Loop identification - XIV

Time for some testing.

Circuit 1 - Single phase diode rectifier

Result:

>>>
Number of nodes 6
Number of branches 9
Number of loops 5
**************************************************
1K 2K 3K 4K 5K 6K 7K 8K 9K 10K 11K 11L 11M 10M 9M 8M 7M 6M 5M 4M 3M 2M 1M 1L 1K
1K 1J 1I 2I 3I 4I 5I 6I 7I 8I 9I 10I 11I 11J 11K 10K 9K 8K 7K 6K 5K 4K 3K 2K 1K
1K 1J 1I 1H 1G 1F 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 11F 11G 11H 11I 11J 11K 10K 9K 8K 7K 6K 5K 4K 3K 2K 1K
1K 1J 1I 2I 3I 4I 5I 6I 6H 7B 7A 6A 5A 5B 5C 5D 5E 6E 7E 8E 9E 10E 11E 11F 11G 11H 11I 11J 11K 11L 11M 10M 9M 8M 7M 6M 5M 4M 3M 2M 1M 1L 1K
1K 1J 1I 1H 1G 1F 1E 2E 3E 4E 5E 5D 5C 5B 5A 6A 7A 7B 6H 6I 7I 8I 9I 10I 11I 11J 11K 11L 11M 10M 9M 8M 7M 6M 5M 4M 3M 2M 1M 1L 1K


One additional loop generated but result is OK.


Circuit 2 - Three phase diode rectifier

Result:

>>>
Number of nodes 10
Number of branches 15
Number of loops 9
**************************************************
1M 1L 1K 1J 1I 2I 3I 4I 5I 6I 6H 7B 7A 8A 9A 9B 6L 6M 5M 4M 3M 2M 1M
1M 1L 1K 1J 1I 1H 1G 1F 1E 2E 3E 4E 5E 5D 5C 5B 5A 6A 7A 8A 9A 9B 6L 6M 5M 4M 3M 2M 1M
11O 11P 11Q 10Q 9Q 8Q 7Q 6Q 5Q 4Q 3Q 2Q 1Q 1P 1O 2O 3O 4O 5O 6O 7O 8O 9O 10O 11O
1M 1L 1K 1J 1I 2I 3I 4I 5I 6I 7I 8I 9I 10I 11I 11J 11K 11L 11M 10M 9M 8M 7M 6M 5M 4M 3M 2M 1M
1M 1L 1K 1J 1I 1H 1G 1F 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 11F 11G 11H 11I 11J 11K 11L 11M 10M 9M 8M 7M 6M 5M 4M 3M 2M 1M
1M 1L 1K 1J 1I 2I 3I 4I 5I 6I 7I 8I 9I 10I 11I 11J 11K 11L 11M 11N 11O 11P 11Q 10Q 9Q 8Q 7Q 6Q 5Q 4Q 3Q 2Q 1Q 1P 1O 1N 1M
1M 1L 1K 1J 1I 2I 3I 4I 5I 6I 7I 8I 9I 10I 11I 11H 11G 11F 11E 10E 9E 8E 7E 6E 5E 5D 5C 5B 5A 6A 7A 8A 9A 9B 6L 6M 5M 4M 3M 2M 1M
1M 1L 1K 1J 1I 1H 1G 1F 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 11F 11G 11H 11I 11J 11K 11L 11M 11N 11O 11P 11Q 10Q 9Q 8Q 7Q 6Q 5Q 4Q 3Q 2Q 1Q 1P 1O 1N 1M
1M 1L 1K 1J 1I 1H 1G 1F 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 11F 11G 11H 11I 10I 9I 8I 7I 6I 6H 7B 7A 8A 9A 9B 6L 6M 5M 4M 3M 2M 1M


Additional 3 loops generated but result is OK.



Circuit 3 - Dc-dc boost converter

Result:

>>>
Number of nodes 4
Number of branches 6
Number of loops 3
**************************************************
1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11C 11B 11A 10A 9A 8A 7A 6A 5A 4A 3A 2A 1A 1B 1C 1D
11F 11G 11H 10H 9H 8H 7H 6H 5H 4H 3H 2H 1H 1G 1F 2F 3F 4F 5F 6F 7F 8F 9F 10F 11F
1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11E 11F 11G 11H 10H 9H 8H 7H 6H 5H 4H 3H 2H 1H 1G 1F


The exact number of loops! This happens quite rarely though.


Circuit 4 - Dc-dc boost converter feeding a single-phase converter without FWDs

Result:
>>>
Number of nodes 14
Number of branches 21
Number of loops 12
**************************************************
1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11C 11B 11A 10A 9A 8A 7A 6A 5A 4A 3A 2A 1A 1B 1C 1D
1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11E 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F
1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11E 11F 11G 11H 10H 9H 8H 7H 6H 5H 4H 3H 2H 1H 1G 1F
1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11E 11F 11G 11H 11I 11J 10J 9J 8J 7J 6J 5J 4J 3J 2J 1J 1I 1H 1G 1F
1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11E 11F 11G 11H 11I 11J 11K 11L 11M 11N 10N 9N 8N 7N 6N 5N 4N 3N 2N 1N 1M 1L 1K 1J 1I 1H 1G 1F
1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11E 11F 11G 11H 11I 11J 11K 11L 11M 11N 11O 11P 11Q 11R 10R 9R 8R 7R 6R 5R 4R 3R 2R 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F
1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11E 11F 11G 11H 11I 11J 11K 11L 11M 11N 10N 9N 8N 7N 6N 6O 7U 7V 8V 9V 9U 6K 6J 5J 4J 3J 2J 1J 1I 1H 1G 1F
1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11E 11F 11G 11H 11I 11J 11K 11L 11M 11N 11O 11P 11Q 11R 10R 9R 8R 7R 6R 5R 5S 5T 5U 5V 6V 7V 8V 9V 9U 6K 6J 5J 4J 3J 2J 1J 1I 1H 1G 1F
1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11E 11F 11G 11H 11I 11J 10J 9J 8J 7J 6J 6K 9U 9V 8V 7V 7U 6O 6N 5N 4N 3N 2N 1N 1M 1L 1K 1J 1I 1H 1G 1F
1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11E 11F 11G 11H 11I 11J 10J 9J 8J 7J 6J 6K 9U 9V 8V 7V 6V 5V 5U 5T 5S 5R 4R 3R 2R 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F
1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11E 11F 11G 11H 11I 11J 11K 11L 11M 11N 10N 9N 8N 7N 6N 6O 7U 7V 6V 5V 5U 5T 5S 5R 4R 3R 2R 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F
1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 11E 11F 11G 11H 11I 11J 11K 11L 11M 11N 11O 11P 11Q 11R 10R 9R 8R 7R 6R 5R 5S 5T 5U 5V 6V 7V 7U 6O 6N 5N 4N 3N 2N 1N 1M 1L 1K 1J 1I 1H 1G 1F


Three additional loops generated but result is OK.



Circuit 5 - Dc-dc boost converter feeding a three phase three level diode clamped inverter connected to grid

Result (I am not going to check this!):

>>>

Number of nodes 48

Number of branches 72

Number of loops 70

**************************************************

1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25C 25B 25A 24A 23A 22A 21A 20A 19A 18A 17A 16A 15A 14A 13A 12A 11A 10A 9A 8A 7A 6A 5A 4A 3A 2A 1A 1B 1C 1D

23J 23K 23L 22L 21L 21K 21J 22J 23J

21R 22R 23R 23S 23T 22T 21T 21S 21R

21Z 22Z 23Z 23AA 23AB 22AB 21AB 21AA 21Z

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 14F 13F 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

5J 5K 5L 4L 3L 3K 3J 4J 5J

9J 10J 11J 11K 11L 10L 9L 9K 9J

17J 17K 17L 16L 15L 15K 15J 16J 17J

3R 4R 5R 5S 5T 4T 3T 3S 3R

11R 11S 11T 10T 9T 9S 9R 10R 11R

15R 16R 17R 17S 17T 16T 15T 15S 15R

5Z 5AA 5AB 4AB 3AB 3AA 3Z 4Z 5Z

9Z 10Z 11Z 11AA 11AB 10AB 9AB 9AA 9Z

17Z 17AA 17AB 16AB 15AB 15AA 15Z 16Z 17Z

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 12N 11N 10N 9N 8N 7N 7M 7L 7K 7J 6J 5J 5K 5L 4L 3L 3K 3J 2J 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 25S 25T 25U 25V 25W 25X 25Y 25Z 24Z 23Z 22Z 21Z 20Z 19Z 19AA 19AB 19AC 19AD 18AD 17AD 16AD 15AD 14AD 13AD 12AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 24R 23R 22R 21R 20R 19R 19S 19T 19U 19V 18V 17V 16V 15V 14V 13V 13W 12G 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 24J 23J 23K 23L 22L 21L 21K 21J 20J 19J 19K 19L 19M 19N 18N 17N 16N 15N 14N 13N 13O 15G 15F 14F 13F 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 14F 13F 12F 12G 13W 13V 12V 11V 10V 9V 8V 7V 7U 7T 7S 7R 6R 5R 4R 3R 2R 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 24J 23J 23K 23L 22L 21L 21K 21J 20J 19J 19K 19L 19M 19N 18N 17N 16N 15N 14N 13N 12N 11N 10N 9N 8N 7N 7M 7L 7K 7J 6J 5J 4J 3J 2J 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 14F 13F 12F 11F 10F 9F 9G 11AE 11AD 10AD 9AD 8AD 7AD 7AC 7AB 7AA 7Z 6Z 5Z 5AA 5AB 4AB 3AB 3AA 3Z 2Z 1Z 1Y 1X 1W 1V 1U 1T 1S 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 25S 25T 25U 25V 25W 25X 25Y 25Z 24Z 23Z 22Z 21Z 20Z 19Z 19AA 19AB 19AC 19AD 18AD 17AD 16AD 15AD 14AD 13AD 12AD 11AD 10AD 9AD 8AD 7AD 7AC 7AB 7AA 7Z 6Z 5Z 5AA 5AB 4AB 3AB 3AA 3Z 2Z 1Z 1Y 1X 1W 1V 1U 1T 1S 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 24R 23R 22R 21R 20R 19R 19S 19T 19U 19V 18V 17V 16V 15V 14V 13V 12V 11V 10V 9V 8V 7V 7U 7T 7S 7R 6R 5R 5S 5T 4T 3T 3S 3R 2R 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 14N 15N 16N 17N 18N 19N 19M 19L 19K 19J 20J 21J 22J 23J 24J 25J 25K 25L 25M 25N 25O 25P 25Q 25R 25S 25T 25U 25V 25W 25X 25Y 25Z 24Z 23Z 23AA 23AB 22AB 21AB 21AA 21Z 20Z 19Z 19AA 19AB 19AC 19AD 18AD 17AD 16AD 15AD 14AD 13AD 12AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 14N 15N 16N 17N 18N 19N 19M 19L 19K 19J 18J 17J 17K 17L 16L 15L 15K 15J 14J 13J 12J 11J 10J 9J 8J 7J 6J 5J 5K 5L 4L 3L 3K 3J 2J 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 12N 11N 10N 9N 8N 7N 7M 7L 7K 7J 6J 5J 5K 5L 4L 3L 3K 3J 2J 1J 1K 1L 1M 1N 1O 1P 1Q 1R 1S 1T 1U 1V 1W 1X 1Y 1Z 2Z 3Z 4Z 5Z 6Z 7Z 7AA 7AB 7AC 7AD 8AD 9AD 10AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 14F 13F 12F 12G 13W 13V 14V 15V 16V 17V 18V 19V 19U 19T 19S 19R 20R 21R 21S 21T 22T 23T 23S 23R 24R 25R 25S 25T 25U 25V 25W 25X 25Y 25Z 24Z 23Z 23AA 23AB 22AB 21AB 21AA 21Z 20Z 19Z 19AA 19AB 19AC 19AD 18AD 17AD 16AD 15AD 14AD 13AD 12AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 14F 13F 12F 12G 13W 13V 12V 11V 10V 9V 8V 7V 7U 7T 7S 7R 6R 5R 4R 3R 2R 1R 1S 1T 1U 1V 1W 1X 1Y 1Z 2Z 3Z 4Z 5Z 6Z 7Z 7AA 7AB 7AC 7AD 8AD 9AD 10AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 25S 25T 25U 25V 25W 25X 25Y 25Z 24Z 23Z 22Z 21Z 20Z 19Z 18Z 17Z 17AA 17AB 16AB 15AB 15AA 15Z 14Z 13Z 12Z 11Z 10Z 9Z 8Z 7Z 7AA 7AB 7AC 7AD 8AD 9AD 10AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 24R 23R 22R 21R 20R 19R 19S 19T 19U 19V 18V 17V 16V 15V 14V 13V 13W 12G 12F 13F 14F 15F 15G 13O 13N 12N 11N 10N 9N 8N 7N 7M 7L 7K 7J 6J 5J 4J 3J 2J 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 24J 23J 23K 23L 22L 21L 21K 21J 20J 19J 18J 17J 16J 15J 14J 13J 12J 11J 11K 11L 10L 9L 9K 9J 8J 7J 6J 5J 4J 3J 2J 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 24J 23J 23K 23L 22L 21L 21K 21J 20J 19J 19K 19L 19M 19N 18N 17N 16N 15N 14N 13N 13O 15G 15F 14F 13F 12F 12G 13W 13V 12V 11V 10V 9V 8V 7V 7U 7T 7S 7R 6R 5R 5S 5T 4T 3T 3S 3R 2R 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 14N 15N 16N 17N 18N 19N 19M 19L 19K 19J 20J 21J 22J 23J 24J 25J 25K 25L 25M 25N 25O 25P 25Q 25R 24R 23R 23S 23T 22T 21T 21S 21R 20R 19R 19S 19T 19U 19V 18V 17V 16V 15V 14V 13V 13W 12G 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 14N 15N 16N 17N 18N 19N 19M 19L 19K 19J 18J 17J 17K 17L 16L 15L 15K 15J 14J 13J 13K 17AH 17AI 16AI 15AI 14AI 13AI 13AH 13AA 13Z 14Z 15Z 15AA 15AB 16AB 17AB 17AA 17Z 18Z 19Z 19AA 19AB 19AC 19AD 18AD 17AD 16AD 15AD 14AD 13AD 12AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 14N 15N 16N 17N 18N 19N 19M 19L 19K 19J 18J 17J 17K 17L 16L 15L 15K 15J 14J 13J 13K 17AH 17AI 16AI 15AI 14AI 13AI 13AH 13AA 13Z 12Z 11Z 10Z 9Z 8Z 7Z 7AA 7AB 7AC 7AD 8AD 9AD 10AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 12N 11N 10N 9N 8N 7N 7M 7L 7K 7J 8J 9J 10J 11J 12J 13J 13K 17AH 17AI 16AI 15AI 14AI 13AI 13AH 13AA 13Z 14Z 15Z 15AA 15AB 16AB 17AB 17AA 17Z 18Z 19Z 19AA 19AB 19AC 19AD 18AD 17AD 16AD 15AD 14AD 13AD 12AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 12N 11N 10N 9N 8N 7N 7M 7L 7K 7J 8J 9J 10J 11J 12J 13J 13K 17AH 17AI 16AI 15AI 14AI 13AI 13AH 13AA 13Z 12Z 11Z 10Z 9Z 8Z 7Z 7AA 7AB 7AC 7AD 8AD 9AD 10AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 12N 11N 10N 9N 8N 7N 7M 7L 7K 7J 6J 5J 5K 5L 4L 3L 3K 3J 2J 1J 1K 1L 1M 1N 1O 1P 1Q 1R 2R 3R 4R 5R 6R 7R 7S 7T 7U 7V 8V 9V 10V 11V 12V 13V 13W 12G 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 25S 25T 25U 25V 25W 25X 25Y 25Z 24Z 23Z 22Z 21Z 20Z 19Z 19AA 19AB 19AC 19AD 18AD 17AD 16AD 15AD 14AD 13AD 12AD 11AD 11AE 9G 9F 10F 11F 12F 13F 14F 15F 15G 13O 13N 12N 11N 10N 9N 8N 7N 7M 7L 7K 7J 6J 5J 5K 5L 4L 3L 3K 3J 2J 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 25S 25T 25U 25V 25W 25X 25Y 25Z 24Z 23Z 22Z 21Z 20Z 19Z 19AA 19AB 19AC 19AD 18AD 17AD 16AD 15AD 14AD 13AD 12AD 11AD 11AE 9G 9F 10F 11F 12F 12G 13W 13V 12V 11V 10V 9V 8V 7V 7U 7T 7S 7R 6R 5R 4R 3R 2R 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 24R 23R 22R 21R 20R 19R 18R 17R 17S 17T 16T 15T 15S 15R 14R 13R 12R 11R 10R 9R 8R 7R 7S 7T 7U 7V 8V 9V 10V 11V 12V 13V 13W 12G 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 24R 23R 22R 21R 20R 19R 19S 19T 19U 19V 18V 17V 16V 15V 14V 13V 13W 12G 12F 11F 10F 9F 9G 11AE 11AD 10AD 9AD 8AD 7AD 7AC 7AB 7AA 7Z 6Z 5Z 4Z 3Z 2Z 1Z 1Y 1X 1W 1V 1U 1T 1S 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 24J 23J 23K 23L 22L 21L 21K 21J 20J 19J 18J 17J 16J 15J 14J 13J 13K 17AH 17AI 16AI 15AI 14AI 13AI 13AH 13AA 13Z 14Z 15Z 16Z 17Z 18Z 19Z 19AA 19AB 19AC 19AD 18AD 17AD 16AD 15AD 14AD 13AD 12AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 24J 23J 23K 23L 22L 21L 21K 21J 20J 19J 18J 17J 16J 15J 14J 13J 13K 17AH 17AI 16AI 15AI 14AI 13AI 13AH 13AA 13Z 12Z 11Z 11AA 11AB 10AB 9AB 9AA 9Z 8Z 7Z 7AA 7AB 7AC 7AD 8AD 9AD 10AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 24J 23J 23K 23L 22L 21L 21K 21J 20J 19J 18J 17J 16J 15J 14J 13J 12J 11J 11K 11L 10L 9L 9K 9J 8J 7J 7K 7L 7M 7N 8N 9N 10N 11N 12N 13N 13O 15G 15F 14F 13F 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 24J 23J 23K 23L 22L 21L 21K 21J 20J 19J 19K 19L 19M 19N 18N 17N 16N 15N 14N 13N 13O 15G 15F 14F 13F 12F 11F 10F 9F 9G 11AE 11AD 10AD 9AD 8AD 7AD 7AC 7AB 7AA 7Z 6Z 5Z 4Z 3Z 2Z 1Z 1Y 1X 1W 1V 1U 1T 1S 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 14N 15N 16N 17N 18N 19N 19M 19L 19K 19J 18J 17J 17K 17L 16L 15L 15K 15J 14J 13J 13K 17AH 17AI 16AI 15AI 15AH 13S 13R 14R 15R 15S 15T 16T 17T 17S 17R 18R 19R 19S 19T 19U 19V 18V 17V 16V 15V 14V 13V 13W 12G 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 14N 15N 16N 17N 18N 19N 19M 19L 19K 19J 18J 17J 17K 17L 16L 15L 15K 15J 14J 13J 13K 17AH 17AI 16AI 15AI 15AH 13S 13R 12R 11R 10R 9R 8R 7R 7S 7T 7U 7V 8V 9V 10V 11V 12V 13V 13W 12G 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 12N 11N 10N 9N 8N 7N 7M 7L 7K 7J 8J 9J 10J 11J 12J 13J 13K 17AH 17AI 16AI 15AI 15AH 13S 13R 14R 15R 15S 15T 16T 17T 17S 17R 18R 19R 19S 19T 19U 19V 18V 17V 16V 15V 14V 13V 13W 12G 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 12N 11N 10N 9N 8N 7N 7M 7L 7K 7J 8J 9J 10J 11J 12J 13J 13K 17AH 17AI 16AI 15AI 15AH 13S 13R 12R 11R 10R 9R 8R 7R 7S 7T 7U 7V 8V 9V 10V 11V 12V 13V 13W 12G 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 14F 13F 12F 12G 13W 13V 14V 15V 16V 17V 18V 19V 19U 19T 19S 19R 18R 17R 16R 15R 14R 13R 13S 15AH 15AI 14AI 13AI 13AH 13AA 13Z 14Z 15Z 16Z 17Z 18Z 19Z 19AA 19AB 19AC 19AD 18AD 17AD 16AD 15AD 14AD 13AD 12AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 14F 13F 12F 12G 13W 13V 14V 15V 16V 17V 18V 19V 19U 19T 19S 19R 18R 17R 16R 15R 14R 13R 13S 15AH 15AI 14AI 13AI 13AH 13AA 13Z 12Z 11Z 11AA 11AB 10AB 9AB 9AA 9Z 8Z 7Z 7AA 7AB 7AC 7AD 8AD 9AD 10AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 14F 13F 12F 12G 13W 13V 14V 15V 16V 17V 18V 19V 19U 19T 19S 19R 18R 17R 16R 15R 14R 13R 12R 11R 11S 11T 10T 9T 9S 9R 8R 7R 6R 5R 4R 3R 2R 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 14F 13F 12F 12G 13W 13V 12V 11V 10V 9V 8V 7V 7U 7T 7S 7R 8R 9R 9S 9T 10T 11T 11S 11R 12R 13R 13S 15AH 15AI 14AI 13AI 13AH 13AA 13Z 14Z 15Z 16Z 17Z 18Z 19Z 19AA 19AB 19AC 19AD 18AD 17AD 16AD 15AD 14AD 13AD 12AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 14F 13F 12F 12G 13W 13V 12V 11V 10V 9V 8V 7V 7U 7T 7S 7R 8R 9R 9S 9T 10T 11T 11S 11R 12R 13R 13S 15AH 15AI 14AI 13AI 13AH 13AA 13Z 12Z 11Z 11AA 11AB 10AB 9AB 9AA 9Z 8Z 7Z 7AA 7AB 7AC 7AD 8AD 9AD 10AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 25S 25T 25U 25V 25W 25X 25Y 25Z 24Z 23Z 22Z 21Z 20Z 19Z 18Z 17Z 17AA 17AB 16AB 15AB 15AA 15Z 14Z 13Z 12Z 11Z 10Z 9Z 8Z 7Z 6Z 5Z 5AA 5AB 4AB 3AB 3AA 3Z 2Z 1Z 1Y 1X 1W 1V 1U 1T 1S 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 24R 23R 22R 21R 20R 19R 18R 17R 17S 17T 16T 15T 15S 15R 14R 13R 13S 15AH 15AI 14AI 13AI 13AH 13AA 13Z 14Z 15Z 15AA 15AB 16AB 17AB 17AA 17Z 18Z 19Z 19AA 19AB 19AC 19AD 18AD 17AD 16AD 15AD 14AD 13AD 12AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 24R 23R 22R 21R 20R 19R 18R 17R 17S 17T 16T 15T 15S 15R 14R 13R 13S 15AH 15AI 14AI 13AI 13AH 13AA 13Z 12Z 11Z 10Z 9Z 8Z 7Z 7AA 7AB 7AC 7AD 8AD 9AD 10AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 24R 23R 22R 21R 20R 19R 18R 17R 17S 17T 16T 15T 15S 15R 14R 13R 12R 11R 10R 9R 8R 7R 6R 5R 5S 5T 4T 3T 3S 3R 2R 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 25K 25L 25M 25N 25O 25P 25Q 25R 24R 23R 22R 21R 20R 19R 19S 19T 19U 19V 18V 17V 16V 15V 14V 13V 12V 11V 10V 9V 8V 7V 7U 7T 7S 7R 6R 5R 5S 5T 4T 3T 3S 3R 2R 1R 1S 1T 1U 1V 1W 1X 1Y 1Z 2Z 3Z 3AA 3AB 4AB 5AB 5AA 5Z 6Z 7Z 7AA 7AB 7AC 7AD 8AD 9AD 10AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 24J 23J 23K 23L 22L 21L 21K 21J 20J 19J 18J 17J 16J 15J 14J 13J 13K 17AH 17AI 16AI 15AI 15AH 13S 13R 14R 15R 16R 17R 18R 19R 19S 19T 19U 19V 18V 17V 16V 15V 14V 13V 13W 12G 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 24J 23J 23K 23L 22L 21L 21K 21J 20J 19J 18J 17J 16J 15J 14J 13J 13K 17AH 17AI 16AI 15AI 15AH 13S 13R 12R 11R 11S 11T 10T 9T 9S 9R 8R 7R 7S 7T 7U 7V 8V 9V 10V 11V 12V 13V 13W 12G 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 25G 25H 25I 25J 24J 23J 23K 23L 22L 21L 21K 21J 20J 19J 19K 19L 19M 19N 18N 17N 16N 15N 14N 13N 12N 11N 10N 9N 8N 7N 7M 7L 7K 7J 6J 5J 4J 3J 2J 1J 1K 1L 1M 1N 1O 1P 1Q 1R 1S 1T 1U 1V 1W 1X 1Y 1Z 2Z 3Z 3AA 3AB 4AB 5AB 5AA 5Z 6Z 7Z 7AA 7AB 7AC 7AD 8AD 9AD 10AD 11AD 11AE 9G 9F 8F 7F 6F 5F 4F 3F 2F 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 14N 15N 16N 17N 18N 19N 19M 19L 19K 19J 18J 17J 17K 17L 16L 15L 15K 15J 14J 13J 13K 17AH 17AI 16AI 15AI 14AI 13AI 13AH 13AA 13Z 12Z 11Z 10Z 9Z 8Z 7Z 6Z 5Z 5AA 5AB 4AB 3AB 3AA 3Z 2Z 1Z 1Y 1X 1W 1V 1U 1T 1S 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 14N 15N 16N 17N 18N 19N 19M 19L 19K 19J 18J 17J 17K 17L 16L 15L 15K 15J 14J 13J 13K 17AH 17AI 16AI 15AI 15AH 13S 13R 12R 11R 10R 9R 8R 7R 6R 5R 5S 5T 4T 3T 3S 3R 2R 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 12N 11N 10N 9N 8N 7N 7M 7L 7K 7J 8J 9J 10J 11J 12J 13J 13K 17AH 17AI 16AI 15AI 14AI 13AI 13AH 13AA 13Z 12Z 11Z 10Z 9Z 8Z 7Z 6Z 5Z 5AA 5AB 4AB 3AB 3AA 3Z 2Z 1Z 1Y 1X 1W 1V 1U 1T 1S 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 15G 13O 13N 12N 11N 10N 9N 8N 7N 7M 7L 7K 7J 8J 9J 10J 11J 12J 13J 13K 17AH 17AI 16AI 15AI 15AH 13S 13R 12R 11R 10R 9R 8R 7R 6R 5R 5S 5T 4T 3T 3S 3R 2R 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 14F 13F 12F 12G 13W 13V 14V 15V 16V 17V 18V 19V 19U 19T 19S 19R 18R 17R 16R 15R 14R 13R 13S 15AH 15AI 16AI 17AI 17AH 13K 13J 12J 11J 11K 11L 10L 9L 9K 9J 8J 7J 6J 5J 4J 3J 2J 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 14F 13F 12F 12G 13W 13V 12V 11V 10V 9V 8V 7V 7U 7T 7S 7R 8R 9R 9S 9T 10T 11T 11S 11R 12R 13R 13S 15AH 15AI 16AI 17AI 17AH 13K 13J 12J 11J 11K 11L 10L 9L 9K 9J 8J 7J 6J 5J 4J 3J 2J 1J 1I 1H 1G 1F

1F 1E 1D 2D 3D 4D 5D 6D 7D 8D 9D 10D 11D 12D 13D 14D 15D 16D 17D 18D 19D 20D 21D 22D 23D 24D 25D 25E 25F 24F 23F 22F 21F 20F 19F 18F 17F 16F 15F 14F 13F 12F 11F 10F 9F 9G 11AE 11AD 12AD 13AD 14AD 15AD 16AD 17AD 18AD 19AD 19AC 19AB 19AA 19Z 18Z 17Z 17AA 17AB 16AB 15AB 15AA 15Z 14Z 13Z 12Z 11Z 10Z 9Z 8Z 7Z 6Z 5Z 5AA 5AB 4AB 3AB 3AA 3Z 2Z 1Z 1Y 1X 1W 1V 1U 1T 1S 1R 1Q 1P 1O 1N 1M 1L 1K 1J 1I 1H 1G 1F

Loop identification - XIII

The concept involved in determining loops.

1. branch_map is the array that contains every branch as a list of elements between nodes. The diagonal elements are null because it is assumed that self-loops do not exist. The non-diagonal elements are branched between nodes. So branch_map[i][j] is the branch between node i and node j.

2. branch_map can have multiple lists because there can be parallel branches between two nodes.

3. Every row must have at least three elements because that is how a node is defined - a node is an element from which three or four branches connect it to another node.

4. The number of independent loops = Branches - Nodes +1.

So this is how I find the loops:

1. Pick the first non-null element in the first row.
2. The first loop in progress will be this element.
3. The direction of searching will be horizontal or "horiz". This means we search in the same row for other branches. All searches will be from the first column to last column of a row.
4. For every element in the row, check for parallel branches and add them to loop_list.
5. If not a parallel branch, check if that element or the inverse of it (i.e if [i, j] is the element, [j, i] will also be the same) has been encountered before. If so, then loop is not valid and stop updating that particular list. If not a repeat, append that element to the list.
6. For every element found, create a new list and add it to the elements already in the list. This means, the lists will keep growing in number and size.
7. Check is the loop has ended. This means, are one of the end nodes of the latest branch the same as the end node of the first branch in the loop.
8. If so, take this list and check if the nodes in the branches of the list have been encountered before. That is make a copy of node_list (loop_nodes) and keep deleting the nodes which are found. So it a node in the list exists in loop_nodes, this means the node has not been encountered. A loop which passes through a new nodes is definitely an independent loop, so add this loop to the main loop_list.
9. If the loop does not pass through a new node, it could still be an independent loop. So check if the loop is the same as the loops already found and in loop_list.
10. If so, this means the loop is different from the loops in loop_list. So this may or may not be an independent loop. Add it to loop_list anyway.
11. This completed once cycle. Change the direction of search to vertical or "vert".
12. Check if loop_nodes is null or if number of loops found is less than B-N+1. If either or both are true, continue checking.
13. Take the last element of every loop in progress and look in the columns of those elements starting from first row to last row. Repeat 4-10. Change direction of search again.


The problem is that this method often throws up a number of loops greater than B-N+1 which means some of them will be redundant. This is particularly the case when tightly interconnected circuits are examined. The examples in the next post will make things clear.

Loop identification - XII

Another change in code. Since, this is one of the most critical aspects of the simulator, I need to make sure I get this right. Still not very happy with the result, but need to take a couple of steps forward. The explanation for why I did what I did will come soon in the next post.

Here is the loop finder part (click on "view raw" below the code box to see it in a new window):


And here is the entire code (click on "view raw" below the code box to see it in a new window):

Loop identification - XI

This task never seems to end. Another change in the loop find code.

I was trying out a method where I try to turn at every node in branch_map. However, one major flaw was that the starting point of a loop is the first non-null element in a row in branch_map. Even this will have to be changed to every non-null element in every row in branch_map. So the old code was:


The new code is:


So essentially a for loop has been placed that iterates through the entire starting row.

Loop identification - X

Back to the circuit:

Result:
>>> ================================ RESTART ===========================
>>>
Number of nodes 4
Number of branches 7
Number of loops 6
**************************************************
4D 3D 2D 1D 1E 1F 1G 1H 2H 3H 4H 5H 6H 7H 8H 9H 9G 9F 9E 9D 8D 7D 6D 5D 4D
4D 3D 2D 1D 1E 1F 2F 3F 4F 4E 4D
4D 3D 2D 1D 1E 1F 1G 1H 2H 3H 4H 5H 6H 7H 8H 9H 9G 9F 9E 9D 8D 7D 7E 7F 6F 5F 4F 4E 4D
4D 3D 2D 1D 1E 1F 2F 3F 4F 5F 6F 7F 7E 7D 6D 5D 4D
4D 5D 6D 7D 7C 7B 7A 6A 5A 4A 4B 4C 4D
4F 4E 4D 5D 6D 7D 7E 7F 6F 5F 4F
>>> node_list
[[0, 5], [3, 3], [3, 5], [6, 3]]



Circuit 4:

Created two more nodes by putting an element at 6G
Result:
>>> ================================ RESTART ====================
>>>
Number of nodes 6
Number of branches 10
Number of loops 8
**************************************************
4D 3D 2D 1D 1E 1F 2F 3F 4F 4E 4D
4D 3D 2D 1D 1E 1F 1G 1H 2H 3H 4H 5H 6H 7H 8H 9H 9G 9F 9E 9D 8D 7D 6D 5D 4D
4D 3D 2D 1D 1E 1F 1G 1H 2H 3H 4H 5H 6H 6G 6F 5F 4F 4E 4D
4D 3D 2D 1D 1E 1F 1G 1H 2H 3H 4H 5H 6H 7H 8H 9H 9G 9F 9E 9D 8D 7D 7E 7F 6F 5F 4F 4E 4D
4D 5D 6D 7D 7C 7B 7A 6A 5A 4A 4B 4C 4D
4F 4E 4D 5D 6D 7D 7E 7F 6F 5F 4F
4F 4E 4D 5D 6D 7D 8D 9D 9E 9F 9G 9H 8H 7H 6H 6G 6F 5F 4F
6H 6G 6F 7F 7E 7D 8D 9D 9E 9F 9G 9H 8H 7H 6H



Circuit 5:

Added a jump statement.
Result:
>>> ================================ RESTART =========================
>>>
Number of nodes 8
Number of branches 13
Number of loops 12
**************************************************
1F 1E 1D 1C 10D 9D 9E 9F 9G 9H 8H 7H 6H 5H 4H 3H 2H 1H 1G 1F
1F 1E 1D 2D 3D 4D 4E 4F 3F 2F 1F
7D 6D 5D 4D 4C 4B 4A 5A 6A 7A 7B 7C 7D
1F 1E 1D 1C 10D 9D 8D 7D 6D 5D 4D 4E 4F 3F 2F 1F
1F 1E 1D 1C 10D 9D 8D 7D 7E 7F 6F 5F 4F 3F 2F 1F
1F 1E 1D 1C 10D 9D 8D 7D 7E 7F 6F 6G 6H 5H 4H 3H 2H 1H 1G 1F
1F 1E 1D 1C 10D 9D 9E 9F 9G 9H 8H 7H 6H 6G 6F 5F 4F 3F 2F 1F
4F 3F 2F 1F 1G 1H 2H 3H 4H 5H 6H 6G 6F 5F 4F
4D 5D 6D 7D 7C 7B 7A 6A 5A 4A 4B 4C 4D
4F 4E 4D 5D 6D 7D 7E 7F 6F 5F 4F
4F 4E 4D 5D 6D 7D 8D 9D 9E 9F 9G 9H 8H 7H 6H 6G 6F 5F 4F
6H 6G 6F 7F 7E 7D 8D 9D 9E 9F 9G 9H 8H 7H 6H



OK. So much for basic circuits. I'll plot some power electronics layout tomrrow and check again.

Loop identification -IX

The last circuit was short of one node because of an error in the node_checking function.

Here is the function:


The difference is caused by the last block:

if (row>0 and row<x_row-1 and col>0 and col<x_col-1):
    # If the element is not on the outer boundary
    if (x_mat[row][col+1]!='' and x_mat[row][col-1]!=''):
        # Check if the elements in next and
        # previous columns and same row are connected
        if (x_mat[row+1][col]!='' or x_mat[row-1][col]!=''):
            # Then check if elements in either the next and
            # previous row and same column are connected
            x_list.append([row, col])
    elif (x_mat[row+1][col]!='' and x_mat[row-1][col]!=''):
        # Check if the elements in next and
        # previous rows and same column are connected
        if (x_mat[row][col+1]!='' or x_mat[row][col-1]!=''):
            # Then check if elements in either the next and
            # previous column and same row are connected
            x_list.append([row, col])
The second elif statement had an extra indent!

Loop identification - VIII

Time for some testing.

Circuit 1:

I deliberately started the circuit from row 3 just to see if it still works.

Result:
>>> ================================ RESTART ===================
>>>
Number of nodes 2
Number of branches 3
Number of loops 3
**************************************************
1D 2D 3D 4D 4E 4F 3F 2F 1F 1E 1D
1D 2D 3D 4D 4C 4B 4A 3A 2A 1A 1B 1C 1D
1D 1E 1F 2F 3F 4F 4E 4D 4C 4B 4A 3A 2A 1A 1B 1C 1D
>>>


Circuit 2:

Three parallel branches between 2 nodes.

Result:
>>> ================================ RESTART =====================
>>>
Number of nodes 2
Number of branches 4
Number of loops 6
**************************************************
3D 4D 5D 6D 6E 6F 5F 4F 3F 3E 3D
3D 4D 5D 6D 7D 8D 8E 8F 8G 8H 7H 6H 5H 4H 3H 2H 1H 1G 1F 1E 1D 2D 3D
3D 4D 5D 6D 6C 6B 6A 5A 4A 3A 3B 3C 3D
3D 3E 3F 4F 5F 6F 6E 6D 7D 8D 8E 8F 8G 8H 7H 6H 5H 4H 3H 2H 1H 1G 1F 1E 1D 2D 3D
3D 3E 3F 4F 5F 6F 6E 6D 6C 6B 6A 5A 4A 3A 3B 3C 3D
3D 2D 1D 1E 1F 1G 1H 2H 3H 4H 5H 6H 7H 8H 8G 8F 8E 8D 7D 6D 6C 6B 6A 5A 4A 3A 3B 3C 3D



Circuit 3:

Result:
>>> ================================ RESTART ======================
>>>
Number of nodes 3
Number of branches 5
Number of loops 3
**************************************************
1F 2F 3F 4F 4E 4D 3D 2D 1D 1E 1F
4D 4E 4F 3F 2F 1F 1G 1H 2H 3H 4H 5H 6H 7H 8H 9H 9G 9F 9E 9D 8D 7D 6D 5D 4D
4D 5D 6D 7D 7C 7B 7A 6A 5A 4A 4B 4C 4D


WRONG!!!!!! Number of nodes is 4.
>>> node_list
[[0, 5], [3, 3], [6, 3]]

So it hasn't picked up [3,5] as a node. Time to check the code!

Loop identification - VII

Another couple of changes. Put in another check for repetitions of loops in loop_list. Also, took care of more than two parallel branches possible between two nodes.

Another major comment. If the number of nodes (including the reference or ground node) is N and the number of branches is B, the number of independent loops will be B-N+1. However, while trying to generate just that many number of independent loops, the code was beginning to fail. So the code posted will show all the possible "distinct" loops out of which many of them will simply be linear combinations of the others. I hope this will get sorted out while solving the equations, since the upper triangularization of the matrices will result in a number of rows to be zero. Anyway, this comes later.

As before, click on "view raw" to see the code that goes out of the box.

Loop identification - VI

Before I start checking whether the results of the loop identification code is correct, a small addition to generate the sequence of elements in a loop and also to generate them in a manner that they can read off directly from the spread sheet describing the circuit.

Here is the added code. The final code I'll put up again after verification.

Click on "View Raw" at the bottom of the box to see the entire code that goes out view.

Loop identification - V

Code is ready but roughly written. Seems to work with 3 different types of circuits. But still need to test it out.

Here is the code. Click on "View Raw" at the bottom of the box to see the entire code that goes out of the page.

Loop identification - IV

An error in the previous code. The code fails with certain types of circuits. This is why:

I don't move right except after the first element after the diagonal. This is OK as long as I cover all elements with each movement. That is when I am moving down, all existing elements must be covered. When left, and up also. But I am only touching the nearest element. Which will only work when the loops connect the closest nodes together.

So, the code will have to be rewritten and significantly. The logic will be:

1. Start from the first element after the diagonal. Check how many elements exist in that row and create that many lists with these two elements.

2. For each of these lists, look "down" and see how many elements exist in that column. Create those many copies of the original list with three elements now and so on.

3. The termination condition will be is a loop is found or if no other element is found.

This will need repeated copies of lists.

Loop identification - III

No update as such. Just cleaned up the code a bit. Broke up the code into functions to reduce the level of indents. The idea is try to fit the code in the visible window but I see from the preview that its still going beyond it. I guess I can't rewrite the code again.

Here is the code. Click on "View Raw" if you need to see the entire code.

Loop identification - II

This part actually turned out a whole lot trickier than I thought it would. I figured the best way to go about is by a two step process: first identify the route every loop must take and then actually build the loop.

So, this is the first part - identifying the loop.

To begin with, here is the entire code (including node and branch identification):

The loop identification part is:

This works for a couple of circuits. But I'll have to test it for all kinds of circuits (or layouts rather) before moving to the next step.

Some things that I assumed:

1. The branch_map matrix is symmetrical (at least in branch information if not exactly). So this means branches will be picked up sooner or later if a reasonably detailed search method is used.

2. To elaborate on what a "reseaonably detailed" search method is.

3. I start from an element in the row which is the first after the null diagonal element. So this is the first branch. I touch EVERY element in this first row. This means, I take a turn (turning down) at all the other nodes (columns) that this node (row) is connected.

4. I then move left from the first element in the column where I turned. The other nodes in that column are not touched. Will this affect later? Will have to think about it.

5. Similarly, the other searches will also turn a the first node they find.


This is the output from the latest circuit that I pasted. It works for a few simple other ones, but will have to test specifically if the code will break at those assumptions.

Loop identification

Moving on from branch identification (for the time being at least), I now take on the task of identifying the loops. Which actually is a little tricky.

Anyway, pasting what all the branches that have been identified look like as an matrix on a spreadsheet:

Its a pretty huge spreadsheet, so can only capture a small part of it as a snapshot. But this is just the matrix "branch_map" computed in the previous blog pasted into cells of a spreadsheet.

For any circuit, the number of independent loops is equal to (B-N+1) where B is the number of branches, N is the number of nodes. The length of "node_list" will give us N and the number of elements (non-null) in the upper triangular part of branch_matrix will give us B. This can be found by this simple block of code:
---------------------------------------------------------------------------------------------------------
number_of_branches=0
for c1 in range(len(node_list)):
                for c2 in range(c1+1, len(node_list)):
                                for parallel_branches in branch_map[c1][c2]:
                                                number_of_branches+=1
print number_of_branches
---------------------------------------------------------------------------------------------------------

So we can now set the number of loops we are expecting to find.

A basic starting idea on how to get loops.

1. Take the branch_map matrix and start from the first element in the upper triangular part.
2. The way nodes have been determined, this will be the uppermost row in the connected circuit of the input csv file. Nodes will then be in later columns of the same row and then in later rows. So esentially moving left to right and then down and then again left to right.
3. So by moving to the right from the first element (say element [0, 1] which is [0 5] ;[0 6] ;[0 7] ;[0 8]), we encounter element [0,2] which is [0 5] ;[0 4] ;[0 3] ;[0 2] ;[0 1] ;[1 1] ;[2 1].
4. Element [0,1] contains the branch which connects node [0, 5] to [0, 8]. Element [0,2] contains the branch which connects node [0, 5] to [2,1].
5. Since, we are on row 0 of branch_map, the common element in node 0 which is [0,5].
6. So, if we traverse element [0, 1] in the reverse direction and element [0, 2] in the forwarsd direction, we are moving from right to left and then down.
7. Now, in an attempt to complete the loop, we move down from element [0, 2]. The first non-empty element encountered is [1,2].
8. This is [0 8] ;[1 8] ;[2 8] ;[2 2] ;[2 1].
9. This connects node [2, 1] to [0, 8] through the the "jump1" jump label. And this essentially completes a loop because [0,8] was where we started.


10. Repeating this sequence gives some very good results on other loops.
11. [0 5] ;[0 6] ;[0 7] ;[0 8] in element [0, 1] in reverse direction and move right
[0 5] ;[1 5] ;[2 5] ;[3 5] ;[4 5] ;[5 5] ;[6 5] in forward direction and then move down.
[6 3] ;[6 4] ;[6 5] in the reverse direction and then move left
[6 3] ;[6 2] ;[6 1] ;[6 0] in the forward direction and then move up
[2 1] ;[2 0] ;[3 0] ;[4 0] ;[5 0] ;[6 0] in the reverse direction and then move left
[2 1] ;[2 2] ;[2 8] ;[1 8] ;[0 8] in the forward direction and the loop ends.

So this seems to be an algorithm! Need to code it. But still need to keep thinking about loopholes.

Branch identification -IV

Another small addition to the code.

While adding jump labels, as mentioned in the previous post, the jump label should not be adjacent to a node as jumps should not happen from one node directly to the other but along segments of a branch. To ensure this doesn't happen:






No need to post the entire code again.

A couple of additional comments:

1. Quite a lot of rules have been fabricated and messages printed, but no exceptions have been generated. This will be left for later.
2. Can different sheets of the same spreadsheet be used maybe for larger circuits? Worth looking into.

Branch identification - III

Another round of changes.

When a spreadsheet is saved as a csv file, a couple of things could be done depending on the settings:

1. The contents of the cells could be padded with an additional set of quotes.

2. The last element of every row contains a carriage return "\n".


An absolute requirement is that the column separator is a comma and not a semicolon.

With respect to the above, added the following block of code:



So this ensures, that every element of the array (list of lists actually) conn_matrix is a regular string without an additional set of quotes or a carriage return at the end.

The next change is a huge one. In any circuit, it is always possible that wires may cross each other without forming a connection. So a jumper has to be included. The jumper also performs another task. In a large circuit where smaller networks may be included conveniently as modules with electrical connections, the jumper connections could make a huge difference because the modules can be conveniently lined up maybe at the top of the spreadsheet and the main circuit could be below.

So this means we need to add jumper connections to the circuit. A few rules devised:

1. A jumper connection has to be the end-point. It can't be a node and it can't have elements (wires or devices) both before and after it.
2. Also, jumper can be adjacent to a node. Bring the branch out from the node explicitly with a "wire" or a device and then connect a jumper. This is to make sure that we don't have to jump directly from one node to another. The jumps are between two branches. So there has to be at least one separator from a node.
3. The jumper name has to start with "jump". Case does not matter so "jump_a" is the same as "Jump_a" but the need to be sensible about labeling remains.
4. Can't have more than two jumpers of the same label. If there is a need t join more than two separate branches at a give node, split that terminating node up into two receiving branches and add two separate receiving jumper labels.
5. Every jumper must have another jumper.
6. Two jumps can't be next to each other - in the adjacent cells that is.

So with this, here is the code:


The logic is as follows:

1. First create a list of jump labels, their co-ordinates, and the direction to move in to reach the adjacent element.
2. So, here when an jump is encountered, the checks performed are:
-Is it a node?
-Is it next to another jump?
-Is it a terminal element?





3. Next is jump_matrix is created where the jump labels are keys in a dictionary and their corresponding values are the two co-ordinates and the direction to move in to reach the next element.




 4. Finding the node is almost the same except that it can't be a jump so a small bit of code to check that:



 5. Identifying a branch.
- Start from a node as usual and move in one of the valid directions.
- Then check if the next element is a jump.
- If it is go to the jump matrix and find out which co-ordinates, the jump tag links.
- Find out which co-ordinate we are currently at a pick the other.
- Move in the direction indicated by the other co-ordinate.
- This brings us to the next valid element after the jump.
- Store this direction of jumping.

Check which direction we can move in from the new element and check if that is not opposite to the direction that a jump was made.
If OK, move in that direction and make the jump direction a null string.
Continue until a node is reached.







Chose another test circuit.

Here two jumps are defined.

The output of the program is:
----------------------------------------------------------------------------------------------------
************************************************************
[[0, 5], [0, 8], [2, 1], [6, 0], [6, 3], [6, 5], [6, 7], [6, 12], [8, 12], [9, 5]]
************************************************************
************************************************************
************************************************************
************************************************************
down
[[0, 5], [1, 5], [2, 5], [3, 5], [4, 5], [5, 5], [6, 5]]
**********************************************************************
right
[[0, 5], [0, 6], [0, 7], [0, 8]]
**********************************************************************
left
[[0, 5], [0, 4], [0, 3], [0, 2], [0, 1], [1, 1], [2, 1]]
**********************************************************************
down
[[0, 8], [1, 8], [2, 8], [2, 2], [2, 1]]
**********************************************************************
right
[[0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [1, 12], [2, 12], [3, 12], [4, 12], [5, 12], [6, 12]]
**********************************************************************
left
[[0, 8], [0, 7], [0, 6], [0, 5]]
**********************************************************************
right
[[2, 1], [2, 2], [2, 8], [1, 8], [0, 8]]
**********************************************************************
up
[[2, 1], [1, 1], [0, 1], [0, 2], [0, 3], [0, 4], [0, 5]]
**********************************************************************
left
[[2, 1], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0]]
**********************************************************************
down
[[6, 0], [7, 0], [8, 0], [9, 0], [9, 1], [9, 2], [9, 3], [9, 4], [9, 5]]
**********************************************************************
right
[[6, 0], [6, 1], [6, 2], [6, 3]]
**********************************************************************
up
[[6, 0], [5, 0], [4, 0], [3, 0], [2, 0], [2, 1]]
**********************************************************************
right
[[6, 3], [6, 4], [6, 5]]
**********************************************************************
up
[[6, 3], [5, 3], [5, 7], [6, 7]]
**********************************************************************
left
[[6, 3], [6, 2], [6, 1], [6, 0]]
**********************************************************************
down
[[6, 5], [7, 5], [8, 5], [9, 5]]
**********************************************************************
right
[[6, 5], [6, 6], [6, 7]]
**********************************************************************
up
[[6, 5], [5, 5], [4, 5], [3, 5], [2, 5], [1, 5], [0, 5]]
**********************************************************************
left
[[6, 5], [6, 4], [6, 3]]
**********************************************************************
right
[[6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12]]
**********************************************************************
up
[[6, 7], [5, 7], [5, 3], [6, 3]]
**********************************************************************
left
[[6, 7], [6, 6], [6, 5]]
**********************************************************************
down
[[6, 12], [7, 12], [8, 12]]
**********************************************************************
up
[[6, 12], [5, 12], [4, 12], [3, 12], [2, 12], [1, 12], [0, 12], [0, 11], [0, 10], [0, 9], [0, 8]]
**********************************************************************
left
[[6, 12], [6, 11], [6, 10], [6, 9], [6, 8], [6, 7]]
**********************************************************************
down
[[8, 12], [9, 12], [10, 12], [11, 12], [11, 11], [11, 10], [11, 9], [11, 8], [11, 7], [11, 6], [11, 5], [10, 5], [9, 5]]
**********************************************************************
up
[[8, 12], [7, 12], [6, 12]]
**********************************************************************
left
[[8, 12], [8, 11], [8, 10], [8, 9], [8, 8], [9, 8], [9, 7], [9, 6], [9, 5]]
**********************************************************************
down
[[9, 5], [10, 5], [11, 5], [11, 6], [11, 7], [11, 8], [11, 9], [11, 10], [11, 11], [11, 12], [10, 12], [9, 12], [8, 12]]
**********************************************************************
right
[[9, 5], [9, 6], [9, 7], [9, 8], [8, 8], [8, 9], [8, 10], [8, 11], [8, 12]]
**********************************************************************
up
[[9, 5], [8, 5], [7, 5], [6, 5]]
**********************************************************************
left
[[9, 5], [9, 4], [9, 3], [9, 2], [9, 1], [9, 0], [8, 0], [7, 0], [6, 0]]
**********************************************************************
16

----------------------------------------------------------------------------------------------------

Branch identification - II

A mistake in the previous code. If there are parallel branches between two nodes, there will be a problem. Take a look at the circuit again.

Between Elements 9E ([8,4]) and 8I ([7,8]) there are two parallel branches. The first one goes: 9E-9F-9G-8G-8H-8I. The second one goes: 9E-10E-11E-11F-11G-11H-11I-10I-9I-8I.

But the code that updates the branch matrix is:
----------------------------------------------------------------------------
branch_map[c1][node_list.index([next_node_row, next_node_column])] = branch_iter
----------------------------------------------------------------------------

This will overwrite the second branch when that is detected. So the statement needs to be changed as:
------------------------------------------------------------------------------
branch_map[c1][node_list.index([next_node_row, next_node_column])].append(branch_iter)
------------------------------------------------------------------------------

This adds the new branch to the existing branch found between the nodes. Again an array (list of lists) where an element is a list of lists of lists!

Branch identification

The previous program was to find the number of nodes in the circuit. A node was defined as a junction of three or four nodes. The next step is to be able to identify the branches between these nodes.

The method I have used is a search routine that starts from a node and continues until another node has reached. This is because of one major constraint imposed on the spreadsheet. Connections have to be made either vertical or horizontal and can't be made diagonal. So if you need a diagonal connection you have to go along a column and then a row.

So when starting from a node, there are certain search directions depending on the number of branches at that node - if is a +, all four search directions (up, down, right and left) are possible while if it is a T junction, three search directions may be possible (for example, up, right and left).

If the next element in the search direction is not a node, there can be two directions of searching - forward or backward. To ensure forward search, check if the new element has already been encountered. If so, that is the wrong direction.

If the next element is a node, stop the search.

If it is not a node, but another new element, continue as above.

Another test circuit has been taken:

Anyway, here is the code:




And this is the result:
---------------------------------------------------------------------------------------------------------
************************************************************
[[0, 4], [0, 6], [2, 1], [2, 4], [5, 0], [5, 4], [5, 8], [7, 8], [8, 4]]
************************************************************
************************************************************
************************************************************
************************************************************
down
[[0, 4], [1, 4], [2, 4]]
**********************************************************************
right
[[0, 4], [0, 5], [0, 6]]
**********************************************************************
left
[[0, 4], [0, 3], [0, 2], [0, 1], [1, 1], [2, 1]]
**********************************************************************
down
[[0, 6], [1, 6], [2, 6], [2, 5], [2, 4]]
**********************************************************************
right
[[0, 6], [0, 7], [0, 8], [1, 8], [2, 8], [3, 8], [4, 8], [5, 8]]
**********************************************************************
left
[[0, 6], [0, 5], [0, 4]]
**********************************************************************
right
[[2, 1], [2, 2], [2, 3], [2, 4]]
**********************************************************************
up
[[2, 1], [1, 1], [0, 1], [0, 2], [0, 3], [0, 4]]
**********************************************************************
left
[[2, 1], [2, 0], [3, 0], [4, 0], [5, 0]]
**********************************************************************
down
[[2, 4], [3, 4], [4, 4], [5, 4]]
**********************************************************************
right
[[2, 4], [2, 5], [2, 6], [1, 6], [0, 6]]
**********************************************************************
up
[[2, 4], [1, 4], [0, 4]]
**********************************************************************
left
[[2, 4], [2, 3], [2, 2], [2, 1]]
**********************************************************************
down
[[5, 0], [6, 0], [7, 0], [8, 0], [8, 1], [8, 2], [8, 3], [8, 4]]
**********************************************************************
right
[[5, 0], [5, 1], [5, 2], [5, 3], [5, 4]]
**********************************************************************
up
[[5, 0], [4, 0], [3, 0], [2, 0], [2, 1]]
**********************************************************************
down
[[5, 4], [6, 4], [7, 4], [8, 4]]
**********************************************************************
right
[[5, 4], [5, 5], [5, 6], [5, 7], [5, 8]]
**********************************************************************
up
[[5, 4], [4, 4], [3, 4], [2, 4]]
**********************************************************************
left
[[5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]
**********************************************************************
down
[[5, 8], [6, 8], [7, 8]]
**********************************************************************
up
[[5, 8], [4, 8], [3, 8], [2, 8], [1, 8], [0, 8], [0, 7], [0, 6]]
**********************************************************************
left
[[5, 8], [5, 7], [5, 6], [5, 5], [5, 4]]
**********************************************************************
down
[[7, 8], [8, 8], [9, 8], [10, 8], [10, 7], [10, 6], [10, 5], [10, 4], [9, 4], [8, 4]]
**********************************************************************
up
[[7, 8], [6, 8], [5, 8]]
**********************************************************************
left
[[7, 8], [7, 7], [7, 6], [8, 6], [8, 5], [8, 4]]
**********************************************************************
down
[[8, 4], [9, 4], [10, 4], [10, 5], [10, 6], [10, 7], [10, 8], [9, 8], [8, 8], [7, 8]]
**********************************************************************
right
[[8, 4], [8, 5], [8, 6], [7, 6], [7, 7], [7, 8]]
**********************************************************************
up
[[8, 4], [7, 4], [6, 4], [5, 4]]
**********************************************************************
left
[[8, 4], [8, 3], [8, 2], [8, 1], [8, 0], [7, 0], [6, 0], [5, 0]]
**********************************************************************

---------------------------------------------------------------------------------------------------------


Which is the correct result.

1. One thing I could do to speed up the result is take advantage of the symmetry of the matrix. If node 1 is connected to node 3, node 3 is connected to node 1. No need to do the search again. So I need to to do the search for node i and node k if k>i. Then just take the lower triangular part to be equal to the upper triangular part.

2. The diagonal elements are null. What will happen if there is a self loop - a loop originating and terminating at a node? But will something like that happen in practical electrical circuits?

More issues will be examined with other circuits. Probably will be at least two more versions of this code.

Here, I need to stop and comment about Python. The fact that an embedded objects are possible and that too of any dimension is fantastic. In the above code, we have an array with the elements being lists of lists! And add to that, the lists are not of the same length. Anything goes! Makes like a whole lot simpler.

Network representation

I need a way to describe a circuit that is both convenient to the user but won't require horrendous effort in programming or be a drain on the system. So would like to avoid GUI based circuit drawing. Also, to ask the user to describe the circuit as a net list will drive most people away.

One way I can think of is a spreadsheet that is saved as a csv file. This can be done with just about any spread sheet software. A sample case:

The above is a circuit description.

1. I haven't bothered about the objects yet so they are just named as "a", "b", "c" etc.
2. Connections that are zero impedance are named as "wire".
3. Empty cells imply no connection.
4. Connections have to be along a row or a column. Can't make diagonal connections.

The .csv file as a text file looks like this:
------------------------------------------------------------
,"wire","wire","b","wire","wire","d","wire"
,"wire",,,"wire",,,"wire"
"wire","wire",,,"wire",,,"wire"
"a",,,,"c",,,"wire"
"wire",,,,"wire",,,"wire"
"wire","wire","f","wire","wire",,"wire","wire"
"wire",,,,"k",,,"h"
"wire",,,,,,,"wire"
"wire","i","wire","wire","wire","wire","e","wire"
,,,,"g",,,"wire"
,,,,"wire","wire","wire","wire"
------------------------------------------------------------

The code to interpret this is:





The output is:
-------------------------------------------------------------------------------------
,"wire","wire","b","wire","wire","d","wire"

,"wire",,,"wire",,,"wire"

"wire","wire",,,"wire",,,"wire"

"a",,,,"c",,,"wire"

"wire",,,,"wire",,,"wire"

"wire","wire","f","wire","wire",,"wire","wire"

"wire",,,,"k",,,"h"

"wire",,,,,,,"wire"

"wire","i","wire","wire","wire","wire","e","wire"

,,,,"g",,,"wire"

,,,,"wire","wire","wire","wire"

************************************************************
[[0, 4], [5, 0], [5, 4], [5, 7], [8, 4], [8, 7]]
-------------------------------------------------------------------------------------


A couple of comments:

1. A break in the network won't be detected. For example, E8 and F6 are empty. Which means E6 or [5,4] is not a node. This will have to be dealt later maybe by filling up breaks with high resistances or simply throwing error exceptions. The user has to ensure all connections. If its open, connect a large resistance.

2. The circuit starts from the top of the spreadsheet. But even if there are a couple of empty lines, the program still works. There will be an offset in the row indices, that can be removed by detecting the number of empty rows.


The concept behind this node list is that while finding the loops to apply KVL, you can start at a node and snake your way until you other nodes and make your way back to the starting node. I will also need the number of branches so that I can determine the number of loops. That will be the next task.

Ahead, the actual objects will have to be embedded. For example, AC_Voltage(mag=100, freq=60, res=0.1) could be one of the elements above. This may need something like regular expressions.

Network interpreter

Happy New Year to all my blog readers. I hope this project reaches a significant stage by the end of this year.

There are two significant tasks to be taken up next:

1. Deciding on a manner in which a circuit will be represented that is convenient to the user and also that can be translated to matrices E, A and B in the ODE solver.

2. The ODE was solved with a fixed time step which may not work later. Reason - there may be branches of the circuit with ridiculously small time constants for which the integration time step will have to be decreased. Also, the control may use methods such as sine triangle pulse width modulation where to determine the crossing between the modulation signal and the carrier wave would need to the integration time step to be chosen according to the value of the modulation signal during a carrier wave.

I am going to take up task 1 first and will spend quite some time on it. My initial approach would be to use spreadsheets to design the circuit. The spreadsheet can be saved as a csv file that will be read by Python. The circuit will have to be represented as a connectivity matrix first from which the loops will have to be determined.