## 7 Conclusions  
The article presents the results of tests of two selected methods of integrating the secondary voltage waveforms of a voltage transformer, generated using a simulation model, in order to determine the linkage waveforms in the transformer core. The secondary voltage integration was performed using an analogue method on a prepared electronic integrator and a digital method using the proposed numerical integration algorithm (trapezoidal method) with the elimination of the constant component implemented in the STM32 microcontroller. The estimated flux waveforms were then compared with the reference flux waveforms generated by simulation in order to qualitatively assess the results obtained for the tested integration methods. Based on the tests of selected integration methods, the following was found:  
1. Both the analogue and digital methods are able to relatively accurately estimate the periodic component of the associated flux in steady states;
2. None of the applied integration methods is able to estimate the constant component of the associated flux in the core (magnetic remanence). This results from the necessity of eliminating the offset of the integration operation, both in the case of the analogue and digital methods and eliminating the constant component from the input signal;
3. For the adopted parameters of both applied integration methods, the elimination of the constant component is faster for the proposed digital method;
4. For the analogue method, the speed of eliminating the constant component depends on the adopted values of the parameters of the integrating element and the parameters of the differentiating element (high-pass filter used to eliminate the constant component of the input signal);
5. For the digital method, the speed of eliminating the constant component depends on the adopted widths of the measurement windows of the average value filters. Extending the width of the measurement window results in a slower filtration speed but improves the accuracy of estimating the periodic components of the slowly changing flux;
6. For a signal with a frequency of 25 Hz, the analogue method estimates the waveform of the linkage with a larger angular error than the proposed digital method. This results from the use of a differentiating term and the parameters of the integrating term. Reducing the angular error is possible by increasing the time constant and, therefore, by slowing down the dynamics of the system (slower elimination of the constant component);
7. The applied analogue method allowed for a more accurate estimation of the oscillatory decaying component compared to the proposed digital method. The errors in estimating slowly changing components result from the selected parameters and the properties of the mean value filters;
8. The advantage of the applied digital method is its flexibility due to its implementation in a microcontroller. This algorithm can be relatively easily modified, unlike the electronic system (analogue method) implemented in hardware;
9. Both the analogue and digital methods can be used as methods for estimating the linkage within the core in order to identify ferroresonance, provided, however, that the detection criterion is based only on measurements of the periodic component in the steady state;
10. Studies of the analogue input circuit have shown that the use of an operational amplifier operating in an inverting differential circuit allows for obtaining smaller interferences in the output signal than in the case of the used summation circuit. The input signal should then first pass through the inverting amplifier and then be fed to the inverting (negative) input of the differential circuit. A constant offset voltage would be fed to the non-inverting (adding) input;
* In the case of an attempt to estimate the flux waveform from the secondary voltage waveform, it is necessary not to use galvanic separation. Otherwise, the integration operation will, as it were, estimate the flux in the separating transformer and not in the core of the voltage transformer.