Computational issues and compensation algorithms

AN3322

24/38

DocID18304 Rev 1

2.2

Timer evaluation for coherent sampling triggering

In order to introduce coherent sampling into the system, it must be evaluated, if the timer

and its resolution is precise enough to ensure precise outputs (instant power, RMS voltage

and current). This section evaluates the quality of the synchronization with the network

which is possible with the given system. It evaluates errors in respect to the distance from

ideal synchronization to the network.

Sampling frequency for 44 samples per 20 ms (per one cycle of mains 50 Hz) results in the

ADC sample time of 454.5

s.

The STM32 timer used for synchronization with the network and for triggering of the ADC

sampling is a 16-bit timer. This timer has a time stamp generation resolution: 27.777 ns

when the STM32 is running on 36 MHz.

Precision of sampling frequency generation

One cycle of 50 Hz can be divided exactly into 720.000 steps when using the given timer.

The timer generates 16363 time stamp events within two subsequent sampling triggers out

of 44.

The error of the trigger generation for one sample position is:

Equation 27

1 / 16363 = 0.000061 = 0.0061% ~ 0.01%

Experimental results in Figure 13 show the influence of the sampling instant generation

correctness on the instant power error.

Table 4. Precision vs. timer setting. Simulated on signal u (t) = sin (2 x pi x 50 x t)

Distance from

ideal sampling

(timer steps)

Sample time error

(%)

URMS

(V)

(%)

P at 1



(W)

Error P (%)

1

0.0089

0.707075

0.004

0.499956

0.009

10

0.0889

0.706794

0.044

0.499557

0.089

100

0.8889

0.703984

0.443

0.467189

0.881

500

4.4444

0.692307

2.093

0.479290

4.142

1000

8.8888

0.681974

3.554

0.465089

6.982

1406

12.4965

0.678874

3.993

0.460870

7.826

2812

24.9956

0.701548

0.786

0.492170

1.566

4218

37.4895

0.724468

-2.455

0.524853

-4.971

1. 5625 = 11250/2 is exactly half of the sampling period, so the error is zero. Table 4 was computed for the

same setting taking 64 samples per period instead of 44. For 44 samples per second, the errors indicated

are even lower, see the text above Table 4.

50.0000

0.707107

0.000

0.500000

0.000