# Enhanced Control for Improving the Operation of Grid-Connected Power Converters under Faulty and Saturated Conditions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Control Strategy

_{f}, improves the transient response and decrease startup current [25], but, on the other hand, it makes the loop more sensitive to distortions that may affect the voltage.

_{q}

_{±}is defined based on the PCC voltage drop/rise multiplied by the droop coefficient k

_{v}

_{±}. As in many applications, a dead-band is considered in this case. The value of ${I}_{r+}^{*}$ is obtained from the reactive current command ${I}_{q+}^{*}$ plus i

_{q}

_{+}. The ${I}_{a-}^{*}$ equals to zero according to standard and the ${I}_{r-}^{*}$ is equal to i

_{q}

_{−}. The contribution of GC-VSC to the PCC voltage support is mathematically written in (3) and (4) according to VDE-AR-N 4120 [23,28].

_{band}

_{±}is the threshold voltage in which GC-VSC has to work in voltage supporting mode by injecting reactive current to the PCC. Also, $\Delta \left|{V}_{+}\right|$ and $\left|{V}_{-}\right|$ are equal to $1-\left|{V}_{+}\right|$ and $\left|{V}_{-}\right|$, in per unit, respectively.

#### 2.1. Saturation and Uncontrollability Scenarios of a GC-VSC

_{i}which is connected to the PCC through a LC filter, as shown in Figure 3. The grid is simplified as a voltage source, V

_{g}, connected in series with an impedance Z

_{g}. Only the voltage at the PCC and the inverter current are measured to control the system. In the case of the inductor of the LC filter, the resistive part is neglected as its value is not significant compared to the inductive part. Moreover, the inherent resistor in a real application would introduce damping, what benefits the performance. Therefore, avoiding the resistor makes the analysis even more restrictive and hence the proposed method should perform even better. In this case, the GC-VSC is controlled within the following operating boundaries:

- (1)
- Using a space vector modulation the linear control range of the output fundamental component can be extended a 15%. However, for a six-step square-wave controlled inverter, the magnitude of the output fundamental voltage is equal to (2/π) V
_{dc}= 0.6366 V_{dc}. Increasing the output voltage of a PWM-controlled inverter from 0.575 V_{dc}to the limit of 0.6366 V_{dc}, is done by entering to the nonlinear region. The region of operation between the loss of linear control (m = 1.15) and complete loss of control (uncontrollability) (m = 1.27) is called the over-modulation region. When over modulation occurs, the modulation index m exceeds the triangle wave in modulator. Note that when m > 1, or m > 1.15 as appropriate, the actual resultant fundamental component does not linearly follow m, and the controller is saturated. Consequently, the shape of the output voltage waveform is only partially under control. Since the modulator effectively loses control of the output waveform during the saturation intervals, the output waveform becomes progressively distorted and includes low-frequency harmonics [29]. Therefore, the amplitude and phase of V_{i}is determined by the input voltage of the switching modulator, the switching method and the dc bus voltage V_{dc}. The peak of V_{i}cannot be higher than 0.6366 V_{dc}for any switching methods. When an inverter works in grid-supporting mode or grid-feeding mode, the inverter voltage has to be higher than the PCC voltage to deliver reactive power to the grid. To inject reactive power, if the input of switching modulator is higher than triangle wave, the current controller becomes saturated, hence the inverter becomes uncontrollable and the waveforms of the injected current gets distorted. - (2)
- The GC-VSC current has to be under the semiconductor’s current rating. In transient conditions, as for instance: power/current reference sudden change, inverter’s start-up or when there is a grid fault, the inverter current may experience some overshoots, due to the delay of the current controller, and the wind-up effect at the integrators of the controllers. However, a high current overshoot might give rise to an undesired converter trip or to a critical damage of the semiconductors.
- (3)
- The GC-VSC should help the grid in case of grid faults according to the Low Voltage Ride Through (LVRT) curve. Typically the reactive current coefficient k
_{v}_{±}is higher than 2 [23,28]; therefore the active current should be set to zero under severe grid faults to keep the VSC current under the rated value.

_{i}, can be decomposed into its symmetrical components. In this case, just the positive and negative sequence will be considered, as it is a three-phase three-wire system and thus zero-sequence circuit analysis is not required due to the absence of zero sequence current components. For the positive sequence, the active current, responsible of the active power delivery and the positive sequence voltage are in phase, but the reactive current is shifted 90 degrees with respect to the positive sequence voltage. Regarding the negative sequence, only reactive current is injected to the PCC according to the VDE-AR-N 4120. The negative sequence reactive current is shifted 90 degrees with respect to the negative sequence voltage. In Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9, the phasor diagrams and numerical results of GC-VSI are shown based on several simulations. The values of voltages and currents are captured from simulation results.

_{v}

_{±}. For i

_{q}

_{+}and i

_{q}

_{−}equal to −0.79 and −0.517 p.u., the V

_{i}

_{+}and V

_{i}

_{−}have to 1.04 p.u. and 0.21 p.u. respectively. Therefore, the inverter has to produce a V

_{i}around 1.25 p.u., which is quite the controllability limit. In these conditions, the controller will become saturated because the value of reactive current (i

_{q}

_{+}) is not suitable, so the value of i

_{q}

_{+}needs to be modified and limited by the saturation scheme.

#### 2.2. Development of the Proposed Anti-Saturation Scheme

_{g}) or the grid voltage (V

_{g}) and permits the converter to remain stable at normal and faulty situations. The importance of this anti-saturation block is once the vector diagrams of currents and voltages in different conditions were reviewed in the previous section.

_{q}

_{−}can be positive or negative depending on the transformations, but the Equation (6) is correct for any value of i

_{q}

_{−}. The negative sequence voltage rotates at twice the frequency with respect to the positive sequence voltage. In the worst case, the maximum value of the inverter voltage can be found when the positive sequence voltage and negative sequence voltage have the same direction as shown in Figure 4, Figure 5, Figure 6, Figure 7 and Figure 8. Therefore:

_{q}

_{−}is found by multiplying k

_{v}

_{−}by the negative sequence voltage, meanwhile i

_{q}

_{+}is related to the reactive power set point and droop function of the PCC’s positive sequence voltage. The DC bus voltage measurement is filtered in order to remove ripples and high frequency noises. In (9) and Figure 9, i

_{p}

_{+}is equal to ${I}_{a+}^{*}$.

#### 2.3. PR Controller with Anti-Windup Capability

_{p}, K

_{i}, ω

_{o}and ω

_{c}are the proportional gain, the resonant gain, the resonant frequency and the resonant bandwidth, respectively. The PR controller is used to ensure zero steady-state error and a fast dynamic response. Because of limitations in practical implementations an ideal resonant controller (ω

_{c}= 0) cannot be used. The frequency response of PR controller, at frequencies higher than or lower than the resonant frequency all the plots converge to the 20 dB per decade asymptotic response regardless of the value of ω

_{c}. The major difference between the different plots is the increasing peak amplitude at the resonant frequency (ω

_{o}) for smaller values of ω

_{c}. The infinite gain benefit of the ideal resonant term only happens at the resonant frequency and any perturbation will lead to a reduction of the generated gain. Hence, the resonant regulator is potentially sensitive to the alignment between the regulator’s resonant frequency (ω

_{o}) and the fundamental frequency of the grid. To solve this issue, instantaneous estimation of frequency from FLL is fed to PR controller and the value of resonant bandwidth is set 2 rad/s in this paper. The implemented PR controller based on two integrators is shown in Figure 12.

_{max}, otherwise there will be over modulation. In over modulation, the switching frequency is reduced and the waveforms at the inverter’s output are distorted [29]. The proposed AC limiter (ACL) to limit the input of SM can be expressed as:

_{max}is chosen based on the switching method.

_{max}is the main important variable in the anti-windup strategy, which should be selected based on V

_{dc}. The value of O

_{max}(V

_{i}

_{max}) depends on the switching method of inverter according to (8). The V

_{i}

_{max}is needed for two parts: anti-saturation scheme and anti-windup of PR controller. For anti-saturation scheme is set ${V}_{dc}/\sqrt{3}$ to prevent uncontrollability. For PR controller with anti-windup, m

_{max}is chosen based on the switching method according to Equations (21) and (22). Therefore, the allowed maximum value of for three different switching methods: Sinusoidal pulse width modulation (SPWM), Space Vector Pulse Width Modulation (SV-PWM) and Square wave modulation can be found from:

_{dead}and Ts are the switching dead time and the switching period, respectively.

## 3. Real Time Simulation Results

_{max}is 7200A (1.5211 p.u.) and V

_{i}

_{max}is considered ${V}_{dc}/\sqrt{3}$ (1.1785 p.u.). The SCR of grid from high voltage side of transformer and X/R of grid impedance are chosen to be 5 and 7, respectively.

_{p}, K

_{i}and k

_{f}) is the one described in [25]. In this study case V

_{band}

_{±}in (3) and (4) is considered to be 0.1 p.u. and also the droop coefficients k

_{v}

_{±}have to be higher than 2 according to VDE-AR-N 4120.

#### 3.1. Test of the PR Controller with Anti-Windup Capability

#### 3.2. Test of the Entire Proposed Scheme

_{ag}= 0.5 p.u., V

_{bg}= 1.8 p.u. and V

_{cg}= 1.8 p.u. is considered. It worth to mention that without anti-saturation the system becomes unstable. The results for SCR = 5 are shown from Figure 16, Figure 17 and Figure 18, where the voltage fault happens from t = 0.25 s until t = 0.4 s.

_{v}

_{+}droop coefficient is set to 6 to show the performance of anti-saturation scheme. The obtained results are shown in Figure 19, Figure 20 and Figure 21.

_{band}is 0.1 p.u. and the magnitude of positive sequence voltage is lower 0.9 and it has some fluctuations. Hence, ΔV

_{+}= 1 − |V

_{+}| is higher than 0.1 and the inverter has to inject reactive current (reactive power) to PCC. Based on (3): i

_{q}

_{+}= K

_{v}

_{+}(ΔV

_{+}− 0.1). According to [28], k

_{v}

_{+}droop coefficient has to be higher than 2. To show performance of proposed scheme in limiting reactive current set point (${I}_{r+}^{*}$), k

_{v}

_{+}is set 6.

_{q}

_{+}is around 0.6 p.u., which leads to the controller saturation. Therefore, i

_{q}

_{+}is cropped by the anti-saturation scheme to around 0.25 p.u. to prevent uncontrollability. Therefore, i

_{q}

_{+}is around 0.6 p.u. and ${I}_{r+}^{*}$ is around 0.25 p.u. The results in Figure 20 show the set points of positive sequence active and reactive currents. The active current is not limited because the converter current is lower than the nominal value.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

AC | Alternating Current |

DC | Direct Current |

C_{f} | capacitor of LC filter |

IGBT | Insulated-Gate Bipolar Transistor |

i_{abc} | current of the converter |

i_{abcg} | current of the grid |

i^{*}_{α+}, i^{*}_{β+} | positive sequence components of converter current reference in stationary reference frame |

i^{*}_{α−}, i^{*}_{β−} | negative sequence components of converter current reference in stationary reference frame |

i_{p+}, i_{q+} | active and reactive components of inverter current in positive sequence |

i_{p−}, i_{q−} | active and reactive components of inverter current in negative sequence |

I^{*}_{a+}, I^{*}_{r+} | set points of active and reactive current in positive sequence |

I^{*}_{a−}, I^{*}_{r−} | set points of active and reactive current in negative sequence |

I^{*}_{p+}, I^{*}_{q+} | active and reactive current command in positive sequence |

f | fundamental frequency in Hz |

FLL | frequency locked loop |

k_{f} | feedforward gain |

K_{p} | proportional gain |

K_{i} | resonant gain |

K_{w} | anti-windup gain |

k_{v±} | droop coefficient |

LC filter | Inductor-Capacitor filter |

LPF | Low Pass Filter |

KVL | Kirchhoff’s Voltage Law |

LVRT | Low Voltage Ride Through |

L_{f} | inductor of LC filter |

m | modulation index |

m_{max} | maximum modulation index |

O_{α}, O_{β} | output of PR controller with two integrators |

O^{*}_{α}, O^{*}_{β} | output of PR controller after modification by anti-wind up or limiter |

PCC | point of common coupling |

P* | active power reference |

P | active power injected by the inverter to the PCC |

PR | proportional-resonant |

Q | reactive power injected by the inverter to the PCC |

Q* | reactive power reference |

S | apparent power injected by the inverter to the PCC |

SCR | short circuit ratio |

SPWM | Sinusoidal Pulse Width Modulation |

SVPWM | Space Vector Pulse Width Modulation |

t_{dead} | switching dead time |

Ts | switching period |

V_{dc} | DC bus voltage |

V_{abc} | phase voltages of the PCC |

V_{abcg} | phase voltages of the grid |

V_{abci} | output voltage of inverter |

V_{i} | space vector of output voltage of inverter |

V_{g} | space vector of grid voltage |

V_{α1+}, V_{β1+} | fundamental components of positive sequence of PCC voltage in stationary reference frame |

V_{α1−}, V_{β1−} | fundamental components of negative sequence of PCC voltage in stationary reference frame |

V_{+}, V_{−} | space vector of PCC voltage in positive and negative sequences |

V_{αg1+}, V_{βg1+} | fundamental components of positive sequence of grid voltage in stationary reference frame |

V_{αg1−}, V_{βg1−} | fundamental components of negative sequence of grid voltage in stationary reference frame |

V_{g+}, V_{g−} | space vector of grid voltage in positive and negative sequences |

Zg | equivalent grid impedance |

Z_{f} = X_{f} = 2πfL_{f} | impedance of L_{f} |

ω_{o}, ω_{c} | resonant frequency in rad/s and resonant bandwidth in rad/s |

## Subscripts and Superscripts

a,b,c | Phase |

i | Inverter |

g | Grid |

max | Maximum |

+,− | Positive sequence and negative sequence, respectively |

* | Reference |

– | complex conjugate |

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**Figure 2.**Schematic of the outer loop including the proposed anti-saturation scheme to generate the current reference.

**Figure 4.**Vector representation of voltages and currents of GC-VSC working at normal grid conditions or balanced voltage changes while injecting reactive power.

**Figure 5.**Vector representation of voltages and currents GC-VSC when there is an unbalanced voltage sag. (

**a**) Positive sequence. (

**b**) Negative sequence. (

**c**) Inverter voltage in the worst case.

**Figure 6.**Vector representation of voltages and currents GC-VSC for unbalanced voltage sag without injecting negative sequence current during the fault. (

**a**) Positive sequence. (

**b**) Negative sequence. (

**c**) Inverter voltage in the worst case.

**Figure 7.**Vector representation of voltages and currents of GC-VSC for unbalanced one phase 100% voltage sag injecting negative sequence current during the fault. (

**a**) Positive sequence. (

**b**) Negative sequence. (

**c**) Inverter voltage in worst case.

**Figure 8.**Vector representation of voltages and currents of GC-VSC for voltage swell. (

**a**) Positive sequence. (

**b**) Negative sequence. (

**c**) Inverter voltage in the worst case.

**Figure 10.**Vector representation of voltages of Figure 3.

**Figure 15.**The Real Time Simulation results of inverter with different PR controller for SCR = 5. From top to bottom: in first figure active and reactive current references; in second figure actual and reference currents in αβ axes; in third figure duty cycle; and in fourth figure converter current and in fifth figure PCC voltage.

**Figure 16.**Voltage faults: V

_{ag}= 0.5 p.u., V

_{bg}= 1.8 p.u., V

_{cg}= 1.8 p.u., with anti-saturation for SCR = 5. From top to bottom: in first figure active current reference, reactive current reference and the maximum available reactive current reference; in second figure active and reactive output power of converter; in third figure duty cycle; and in fourth figure magnitude of positive and negative sequence of PCC voltage and grid voltage.

**Figure 17.**Set points of active and reactive currents in positive sequence for voltage faults: V

_{ag}= 0.5 p.u., V

_{bg}= 1.8 p.u., V

_{cg}= 1.8 p.u., with anti-saturation for SCR = 5.

**Figure 18.**Voltage faults: V

_{ag}= 0.5 p.u., V

_{bg}= 1.8 p.u., V

_{cg}= 1.8 p.u. From top to bottom: in first figure the voltage of grid; in second figure PCC voltage; in third figure converter current; and in fourth figure the current of grid and in fifth figure actual and reference currents in αβ axes.

**Figure 19.**Voltage faults: 1ph 100% voltage sag without injecting negative sequence current with anti-saturation for SCR = 2. From top to bottom: in first figure active current reference, reactive current reference and the maximum available reactive current reference; in second figure active and reactive output power of converter; in third figure duty cycle; and in fourth figure magnitude of positive and negative sequence of PCC voltage and grid voltage.

**Figure 20.**Set points of active and reactive currents in positive sequence in case of 1ph 100% voltage sag without injecting negative sequence current.

**Figure 21.**Voltage faults: 1ph 100% voltage sag without injecting negative sequence current. From top to bottom: in first figure the voltage of grid; in second figure PCC voltage; in third figure converter current; and in fourth figure the current of grid and in fifth figure actual and reference currents in αβ axes.

Variable | Value | Variable | Value |
---|---|---|---|

V (V_{rms}) | 690 | C_{f} (μF) | 1000 |

S_{NOM} (MVA) | 4 | f_{O} (Hz) | 50 |

V_{dc} (V) | 1150 | f_{S} (kHz) | 2 |

L_{f} (μH) | 65 | SCR | 5 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Shahparasti, M.; Catalán, P.; Roslan, N.F.; Rocabert, J.; Muñoz-Aguilar, R.-S.; Luna, A.
Enhanced Control for Improving the Operation of Grid-Connected Power Converters under Faulty and Saturated Conditions. *Energies* **2018**, *11*, 525.
https://doi.org/10.3390/en11030525

**AMA Style**

Shahparasti M, Catalán P, Roslan NF, Rocabert J, Muñoz-Aguilar R-S, Luna A.
Enhanced Control for Improving the Operation of Grid-Connected Power Converters under Faulty and Saturated Conditions. *Energies*. 2018; 11(3):525.
https://doi.org/10.3390/en11030525

**Chicago/Turabian Style**

Shahparasti, Mahdi, Pedro Catalán, Nurul Fazlin Roslan, Joan Rocabert, Raúl-Santiago Muñoz-Aguilar, and Alvaro Luna.
2018. "Enhanced Control for Improving the Operation of Grid-Connected Power Converters under Faulty and Saturated Conditions" *Energies* 11, no. 3: 525.
https://doi.org/10.3390/en11030525