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In the context of this document power quality refers to the rms voltage of each harmonic of 60 Hz. When power is obtained from the electricity grid the harmonic content is usually quite small. However, when power is obtained from a standby power source the harmonic content can be much higher. The Premium and Super Premium Circuit Filters used in the SPI PLC Lighting Control System will absorb and dissipate energy from voltage harmonics, so it is essential to keep these harmonics below specified maxima.

The Canadian Standards Association has adopted a standard that sets out the maximum current harmonic content for a generator that is directly connected to the electricity grid. SPI is concerned about voltage harmonics as opposed to current harmonics. Nevertheless, the CSA standard is a good starting point. CSA C22.2 107.1 - 01 contains a table of maximum rms current harmonics for a grid connected generator as follows:

HARMONIC NO. | EVEN | ODD |
---|---|---|

2 - 9 | 1% | 4% |

10 - 15 | .5% | 2% |

16 - 21 | .4% | 1.5% |

22 - 33 | .2% | .6% |

>33 | .1% | .3% |

The standard further specifies that when connected to the grid the total harmonic output cannot be greater than 5% and that when disconnected from the grid the total harmonic output cannot exceed 10%. The standard further states that when disconnected from the grid the maximum energy in any single harmonic must be less than 6%.

In interpreting this standard it is important to remember that the voltage and the frequency are both fixed by the grid. The harmonic current results when the generator output current is not sinusoidal as is the grid current. If this same generator output current waveform is applied to a fixed resistor, there are resulting voltage harmonics in proportion to the current harmonics. It is the voltage harmonics that affect the SPI equipment. However, if in the process of being disconnected from the grid the inverter's output voltage reference waveform becomes non-sinusoidal, then we are completely uncertain regarding the magnitude of the voltage harmonics.

The above data suggests that a reasonable standard of performance for voltage harmonics from a good quality inverter type backup power supply that operates independent of the grid is as follows:

HARMONIC NO. | EVEN | ODD |
---|---|---|

2 - 9 | 2% | 8% |

10 - 15 | 1% | 4% |

16 - 21 | .8% | 3% |

22 - 33 | .4% | 1.2% |

>33 | .2% | .6% |

Using this table we can calculate the maximum rms Voltage that is applied to the resistors in the Circuit Filters and hence calulate the amount of heating. This heating can be compared to the heat dissipation rating of the resistors. To simplify the calculation, all the energy can be concetrated in the worst case harmonic of each group. Thus for heating calculation purposes we can consider:

HARMONIC NO. | % | Voltage |
---|---|---|

1 | 100% | 120V |

9 | 10% | 12V |

15 | 5% | 6V |

21 | 3.8% | 4.56V |

33 | 1.6% | 1.92V |

>33 | .8% | .96V |

The voltage applied to the resistor in the circuit filter is further reduced by the transfer function of the filter itself. The magnitude of this transfer function is given by:

|T| = R / (R^2 + (WL - (1 / WC))^2)^0.5

At low frequencies:

|T| ~ RWC

At the fundamental (60 Hz) the voltage applied to the resistor is:

120 V X (1.5 X 6.28 X 60 X 10^-5) = .68 V

At the 9th harmonic the voltage applied to the resistor is:

12 V X (1.5 X 6.28 X 9 X 60 X 10^-5) = .62 V

At the 15th harmonic the voltage applied to the resistor is:

6 V X (1.5 X 6.28 X 15 X 60 X 10^-5) = .50 V

At the 21st harmonic the voltage applied to the resistor is:

4.56 X (1.5 X 6.28 X 21 X 60 X 10^-5) = .54 V

At the 33rd harmonic |T| is given by:

|T| = 1.5 / (2.25 + (.6217 - 8.04)^2)^0.5

= 1.5 / 7.568

= .198,

so the voltage applied to the resistor is:

1.92 X .198 = .38 V.

Above the 33 harmonic the worst case is for the entire voltage to be applied to the resistor:

|T| = 1

and the voltage contribution is:

.96 V X 1 = .96 V

The total voltage Vt rms across the resistor is given by:

Vt rms = (.68^2 + .62^2 + .50^2 + .54^2 + .38^2 +.96^2)^0.5

= (.462 + .384 + .250 + .292 + .144 + .922)^0.5

= 1.56 V rms

Since the resistor is 1.5 ohms this voltage results in slightly over a watt of heat. We are using 10 watt resistiors, so we can potentially allow this voltage to increase three fold. A more practical limitation is the ability of the enclosure to absorb the heat from three such resistors per PCB. Hence, the above table is a good practical limit on the voltage quality.

Note that due to the use of 10 watt power resistors, for short periods of time the harmonic voltage could increase by a factor of three without damaging the SPI equipment. However, the Circuit Filter enclosures are not designed to continuously dissipate 10 watts per branch lighting circuit.

This web page last updated September 20, 2005

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