Sizing of a Filter (L-C) for a 180 ̊ Control Inverter Connected to a Medium Voltage Network

This paper studies the design and sizing of a filter (L-C) for an inverter with 180 ̊ control in Medium voltage (MV), based on formulas of the capacitance of the capacitor C and the inductance L of the filter (L-C) of an SPWM inverter. These formulas were obtained by minimizing two parameters: the reactive power of the capacitor (capped at 5% of the apparent power of the load) and the ripple of the current flowing through inductance L (capped at 10% of the current supplying the load). The application of these formulas for the calculation of the filter (L-C) of the 180 ̊ control inverter in MV is not conclusive. Studies have been carried out to make them applicable. The results show that limiting the current ripple in the inductor to 10% of the load current is a valid assumption and that limiting the reactive power of the capacitor to 5% of the apparent power of the load presents shortcomings. The results also show that setting the inductance L of the filter to Lmaxi and the capacitor C from 35 × Cmaxi to 400 × Cmaxi gives voltage and current THDs that meet the 519 IEEE-2014 standards.


Introduction
In recent decades, the countries of sub-Saharan Africa have started to build photovoltaic plants with peak powers of around tens of megawatts [1]. These photovoltaic plants are built to reinforce the energy demand of these countries which does not cease growing.
For the transmission and distribution in MV in localities far from the national grid, of the energy produced in these photovoltaic plants, the use of three-phase voltage inverters is necessary. It is with this in mind that we propose to design and size a filter (L-C) for a 180˚ control inverter. This is because inverters do not provide sinusoidal voltage and current signals [2]. These signals contain harmonics generated by semiconductors. These harmonics hamper the proper functioning of electrical equipment [3].
The measurement parameter of these harmonics is the THD. It characterizes the quality of the voltage and current signals, and therefore the quality of the power. The lower the THD, the better the quality of the signal power, and the signal becomes closer to sinusoidal shape [3].
In order to obtain better filter efficiency (L-C) for the operation of an inverter with 180˚ control in MV, the main contribution proposed in this research article is: -on the one hand, to discuss the applicability of existing formulas in newspapers [4]; -on the other hand, to improve them from studies so that they are applicable to the sizing of the filter (L-C) of the 180˚ control inverter connected to an MV network [5].
The document is structured as follows: section II presents the system model and the formulation of the problem; the filter (L-C) and its calculation formulas for the three-phase inverter with SPWM control are studied; in section III, the 180˚ control inverter is analysed; section IV presents the applicability of the filter formulas (L-C) of the three-phase inverter SPWM to the inverter with 180˚ control; in section V, studies to improve the parameters of the filter (L-C) for an inverter with control 180˚. Finally, section VI concludes the article.

System Model and Problem Formulation
The model is based on a medium voltage direct current (MVDC) electrical power transmission system. This is to improve the quality of the voltage and current signals on the AC side of the 180˚ control inverter connected to an MV network.
The scientific literature has been used to the best of our knowledge. No method of calculating a filter (L-C) for a 180˚ control inverter operating in MV.
Then a method of calculating a filter (L-C) of the 180˚ control inverter operating in MV based on that of the filter (LC) of the SPWM control inverter is adopted, after verifying the applicability of the formulas of articles [4] [5] [6]. This is to reformulate the filter calculation method (L-C) of articles so that it can be used for a 180˚ control inverter connected to the MV network.

Filter (L-C)
Consider the diagram of a single-phase circuit of a filter (L-C) given in Figure   1.
Formulas of inductance L and capacitor C According to articles [4] [5] [6], the calculation of L and C of the filter (L-C) for a three-phase inverter with SPWM control is done as follows: These formulas given by Equation (2) were obtained by minimizing two parameters: the reactive power of capacitor C (capped at 5% of the apparent power of the alternating load) and the ripple of the current flowing through inductor L (capped at 10% of the phase-to-neutral voltage supplying the alternating charge).

180˚ Control Inverter (Full Wave)
Consider the diagram of a three-phase inverter below ( Figure 2).
In the three-phase two-level inverter ( Figure 2), there are three arms. Each arm has two controllable switches K i = (T i ; D i ) (with i = 1, 2, 3, 4, 5, 6). Each controllable switch consists of: -Bipolar power transistor or IGBT or thyristor (controllable component); -Diode mounted head-to-tail (antiparallel) on each controllable component.

The inverter is supplied by a DC source E.
In 180˚ control, each switch K i of Figure 2 conducts for 180˚ (π radians).
Two switches of the same arm have their control shifted by 180˚ (π radians).
Two consecutive switches have their control shifted by 120˚ (2π/3 radians). Table 1 gives a summary of the operation of the 180˚ control inverter and Figure 3 represents the voltage signals The Fourier series decomposition based on Figure 3, gives us:     The effective fundamentals of voltage and current are: Remember that, without the filter (L-C), the harmonic distortion rate (THD = 31.08%). This does not comply with the IEEE 519 [7] standard, which requires that in MV, this THD is 8%.

Applicability of the Filter Formulas (L-C) of the Three-Phase Inverter SPWM to the Inverter with 180˚ Control
This is to use the formulas for calculating the inductance L and capacitance C of The formulas of Equation (5)

Studies to Improve the Filter Parameters (L-C) for a 180˚ Control Inverter
In the scientific literature, the only method of calculating the filter (LC) for an inverter with 180˚ control is found in article [8], where it is a question of calculating a resistance R related to the quality factor Q, after having set the resonant frequency f Res and the capacitor C and deduce the inductance L.
The SPWM inverter filter (L-C) formula verification approach applied to the 180˚ control inverter filter (L-C) has been completed. The results are inconclusive, ie the IEEE 519 [7] standard is not met.  For this reason, a first study is carried out in order to determine the choice ranges of the capacitor C and the inductance L of the filter (L-C) of the 180˚ control inverter. In this study, C maxi is varied by multiplying it by q varying from 1 to 1000 and the value of L maxi is kept unchanged.
From Table 2, Figures 5-7 are shown below. Table 2 shows that from C = 35 × C maxi , the THD% obtained comply with the IEEE 519 standard [7]. But for Figure 6 and Figure 7, a resonance is observed beyond C = 100 × C maxi . Between C = 35 × C maxi and C = 100 × C maxi , the THD% obtained in Table 2 comply with the IEEE 519 standard [7]. The choice of capacitance C of the capacitor can be made in the range [35 × C maxi ; 100 × C maxi ] because of the resonance phenomenon observed in Figure 2 and Another study is carried out by varying L maxi . The inductance L maxi is multiplied by q which varies from 0.01 to 25 while keeping the value of C = C maxi unchanged.
From Table 3        If a damping resistor is not used in series with inductor L. If a damping resistor is used in series with inductance L, the tuning range of capacitor C could reach 400 × C 0 because between 100 × C 0 and 400 × C 0 , there is resonance. Figures 11-14 show three operating cases with the different values of L and C:

Conclusions
In this article, a method was adopted: that of using the formulas of a filter (L-C) of a three-phase inverter with SPWM control obtained by minimizing the reactive power of the capacitor C and the current ripple in the inductor. L, that is to say, limits the reactive power of the capacitor to 5% of the apparent power of the load and limits the ripple of the current flowing through the inductor L to 10% of the current in the load.
The formulas applied to the filter (L-C) of the 180˚ MV control inverter did not allow the voltage and current THDs to be obtained which comply with the IEEE 519 standard.
Therefore, from these formulas, studies have been carried out with a view to obtaining a good compromise, where the voltage and current THDs comply with the IEEE 519 standard. From these studies, it emerges that taking the inductance L = L maxi is a valid assumption and that the limitation of the reactive power of the capacitor to 5% of the apparent power of the load has shortcomings. The results also show that setting the inductance L of the filter to L maxi and the capacitor C from 35 × C maxi to 400 × C maxi gives voltage and current THDs that meet the IEEE 519 standard. The simulations on the MATLAB/Simulink software made it possible to justify this method. Also for the range, 100 × C 0 to 400 × C 0 , the sizing of a resonance damping resistor is to be expected.