Double-loop control structure using proportional resonant and sequence-decoupled resonant controllers in static coordinates for dynamic voltage restorer

Among incidents on grids, the sag/swell voltage is considered as the most frequent incident. To solve this problem, custom power devices are used. In particular, the dynamic voltage restorer (DVR) is a modern and efficient customer device. DVRs are used to mitigate voltage sag/swells and harmonics on the load bus, thus protecting the sensitive loads. The DVR is a serial compensator that applies a voltage to the point of common coupling to maintain the voltage of sensitive load at the nominal value. To improve the performance of DVRs, in this study, the control strategy of the two-stage loop circuit is implemented. The external voltage control loop uses a sequence-decoupled resonant (SDR) controller, and the inner current-control loop uses the proportional resonant (PR) controller implemented in the stationary frame αβ.


Introduction 
The sag/swell voltage is a problem that entails several hazards for the operation of voltage-sensitive systems and devices [1][2][3] . Using DVRs to mitigate the sag/swell voltage and protect sensitive devices is one of the effective solutions. In the past, DVRs often used the proportional-integral (PI) feedback controller in a synchronous reference frame (SRF) [3][4][5][6][7][8][9][10][11] . By converting the feedback signals into SRFs, they become DC quantities. As the PI controller has a very large DC gain, the steady-state error can be effectively eliminated. However, besides converting between the reference frames, when the grid unbalanced, it is required to use double controllers and cross-decoupling, leading to increased computation and complexity in digital signal processing. In addition, PI controllers have disadvantages such as steady-state errors in the stationary frame and the need to decouple the phase dependency in three-phase systems. To improve overall performance, several solutions have been proposed, including the addition of a feedforward voltage path, multi-state feedback, and increasing the proportional gain. These changes help extend the bandwidth of the PI controller, but they also push the systems towards their stability limits, and can distort the line current caused by background harmonics introduced along the feedforward path if the grid voltage is distorted [9] .
To reduce the amount of computation and still obtain the same frequency response as the PI controller in SRF [5-6, 9, 12-14] , PR controllers need to be developed in the static coordinate system. The main advantage of the PR controller is an extremely high gain at the resonant frequency, which eliminates the steady-state error at this frequency. It is equivalent to an integrator, which has a very large DC gain coefficient that makes the DC static error equal to 0. The PR controllers are used to adjust the AC signal without any SRF conversion. They can achieve good grip properties and control stability. Compared with conventional PI controllers in SRF, the control complexity of PR controllers has been reduced to a certain extent.
With the unbalanced sag/swell voltage, conventional resonance controllers lose their advantages as it is not possible to separate the positive and negative sequences for individual adjustment. In Ref. [10], it is shown that better system performance can be achieved if the gains for each sequence quantity can be adjusted individually. The SDR controller has all the advantages of conventional resonant controllers, and its control structure is easy to implement because the multi-state-variable structure uses the second-order resonant controller. With this controller, the abc quantities of the three-phase three-wire system are independently controlled for positive and negative sequence components in the stationary coordinate system αβ.
Owing to these advantages of resonant controller, researchers have used this type of controller for DVRs. Ref. [14] provides a control strategy for resonant controllers that does not cause oscillation, but due to the existence of the integral stage, it is difficult to use simple resonance control to satisfy the dynamic speed. The authors of Ref. [8] use the PR controller to eliminate the steady-state error while increasing the dynamic response speed. However, the inclusion of the proportional stage leads to poor load adaptability. Ref. [15] provides a combined strategy: resonance control to perform voltage compensation without static error and feedforward control to improve the dynamic response of the system. Additionally, a method of suppression of harmonic voltages on the capacitance is included to increase adaptability to non-linear loads. The essence is to use the resonant control in the voltage loop structure, without using a loop according to the current. A capacitive harmonic feedback signal is sent to the DVR to generate an opposite harmonic current, indirectly removing the harmonic component in the output compensation voltage of the DVR.
It should be noted that in the control process, the current flowing through the filter inductance has a very large instantaneous fluctuation, becoming a source of interference that directly affects the output voltage of the DVR. It affects the current flowing through both the filter capacitor and the transformer, affecting the current of the source. Therefore, simply regulating the harmonic components through the capacitor is not sufficient. In contrast, the control loop of the external voltage mainly involves tracking to the set voltage value, and it acts as a filter with voltage harmonics on the filter capacitor. It is necessary to use a loop circuit according to the current of the filter inductance to quickly identify the electrical current disturbance on the system, from which the current controller will effectively eliminate or significantly reduce its influence on the output voltage of the DVR, thus improving the dynamic characteristics of the DVR.
To enhance the DVR's protection performance against balanced and unbalanced sag/swell events, as well as to maximize the advantages of PR and SDR controllers, the author proposes the use of a two-loop control structure in which an external voltage control loop uses an SDR controller for independent control of positive and negative sequence components, and an inner current control loop uses a PR controller. Such a structure combines the advantages of the both controller types, simplifies the control structure, reduces the computation, and improves the dynamics and adaptability to nonlinear loads. Fig. 1 shows a structure diagram of a practical and an ideal PR controller [9] .   Fig. 2 shows the positive-and negative-sequence Bode diagrams of practical and ideal PR controllers. adjusting ω c appropriately to reduce sensitivity to frequency changes in the grid. In addition, system delay compensation (load delay, calculation delay and regulating delay) and harmonic compensation are discussed in detail in Ref. [9].

SDR controller
The multi-state-variable structure of ideal SDR is as follows [10] .
Here, e  and e  respectively are the feedback error signals caused by coordinates α and β; K I is the SDR controller's integral factor; () ys   and () ys   are the positive and negative sequence output operators in the synchronous frame. Fig. 3 shows the multi-state-variable structure diagram of an ideal SDR controller [10] .
The multi-state-variable structure of a practical SDR can be described as follows [10] .
Here, ω b represents the cutoff frequency of the practical SDR controller.  Multi-state-variable structure diagram describes the practical SDR controller [10].
The gain factor of the ideal SDR controller can lead to serious issues related to the center frequency. To address this, the practical SDR controller described by the multi-state-variable structure (Fig. 4) [10] is regularly used. Fig. 5 shows the positive-and negative-sequence Bode diagrams of an ideal and a practical PR controller.   Fig. 6 shows a simple model of a voltage source converter (VSC) and LC filter connected to a grid [11] . VSC is represented as a voltage source u inv , i f is the current running through the filter inductor, u dc is DC-Link voltage. From the structure diagram in Fig. 6, Kirchhoff's law is applied to the three-phase voltage and current, yielding the following equations

Control model and algorithm
Applying the Clarke conversion on the static frame αβ yields Conduct interruption Eqs. (9) and (10), we get where T S is the sample period. The load voltage control algorithm is described in the form of mathematical equations and the following diagrams: (1) Voltage regulator From Eq. (12), we obtain the equation describing the voltage regulator using the SDR controller, as follows (2) Current regulator From Eq. (11), the equation describing the current regulator using the PR resonant controller is obtained, as follows where G PR is the transfer function of PR controller. The current regulator and voltage regulator structures are designed using from Eqs. (13) and (14), as shown in Fig. 7.
The synthesized structure of the two regulating loops on the stationary frame αβ is shown in Fig. 8.
A schematic diagram of the DVR connected to the grid is shown in Fig. 9.

Simulation results
The performance of the proposed control strategy for sag/swell voltage incidents is evaluated using the simulation results; this evaluation uses a complete voltage compensation strategy and a space vector modulation method. The grid model, load model, and DVR model are set up using tools such as Simulink and SimPowerSystem of MATLAB.
The simulation results show that when there are balanced or unbalanced sag/swell voltage problems on the grid, the DVR shows good protection performance: The output characteristics are not significantly affected by the harmonics, and the THD index of the load voltage is very low. With this control strategy, the adaptability to nonlinear load is adequate.

Conclusions
With the proposed DVR control method, it can be seen that the control structure on the static coordinate system αβ is considerably simpler. It is not necessary to use the channel interleaving as well as the transitions of αβ/dq, which reduces the computational burden on the control algorithms; the dynamics of the system are thus improved. Prior to balanced/ unbalanced sag/swell voltage events, even with a significant disturbance, the DVR shows very good performance: it quickly restores and stabilizes the load voltage and shows sufficient adaptability to nonlinear loads.
The design and calculation of the parameters of the DVR controller should be noted, owing to the very large fluctuation in the current flowing through the filter inductance. The first step requires the design of the inner current loop to be considerably faster than the external voltage regulation loop. This is achieved by the current control loop using the PR controller, which has sufficiently fast dynamic characteristics. The next step is to design and regulate the SDR controller parameter for the external voltage control loop to track to the set value, so that the control quality of the new system is ensured. Further, as the harmonic voltage regulates the resonant controllers for the frequencies outside the resonant frequency range, the output characteristics are less affected by the harmonics. However, this causes additional energy loss. To restore the voltage on the load to 1 pu when there is a sag/swell voltage event, as well as increase the adaptability to nonlinear loads, the DC power capacity requirement must be greater than that for the control strategy that uses the PI in SRF, where the requirement depends on the resonant controller parameters and the nonlinearity of the load.