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#### The Transactions of the Korean Institute of Electrical Engineers

##### ISO Journal TitleTrans. Korean. Inst. Elect. Eng.
• SCOPUS
• KCI Accredited Journal

1. (School of Electrical and Electronic Engineering, Chung-Ang University, Korea.)

Three-phase PWM rectifier, grid condition, total harmonic distortion, dc voltage ripple

## 1. ์ ๋ก

๊ณ ์กฐํ ๋ฐ ๋ถํํ ์ฑ๋ถ์ ํฌํจํ๋ 3์ ๊ณํต ํ๊ฒฝ์๋ ๋ถ๊ตฌํ๊ณ , ๋์ ํ์ง์ ์ ํํ ๊ต๋ฅ ์ ๋ฅ๋ฅผ ์์ฑํ๋ ๋์์ ๋ฎ์ ๋ฆฌํ๊ฐ์ ๊ฐ์ง๋ ์์ ๋ ์ง๋ฅ ์ถ๋ ฅ ์ ์์ ๋ง๋ค์ด ๋ด๊ธฐ ์ํ ๊ต๋ฅ-์ง๋ฅ ์ ๋ ฅ ๋ณํ์ ํ์์ฑ์ด ์ง์์ ์ผ๋ก ์ฆ๊ฐํ๊ณ  ์๋ค(1-4). ์ด๋ฌํ ํ์์ฑ์ ๋ง์กฑํ๊ธฐ ์ํ์ฌ, ๋ฎ์ ์๋ ฅ ์ ๋ฅ ๊ณ ์กฐํ ์๊ณก (total harmonic distortion: THD), ๋์ ์ญ๋ฅ  ๋ฐ ์ฐ์ํ ์ง๋ฅ ์ถ๋ ฅ ์ ์ ์กฐ์  ๋ฅ๋ ฅ์ ๊ฐ์ง๋ 3์ ํ์คํญ๋ณ์กฐ (pulse width modulation: PWM) ์ ๋ฅ๊ธฐ๊ฐ 3์ ๋ค์ด์ค๋ ์ ๋ฅ๊ธฐ ๋ฐ ์์์ ์ด ์ ๋ฅ๊ธฐ๋ฅผ ๋์ฒดํ์ฌ ์ฌ์ฉ๋  ์ ์๋ค(5,6). ๋ํ, 3์ ํ์คํญ๋ณ์กฐ ์ ๋ฅ๊ธฐ์ ๋์์ ์ ์ดํ๊ธฐ ์ํ์ฌ ๋ค์ํ ์ ์ด ๊ธฐ๋ฒ๋ค์ด ๊ฐ๋ฐ๋์ด ์๋ค(7-9). ๊ฐ์ฅ ๋ํ์ ์ธ ์ ์ด ์๊ณ ๋ฆฌ์ฆ์ 3์ ์ ๋ฅ๊ธฐ์ 3์ ๊ต๋ฅ ์๋ ฅ ์ ๋ฅ๋ค์ ์ ์ด ๋ณ์๋ก ํ์ฉํจ์ผ๋ก์จ, 3์ ๊ต๋ฅ ์ ๋ฅ์ ํฌ๊ธฐ ๋ฐ ์์์ ๋ณํ์ํค๊ธฐ ์ํด 3์ ์ ๋ฅ๊ธฐ ์๋ ฅ ์ ์์ ๋ณํ์ํค๋ ์ ๋ฅ์ ์ดํ (Voltage Oriental Control: VOC) ๋ฐฉ๋ฒ์ด ์๋ค(10,11). ์ ๋ฅ์ ์ดํ ์ ๋ฅ๊ธฐ๋ 3์ ๊ต๋ฅ ์ ๋ฅ์ ์์์ ๊ต๋ฅ ์ ์๊ณผ ์ผ์น์ํค๊ณ  ์ ๋ฅ์ ํํ๋ฅผ ์ ํํ ํํ๋ก ์ ์ดํจ์ผ๋ก์จ ๋จ์ผ ์ญ๋ฅ ์ ๊ฐ์ง๋ ๊ณ ํ์ง ์ ํํ ์๋ ฅ ์ ๋ฅ ํํ์ ์์ฑํ๋ค. ๋ํ, 3์ ๊ต๋ฅ ์๋ ฅ ์ ๋ฅ๋ณด๋ค ์ง๋ฅ ํํ์ ์ ์ด ๋ณ์๊ฐ ๋  ์ ์๋ ์ ํจ ์ ๋ ฅ๊ณผ ๋ฌดํจ ์ ๋ ฅ์ ์ฌ์ฉํจ์ผ๋ก์จ 3์ ํ์คํญ๋ณ์กฐ ์ ๋ฅ๊ธฐ๋ฅผ ์ ์ดํ๋ ์ ๋ ฅ์ ์ดํ (Direct Power Control: DPC) ๋ฐฉ๋ฒ์ด ์๋ค(12). ์ ๋ ฅ์ ์ดํ ์ ๋ฅ๊ธฐ๋ ์ง๋ฅ ๋ถํ๊ฐ ํ์๋ก ํ๋ ์ ํจ ์ ๋ ฅ ์ฑ๋ถ๊ณผ ์ญ๋ฅ ์ ์ ์ดํ๊ธฐ ์ํ ๋ฌดํจ ์ ๋ ฅ ์ฑ๋ถ์ ๋๋ฆฝ์ ์ผ๋ก ์ ์ดํจ์ผ๋ก์จ, ํจ๊ณผ์ ์ธ ๊ต๋ฅ-์ง๋ฅ ๋ณํ๊ณผ ๋์์ ๋จ์ผ ์ญ๋ฅ ์ ์ ๋ฅ๊ธฐ ๋์์ ๊ตฌํํ  ์ ์๋ค. ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์ ๊ธฐ๋ณธ์ผ๋ก ํ๋ ๋ค์ํ ํํ์ ๊ฐ์ ๋ ์ฑ๋ฅ์ ์ถ๊ตฌํ๋ 3์ ํ์คํญ๋ณ์กฐ ์ ๋ฅ๊ธฐ ์ ์ด๊ธฐ๋ฒ๋ค์ด ๊ฐ๋ฐ๋์ด ์๋ค[1,2,5]. ์ด๋ฌํ ์ฐ๊ตฌ๊ฐ๋ฐ๊ณผ์ ์ ํตํ์ฌ, ๋ชจ๋ธ์์ธก์ ์ด๊ธฐ๋ฒ์ ์ ์ด ํ๋ซํผ์ผ๋ก ํ ๊ธฐ๋ณธํ ์ ๋ฅ์ ์ดํ๊ณผ ๊ธฐ๋ณธํ ์ ๋ ฅ์ ์ดํ ์๊ณ ๋ฆฌ์ฆ๋ค์ด ๊ณ ์๋์๋ค. ๊ธฐ๋ณธํ ์๊ณ ๋ฆฌ์ฆ๋ค์ ๊ธฐ๋ฐ์ผ๋ก ํ์ฌ ๊ฐ ์ ์ดํ์์ ์ค์์นญ ์์ค์ ๊ฐ์์ํค๊ธฐ ์ํ 2๊ฐ์ง ๊ณ ํจ์จํ ์๊ณ ๋ฆฌ์ฆ๋ค์ด ๋ํ ๊ฐ๋ฐ๋์๋ค(13-17). 3์ ํ์คํญ๋ณ์กฐ ์ ๋ฅ๊ธฐ๋ฅผ ๋์์ํค๊ธฐ ์ํด ์ฌ์ฉ๋  ์ ์๋ ๋ค์ํ ์ ์ด ๊ธฐ๋ฒ๋ค ์ค, ๊ณ ์กฐํ ๋ฐ ๋ถํํ ์ฑ๋ถ์ ์ํด ์๊ณก๋ ๊ณํต ํ๊ฒฝ์์ ๊ฐ๊ฑดํ ์ฑ๋ฅ์ ๋ณด์ผ ์ ์๋ ๊ธฐ๋ฒ๋ค์ ๋ํ ๋น๊ต ํ๊ฐ๊ฐ ํ์ํ๋ค.

๋ณธ ๋ผ๋ฌธ์์๋ ๊ณ ์กฐํ ๋ฐ ๋ถํํ ์ฑ๋ถ์ ๊ฐ์ง๋ ๊ณํตํ๊ฒฝ์์, ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ ๊ธฐ๋ฐ์ ๊ฐ 3๊ฐ์ง ์์ดํ ์ ์ด ๊ธฐ๋ฒ๋ค์ ์ํด ๋์ํ๋ 3์ ํ์คํญ ๋ณ์กฐ ์ ๋ฅ๊ธฐ์ ์์ถ๋ ฅ ์ฑ๋ฅ์ ๋น๊ต ๋ถ์ํ์๋ค. ๊ธฐ๋ณธํ๊ณผ ๊ณ ํจ์จํ์ ๊ด๊ณ์์ด, ๋์ผํ ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ ๊ธฐ๋ฒ๋ค์ ์๊ณก ๋ฐ ๋ถํํ ๊ณํต ํ๊ฒฝ์์ ์ ์ฌํ ์ฑ๋ฅ์ ๋ณด์๋ค. 3์ ์๋ ฅ ์ ์ ์ค ํ ์์๋ง 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋ ๊ฒฝ์ฐ์๋ ์ ๋ฅ์ ์ดํ์ด ์ ๋ ฅ์ ์ดํ๋ณด๋ค ๋ค์ ๊ฐ์ ๋ ์๋ ฅ์ ๋ฅ ํ์ง์ ๋ณด์๋ค. ๋ํ, ๋ถํํ ์ฑ๋ถ์ด ํฌํจ๋ ๊ณํต ํ๊ฒฝ์์๋ ์ ๋ฅ์ ์ดํ ์ ๋ฅ๊ธฐ์ ์ํด ์์ฑ๋ ์๋ ฅ ์ ๋ฅ ํํ์ด ์ ๋ ฅ์ ์ดํ๋ณด๋ค ๋ค์ ๋ฎ์ THD ๊ฐ์ ๊ฐ์ก๋ค. ํํธ ํ ์์๋ง 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋ ๊ฒฝ์ฐ์ 3์ ๋ชจ๋์ 5์ฐจ ๋ฐ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋ ๊ฒฝ์ฐ์๋, ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์ ์ํด ์์ฑ๋ ์๋ ฅ ์ ๋ฅ THD ๊ฐ์ด ์ ์ฌํ ๊ฒฐ๊ณผ๋ฅผ ๋ณด์๋ค. ๊ณ ์กฐํ ๋ฐ ๋ถํํ ์ฑ๋ถ์ ๊ฐ์ง๋ ๋ชจ๋  ๊ณํต ํ๊ฒฝ์์, ์ ๋ ฅ์ ์ดํ ์ ๋ฅ๊ธฐ์ ์ํ ์ถ๋ ฅ ์ ์์ด ์ ๋ฅ์ ์ดํ ์ ๋ฅ๊ธฐ์ ์ํ ์ถ๋ ฅ ์ ์๋ณด๋ค ๋ ๋ฎ์ ๋ฆฌํ๊ฐ์ ๊ฐ์ก๋ค. ๋ฐ๋ผ์, ์ถ๋ ฅ ์ ์ ๋ฆฌํ ์ธก๋ฉด์์๋ ์ ๋ ฅ์ ์ดํ ์ ๋ฅ๊ธฐ๊ฐ ๊ณํต ์ ์์ ์๊ณก ๋ฐ ๋ถํํ ํ๊ฒฝ์ ๋ ๊ฐ๊ฑดํ ํน์ฑ์ ๋ณด์์ ํ์ธํ์๋ค.

## 2. ์ ๋ฅ์ ์ด ๋ฐ ์ ๋ ฅ์ ์ด ๊ธฐ๋ฐ์ ์ ์ด ์๊ณ ๋ฆฌ์ฆ์ ๊ฐ์ง๋ 3์ ํ์คํญ๋ณ์กฐ ์ ๋ฅ๊ธฐ

๊ทธ๋ฆผ. 1. 3์ ํ์คํญ ๋ณ์กฐ ์ ๋ฅ๊ธฐ

Fig. 1. Three-phase pulsewidth modulated rectifier

๊ทธ๋ฆผ 1์ 3์ ํ์คํญ ๋ณ์กฐ ์ ๋ฅ๊ธฐ๋ฅผ ๋ํ๋ธ๋ค. ๊ทธ๋ฆผ 1์์ ina์ ina๋ ๊ฐ๊ฐ ์์ ์๋ ฅ ์ ์๊ณผ ์๋ ฅ ์ ๋ฅ๋ฅผ ๋ํ๋ธ๋ค. ๋ํ o๋ ์ ๋ฅ๊ธฐ ์ถ๋ ฅ ์ธก ์ปคํจ์ํฐ๋ฅผ ์๋ฏธํ๋ค. ์ ๋ฅ๊ธฐ์ ์ upper์ lower ์ค์์น๋ ๊ฐ๊ฐ S, S์ด๊ณ  ์์ upper ๋ฐ lower ์ค์์น๋ S, S์ด๋ค. S์ S๋ ๊ฐ๊ฐ ์์ upper ์ lower ์ค์์น๋ฅผ ์๋ฏธํ๋ค. ๊ทธ๋ฆผ 1๊ณผ ๊ฐ์ 3์ ํ์คํญ ๋ณ์กฐ ์ ๋ฅ๊ธฐ๋ฅผ ์ ์ดํ๊ธฐ ์ํด ๋ชจ๋ธ์์ธก์ ์ด์์๋ ํฌ๊ฒ ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์ ์ ์ด ๊ธฐ๋ฒ์ด ์ ์๋์๋ค(17,18). ์ ๋ฅ์ ์ดํ์ ๋ชจ๋ธ์์ธก์ ์ด๊ธฐ๋ฒ์์๋ ๋ชจ๋ธ์์ธก์ ์ด๋ฅผ ์ํ ๋น์ฉํจ์๊ฐ ๋ค์ ์คํ(+1 ๋ฒ์งธ)์ ๊ธฐ์ค ๋ถํ ์ ๋ฅ์ ๋ค์ ์คํ(+1 ๋ฒ์งธ)์ ์์ธก ๋ถํ ์ ๋ฅ๋ก ๊ตฌ์ฑ๋์ด ์๋ค. +1 ๋ฒ์งธ์ ๊ธฐ์ค ๋ถํ ์ ๋ฅ๋ ์๋ ฅ ์ ์์ ์์์ ํ ์คํ ๋๋ ์ด์ํจ ๊ฐ์ ์ด์ฉํด ๊ตฌํ  ์ ์๋ค. ๋ํ +1 ๋ฒ์งธ์ ์์ธก ๋ถํ ์ ๋ฅ๋ ๋ถํ์ ์ ๋ฅ๊ธฐ์ ๋์  ๋ฐฉ์ ์์ ํตํด ์ ๋ํ  ์ ์๋ค. ์ ๋ ฅ์ ์ดํ์ ๋น์ฉํจ์๊ฐ +1 ๋ฒ์งธ์ ์ ํจ ์ ๋ ฅ (real power: P)๊ณผ ๋ฌดํจ์ ๋ ฅ (reactive power: Q) ๊ทธ๋ฆฌ๊ณ  ๊ทธ์ ๋ํ ๊ฐ๊ฐ์ ๊ธฐ์ค ๊ฐ์ผ๋ก ๊ตฌ์ฑ๋๋ค. ์ ํจ ์ ๋ ฅ๊ณผ ๋ฌดํจ ์ ๋ ฅ์ ์์ ์ ๋ ฅ์์ ํตํด ์ป์ ์ ์๋ค. ๋ํ ์ ํจ ์ ๋ ฅ์ ๊ธฐ์ค ๊ฐ์ ๋ถํ ์ ์๊ณผ ๋น๋ก์ ๋ถ(proportional-integral: PI) ์ ์ด๊ธฐ๋ฅผ ํตํด ๊ตฌํ  ์ ์๊ณ  ๋ฌดํจ ์ ๋ ฅ์ ๊ธฐ์ค์น๋ ๋จ์ผ ์ญ๋ฅ  ์ ์ด๋ฅผ ์ํด 0์ผ๋ก ์ค์ ํ๋ค. ์ด๋ฌํ ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์ ๊ธฐ๋ณธ์ผ๋ก ํ์ฌ 3์ ํ์คํญ ๋ณ์กฐ ์ ๋ฅ๊ธฐ์ ํจ์จ์ ๋์ด๊ธฐ ์ํด ์ ๋ฅ๊ธฐ ์ ์ด ๋์ ์ค 3์์ ํ ์์ ํด๋จํ ์ํค๋ ๊ธฐ๋ฒ๋ค์ด ์ ์๋์ด ์๋ค(13-16). ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์์ ํ ์์ ํด๋จํ ์ํค๊ธฐ ์ํด ์ฌ๋ฌ ์ค์์นญ ๋์ ์ค ํ ์์ ํด๋จํ ์ํฌ ์ ์๋ ์ ์ ๋ฒกํฐ๋ค๋ง ์ด์ฉํ์ฌ ๋น์ฉํจ์๋ฅผ ํตํด ์ต์ ์ ์ค์์นญ ๋์์ ํ๊ฒ ํ๋ ๊ธฐ๋ฒ๋ค์ด ๊ฐ๊ฐ ์ ์๋์๋ค(13,15). ์ ๋ฅ๊ธฐ ์ ์ ๋ฒกํฐ๋ฅผ ๋ฏธ๋ฆฌ ์ ์ ํ๊ธฐ ์ํด +1 ๋ฒ์งธ์ ์ ๋ฅ๊ธฐ ์ ์๊ณผ ์๋ ฅ ์ ๋ฅ์ ํฌ๊ธฐ๋ฅผ ์ด์ฉํ๋ค. +1 ๋ฒ์งธ์ ์ ๋ฅ๊ธฐ ์๋ ฅ ์ ์๊ณผ ์๋ ฅ ์ ๋ฅ ๋ถํ์ ์ ๋ฅ๊ธฐ์ ๋์  ๋ฐฉ์ ์์ ํตํด ๊ตฌํ  ์ ์๋ค. ์ ๋ฅ์ ์ดํ์ preselection ๊ธฐ๋ฒ์ ํตํ ์ ๋ฅ๊ธฐ ํจ์จ ์ฆ๊ฐ ๊ธฐ๋ฒ์ ๋น์ฉ ํจ์๋ฅผ 3์์ ์ ๋ฅ๊ธฐ ์ ์๊ณผ ๊ทธ์ ๋ํ ๊ธฐ์ค์น๋ก ์ค์ ํ๋ค. ๋ํ ์ ๋ ฅ์ ์ดํ์ preselection ๊ธฐ๋ฒ์ ๊ธฐ๋ณธ ์ ๋ ฅ์ ์ดํ๊ณผ ๊ฒ์ผ๋ก๋ ๋์ผํ์ง๋ง ์ ๋ฅ๊ธฐ ์ ์ ๋ฒกํฐ์ ํ๋ณด๊ตฐ์ด ๋ค๋ฅด๋ค. ํํธ, ์ต์ ์ ์์ ์ธ๊ฐํ์ฌ 3์ ์ค ํ ์์ ํด๋จํ ์ํค๋ ๋ชจ๋ธ์์ธก์ ์ด๊ธฐ๋ฒ์ด ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์์ ๊ฐ๊ฐ ์ ์๋์๋ค(14,16). ์ค์์นญ ์์ค์ ์ค์ด๊ธฐ ์ํด ์ธ๊ฐ๋  ์ต์ ์ ์์ ์๋ ฅ ์ ๋ฅ์ ์ต๋๊ฐ, ์ต์๊ฐ, ์ ๋ฅ๊ธฐ ์ถ๋ ฅ DC ์ ์, ๊ทธ๋ฆฌ๊ณ  ์ ๋ฅ๊ธฐ ์ ์์ ํตํด ์ ํด์ง๋ค. ์ต์ ์ ์์ ์ด์ฉํ ์ ๋ฅ์ ์ดํ ๋ชจ๋ธ์์ธก์ ์ด ๊ธฐ๋ฒ์ ๋น์ฉํจ์๋ ์ต์ ์ ์์ด ์ธ๊ฐ๋ ์ ๋ฅ๊ธฐ ์ ์๊ณผ ๊ทธ์ ๋ํ ๊ธฐ์ค์น๋ก ๊ตฌ์ฑ๋๋ค. ๋ํ ์ต์ ์ ์์ ์ด์ฉํ ์ ๋ ฅ์ ์ดํ ๋ชจ๋ธ์์ธก์ ์ด ๊ธฐ๋ฒ์ ๋น์ฉํจ์๋ ๊ฒ์ผ๋ก๋ ๊ธฐ๋ณธ ์ ๋ ฅ์ ์ดํ ๊ธฐ๋ฒ๊ณผ ๋์ผํ์ง๋ง ์์ธก ์ ํจ ์ ๋ ฅ๊ณผ ๋ฌดํจ ์ ๋ ฅ์ ๊ณ์ฐ ๋ฐฉ์์ด ๋ค๋ฅด๋ค. ๋ณธ ๋ผ๋ฌธ์์๋ ๊ธฐ๋ณธ ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์ ๊ฐ๊ฐ VOC(conv)์ DPC(conv)๋ก ๋ช๋ชํ๋ค. ๋ํ ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์์ ์ ์๋ฒกํฐ์ ํ๋ณด๊ตฐ ์ค ํ์์ ํด๋จํ์ ์ํค๋ ์ ์๋ฒกํฐ๋ง์ ์ฌ์ฉํ์ฌ ์ต์ ์ ์ ์ ๋ฒกํฐ๋ฅผ ์ ํํ๋ ๋ชจ๋ธ์์ธก์ ์ด๊ธฐ๋ฒ์ ๊ฐ๊ฐ VOC (mod1)๊ณผ DPC(mod2)๋ก ๋ถ๋ฅธ๋ค. ์ต์ ์ ์์ ์ธ๊ฐํ์ฌ ํ์์ ํด๋จํ์ ์ํค๋ ๋ชจ๋ธ์์ธก์ ์ด๊ธฐ๋ฒ์ ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์ ๊ฐ๊ฐ VOC(mod2)์ DPC(mod2)๋ก ๋ช๋ชํ๋ค.

๊ทธ๋ฆผ. 2. ์ ์ด ๋ธ๋ก ๋ค์ด์ด๊ทธ๋จ (a) ์ ๋ฅ์ ์ดํ (b) ์ ๋ ฅ์ ์ดํ

Fig. 2. Control block diagram based on (a) current control (b) power control

๊ทธ๋ฆผ. 3. a์ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ (20%)์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ์์ ์๋ ฅ ์ ๋ฅ ํํ (a) 3์ ์๋ ฅ์ ์ (b) VOC(conv) (c) DPC(conv) (d) VOC(mod1) (e) DPC(mod1) (f) VOC(mod2) (g) DPC(mod2)

Fig. 3. Input current waveform in the grid system with the 5th harmonic component (20%) in a-phase input voltage (a) 3-phase input voltage (b) VOC(conv) (c) DPC(conv) (d) VOC(mod1) (e) DPC(mod1) (f) VOC(mod2) (g) DPC(mod2)

## 3. ๊ณ ์กฐํ ์ฑ๋ถ์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ์์ 3์ ํ์คํญ๋ณ์กฐ ์ ๋ฅ๊ธฐ ํน์ฑ ๋น๊ต

๊ณ ์กฐํ ๋ฐ ๋ถํํ์ด ํฌํจ๋ ๊ณํต ํ๊ฒฝ์์, ์์ดํ ์ ์ด ์๊ณ ๋ฆฌ์ฆ์ ๊ฐ์ง๋ 3์ ์ ๋ฅ๊ธฐ์ ์ฑ๋ฅ์ ๋น๊ต ๋ถ์ํ๊ธฐ ์ํ์ฌ ๋์ผํ ์ปจ๋ฒํฐ ํ๋ผ๋ฏธํฐ ๋ฐ ๊ณํต ์กฐ๊ฑด์ ์ฌ์ฉํ๋ค. ์ฌ์ฉํ ์๋ ฅ ์ ์์ root mean sqare (rms) ๊ฐ์ 110 V, ์ฃผํ์ 60 Hz, ์ ๋ฅ๊ธฐ ์๋ ฅ ์ธ๋ํด์ค 10 mH, ์๋ ฅ ์ ํญ 1 ฮฉ, ์ถ๋ ฅ ์ ํญ 100 ฮฉ, ์ํ๋ง ์ฃผํ์๋ 20 kHz์ด๋ค. ๋ํ, ์คํ์ค ํ๊ฒฝ์์ 3์ ๊ต๋ฅ ์ ์์ Chroma 61702๋ฅผ ์ด์ฉํ์ฌ ๊ณ ์กฐํ ๋ฐ ๋ถํํ ์ฑ๋ถ์ ๊ฐ์ง๋ 3์ ๊ณํต ํ๊ฒฝ์ ๋ชจ์ฌํ์์ผ๋ฉฐ, 3์ ์ ๋ฅ๊ธฐ์ ์ ์ด ์๊ณ ๋ฆฌ์ฆ๋ค์ ๋์งํธ ์ ํธ ์ฒ๋ฆฌ ๋ณด๋ (TMS320F28335)๋ฅผ ์ด์ฉํ์ฌ ๊ตฌํ๋์๋ค. 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ ํฌํจํ๋ 3์ ๊ณํต ์ ์์ ๋ค์๊ณผ ๊ฐ๋ค.

##### (1)
\begin{aligned} &v_{i n a}(t)=V_{m} \sin (u t)+a_{5} V_{m} \sin (5 u t) \\ &v_{i n b}(t)=V_{m} \sin \left(u t-\frac{2 \pi}{3}\right)+b_{5} V_{m} \sin \left(5 u t+\frac{2 \pi}{3}\right) \\ &v_{i n c}(t)=V_{m} \sin \left(u t+\frac{2 \pi}{3}\right)+c_{5} V_{m} \sin \left(5 u t-\frac{2 \pi}{3}\right) \end{aligned}

์(1)์์ $a_{5},\: b_{5},\: c_{5}$์ ๊ฐ ์์ ํฌํจ๋ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ๋ฅผ ๋ํ๋ด๋ ํญ์ด๋ค. ๋ํ m์ 3์ ๊ณํต ์ ์์ ๊ธฐ๋ณธ์ฃผํ์์ ํฌ๊ธฐ๋ฅผ ์๋ฏธํ๋ค. $\omega$๋ ๊ฐ์ฃผํ์๋ฅผ ๋ํ๋ธ๋ค.

๊ทธ๋ฆผ 3๋ ์์ 20%์ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ ๊ฐ์ง๋ ๊ณํตํ๊ฒฝ ํ์์ ๊ฐ ์ ์ด๊ธฐ๋ฒ๋ค์ ์ํด ์์ฑ๋๋ 3์ ์๋ ฅ ์ ๋ฅํํ์ ๋ณด์ธ๋ค. ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์ ๋ฐ๋ผ ์๋ ฅ์ ๋ฅ ํํ๋ ์์ดํ์ง๋ง, ๋ชจ๋ ์๋ ฅ์ ๋ฅ ํํ๊ฐ ์๊ณก๋จ์ ์ ์ ์๋ค. ์ ๋ฅ์ ์ดํ์ ๊ฒฝ์ฐ, 5์ฐจ ๊ณ ์กฐํ ์ ์ ์ฑ๋ถ์ด ํฌํจ๋ ์ ์ ๋ฅ๊ฐ ์ ๋ฐ ์ ์ ๋ฅ๋ณด๋ค ๋ ํฐ ๊ณ ์กฐํ ์ฑ๋ถ์ ๊ฐ์ง๊ณ  ์๊ณก๋๋ ํ์์ ๋ณด์ธ๋ค. ๋ฐ๋ฉด, ์ ๋ ฅ์ ์ดํ์ ๊ฒฝ์ฐ, ์ ๋ฅ์ ์ดํ๋ณด๋ค 3๊ฐ์ ์์ ๋ฅ๊ฐ ์ ์ฌํ ํํ๋ก ์๊ณก๋จ์ ์ ์ ์๋ค. 3๊ฐ์ ์ ๋ฅ์ ์ดํ ๋ฐ 3๊ฐ์ ์ ๋ ฅ์ ์ดํ์ ์ํด ์์ฑ๋ ์๋ ฅ์ ๋ฅ ํํ์ ๊ธฐ๋ณธํ ๋ฐ ๊ณ ํจ์จํ์ ๊ด๊ณ์์ด ์ ์ฌํจ์ ๋ณด์ธ๋ค. ์๋ ฅ ์์ ํฌํจ๋ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ 3์ ์ ๋ฅ๊ธฐ ์๋ ฅ์ ๋ฅ THD ๊ฐ์ด ๊ทธ๋ฆผ 4์ ๋ณด์ธ๋ค. 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ ํฌ๊ธฐ๊ฐ ์ฆ๊ฐํ ์๋ก ์๋ ฅ ์ ๋ฅ์ ์๊ณก์ด ์ฌํด์ง๋ค. ๊ธฐ๋ณธํ์ ๊ฒฝ์ฐ, ํฐ ๊ณ ์กฐํ ์ฑ๋ถ(15% ์ด์)์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ์์๋ ์ ๋ ฅ์ ์ดํ์ด ์ ๋ฅ์ ์ดํ๋ณด๋ค ํฐ THD๋ฅผ ๋ง๋ ๋ค๋ ๊ฒ์ ์ ์ ์๋ค. ๋ํ, ๊ณ ํจ์จํ์ ๊ฒฝ์ฐ, ์ ๋ ฅ์ ์ดํ์ ์ํ ๋ฐฉ๋ฒ์ด ์ ๋ฅ์ ์ดํ๋ณด๋ค ๋ค์ ๋ฎ์ THD๋ฅผ ์ป๋๋ค.

๊ทธ๋ฆผ. 4. ๊ณํต์ ํฌํจ๋ a์ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์๋ ฅ์ ๋ฅ THD (a) ๊ธฐ๋ณธํ (b) ๊ณ ํจ์จํ

Fig. 4. Input current THD according to the magnitude of the a-phase 5th harmonic component included in the grid system (a) Basic type (b) High-efficiency type

๊ทธ๋ฆผ 5๊ณผ ๊ทธ๋ฆผ 6๋ ์ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ(20%)์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ ํ์์ ์ถ๋ ฅ์ ์ ๋ฆฌํ ํํ ๋ฐ ์ฃผํ์ ์คํํธ๋ผ์ ๋ณด์ธ๋ค. ์๊ฐ ์์ญ๊ณผ ๋ชจ๋  ์ ๋ฅ์ ์ดํ์ด ์ ๋ ฅ์ ์ดํ๋ณด๋ค ์ถ๋ ฅ ์ ์์ ๋ฆฌํ๊ฐ์ด ์ฝ 2๋ฐฐ ํฌ๋ค๋ ๊ฒ์ ํ์ธํ  ์ ์๊ณ , ์ด๋ ์ฃผํ์ ์์ญ์์ ์คํํธ๋ผ์ ํฌ๊ธฐ๋ก๋ถํฐ๋ ๋์ผํ ๊ฒฐ๊ณผ๊ฐ ํ์ธ๋๋ค. 3๊ฐ์ ์ ๋ฅ์ ์ดํ ๋ฐ 3๊ฐ์ ์ ๋ ฅ์ ์ดํ์ ์ํด ์์ฑ๋ ์ถ๋ ฅ์ ์ ํํ ๋ฐ ์ฃผํ์ ์คํํธ๋ผ์ ๊ธฐ๋ณธํ ๋ฐ ๊ณ ํจ์จํ์ ๊ด๊ณ์์ด ์ ์ฌํจ์ ๋ณด์ธ๋ค. ๊ทธ๋ฆผ 7์ ๊ณํต์ ํฌํจ๋ ์ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์ถ๋ ฅ ์ ์ ํผํฌ ๋ฆฌํ ๊ฐ์ ๋ณด์ธ๋ค. ๊ณํต์ ํฌํจ๋๋ ๊ณ ์กฐํ ์ฑ๋ถ์ ํฌ๊ธฐ๊ฐ ์ฆ๊ฐํ ์๋ก, ์ถ๋ ฅ ์ ์์ ๋ฆฌํ ๊ฐ์ด ์ฆ๊ฐํ๋ ๊ฒฝํฅ์ ๋ณด์ธ๋ค. ๋ํ, ๊ธฐ๋ณธํ ๋ฐ ๊ณ ํจ์จํ ๋ชจ๋์์, ์ ๋ฅ์ ์ดํ๋ณด๋ค ์ ๋ ฅ์ ์ดํ์ด ์๋์ ์ผ๋ก ๋ฎ์ ์ถ๋ ฅ ์ ์ ๋ฆฌํ ๊ฐ์ ์์ฑํ๋ค.

๊ทธ๋ฆผ. 5. a์ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ(20%)์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ ํ์์ ์ถ๋ ฅ์ ์ ๋ฆฌํ ํํ (a) VOC(conv) (b) DPC(conv) (c) VOC(mod1) (d) DPC(mod1) (e) VOC(mod2) (f) DPC(mod2)

Fig. 5. Ripple of the output voltage in the grid system with a-phase 5th harmonic component (20%) (a) VOC(conv) (b) DPC(conv) (c) VOC(mod1) (d) DPC(mod1) (e) VOC(mod2) (f) DPC(mod2)

๊ทธ๋ฆผ. 6. a์ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ(20%)์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ ํ์์ ์ถ๋ ฅ์ ์ ๋ฆฌํ FFT (Fast Fourier Transform) ํํ (a) VOC(conv) (b) DPC(conv)

Fig. 6. FFT (Fast Fourier Transform) results of the output voltage ripple in the grid system with a-phase 5th harmonic component (20%) (a) VOC(conv) (b) DPC(conv)

๊ทธ๋ฆผ. 7. ๊ณํต์ ํฌํจ๋ ์ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์ถ๋ ฅ ์ ์ ํผํฌ ๋ฆฌํ ๊ฐ (a) ๊ธฐ๋ณธํ (b) ๊ณ ํจ์จํ

Fig. 7. Peak ripple value of the output voltage according to the magnitude of the a-phase 5th harmonic component included in the grid system (a) Basic type (b) High-efficiency type

๊ทธ๋ฆผ. 8. ๊ณํต์ ํฌํจ๋ 3์ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์๋ ฅ์ ๋ฅ THD (a) ๊ธฐ๋ณธํ (b) ๊ณ ํจ์จํ

Fig. 8. Input current THD according to the magnitude of the three-phase 5th harmonic component included in the grid system (a) Basic type (b) High-efficiency type

๊ทธ๋ฆผ 8๋ 3์ ๊ณํต์ ๋์ผํ ํฌ๊ธฐ์ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋๋ ๊ฒฝ์ฐ, ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์๋ ฅ์ ๋ฅ THD๊ฐ์ ๋ณด์ธ๋ค. ์์๋ง 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋ ๊ฒฝ์ฐ์ ๋ง์ฐฌ๊ฐ์ง๋ก, 3์ ๋ชจ๋์ ํฌํจ๋ ๊ณ ์กฐํ ์ฑ๋ถ์ ํฌ๊ธฐ๊ฐ ์ฆ๊ฐํ ์๋ก ์๋ ฅ์ ๋ฅ THD๋ ์ฆ๊ฐํ๋ค. ๊ทธ๋ฆผ 4์ ๊ทธ๋ฆผ 8๋ฅผ ๋น๊ต์, ์๋ ฅ์ ๋ฅ ์๊ณก์ ์ ๋๋ ์์๋ง ๊ณ ์กฐํ๊ฐ ํฌํจ๋ ๊ฒฝ์ฐ๋ณด๋ค ๋ ํฌ๊ฒ ์ฆ๊ฐํจ์ ์ ์ ์๋ค. ๋ํ, 3์ ๋ชจ๋์ ๊ณ ์กฐํ๊ฐ ํฌํจ๋ ๊ณํต ํ๊ฒฝ ํ์์๋ ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์ THD๊ฐ์ด ๋ ์ ์ฌํด์ง๋ ๊ฒฝํฅ์ ๋ณด์ธ๋ค. ๊ทธ๋ฆผ 9์ ๊ณํต์ ํฌํจ๋ 3์ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์ถ๋ ฅ ์ ์ ํผํฌ ๋ฆฌํ๊ฐ์ ๋ณด์ธ๋ค. ํ์์๋ง ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋ ๊ฒฝ์ฐ๋ณด๋ค, 3์ ๋ชจ๋์ ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋์์ ๋ ์ถ๋ ฅ ์ ์์ ๋ฆฌํ์ด ๋ ์ฆ๊ฐํจ์ ์ ์ ์๋ค. ๊ทธ๋ฆผ 7๊ณผ ๊ทธ๋ฆผ 9์ ๋น๊ต์ ์์๋ง ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋ ๊ฒฝ์ฐ์ ๋์ผํ๊ฒ ์ ๋ ฅ์ ์ดํ์ด ์ ๋ฅ์ ์ดํ๋ณด๋ค ๋ ๋ฎ์ ๋ฆฌํ๊ฐ์ ๋ณด์ด๊ณ , ๊ทธ ์ฐจ์ด๋ ์์๋ง ๊ณ ์กฐํ๊ฐ ํฌํจ๋ ๊ฒฝ์ฐ๋ณด๋ค ๋ ํฌ๋ค.

๊ทธ๋ฆผ. 9. ๊ณํต์ ํฌํจ๋ 3์ 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์ถ๋ ฅ ์ ์ ํผํฌ ๋ฆฌํ๊ฐ (a) ๊ธฐ๋ณธํ (b) ๊ณ ํจ์จํ

Fig. 9. Peak ripple value of the output voltage according to the magnitude of the three-phase 5th harmonic component included in the grid system (a) Basic type (b) High-efficiency type

๊ทธ๋ฆผ 10์ ์์ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ (20%)์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ์์ ๊ฐ ์ ์ด๊ธฐ๋ฒ๋ค์ ์ํด ์์ฑ๋๋ 3์ ์๋ ฅ ์ ๋ฅํํ์ ๋ณด์ธ๋ค. 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ ์ฃผ์ํ์ ๋์ ๋์ผํ๊ฒ, ๊ธฐ๋ณธํ๊ณผ ๊ณ ํจ์จํ์ ๊ด๊ณ์์ด ์ ์ฌํ ํํ๋ฅผ ๋ณด์ด๊ธฐ ๋๋ฌธ์ ๊ธฐ๋ณธํ ์ ๋ฅ์ ์ด์ ๊ธฐ๋ณธํ ์ ๋ ฅ์ ์ด์ ์ํด ์์ฑ๋ ์คํ ํํ๋ค๋ง ๋ณด์ธ๋ค. ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์ ๋ฐ๋ผ ์๋ ฅ์ ๋ฅ ํํ๋ ์์ดํ์ง๋ง, ๋ชจ๋ ์๋ ฅ์ ๋ฅ ํํ๊ฐ ์๊ณก๋๋ค. ์ ๋ฅ์ ์ดํ์ ๊ฒฝ์ฐ 7์ฐจ ๊ณ ์กฐํ ์ ์ ์ฑ๋ถ์ด ํฌํจ๋ ์ ์ ๋ฅ๊ฐ ์ ๋ฐ ์ ์ ๋ฅ๋ณด๋ค ๋ ํฐ ๊ณ ์กฐํ ์ฑ๋ถ์ ๊ฐ์ง๊ณ  ์๊ณก๋๋ ํ์์ ๋ณด์ด๋ ๋ฐ๋ฉด, ์ ๋ ฅ์ ์ดํ์ ๊ฒฝ์ฐ 3๊ฐ์ ์์ ๋ฅ๊ฐ ์ ์ฌํ ํํ๋ก ์๊ณก๋จ์ ์ ์ ์๋ค. ์๋ ฅ ์์ ํฌํจ๋ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ 3์ ์ ๋ฅ๊ธฐ ์๋ ฅ์ ๋ฅ THD ๊ฐ์ ๊ทธ๋ฆผ 11์ ๋ณด์ธ๋ค. 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ ํฌ๊ธฐ๊ฐ ์ฆ๊ฐํ ์๋ก ์๋ ฅ ์ ๋ฅ์ ์๊ณก์ด ์ฌํด์ง๋ค. ๊ธฐ๋ณธํ์ ๊ฒฝ์ฐ ์ ๋ ฅ์ ์ดํ๊ณผ ์ ๋ฅ์ ์ดํ์ด ์ ์ฌํ๊ณ , ๊ณ ํจ์จํ์ ๊ฒฝ์ฐ ์ ๋ ฅ์ ์ดํ์ ์ํ ๋ฐฉ๋ฒ์ด ์ ๋ฅ์ ์ดํ๋ณด๋ค ๋ค์ ๋ฎ์ THD๋ฅผ ์์ฑํ๋ค.

๊ทธ๋ฆผ. 10. a์ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ(20%)์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ์์ ์๋ ฅ์ ๋ฅ ํํ๋ค (a) 3์ ์๋ ฅ์ ์ (b) VOC(conv) (c) DPC(conv)

Fig. 10. Input current waveform in the grid system with a-phase 7th harmonic component (20%) (a) three-phase input voltage (b) VOC(conv) (c) DPC(conv)

๊ทธ๋ฆผ 12๋ ์ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ(20%)์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ์์ ์ถ๋ ฅ์ ์ ๋ฆฌํ ํํ ๋ฐ ์ฃผํ์ ์คํํธ๋ผ์ ๋ณด์ธ๋ค. 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ ์ฃผ์ํ์ ๋์ ๋์ผํ๊ฒ, ๊ธฐ๋ณธํ๊ณผ ๊ณ ํจ์จํ์ ๊ด๊ณ์์ด ์ ์ฌํ ํํ๋ฅผ ๋ณด์ด๊ธฐ ๋๋ฌธ์ ๊ธฐ๋ณธํ ์ ๋ฅ์ ์ด์ ๊ธฐ๋ณธํ ์ ๋ ฅ์ ์ด์ ์ํด ์์ฑ๋ ์คํ ํํ๋ค๋ง ๋ณด์ธ๋ค. ์๊ฐ ์์ญ๊ณผ ๋ชจ๋  ์ ๋ฅ์ ์ดํ์ด ์ ๋ ฅ์ ์ดํ๋ณด๋ค ์ถ๋ ฅ ์ ์์ ๋ฆฌํ๊ฐ์ด ๋ค์ ์ปค์ง๋ง, 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ ํฌํจํ ๊ฒฝ์ฐ๋ณด๋ค๋ ์๋ค๋ ๊ฒ์ ํ์ธํ  ์ ์๋ค. ๊ทธ๋ฆผ 13์ ๊ณํต์ ํฌํจ๋ ์ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์ถ๋ ฅ ์ ์ ํผํฌ ๋ฆฌํ ๊ฐ์ ๋ณด์ธ๋ค. ๊ณํต์ ํฌํจ๋๋ ๊ณ ์กฐํ ์ฑ๋ถ์ ํฌ๊ธฐ๊ฐ ์ฆ๊ฐํ ์๋ก, ์ถ๋ ฅ ์ ์์ ๋ฆฌํ ๊ฐ์ด ์ฆ๊ฐํ๋ ๊ฒฝํฅ์ ๋ณด์ธ๋ค. ๋ํ, ๊ธฐ๋ณธํ ๋ฐ ๊ณ ํจ์จํ ๋ชจ๋์์, ์ ๋ฅ์ ์ดํ๋ณด๋ค ์ ๋ ฅ์ ์ดํ์ด ์๋์ ์ผ๋ก ๋ฎ์ ์ถ๋ ฅ ์ ์ ๋ฆฌํ ๊ฐ์ ์์ฑํ๋ค.

๊ทธ๋ฆผ. 11. ๊ณํต์ ํฌํจ๋ a์ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์๋ ฅ์ ๋ฅ THD (a) ๊ธฐ๋ณธํ (b) ๊ณ ํจ์จํ

Fig. 11. Input current THD according to the magnitude of the a-phase 7th harmonic component included in the grid system (a) Basic type (b) High-efficiency type

๊ทธ๋ฆผ. 12. a์ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ (20%)์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ์์ ์ถ๋ ฅ์ ์ ๋ฆฌํ ๋ฐ ์ฃผํ์ ์คํํธ๋ผ ํํ (a) VOC(conv) (b) DPC(conv)

Fig. 12. Output voltage ripple and frequency spectrum in the grid system with a-phase 7th harmonic component (20%) (a) VOC(conv) (b) DPC(conv)

๊ทธ๋ฆผ. 13. ๊ณํต์ ํฌํจ๋ a์ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์ถ๋ ฅ ์ ์ ํผํฌ ๋ฆฌํ๊ฐ (a) ๊ธฐ๋ณธํ (b) ๊ณ ํจ์จํ

Fig. 13. Peak ripple value of the output voltage according to the magnitude of the a-phase 7th harmonic component included in the grid system (a) Basic type (b) High-efficiency type

๊ทธ๋ฆผ 14๋ 3์ ๊ณํต์ ๋์ผํ ํฌ๊ธฐ์ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋๋ ๊ฒฝ์ฐ, ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์๋ ฅ์ ๋ฅ THD๊ฐ์ ๋ณด์ธ๋ค. ์์๋ง 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋ ๊ฒฝ์ฐ์ ๋ง์ฐฌ๊ฐ์ง๋ก, 3์ ๋ชจ๋์ ํฌํจ๋ ๊ณ ์กฐํ ์ฑ๋ถ์ ํฌ๊ธฐ๊ฐ ์ฆ๊ฐํ ์๋ก ์๋ ฅ์ ๋ฅ THD๋ ์ฆ๊ฐํ๋ค. ๊ทธ๋ฆผ 11์ ๊ทธ๋ฆผ 14๋ฅผ ๋น๊ต์, ์๋ ฅ์ ๋ฅ ์๊ณก์ ์ ๋๋ ์์๋ง ๊ณ ์กฐํ๊ฐ ํฌํจ๋ ๊ฒฝ์ฐ๋ณด๋ค ๋ ํฌ๊ฒ ์ฆ๊ฐํจ์ ์ ์ ์๋ค. ๋ํ, 3์ ๋ชจ๋์ ๊ณ ์กฐํ๊ฐ ํฌํจ๋ ๊ณํต ํ๊ฒฝํ์์๋ ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์ THD๊ฐ์ด ๋ ์ ์ฌํด์ง๋ ๊ฒฝํฅ์ ๋ณด์ธ๋ค. ๊ทธ๋ฆผ 15์ ๊ณํต์ ํฌํจ๋ 3์ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์ถ๋ ฅ ์ ์ ํผํฌ ๋ฆฌํ ๊ฐ์ ๋ณด์ธ๋ค. ํ์์๋ง ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋ ๊ฒฝ์ฐ๋ณด๋ค, 3์ ๋ชจ๋์ ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋์์ ๋ ์ถ๋ ฅ ์ ์์ ๋ฆฌํ์ด ๋ ์ฆ๊ฐํจ์ ์ ์ ์๋ค. ๊ธฐ๋ณธํ๊ณผ ๊ณ ํจ์จํ์์, ์ ๋ ฅ์ ์ดํ์ด ์ ๋ฅ์ ์ดํ๋ณด๋ค ๋ ๋ฎ์ ๋ฆฌํ ๊ฐ์ ๋ณด์์ ์ ์ ์๋ค.

๊ทธ๋ฆผ. 14. ๊ณํต์ ํฌํจ๋ 3์ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์๋ ฅ์ ๋ฅ THD (a) ๊ธฐ๋ณธํ (b) ๊ณ ํจ์จํ

Fig. 14. Input current THD according to the magnitude of the three-phase 7th harmonic component included in the grid system (a) Basic type (b) High-efficiency type

๊ทธ๋ฆผ. 15. ๊ณํต์ ํฌํจ๋ 3์ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์ถ๋ ฅ ์ ์ ํผํฌ ๋ฆฌํ ๊ฐ (a) ๊ธฐ๋ณธํ (b) ๊ณ ํจ์จํ

Fig. 15. Peak ripple value of the output voltage according to the magnitude of the three-phase 7th harmonic component included in the grid system (a) Basic type (b) High-efficiency type

๊ทธ๋ฆผ. 16. a์ ๋ถํํ ์ฑ๋ถ(20%)์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ์์ ์๋ ฅ์ ๋ฅ ํํ๋ค (a) 3์ ์๋ ฅ์ ์ (b) VOC(conv) (c) DPC(conv)

Fig. 16. Input current waveform in the grid system with a-phase unbalance component (20%) (a) three-phase input voltage (b) VOC(conv) (c) DPC(conv)

## 4. ๋ถํํ ์ฑ๋ถ์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ์์ 3์ ํ์คํญ๋ณ์กฐ ์ ๋ฅ๊ธฐ ํน์ฑ ๋น๊ต

์์ดํ ์ ์ด ์๊ณ ๋ฆฌ์ฆ์ ๊ฐ์ง๋ 3์ PWM ์ ๋ฅ๊ธฐ๊ฐ ๋ถํํ ๊ณํต ํ๊ฒฝ์ ๋ธ์ถ๋์์ ๋ ์๋ ฅ ์ ๋ฅ ํ์ง ๋ฐ ์ถ๋ ฅ ์ ์ ๋ฆฌํ ํน์ฑ์ด ์กฐ์ฌ๋์๋ค. ๋ถํํ ์ํ์ 3์ ๊ณํต ์ ์์ ๋ค์๊ณผ ๊ฐ๋ค.

##### (2)
\begin{align*} v_{"\in " a}(t)=V_{m}\sin(\omega t)+a_{un}V_{m}\sin(\omega t)\\ v_{"\in " b}(t)=V_{m}\sin(\omega t-\dfrac{2\pi}{3})+b_{un}V_{m}\sin(\omega t+\dfrac{2\pi}{3})\\ v_{"\in " c}(t)=V_{m}\sin(\omega t+\dfrac{2\pi}{3})+c_{un}V_{m}\sin(\omega t-\dfrac{2\pi}{3}) \end{align*}

์ฌ๊ธฐ์, $a_{un},\: b_{un},\: c_{un}$์ ๊ฐ ์์ ๋ถํํ ์ง์๋ฅผ ๋ํ๋ด๋ ํญ์ด๋ค.

๊ทธ๋ฆผ. 17. ๋ถํํ ์ ์ ํ๊ฒฝ์์ ์ ๋ถํํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์๋ ฅ์ ๋ฅ THD (a) ๊ธฐ๋ณธํ (b) ๊ณ ํจ์จํ

Fig. 17. Input current THD according to the magnitude of the a-phase unbalanced component in an unbalanced voltage environment (a) Basic type (b) High- efficiency type

๊ทธ๋ฆผ 16์ ์ ๋ถํํ ์ฑ๋ถ(20%)์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ์์ ๊ฐ ์ ์ด๊ธฐ๋ฒ๋ค์ ์ํด ์์ฑ๋๋ 3์ ์๋ ฅ ์ ๋ฅํํ์ ๋ถํํ ๊ณํต ์ ์๊ณผ ํจ๊ป ๋ณด์ฌ์ค๋ค. ๊ณ ์กฐํ ์ฑ๋ถ์ ์ฃผ์ํ์ ๋์ ๋์ผํ๊ฒ ๊ธฐ๋ณธํ๊ณผ ๊ณ ํจ์จํ์ ๊ด๊ณ์์ด ์ ์ฌํ ํํ๋ฅผ ๋ณด์ด๊ธฐ ๋๋ฌธ์ ๊ธฐ๋ณธํ ์ ๋ฅ์ ์ด์ ๊ธฐ๋ณธํ ์ ๋ ฅ์ ์ด์ ์ํด ์์ฑ๋ ์คํ ํํ๋ค๋ง ๋ณด์ธ๋ค. ๋ถํํ ๊ณํต ํ๊ฒฝ์์๋ ์ ๋ฅ์ ์ดํ์ ์ํด ์์ฑ๋ 3์ ์ ๋ฅ ํํ๋ค์ด ์ ๋ ฅ์ ์ดํ์ ์ํ ํํ๋ค๋ณด๋ค ์ฐ์ํ ํ์ง์ ๋ณด์ด๋ ๊ฒ์ ํ์ธํ  ์ ์๋ค. ๊ทธ๋ฆผ 17๋ ๋ถํํ ์ ์ ํ๊ฒฝ์์ ์ ๋ถํํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์๋ ฅ์ ๋ฅ THD ๊ฐ์ ๋ณด์ธ๋ค. ๋ถํํ ์ ์ ์ฑ๋ถ์ ํฌ๊ธฐ๊ฐ ์ฆ๊ฐํ ์๋ก ์๋ ฅ ์ ๋ฅ์ ์๊ณก์ด ์ฌํด์ง๋ค. ๊ธฐ๋ณธํ์ ๊ฒฝ์ฐ, ํฐ ๊ณ ์กฐํ ์ฑ๋ถ(15% ์ด์)์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ์์๋ ์ ๋ ฅ์ ์ดํ์ด ์ ๋ฅ์ ์ดํ๋ณด๋ค ์๋นํ ํฐ THD๋ฅผ ๋ง๋ ๋ค๋ ๊ฒ์ ์ ์ ์๋ค. ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ ๋ชจ๋์์, ๊ณ ํจ์จํ ์ ์ด ๊ธฐ๋ฒ๋ค์ด ๊ธฐ๋ณธํ ์ ์ด ๊ธฐ๋ฒ๋ค๋ณด๋ค ๋ค์ ๋ฎ์ THD๋ฅผ ์์ฑํจ์ ์ ์ ์๋ค.

๊ทธ๋ฆผ. 18. a์ ๋ถํํ ์ฑ๋ถ(20%)์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ์์ ์ถ๋ ฅ์ ์ ๋ฆฌํ ํํ ๋ฐ ์ฃผํ์ ์คํํธ๋ผ (a) VOC(conv) (b) DPC(conv)

Fig. 18. Output voltage ripple waveform and frequency spectrum in the grid system with a-phase unbalance component (20%) (a) VOC(conv) (b) DPC(conv)

๊ทธ๋ฆผ 18์ ์ ๋ถํํ ์ฑ๋ถ์ ๊ฐ์ง๋ ๊ณํต ํ๊ฒฝ์์ ์ถ๋ ฅ์ ์ ๋ฆฌํ ํํ ๋ฐ ์ฃผํ์ ์คํํธ๋ผ์ ๋ณด์ธ๋ค. ์๋ ฅ ์ ๋ฅ ํํ๊ณผ ๋์ผํ๊ฒ, ๊ธฐ๋ณธํ๊ณผ ๊ณ ํจ์จํ์ ๊ด๊ณ์์ด ์ ์ฌํ ํํ๋ฅผ ๋ณด์ด๊ธฐ ๋๋ฌธ์ ๊ธฐ๋ณธํ ์ ๋ฅ์ ์ด์ ๊ธฐ๋ณธํ ์ ๋ ฅ์ ์ด์ ์ํด ์์ฑ๋ ์คํ ํํ๋ค๋ง ๋ณด์ธ๋ค. ์๊ฐ ์์ญ๊ณผ ์ฃผํ์ ์์ญ ๋ชจ๋์์ ์ ๋ฅ์ ์ดํ์ด ์ ๋ ฅ์ ์ดํ๋ณด๋ค ๋ ํฐ ์ถ๋ ฅ ์ ์ ๋ฆฌํ์ ์์ฑํ๋ค๋ ๊ฒ์ ํ์ธํ  ์ ์๋ค. ๊ทธ๋ฆผ 19๋ ๋ถํํ ์ ์ ํ๊ฒฝ์์ ์ ๋ถํํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์ถ๋ ฅ ์ ์ ํผํฌ ๋ฆฌํ ๊ฐ์ ๋ณด์ธ๋ค. ๊ณํต์ ํฌํจ๋๋ ๋ถํํ ์ฑ๋ถ์ ํฌ๊ธฐ๊ฐ ์ฆ๊ฐํ ์๋ก, ์ถ๋ ฅ ์ ์์ ๋ฆฌํ๊ฐ์ด ์ฆ๊ฐํ๋ ๊ฒฝํฅ์ ๋ณด์ธ๋ค. ๋ํ, ๊ธฐ๋ณธํ ๋ฐ ๊ณ ํจ์จํ ๋ชจ๋์์, ์ ๋ฅ์ ์ดํ๋ณด๋ค ์ ๋ ฅ์ ์ดํ์ด ์๋์ ์ผ๋ก ๋ฎ์ ์ถ๋ ฅ ์ ์ ๋ฆฌํ๊ฐ์ ์์ฑํจ์ ํ์ธํ  ์ ์๋ค.

๊ทธ๋ฆผ. 19. ๋ถํํ ์ ์ ํ๊ฒฝ์์ a์ ๋ถํํ ์ฑ๋ถ ํฌ๊ธฐ์ ๋ฐ๋ฅธ ์ถ๋ ฅ ์ ์ ํผํฌ ๋ฆฌํ ๊ฐ (a) ๊ธฐ๋ณธํ (b) ๊ณ ํจ์จํ

Fig. 19. Peak ripple value of the output voltage according to the magnitude of the a-phase unbalanced component in an unbalanced voltage environment (a) Basic type (b) High-efficiency type

## 5. ๊ฒฐ ๋ก

๋ณธ ๋ผ๋ฌธ์์๋ ๊ณ ์กฐํ ๋ฐ ๋ถํํ ์ฑ๋ถ์ ๊ฐ์ง๋ ๊ณํตํ๊ฒฝ์์, ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ ๊ธฐ๋ฐ์ ๊ฐ 3๊ฐ์ง ์์ดํ ์ ์ด ๊ธฐ๋ฒ๋ค์ ์ํด ๋์ํ๋ 3์ ํ์คํญ ๋ณ์กฐ ์ ๋ฅ๊ธฐ์ ์์ถ๋ ฅ ์ฑ๋ฅ์ ๋น๊ต ๋ถ์ํ์๋ค. ๊ธฐ๋ณธํ๊ณผ ๊ณ ํจ์จํ์ ๊ด๊ณ์์ด, ๋์ผํ ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ ๊ธฐ๋ฒ๋ค์ ์๊ณก ๋ฐ ๋ถํํ ๊ณํต ํ๊ฒฝ์์ ์ ์ฌํ ์ฑ๋ฅ์ ๋ณด์๋ค. 3์ ์๋ ฅ ์ ์ ์ค ํ ์์๋ง 5์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋ ๊ฒฝ์ฐ์๋ ์ ๋ฅ์ ์ดํ์ด ์ ๋ ฅ์ ์ดํ๋ณด๋ค ๋ค์ ๊ฐ์ ๋ ์๋ ฅ์ ๋ฅ ํ์ง์ ๋ณด์๋ค. ๋ํ, ๋ถํํ ์ฑ๋ถ์ด ํฌํจ๋ ๊ณํต ํ๊ฒฝ์์๋ ์ ๋ฅ์ ์ดํ ์ ๋ฅ๊ธฐ์ ์ํด ์์ฑ๋ ์๋ ฅ ์ ๋ฅ ํํ์ด ์ ๋ ฅ์ ์ดํ๋ณด๋ค ๋ค์ ๋ฎ์ THD๊ฐ์ ๊ฐ์ก๋ค. ํํธ ํ ์์๋ง 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋ ๊ฒฝ์ฐ์ 3์ ๋ชจ๋์ 5์ฐจ ๋ฐ 7์ฐจ ๊ณ ์กฐํ ์ฑ๋ถ์ด ํฌํจ๋ ๊ฒฝ์ฐ์๋, ์ ๋ฅ์ ์ดํ๊ณผ ์ ๋ ฅ์ ์ดํ์ ์ํด ์์ฑ๋ ์๋ ฅ ์ ๋ฅ THD๊ฐ์ด ์ ์ฌํ ๊ฒฐ๊ณผ๋ฅผ ๋ณด์๋ค. ๊ณ ์กฐํ ๋ฐ ๋ถํํ ์ฑ๋ถ์ ๊ฐ์ง๋ ๋ชจ๋  ๊ณํต ํ๊ฒฝ์์, ์ ๋ ฅ์ ์ดํ ์ ๋ฅ๊ธฐ์ ์ํ ์ถ๋ ฅ ์ ์์ด ์ ๋ฅ์ ์ดํ ์ ๋ฅ๊ธฐ์ ์ํ ์ถ๋ ฅ ์ ์๋ณด๋ค ๋ ๋ฎ์ ๋ฆฌํ๊ฐ์ ๊ฐ์ก๋ค. ๋ฐ๋ผ์, ์ถ๋ ฅ ์ ์ ๋ฆฌํ ์ธก๋ฉด์์๋ ์ ๋ ฅ์ ์ดํ ์ ๋ฅ๊ธฐ๊ฐ ๊ณํต ์ ์์ ์๊ณก ๋ฐ ๋ถํํ ํ๊ฒฝ์ ๋ ๊ฐ๊ฑดํ ํน์ฑ์ ๋ณด์๋ค.

### Acknowledgements

์ด ๋ผ๋ฌธ์ ์ ๋ถ(๊ณผํ๊ธฐ์ ์ ๋ณดํต์ ๋ถ)์ ์ฌ์์ผ๋ก ํ๊ตญ์ฐ๊ตฌ์ฌ๋จ์ ์ง์์ ๋ฐ์ ์ํ๋ ์ฐ๊ตฌ (No. 2020R1A2C1013413)๋ก์, ๊ด๊ณ๋ถ์ฒ์ ๊ฐ์ฌ๋๋ฆฝ๋๋ค.

### References

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Y. Cho, K.-B. Lee, Apr 2016, Virtual-flux-based predictive direct power control of three-phase PWM rectifiers with fast dynamic response, IEEE Trans. Power Electron., Vol. 31, No. 4, pp. 3348-3359
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P. Antoniewicz, M. P. Kazmierkowski, Dec 2008, Virtual-fluxbased predictive direct power control of AC/DC converters with online inductance estimation, IEEE Trans. Ind. Electron., Vol. 55, No. 12, pp. 4381-4390
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M. Malinowski, M. P. Kazmierkowski, A. M. Trzynadlowski, Nov 2003, A comparative study of control techniques for PWM rectifiers in AC adjustable speed drives, IEEE Trans. Power Electron., Vol. 18, No. 6, pp. 1390-1396
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Y. Zhang, J. Jiao, J. Liu, J. Gao, May 2019, Direct power control of PWM rectifier with feedforward compensation of DC-bus voltage ripple under unbalanced grid conditions, IEEE Trans. Ind. Appl., Vol. 55, No. 3, pp. 2890-2901
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H.-S. Song, I.-W. Joo, K. Nam, Dec 2003, Source voltage sensorless estimation scheme for PWM rectifiers under unbalanced conditions, IEEE Trans. Ind. Electron., Vol. 50, No. 6, pp. 1238-1245
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J. L. Duarte, A. Van Zwam, C. Wijnands, A. Vandenput, June 1999, Reference frames fit for controlling PWM rectifiers, IEEE Trans. Ind. Electron., Vol. 46, pp. 628-630
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B. H. Kwon, J. H. Youm, J. W. Lim, Sept 1999, A linevoltage-sensorless synchronous rectifier, IEEE Trans. Power Electron., Vol. 14, pp. 966-972
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Zhang Yongchang, Wang Zeting, Jiao Jian, Liu Jie, 2020, GridVoltage Sensorless Model Predictive Control of ThreePhase PWM Rectifier Under Unbalanced and Distorted Grid Voltages, Power Electronics IEEE transactions on, Vol. 35, No. 8, pp. 8663-8672
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S. Hansen, M. Malinowski, F. Blaabjerg, M. P. Kazmierkowski, 2000, Control strategies for PWM rectifiers without line voltage sensors, in Proc. IEEE APEC, Vol. 2, pp. 832-839
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B. T. Ooi, J. W. Dixon, A. B. Kulkarni, M. Nishimoto, 1986, An integrated AC drive system using a controlled current PWM rectifier/inverter link, in Proc. IEEE PESCโ86, pp. 494-501
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T. Ohnishi, 1991, Three-phase PWM converter/inverter by means of instantaneous active and reactive power control, in Proc. IEEE IECONโ91, pp. 819-824
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S. Kwak, J. Park, Sept 2014, Switching Strategy Based on Model Predictive Control of VSI to Obtain High Efficiency and Balanced Loss Distribution, in IEEE Transactions on Power Electronics, Vol. 29, No. 9, pp. 4551-4567
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S. Kwak, J. Park, Mar 2015, Predictive Control Method With Future Zero-Sequence Voltage to Reduce Switching Losses in Three-Phase Voltage Source Inverters, in IEEE Transactions on Power Electronics, Vol. 30, No. 3, pp. 15581566-
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## ์ ์์๊ฐ

##### ๊น๋์ฐ(Dongyeon Kim)

Dongyeon Kim received the M.S. degree in electrical and electronics engineering from Chung-Ang University, Seoul, South Korea, in 2021.

##### ๊ณฝ์์ (Sangshin Kwak)

Sang-Shin Kwak received the Ph.D. degree in electrical engineering from Texas A&M University, College Station, TX, USA, in 2005.

From 1999 to 2000, he was a Research Engineer with LG Electronics, Changwon, South Korea.

He was also with Whirlpool R&D Center, Benton Harbor, MI, USA, in 2004.

From 2005 to 2007, he was a Senior Engineer with Samsung SDI R&D Center, Yongin, South Korea.

From 2007 to 2010, he was an Assistant Professor with Daegu University, Gyeongsan, South Korea.

Since 2010, he has been with ChungAng University, Seoul, South Korea, where he is currently a Professor.

His research interests include design, modulation, and control of power converters, multilevel converters, renewable energy systems, deep learning applied power conversion, and reliability.

##### ๊น์ฌ์ฐฝ(Jae-Chang Kim)

Jae-Chang Kim received the B.S. degree in electrical and electronics engineering from Chung-Ang University, Seoul, South Korea, in 2017, where he is currently pursuing the combined M.S and Ph.D. degrees in electrical and electronics engineering.

His research interests include control and analysis for two-level, multilevel, and matrix converters.