# US 7,411,801 B2 · Method and apparatus for controlling voltage linearity of voltage source inverters > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 7,411,801 B2 - Document ID: US7411801B2 - Status: Granted - Kind: B2 - Application number: 11/300,249 - Filed: 2005-12-14 - Published: 2007-06-14 - Granted: 2008-08-12 - Earliest claimed: 2005-12-14 - Assignees: GM Global Technology Operations LLC - Inventors: Brian Welchko; Steven E. Schulz; Silva Hiti - Web page: https://patentgrep.com/patent/US7411801B2 ## CPC - H02M 7/53871: {with automatic control of output voltage or current} - H02M: APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF (transformers H01F; dynamo-electric converters H02K47/00; controlling transformers, reactors or choke coils, control or regulation of electric motors, generators or dynamo-electric converters H02P) ## Abstract Methods and apparatus are provided for modifying a pulse width modulation signal controlling a voltage source inverter. The method comprises the steps of determining a duty cycle of the signal, clipping the duty cycle when a modulation index is greater than a minimum modulation index and less than a maximum modulation index, clipping the duty cycle when the modulation index is greater than or equal to the maximum modulation index, and transmitting the duty cycle to the voltage source inverter. The minimum modulation index indicates a distortion range. ## Claims ### Claim 1 A method of modifying a signal controlling a voltage source inverter, the method comprising the steps of: determining a duty cycle limit (dmax) based on the signal; limiting the signal to the duty cycle limit when a modulation index (Mi) is greater than a minimum modulation index (Mi—min) to produce an output signal when a duty cycle of the signal reaches a first phase angle (α1) determined as a function of the modulation index (Mi); and transmitting the output signal to the voltage source inverter. ### Claim 2 (depends on 1) A method according to claim 1, wherein said limiting step comprises limiting the signal to the duty cycle limit when the modulation index (Mi) is greater than the minimum modulation index (Mi_min) and less than a maximum modulation index (Mi_max), the minimum modulation index (Mi_min) indicating a distortion range. ### Claim 3 (depends on 1) A method according to claim 1 further comprising the step of limiting the signal to a second duty cycle limit (dclip) when the modulation index (Mi) is greater than the maximum modulation index (Mi_max), the maximum modulation index (Mi_max) indicating an overmodulation range. ### Claim 4 (depends on 1) A method according to claim 1, wherein said step of limiting the signal at the duty cycle limit (dmax) comprises clamping the signal at a first potential when a duty cycle of the signal reaches the first phase angle (α1) indicating a maximum duty cycle. ### Claim 5 (depends on 1) A method according to claim 1, wherein the first phase angle (α1) is based on d max = M i ⁢ k ⁢ ⁢ sin ⁡ ( α 1 ) - 1 2 - M i ⁢ k ⁢ ⁢ sin ⁡ ( α i - 2 ⁢ π 3 ) , wherein α1 is a phase angle corresponding to the modulation index (Mi) and k is a factor k = 2 ⁢ V d ⁢ ⁢ c π , and wherein Vdc is a supply potential to the voltage source inverter. ### Claim 6 (depends on 1) A method according to claim 1, wherein said step of limiting the signal at the duty cycle limit comprises: clamping the signal at a first potential when a duty cycle of the signal reaches the first phase angle (α1) indicating a maximum duty cycle (dmax); and clamping the signal at a second potential when the duty cycle of the signal reaches a second phase angle (α2). ### Claim 7 (depends on 6) A method according to claim 6, wherein M i ⁢ k = 1 π 2 ⁡ [ 2 ⁢ M i ⁢ k ⁢ ⁢ πα 1 + 2 ⁢ M i ⁢ α 1 + 3 ⁢ M i - 2 ⁢ π ] + 1 π 2 ⁡ [ 2 ⁢ π ⁢ ⁢ cos ⁡ ( α 1 ) - M i ⁢ k ⁢ ⁢ π ⁢ ⁢ sin ⁡ ( 2 ⁢ α 1 ) - 2 ⁢ M i ⁢ sin ⁡ ( 2 ⁢ α 1 + π 3 ) ] + 4 π ⁢ d max ⁡ [ cos ⁡ ( α 1 ) - cos ⁡ ( α 2 ) ] + 2 π ⁢ cos ⁡ ( α 2 ) wherein k is a factor k = 2 ⁢ V d ⁢ ⁢ c π , and wherein Vdc is a supply potential to the voltage source inverter. ### Claim 8 (depends on 1) A method according to claim 1, wherein the duty cycle limit (dmax) indicates a maximum duty cycle, wherein M i_min = d max + 0.5 3 ⁢ k , wherein k is a factor k = 2 ⁢ V d ⁢ ⁢ c π , and wherein Vdc is a supply potential to the voltage source inverter. ### Claim 9 A method of modifying a signal controlling a voltage source inverter, the method comprising the steps of: determining a duty cycle for a phase-leg of the signal; clamping the signal at a first potential when the duty cycle is between a first duty cycle limit (dmax) and a second duty cycle limit (dclip) indicating a distortion range when the duty cycle reaches a first phase angle (α1) determined as a function of the modulation index (Mi); clamping the signal at a second potential when the duty cycle≧the second duty cycle limit (dclip); clamping the signal at a third potential when the duty cycle is between a third duty cycle limit (dmin) and a fourth duty cycle limit indicating the distortion range; and clamping the signal at a fourth potential when the duty cycle≦the fourth duty cycle limit. ### Claim 10 (depends on 9) A method according to claim 9, wherein said step of clamping the signal at a first potential comprises determining a first phase angle (α1) corresponding to the first duty cycle limit (dmax). ### Claim 11 (depends on 9) A method according to claim 9, wherein d max = M i ⁢ k ⁢ ⁢ sin ⁡ ( α 1 ) - 1 2 - M i ⁢ k ⁢ ⁢ sin ⁡ ( α i - 2 ⁢ π 3 ) , wherein Mi is a modulation index of the signal and α1 is a phase angle corresponding to the modulation index (Mi). ### Claim 12 (depends on 11) A method according to claim 11, wherein said step of clamping the signal at a first potential further comprises determining a second phase angle (α2) corresponding to the second duty cycle limit (dclip). ### Claim 13 (depends on 12) A method according to claim 12, wherein M i ⁢ k = 1 π 2 ⁡ [ 2 ⁢ M i ⁢ k ⁢ ⁢ πα 1 + 2 ⁢ M i ⁢ α 1 + 3 ⁢ M i - 2 ⁢ π ] + 1 π 2 ⁡ [ 2 ⁢ π ⁢ ⁢ cos ⁡ ( α 1 ) - M i ⁢ k ⁢ ⁢ π ⁢ ⁢ sin ⁡ ( 2 ⁢ α 1 ) - 2 ⁢ M i ⁢ sin ⁡ ( 2 ⁢ α 1 + π 3 ) ] + 4 π ⁢ d max ⁡ [ cos ⁡ ( α 1 ) - cos ⁡ ( α 2 ) ] + 2 π ⁢ cos ⁡ ( α 2 ) wherein k is a factor k = 2 ⁢ V d ⁢ ⁢ c π , and wherein Vdc is a supply potential to the voltage source inverter. ### Claim 14 (depends on 10) A method according to claim 10 further comprising the step of determining third and fourth phase angles prior to said step of clamping the signal at a third potential, the third phase angle corresponding to the third duty cycle limit (dmin), the fourth phase angle corresponding to the fourth duty cycle limit. ### Claim 15 (depends on 10) A method according to claim 10, wherein the signal has a modulation index (Mi) greater than a minimum modulation index (Mi—min) and less than a maximum modulation index (Mi—max); and wherein said step of clamping the signal at a first potential comprises determining first and second phase angles based on the modulation index (Mi), the first phase angle corresponding to the first duty cycle limit (dmax), the second phase angle corresponding to the second duty cycle limit (dclip). ### Claim 16 A voltage source inverter comprising: a controller configured to: receive a first signal having a duty cycle; and limit said duty cycle at a first duty cycle limit (dmax)when a modulation index (Mi) is greater than a minimum modulation index (Mi—min), said minimum modulation index (Mi—min) indicating a distortion range, wherein the duty cycle of the first signal is limited when it reaches a first phase angle(α1) determined as a function of the modulation index (Mi); and a switch network having a first input coupled to said controller and having a second input configured to couple to a reference potential (Vdc), said switch network configured to: convert said reference potential (Vdc) to a voltage based on said first signal; and transmit a second signal having said voltage. ### Claim 17 (depends on 16) A voltage source inverter according to claim 16, wherein said controller is further configured to: clamp said first signal at a first potential when said duty cycle reaches the first phase angle (α1) indicating the first duty cycle limit (dmax); and clamp said first signal at a second potential when said duty cycle reaches a second phase angle (α2). ### Claim 18 (depends on 17) A voltage source inverter according to claim 17, wherein M i_min = d max + 0.5 3 ⁢ k , wherein k is a factor k = 2 ⁢ V dc π . ### Claim 19 (depends on 17) A method according to claim 17, wherein d max = M i ⁢ k ⁢ ⁢ sin ⁡ ( α 1 ) - 1 2 - M i ⁢ k ⁢ ⁢ sin ⁡ ( α i - 2 ⁢ π 3 ) , wherein k is a factor k = 2 ⁢ V dc π . ### Claim 20 (depends on 16) A voltage source inverter according to claim 16, wherein said controller is further configured to: clamp said first signal at a first potential when Mi—min