse transformation is performed and it is given in Equation (3).

According to SRF theory, two phase stationary frame αβ0 current variables are transformed back into three-phase stationary frame abc variables. And also the reference currents are obtained from the following Equation (4). The term T_{abc} is denoted by transformation function and it is shown in Equation (5).

By solving the above equations, reference currents are obtained and given in Equation (6). This equation represents the final calculation for transforming abc variables into dq variables.

For grid connected applications, the voltage control can also be implemented using synchronous reference frame technique in the same way of current control method as explained above. In this control method, the grid voltage and currents are transformed from their three-phase quantities (abc variables) into a two phase quantities (dq variables) using Clarke transformation function. Since the variables are now rotating synchronously with the reference frame, the control variables can be converted into DC variables [

In this system, the major role of PLL is to track the phase angle required for abc to dq transformation. It is also used for grid synchronization. The main advantage of this proposed SRF-PLL based DVR system is that continuous power supply is suppliedtotheloadbytheactiveconversionofDCvariablestoACvariables.The most popularly used synchronization technique is VCO based PLL as shown in _{i}) [

Ingrid-connected renewable system, control algorithm plays a vital role and it allows the synchronization between the renewable energy source and the utility grid [

There are several methods to estimate the phase angle of grid voltage in order to obtain the synchronization of the inverter voltage with the three-phase grid voltages. For grid synchronization, different types of synchronization methods are used. They are Synchronous Reference Frame PLL (SRF-PLL), Positive Sequence Detector based dq PLL (PSD-dq PLL), Dual Second Order Generalized Integrator Phase- Lock Loop (DSOGI-PLL), and Multiple Second Order Generalized Integrator Frequency-Lock Loop (MSOGI-FLL) [

Among the various control techniques, SRF-PLL is very effective control technique. All these techniques might be used in different renewable energy applications and the choice of control method will depend on the grid interfacing requirements and regulations to be fulfilled. To implement the control strategy, it becomes necessary to calculate the reference current [

As already mentioned, a PLL is a closed loop system in which voltage controlled oscillator is controlled to

keep the time and phase of an external periodical signal using a feedback loop [

To convert three-phase quantities into rotating reference frame, the first step is to transform the three-phase quantities into an orthogonal component system (alpha and beta) by taking the projections of the three-phase quantities on an orthogonal axis as shown in

This conversion process is known is called the Clarke transform and it is shown in Equation (8). The alpha - beta components are known as stationary reference frame variables.

In the stationary reference frame, the net voltage vector makes an angle θ with the orthogonal reference frame and rotates at a frequency of ω. The system can then be reduced to DC by taking the projection of the stationary reference frame components on the rotating reference frame [

In three-phase system, the major role of the PLL is to accurately estimate the phase angle difference between input and output waveforms. The angle estimated by PLL is assumed as θ and the actual angle is assumed as ω * t [

Using the trigonometric identities, the above Equation (11) can be reduced to,

When the angle traced by PLL is close to the actual voltage vector angle,

This property is used in the Synchronous Reference Frame PLL for three-phase grid connected application. The three-phase quantities are transformed into the rotating reference frame and the q component is used as the phase detected value [

To solve the transfer function of PLL, small signal analysis is done using the network theory and the PLL transfer function can be expressed as follows:

The closed loop error transfer function for PLL is given as,

This closed loop transfer function can be compared with the second order system transfer function and system transfer function can be expressed by,

In the above equation, ω_{n} is the natural frequency and

In the design of SRF-PLL, designing the values of PI controller (also known as loop filter) is very important. The output equation of PI controller is expressed in Equation (19).

Using z transform, Equation (19) can be re-written as:

By using bilinear transformation,

Replace

In the above equation, T is considered as sampling time. And transfer function of PI controller is rewritten as,

The already obtained Equation (8) and Equation (9) can be compared to map the value of proportional gain and integral gain of the PI controller into the digital domain. It is known that the step response to a general second order equation of H(S) is given by,

By assuming settling time (settling time is defined as the time it takes for the response to settle between an errorband) value of 20 ms and error band of 5%, damping ratio and natural frequency can be obtained. The designed parameters of PI controller are shown in

In _{0} and B_{1} are called as digital filter coefficients and its values are obtained by substituting K_{p} and K_{i} values in the below equation.

In the Equation (22) and Equation (23) is the run rate of PLL and its values is chosen as 10 KHz, B_{0} and B_{1} values are obtained by using the above equations.

In this section, the simulation of three-phase PV fed grid connected system is shown. And also, voltage sag and swell issues are generated. They are compensated by DVR operation. DVR control unit is implemented with the help of SRF based PLL. Therefore, in addition with the voltage sag and swell compensation, grid synchronization is also achieved with this DVR control action.

Before generating the voltage sag and swell, the grid connected system is developed and implemented as shown in

Since the voltage generated from PV array is DC quantity, to convert the DC into AC quantity, inverter is required before interfacing with the grid. Normally voltage source inverters are used for interconnection. But in this proposed system, multi-level inverter is chosen due to their several advantages over conventional inverters. Their advantages are reduced switching frequency, output voltage with very low distortion and reduced dv/dt stress [

In the proposed DVR model, three-phase voltage source inverter is implemented and it is responsible for compensation of voltage sags and swells. It is connected in series to the grid with the help of injection transformer.

Parameters | Value |
---|---|

Damping Ratio ( | 0.7 |

Natural Frequency ( | 168.87 Hz |

K_{p} | 250 |

K_{i} | 231 |

B_{0} | 230.12 |

B_{1} | 243.79 |

Parameters | Value |
---|---|

Series RLC load: R L C | 0.4 Ω 0.15 × 10^{−3} H 0 |

Non-linear load: R L | 1 Ω 0.15 × 10^{−3} H |

DVR parameters: DC input voltage R | 700 0.1 Ω |

Grid Parameters: Grid voltage L-L (rms) Vbase Line Frequency Nominal load power R C | 415 Ω 50 Hz 4000 W 1 Ω 100 × 10^{−6} F |

The inverter system consists of an Insulated Gate Bipolar Transistor (IGBT) module, its gate-driver, and an isolation transformer. To control the series inverter, various methods are presented in the literature, to provide dynamic voltage restoration and most of the methods are injecting a voltage in quadrature with advanced phase, so that reactive power is utilized in voltage restoration [_{ab}, V_{bc}, and V_{ca} are transformed into the d-q variables.

Then, these voltages are normalized to unit sine waves using line-neutral system voltage of 120 V_{rms}. This value is considered as reference value (V_{ref}) and it is compared to with actual system voltages (V_{s}). Based on this value, the amount of injected voltage is calculated to maintain a constant voltage at the load terminals. Therefore whenever voltage sag or swell is occurred in the grid side, a corresponding voltage is injected (V_{inj}) in-phase by the DVR to retain a constant voltage (V_{L}) at the load end.

In this system, three-phase grid is fed by multi-level inverter. With the use of sine PWM modulation scheme, Total Harmonic Distortion (THD) value of inverter can be reduced without any additional control technique. This technique can eliminate the choice of large filter inductor and capacitance [

When additional loads are connected to the grid, grid voltage is severely affected by voltage sag and swell problem. These two major issues are mitigated by DVR. It act as voltage controller and whenever grid voltage is reduced or increased from its nominal range, the change in voltage is detected by DVR, and required amount of voltage is injected by DVR for that entire period of PQ problem. To provide three-phase controllable voltage source, it uses Voltage Source Inverter (VSI).The performance of grid connected system is analyzed under the condition of sag and swell problem. In this system, 30% of decrease in voltage is initiated from the time period

of 0.2 sec to 0.3 sec and 50% of increase in voltage is initiated from the time period of 0.5 sec to 0.6 sec. The disturbed grid voltage and current is shown in

To compensate the load voltage, DVR is designed and interconnected with the grid connected system. DVR is a series connected power electronics based device that can quickly mitigate the voltage sag and swell in the system and restore the load voltage. In this system, 30% of decrease in voltage is initiated for 5 cycles (from 0.2 to 0.3 sec) at the PCC as shown in

By the action of inverter used in DVR, required phase voltage will pass through the injection transformer to mitigate the sag voltage. This injection process will be done continuously unless and until the load voltage meets the rated voltage. The injected voltage required to compensate the voltage sag (

To analyse the performance of SRF-PLL, the same grid connected circuit is implemented with SRF-PLL as

shown in

The MATLAB/Simulink model of three-phase SRF-PLL is shown in _{a}, V_{b} and V_{c}) are multiplied with inverter current variables (I_{a}, I_{b} and I_{c}). In this model, multipliers serve as phase detectors. If the phase difference between two signals is zero degree, then the error signal is zero, which represents the locked state of the PLL. If there is any phase difference, non-zero error signal is produced and it is said to be unlocked state [_{a}, V_{b} and V_{c} are transferred from three phases to a stationary system of two phases V_{d} and V_{q} as presented in _{d} and V_{q} variables are separated into qe and de variables. A low pass filter is designed and it is used to extract the fundamental signal from the grid voltage as a unity sine reference. This sine reference signal is obtained from qe conversion block to sin-cos signal generations block as shown in

In this PLL circuit, the function of PI regulator is to track the phase when the grid frequencies are changed below or above the rated frequency. Initially, the phase angle θ is estimated with θ^{*}. The parameter θ^{*}is the integral value of the estimated frequency ω^{*}. The estimated frequency ω^{*} is the sum of the PI controller output and the feed forward frequency ωf. By using this value and following the Equation (11), gain of the PI-regulator is designed so that estimated frequency ω^{*} is locked on the system frequency ω.

The performance of the proposed SRF- PLL with the injection of 5^{th} and 7^{th} order harmonic contents into the grid voltage is given in ^{th} and 7^{th} order harmonics injection to grid voltage, the phase angle is locked very well.

The performance of PLL is analyzed for various frequency values and the results are obtained. When the grid voltage frequency reduces from 50 to 40 Hz at 0.05 s, PLL tracks the phase angle correctly and maintain the

synchronism between inverter and grid voltage. The performance of the SRF-PLL under this condition is presented in

It is seen from

In this system, 5^{th} and 7^{th} order harmonics are added to the input signal. The designed PLL is working effectively even at the harmonic injection and the phase angle of the fundamental frequency is tracked accurately.The whole system is designed to deliver the power of 4000 W to the load. With the SRF-PLL system, grid active power is maintained as 4300 W during the operation and grid reactive power is obtained as 2000 VAR. The grid active and reactive power with PLL system is shown in

In this work, SRF-PLL has been developed to achieve the grid synchronization under various frequency ranges. The PLL presented in this method is based on trigonometric function transformation and synchronous reference frame theory. The filter used in the PLL is easy to design and implement. And also, 13-level inverter is simulated and connected to grid to supply the power to the grid. Simulation results verify that this type of SRF-PLL method has good phase locked control under wide frequency tracking range when compared with conventional types of PLL methods. To know the performance of SRF-PLL, its results are compared other types of PLLs such as pPLL, Park PLL and Digital PLL. The performance parameters of different PLL methods are shown in

When the grid frequency changes, static error caused is only 3 degrees, but this error is small and all the settling time is shorter compared with other methods. And also, when third order and seventh order harmonics are introduced in the grid voltage this type of PLL can obtain the accurate phase locked control. Because in SRF-PLL method, the low pass filter is correctly designed and implemented to reduce the effect of harmonics in the system.

In order to verify the theoretical concept and above simulation results experimentally, a hardware prototype of the complete single phase DVR system was constructed and is shown in

In this circuit model, load experiences voltage sag of 10% magnitude for 0.5 ms duration as shown in

Whenever DVR detects voltage sag or swell, it must inject the required amount of voltage properly to the load. When DVR is activated, magnitude of load voltage remains constant due to the injected voltage, which increases during the voltage sag event to compensate for the voltage sag. The compensated voltage by DVR action is shown in

Parameters | p PLL | Park PLL | Digital PLL | SRF-PLL |
---|---|---|---|---|

−5 Hz frequency change Settling time Static Error | 9 cycles 0 deg | 9 cycles 0 deg | 2.9 cycles 4 deg | 2.7 cycles 3 deg |

+5 Hz frequency change Settling time Static Error | 7 cycles 0 deg | 7 cycles 0 deg | 2.5 cycles 4 deg | 2.4 cycles 3 deg |

30% increase in voltage Settling time | 5 cycles | 2 cycles | 0.5 cycles | 0.2 cycles |

50% increase in voltage Settling time | 6 cycles | 3 cycles | 0.7 cycles | 0.3 cycles |

5^{th} and 7^{th} order harmonic injection | Un-locked | Un-locked | Well locked | Well locked |

voltage. Therefore, from DVR experimental waveforms, it can be concluded that the designed DVR system hardware setup is able to respond instantaneously to compensate voltage sags.

In this paper, the concept of Synchronous Reference Frame Theory based PLL is explained. This PLL control strategy is implemented to the DVR system to improve its voltage restoration capabilities. With this integration

of PLL, the DVR will be able to independently compensate voltage sags and swells without requiring any additional controller. Design of major components used in PLL circuit is explained. Experimental setup of the single phase DVR system is presented and the ability to provide temporary voltage sag compensation is tested. In addition with the voltage sag and swell compensation, grid synchronization is also achieved effectively for various frequency ranges such as 40 Hz, 45 Hz, 50 Hz, 55 Hz and 60 Hz. In this work, SRF-PLL method has been presented based on synchronous reference frame theory. The filter used in the method is easy to design and implement. With this designed PLL system, phase angle is accurately tracked within acceptable margins. The settling time and static errors for different PLLs are compared and analyzed very well. It is observed that, this SRF-PLL method has good dynamic and static performances under the wide frequency range. Moreover it has the good and accurate phase angle tracking control with wide frequency range. Therefore this type of PLL system with the PI-regulator can be operated in a real life application.

In the future, the proposed SRF-PLL method can be applied for DVR when symmetrical and asymmetrical faults are generated in distributed power generation system to achieve the grid control and synchronization.

Saritha Natesan,Jamuna Venkatesan, (2016) A SRF-PLL Control Scheme for DVR to Achieve Grid Synchronization and PQ Issues Mitigation in PV Fed Grid Connected System. Circuits and Systems,07,2996-3015. doi: 10.4236/cs.2016.710256