# A Flexible Power Electronics Configuration for Coupling Renewable Energy Sources

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## Abstract

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## 1. Introduction

- series and multilevel topologies;
- parallel topologies;
- hybrid topologies.

## 2. System under Investigation

_{rms}= 1, 000 V with frequency f = 60 Hz.

_{dc}= 1.7 kV is taken as the reference, and therefore, it can be written:

_{conv}is the phase voltage reached referring to the neutral point; V dc is the total DC voltage set to V dc = 2 · V max, because in the NPC topology, the switches have only to block half of the DC bus voltage. If the secondary winding is delta connected, the transformer ratio becomes:

_{rms}= 3, 600 A:

_{dc}= 6 kV, the deliverable power by the topology ensuring fault-tolerant operation raises to P = 22 MW. These results are obtained keeping the converter in the linear modulation region that provides the lowest THD.

- Using equal generation plants in the same region;
- Using three-phase insulated winding stators.

_{tot}= P three

_{tot}; this means that the power produced by a single single-phase DC source must be ${\scriptscriptstyle \frac{1}{3}}\cdot P{t}_{tot}$. If this link is removed, the harmonic cancellation will not be perfect, because the voltage phasors applied by three-phase and mono-phase converters will be different. This means that generally, the switching frequency band appears in the voltage waveform centered at 2 · fswitching; changing the power ratios, the reduction of the harmonic band centered at 2 · fswitching will be variable, and a theoretical perfect elimination will be possible with the total power ratios nearly equal to one.

## 3. Control System Design

## 4. Optimization of Power Delivered to the Grid

_{m}and P

_{t}are the single and three-phase powers associated with only one converter (one arm of the single-phase and one three-phase converter). Considering that the connection impedance parameters are known, the total voltage drop phasor on this impedance can be calculated, and finally, the components of the converter voltage (phase δ and amplitude) are known. Finally, the voltage values for each converter can be calculated as:

_{m}and V

_{t}are the mono- and three-phase voltage amplitudes; I is the current module; ϕ is the angle between the grid voltage and current phasors; δ is the angle between the converter voltage phasor and grid voltage phasor; Pm and Pt are the active powers delivered by each converter. The angle ϕ is kept as variable in order to allow the converter to help the grid voltage regulation. For this function, additional conditions must be considered, and in order to keep the problem simple in this analysis, ϕ is equal to zero (a condition that has to be removed obviously if ϕ ≠ 0). The constraints that the solver must take into account are divided into equality and inequality constraints:

_{lim}and Pt

_{lim}are power limits known by environmental measurement; I

_{lim}, V

_{lim}are the switches limits, and the grid voltage is reported to the converter side through the turns ratio of the transformer. δ obviously must be positive, and the conditions on ϕ is dependent on the system: if a frequency and voltage dropfunction must be implemented, the standard limits on power factor can be chosen according to IEEE standards (for example, cos(ϕ) > 0.85 lagging or leading for solar PV systems, IEEE 929).

#### 4.1. Additional Controllers

_{grid}), the power loops are not able to see the equivalent impedance change or the grid voltage dip, and the power reference will remain the same. Since the impedance during a fault is lower, the power reference can be reached with an increasing of the current. The solution would be a simple saturation of the Id and Iq reference values to 1 p.u., but in this hypothesis, if the inverter is injecting both active and reactive currents, the limits would be reached satisfying the single conditions on Id and Iq. As explained in [11], this problem can be solved using a dynamic current limiting control. In the normal operation, the current limits are Id = 1 and Iq = 1. When a fault is detected on the grid (voltage dip, three-phase short circuit or other disturbances), a script is run. If the total current Irms is bigger than the limit, the instantaneous Id value is memorized, and $Iq=\sqrt{I{lim}^{2}-I{d}^{2}}$ is computed. These two parameters are set as new saturation limits, and they will remain unchanged till the fault is removed. When the disturbing action ends, the initial limits are restored. In this way, if the entire converter were delivering the current Id and the reactive current Iq to give voltage assistance to the grid before the fault, after the fault, the values of Id and Iq will remain unchanged (if the transient is neglected), while the powers will change according to the impedance change (or voltage dip).

#### 4.2. Source Models

_{DC}= 1 kV and the current derived by the neutral point is neglected, since its frequency will be much higher than f = 120 Hz. The resultant capacitance is the series of upper and lower capacitance. One of the hypothesis behind Equation (11) was to fix ϕ ≃ 90°, which is verified if the converter injects mostly reactive power into the grid. Therefore, the single capacities will be: C

_{m}

_{−}

_{single}= 2 · C

_{m}= 37.52 mF.

_{m}is the rms value of the current harmonic with the switching frequency, ω

_{hf}is the angular speed associated with the switching frequency and ${\scriptscriptstyle \frac{{V}_{DC}}{2}}$ and C

_{t}

_{−}

_{single}are the voltage and the capacitance of a single capacitor. Since the voltage on the capacitor is regulated by an external controller, one

**PI**(proportional integral regulator) for each DC source is used in order to model the delay and the overshoot of the voltage regulator. The expressions in the open and closed loop, including the PI regulator, are:

#### 4.3. Real Implementation

#### 4.4. Neutral Point Balance

_{switching}, and this high frequency voltage would saturate the PI of the proposed scheme. An interesting solution is proposed by [15] for parallel configurations, where the voltage balancing is obtained through a resonant RLC circuit. In this paper, it is explained that when a voltage unbalance occurs, the output voltage waveform changes its harmonic spectrum, because the switching frequency appears, while normally, it should be canceled because of the unipolar operation, seen as interleaving. In this work, a three-phase RLC circuit has been used as a filter tuned on this frequency, providing the balancing effect.

## 5. Simulation Results and Discussion

_{switching}; while in Figure 6b, the optimal power ratio is achieved, and the first harmonic band is centered at f = 4f

_{switching}. In Figure 7a,b, the waveforms relative to the single-phase converters and three-phase converters are represented: the total single-phase converter voltage with five voltage levels (each single-phase arm introduces three levels), the upper and lower DC current (blue) and AC current (green), the neutral current (blue) and the overall DC power are depicted, respectively. It is easy to see that the single-phase DC current has a second harmonic component, and the current derived from the neutral point is null on average. In the three-phase case, the second harmonic disappears, and the first harmonic is the switching frequency.

## 6. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**Circuit parameters used and optimization results represented as a function of the single-phase and three-phase available power. (

**a**) Simulation positive sequence parameters per unit system; (

**b**) power delivered to the grid in MW; (

**c**) single-phase voltage phasor amplitude, kV; (

**d**) three-phase voltage phasor amplitude, kV; (

**e**) Id and Iq current surfaces, kA.

**Figure 5.**Effect of the dynamic current limit: voltage dip with amplitude −38%. (

**a**) Voltage dip considered from t = 0.1 s till t = 0.2 s; (

**b**) RMScurrent phase without a dynamic limit; (

**c**) RMS current phase with a dynamic limit.

**Figure 6.**Voltage (referring to the ground) FFT measured before the filtering impedance. The fundamental frequency is not fully visualized in order to clearly see the higher harmonics. (

**a**) FFT of phase to ground voltage: interleaving applied, Pm = 0.8 MW, Pt = 1 MW. The power ratio does not achieve the optimal condition; (

**b**) FFT of phase to ground voltage with the optimal power condition: interleaving applied, Pm = 0.33 MW, Pt = 1 MW.

**Figure 7.**Single-phase and three-phase converters waveforms with constant voltage generators and with P m = 0.5 MW, P t = 1 MW. (

**a**) Single-phase converter waveforms; (

**b**) a single three-phase converter waveform.

**Figure 8.**Single-phase balancing circuit operation. (

**a**) DC voltage unbalance with pre-charge voltage in single-phase converter A set to +65 V; (

**b**) result with an initial unbalance set to +65 V with balancing circuit.

**Figure 9.**Three-phase capacitors balancing in different cases. (

**a**) Without balancing; (

**b**) with single-phase balanced circuits; (

**c**) with all balancing circuits.

**Figure 10.**Simulation results for stochastic energy sources after optimization. (

**a**) Single-phase converter DC available power and absorbed power; (

**b**) three-phase converter DC available power and absorbed power; (

**c**) electronic efficiency, magnetic elements efficiency and global efficiency.

**Figure 11.**Capacitors’ voltage in the stochastic simulation. (

**a**) Single-phase converter DC upper and lower capacitor voltage; (

**b**) three-phase converter DC upper and lower capacitor voltage.

**Figure 12.**Neutral point voltage during stochastic simulations expressed as the difference between the upper and lower voltage.

**Figure 13.**Simulation parameters: k

_{transformer}= 0.5, Pbase = 12 MW, f

_{sw}= 1.5 kHz. (

**a**) Global active and reactive powers; (

**b**) electronic, electric and global efficiencies; (

**c**) voltage and current obtained THD.

© 2015 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 license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Filippini, M.; Molinas, M.; Oregi, E.O.
A Flexible Power Electronics Configuration for Coupling Renewable Energy Sources. *Electronics* **2015**, *4*, 283-302.
https://doi.org/10.3390/electronics4020283

**AMA Style**

Filippini M, Molinas M, Oregi EO.
A Flexible Power Electronics Configuration for Coupling Renewable Energy Sources. *Electronics*. 2015; 4(2):283-302.
https://doi.org/10.3390/electronics4020283

**Chicago/Turabian Style**

Filippini, Mattia, Marta Molinas, and Eneko Olea Oregi.
2015. "A Flexible Power Electronics Configuration for Coupling Renewable Energy Sources" *Electronics* 4, no. 2: 283-302.
https://doi.org/10.3390/electronics4020283