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PVC of Three Leg Inverter with LC Filter

Three-phase three-leg inverters have had a rise in popularity over the years, seeing implementations within a wide range of applications and much research has been conducted [1]. In applications where high quality voltages are needed such as standalone power converters (SPC), connecting the output to an LC filter is necessary [1]. The benefits of the LC filter in an SPC application is that the system will achieve a good output voltage even with a nonlinear load and has fast dynamic responses [1]. However, utilizing the LC filter makes the design of the controller more difficult and complicated [1].

As seen in [2, Fig. 1] the neutral point of the DC link is connected to the output terminal by the two center switches [3]. Each phase of the inverter contains four switched and two diodes together, this configurations makes three voltage levels possible with the resulting value depending on the current state of the switches [3]. 27 total switching combinations are possible and of those possible combinations we can derive 19 unique voltage vectors. Using [3, Eqn. 1] V0 through V18 can be calculated.

By utilizing the DC link capacitors differential equations and approximating their derivatives over some sampling time Ts we can create two current equations [3]. Since the currents will be affected by the current switching state of the converter, the value of the switch must also be included in the current equations thus,

Using these same analysis techniques we can also predict the current circuit’s effect on the resulting voltages.
In order to fulfill all of our control requirements we need to develop a cost function that will minimize errors, an example of such cost function can be seen in [3, Eqn. 3].

The first two terms determine the load current errors, because the current may be a complex number both the real and imaginary parts must be checked [3]. The third term checks for the capacitor voltage error, by minimizing this term the designer can achieve voltage balance. Weighting factors must also be included to help assist the designer alter various aspects of circuit operation such as the switching frequency and reference tracking [3]. By increasing γn the switching frequency goes down while the error margin increases [3]. This method also allows the designer to quickly and effectively balance the capacitor voltages [3].

 

References
[1] 2013 International Conference on Control, Decision and Information Technologies (CoDIT 2013) Hammamet, Tunisia, 6-8 May 2013. Piscataway, NJ: IEEE, 2013.
[2] C. Xia, X. Gu, T. Shi, and Y. Yan, “Neutral-Point Potential Balancing of Three-Level Inverters in Direct-Driven Wind Energy Conversion System,” IEEE Transactions on Energy Conversion, vol. 26, no. 3, pp. 18–29, Mar. 2011.
[3] J. Rodriguez and P. Cortes, Predictive control of power converters and electrical drives. New York: John Wiley & Sons Inc, 2012.