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A technique is proposed for the formation of emergency components of current and voltage of a power transmission line by a computational experiment in the MATLAB-Simulink dynamic simulating system (DSS) in order to use them as input information signals of additional stages of microprocessor protections with increased sensitivity. The emergency components of current and voltage are determined using orthogonal components. The emergency component of the short-circuit current is defined as the difference between the vectors (sinusoids) of the main harmonic of the short-circuit current and the current of the previous mode, if the effective value of this difference exceeds some predetermined value. Similarly, the emergency component of the voltage is determined, taking into account the fact that in emergency mode, the voltage at the place of installation of protection does not increase, but decreases. A computer software package (CSP) has been developed in the MATLAB-Simulink DSS to study the functional properties of microprocessor protection using emergency components of currents and phase voltages of a power transmission line of 6(10)–35 kV. The results of the formation of emergency components by models of digital measuring bodies of current and voltage protection are presented, confirming the operability of the developed software package. A CSP has been developed for calculating emergency components of currents and voltages of a power transmission line of 6(10)–35 kV using orthogonal components based on a mathematical model of the power supply unit of the protected line. The results of calculations of emergency components are presented, confirming the operability of the developed software package; a comparison of the results of calculating emergency components obtained by modeling in the MATLAB-Simulink DSS and using a CSP based on a mathematical model is also carried out.

In microprocessor automation and control systems, the amplitude (effective) values of the fundamental harmonic of the input signals are widely used as information parameters of the controlled quantities. They are most often determined by samples of one or a pair of orthogonal components of the signal, for the formation of which digital Fourier filters and their modifications are mainly used. At the rated frequency in the power system, these filters ensure reliable reception of the signal amplitude without additional error. If the frequency deviates from the rated one, the number of samples per signal period is not an integer and the discretization becomes asynchronous. As a result, a corresponding error appears in the amplitude of the signal, and its change becomes oscillating. With minor frequency fluctuations in the normal mode, the amplitude error is insignificant. However, in abnormal situations, the frequency can have significant variations. At the same time, in critical situations, failure of automation and control systems, as well as incorrect operation of their functional algorithms, cannot be excluded. Known methods for determining the amplitude of a signal with frequency fluctuations provide a solution to the existing problem, but they are characterized by a slow response. The proposed high-response method for determining the amplitude during frequency fluctuations is focused on using as initial information samples of instantaneous values of the cosine orthogonal component of the signal, which are formed using an appropriate digital Fourier filter. Based on these samples, the dynamic cosine and sine of the angle of one sample are calculated, the use of which in calculating the amplitude ensures its independence from frequency. Processing of the received amplitude with an amplifying element with a nonlinear coefficient makes it possible to achieve acceptable performance. The effectiveness of the proposed solution was evaluated by a computational experiment using a digital model implemented in the MATLAB-Simulink dynamic modeling environment. In this case, both sinusoidal input signals and complex ones, close to the real secondary signals of measuring transformers, were used as test actions. As a result of the research, it was found that the proposed method for determining the amplitude during frequency fluctuations has a performance at the level of a quarter of the period and provides effective elimination of frequency error both in load modes and in damage modes.

In microprocessor protections, measuring bodies are used that react to individual symmetrical components of signals or a combination of them. This makes the corresponding protection devices more sensitive. Of all the varieties of digital filters of symmetrical components, filters of the negative and zero sequences are mainly used. As for the known algorithms of their software implementation, it is advisable to use filters that form orthogonal components of the required sequence from orthogonal components of phase or phase-to-phase values of signals. Digital Fourier filters, characterized by inertia, are used as formers of the latter. For this reason, their transient modes are accompanied by the appearance of a dynamic error, which can significantly affect the functioning of filters of symmetrical components, worsening their properties. A significant reduction in this effect can be achieved by using shapers with correction of dynamic errors to isolate the orthogonal components of the input signals. They are based on non-recursive digital Fourier filters, the orthogonal components of which are subjected to software correction processing in order to obtain equivalent components characterized by fast-fading dynamic amplitude errors. Correction of the dynamic phase error is realized in the process of obtaining the resulting orthogonal components, which are a combination of Fourier components and calculated ones that have been estimated according to them. Based on the information about the amplitudes and current phases of the signals contained in the equivalent and resultant components, respectively, the resulting orthogonal components are formed, differing in minimal amplitude and phase errors in transient modes. According to these components, the orthogonal components of the signal of the negative and zero sequences in the corresponding filter are calculated. In the dynamic modeling environment of MATLAB-Simulink-SimPowerSystems, a digital model is implemented, which includes a power system, a three-phase group of current transformers, a load, a short-circuit block, as well as models of negative and zero sequence filters. The study of the functioning of these filters was carried out using two types of test actions, viz. a three-phase system of sinusoidal signals and a three-phase system of signals close to real secondary currents in short circuits. The results of the research have demonstrated that the developed digital filters of the negative and zero sequences have 1.1–1.4 times higher performance as compared with similar Fourier filters accepted as reference and that they are distinguished by improved magnitudes of dynamic indicators.

Digital measuring elements in microprocessor protections of electrical installations are implemented mainly with the use of orthogonal components of input signals. To form orthogonal components in microprocessor protections, digital Fourier filters are most widely used, the action of which is al-ways inertial in transient modes. As a result, a dynamic error appears, changing over time and completely disappearing when a steady-state regime occurs. The dynamic error consists of amplitude and phase errors, which can significantly affect the functioning of digital measuring elements and create conditions for their excessive triggering during external short circuits and deceleration of triggering during internal short circuits. Therefore, it is advisable to compensate for the dynamic error, for which it is proposed to determine the amplitude and phase of the fundamental harmonic signal by specially formed orthogonal components. The proposed method of forming orthogonal components of the signal with compensation of dynamic amplitude and phase errors is based on the use of orthogonal components of the digital Fourier filter, followed by the determination of their samples of the final orthogonal components that coincide with the orthogonal components of Fourier in steady-state mode and shifted in phase relative to the latter in transient mode. The amplitude and phase of the signal with minimal dynamic phase errors are calculated from the samples of the final orthogonal components in the digital measuring element. In the dynamic modeling environment of MATLAB-Simulink-SimPowerSystems, a digital model is implemented, which includes a power system, a three-phase group of current transformers, a load, a short-circuit block, as well as a model of a digital measuring element implemented on the basis of the final orthogonal components. The operation of the digital model was checked using two types of test effects, viz. a sinusoidal signal with a frequency of 50 Hz, and a signal close to the real secondary current of a short-circuit current transformer. As a result of the calculations, it was found that digital measuring elements made on the basis of the proposed methodology made it possible to reduce the relative dynamic amplitude and phase errors by three to four times, as compared with the Fourier measuring element taken as a reference.

In microprocessor protections of electric power systems, the controlled information parameters of input signals are determined using their orthogonal components. To form these components, digital Fourier filters which have inertia are most widely used. As a result, transient modes of orthogonal components formation are accompanied by the appearance of a dynamic error. It consists of dynamic amplitude and phase errors, which can significantly affect the functioning of the corresponding measuring elements and cause the possibility of their excessive triggering during external short circuits and slowing down the triggering during internal short circuits. The reduction of the influence of these factors on the behavior of measuring elements is ensured by the use of high-speed shapers to isolate orthogonal components, as well as by compensating for dynamic phase error. The proposed method of forming orthogonal components of a signal with compensation for dynamic phase error is based on obtaining orthogonal Fourier components, followed by determining from their samples the calculated components that coincide or are shifted in phase relative to the orthogonal Fourier components, respectively, in steady-state and transient modes. The resulting orthogonal components with minimal dynamic phase errors are calculated in accordance with samples of calculated orthogonal components and Fourier components. The efficiency of the proposed solution was evaluated by a computational experiment using a digital model implemented in the MATLAB-Simulink dynamic modeling environment. At the same time, both sinusoidal input signals and complex ones with an aperiodic component and higher harmonics were used as test actions. As a result of the studies carried out, it has been found that the proposed method of compensation for dynamic phase error in the formation of orthogonal components is workable and effective for both sinusoidal and complex input signals. The developed compensation method reduces the dynamic phase error of digital Fourier filters by three to four times.

The methods used in the microprocessor protection of electrical equipment for forming orthogonal components of input currents ensure their reliable isolation after changing the mode followed by one or more periods of the fundamental frequency. This is due to the inertia of the functional elements, in particular, digital frequency filters, as well as the saturation of the steel magnetic cores of current transformers. To increase the speed of the selection of orthogonal components of the input currents, it is proposed to form them as equivalent ones in terms of the cosine and sine components obtained using digital Fourier filters by multiplying by the resulting coefficient. The method that has been developed for determining the specified coefficient provides compensation for the delay caused by the inertia of digital filters, as well as the saturation of the steel of magnetic cores of current transformers. The proposed method of forming orthogonal components is highly effective in the modes of strong saturation of the magnetic core with a complex input action in the presence of an aperiodic component with a large damping time constant. The evaluation of the efficiency of the proposed method was performed using a complex digital model implemented in the dynamic modeling environment MatLab-Simulink. As a result of the performed studies, it was found that in the absence of saturation of the magnetic core of current transformers, as well as in the presence of a small and medium degree of saturation, the proposed method for forming equivalent orthogonal components of input currents has dynamic properties close to the ones of those that had been previously proposed. With a strong saturation of the magnetic core of current transformers, the speed of obtaining reliable values of these components is increased by 1.5–2 times.

The use of orthogonal components (OC) underlies the construction of measuring elements of modern protection and automation devices. In most microprocessor-based protections, the orthogonal component of the input signal is extracted using a discrete Fourier transform (DFT). The DFT disadvantages are its low speed, which is more than one period of the fundamental frequency, as well as the sensitivity to the free aperiodic component, which creates significant conversion errors depending on the time constant of its decay. Such a settling time of the true output signal is often unacceptable for the design of high-speed measuring devices. The paper proposes to form the OC of the equivalent signal according to the values of the cosine and sine OC of the fundamental harmonic, formed using the DFT by multiplying them by the resulting correction factor. The developed algorithm for the formation of orthogonal components of input signals in microprocessor protections is characterized by high speed in transient modes and it has wide functionality. So, the proposed digital device for forming the orthogonal components of an equivalent signal, in comparison with digital filter based on the DFT, has an increased operating speed both in the mode of occurrence of a short circuit and during the decay of the monitored signal, while maintaining the same characteristics as in the DFT in other modes. A block diagram of the proposed digital device for forming the OC of an equivalent signal has been developed, all blocks of which can be implemented on a microelectronic and microprocessor element base. A digital model of the specified device has been developed in the dynamic modeling system MatLab-Simulink in accordance with the structural diagram. As a result of the calculations, a significant (up to two times) increase in the performance of the proposed digital device for forming the OC in transient modes has been established in comparison with the shapers based on the DFT.

The magnetizing current inrush appears in electrical power units equipped with transformers in case of no-load energizing of the power transformers and in a number of other cases. This phenomenon could cause a false triggering of the current protection. To prevent incorrect actions of the current protection during the magnetizing current inrush a protection blocking is carrying out. The blocking principle operation is based on the fact that in a three-phase system in normal mode and in case of symmetrical short circuit the first harmonics contained in the phase currents of electrical installations form a direct sequence and the second ones – the negative sequences. In case of an asymmetric mode, including an asymmetric short circuit, the negative sequence appears, formed by the first harmonics that are part of the phase currents of the specified system. In magnetizing current inrush modes, second harmonics of significant magnitude are present in phase currents, which form the negative sequence. Based on the analysis of the information parameters of the specified sequences currents, identification of the magnetizing current inrush and short-circuit modes is performed with the implementation of the protection blocking if necessary. The study of the current protection blocking functioning was performed using computational experiment by analyzing the calculated changes of blocking parameter compared with the threshold setpoint. The specified researching is done by using the digital model that is implemented in the dynamic modeling environment MatLab-Simulink. As a result of the performed calculations, the principal operability of the proposed current protection blocking was confirmed that provides a fairly reliable identification of the magnetizing current inrush and short-circuits modes, regardless of the degree of saturation of current transformers. It was found that the proposed principle of the current protection blocking has a higher sensitivity in comparison with the classical one based on the estimation of the ratio of the second and first harmonics of the phase currents. In short-circuit modes in an electrical power units the proposed blocking causes a current protection operation delay that can be reduced by digital filters performance improvement.

The use of orthogonal components (OS) is the main direction of determining information parameters in microprocessor relay protection and automation of electric power systems. Most of the measuring devices used in modern protection and automation devices can be implemented using known operating systems. Digital non-recursive frequency filters based on discrete Fourier transform are used for OS selection. The main disadvantage of these filters is their low performance that exceeds the period of industrial frequency. For the construction of high-speed measuring devices, this time of establishing the true output signal is often unacceptable. The article proposes to form the equivalent signal OS in microprocessor defenses based on the values of the cosine and sine axes of the main harmonic formed using a discrete Fourier transform, by multiplying them by a correction factor, which is a function of the values of the input signal amplitude and its main harmonic. The proposed algorithm for generating OS input signals in microprocessor defenses is characterized by high performance in transient modes and has wide functionality. A block diagram of an OS equivalent signal generator has been developed, all blocks of which can be implemented according to known schemes on a microelectronic and microprocessor element base. The OS shaper model is implemented in the MatLab-Simulink dynamic modeling environment. The model functioning was checked using two types of test actions, viz. a sinusoidal signal with a frequency of 50 Hz (idealized action) and a signal close to the real secondary current of a short-circuit current transformer. As a result of the performed calculations, a significant (up to two times) in the speed of the proposed method of OS formation in comparison with the formers based on the discrete Fourier transform, frequency properties of both formers being identical.

Digital filters made with the use of discrete Fourier Transform are applied in most microprocessor protections produced both in the home country and abroad. When the input signal frequency deviates from the value to which these filters are configured, a signal is generated at their output with oscillation amplitude that is proportional to the deviation of the signal frequency from the specified one. The article proposes an algorithm for compensating the oscillations of orthogonal components of the output signals of digital filters implemented on the basis of a discrete Fourier transform, when the input signal frequency deviates from the nominal one. A mathematical model of the proposed digital filter with an algorithm for compensating the oscillations of its orthogonal components, as well as a signal model for reproducing input effects, is implemented in the MatLab-Simulink dynamic modeling environment. The digital filter model is provided with two channels, viz. a current channel and a voltage channel, which makes it possible to simulate their operation in relation to protections that use one or two input values, for example, for current and remote protection. Verification of the functioning of the digital filter model with compensation for fluctuations in its output signal was carried out with the use of two types of test effects, viz. a sinusoidal signal with a frequency of 48–51 Hz (idealized effect), and the effects that are close to the real secondary signals of measuring current transformers and voltage transformers in case of short circuits accompanied by a decrease in frequency. The conducted computational experiments with deviation of frequency from the nominal one, revealed the presence of undamped oscillations at the output of standard digital Fourier filters and their almost complete absence in the proposed digital filters. This makes us possible to recommend digital filters based on a discrete Fourier transform supplemented by an algorithm for compensation of fluctuations in the amplitudes of the output signals for the use in microprocessor protection.

The technique is proposed to improve the performance of the measuring element of microprocessor-based protection and its implementation is considered at the software level. Two factors mainly influence on the performance of the measuring elements of microprocessorbased protection of electrical installations. The first one is associated with the appearance of aperiodic and harmonic components in the measured signals due to transients and nonlinearity of the electrical installation elements, and the second–with the inertia of information processing algorithms, in particular–with analog and digital filtering. This leads to the fact that the signal determining time at the output of the measuring element is delayed to unacceptable values that in some cases makes the high-speed protection of electrical equipment ineffective. To solve this problem, it is proposed to form the output signal of the measuring element in the form of special equivalent signals, which are a function of the pre-calculated correction factor and orthogonal components of the controlled signal. In the MatLab-Simulink dynamic modeling environment a mathematical model of the developed measuring element has been implemented, as well as a model of the elements of the power system. Checking the functioning of the model of the measuring element was carried out with the use of 2 types of test effects, viz. a sinusoidal signal with a frequency of 50 Hz (idealized effect), as well as a signal close to the real secondary current of the current transformer in case of short circuit. Computational experiments carried out in relation to the current measuring element using harmonic and close-to-real test effects made it possible to reveal a significant (up to 2 times) increase in the performance of the proposed measuring element as compared to existing ones based on the implementation of the discrete Fourier transform.

The development and implementation of a digital current measurement element for proper operation during current transformer (CT) magnetic core severe saturation are considered. CT transient performance is often accompanied by primary current transformation to secondary one with great errors. In this case the secondary CT current which is an input signal of the digital measurement element differs from the ideally transformed CT current both in shape and magnitude. This causes impermissible signal settling time at the standard digital measurement element output. As a result, main requirements to the protection devices such as reliability and fast operation are violated, that in some cases makes the high-speed protection device ineffective. To solve this problem, it is proposed to form the output signal of the digital current measurement element in depending on the input signal total harmonic distortion (THD) coefficient value. Moreover, it is worthwhile to form the output signal so that for a low CT saturation conditions this output signal slightly differs from the secondary current RMS value, and for a severe CT saturation conditions it exceeds this value. Digital current measurement element model has been developed and implemented in the MatLab-Simulink environment using the following blocks: a digital filter block responsible for the input signal fundamental frequency component magnitude calculation; a digital filter block responsible for the input signal RMS value calculation; and, also, a standard blocks for basic mathematical calculations needed for proper functioning of the proposed measurement element. The functional testing of the proposed digital current measurement element model was carried out using the signal, that was similar in form to the waveform of the secondary current of the severe saturated CT. The tests that had been performed confirmed that the proposed digital current measurement element in comparison with the standard current measurement element ensures stable functioning and enhanced operation time during transients.

The implementation of information support for PC-based and hardware-software based sets for digital overcurrent protection devices and their models testing using MatLab-Simulink environment is considered. It is demonstrated that the mathematical modeling of a part of the power system – viz. of the generalized electric power object – could be based on rigid and flexible models. Rigid models implemented on the basis of mathematical description of electrical and magnetic circuits of a power system can be considered as a reference model for the simulation results that have been obtained with the aid of another simulation system to be compared with. It is proposed to implement flexible models for generalized electric power object in the MatLabSimulink environment that includes the SimPowerSystems component library targeted to power system modeling. The features of the parameters calculation of the SimPowerSystems component library blocks that the power system model is formed of are considered. Out of the Simulink standard blocks the models of a wye-connected current transformers were composed as well as the digital overcurrent protection, missing in the component library. A comparison of simulation results of one and the same generalized electric power object implemented in various PC-based software packages was undertaken. The divergence of simulation results did not exceed 3 %; the latter allows us to recommend the MatLab-Simulink environment for information support creation for hardware-software based sets for digital overcurrent protection devices testing. The structure of the hardware-software based set for digital overcurrent protection device testing using the Omicron CMC 356 has been suggested. Time to trip comparison between the real digital protection device МР 801 and the model with the parameters which are exactly match the parameters of the prototype device was carried out using the identical test inputs. The results of the tests demonstrated a close coincidence of results (the divergence of not more than 8 %), that confirms the possibility of using the suggested hardware-software based test set during the development and debugging of new digital relay protection devices.

This article presents the implementation of digital filters used in digital relay protection current measuring elements. Mathematical descriptions of the considered digital filters as well as the computer programs for their coefficients calculation are described. It has been shown that in order to reliable estimate the digital filter performance its input signals waveforms must be close to the actual secondary current waveform of the current transformer to which the digital protection with the estimated digital filter is connected. For these purposes in MatLab–Simulink dynamic simulation environment the power system and the current measuring element models were developed. Performed calculations allowed to reveal that the exponentially decaying DC component which in some cases contains in primary fault current drives the current transformer core into saturation even when its nominal parameters are not exceeded. This results in distortion of the current transformer secondary current which in this case contains higher and inter-harmonics. Moreover, such harmonic content is not completely taking into account during coefficients calculation of the considered digital filters what results in signal magnitude estimation inaccuracy. Comparison of the digital filters response to the above-mentioned input signals allowed to find out such digital filter implementations which enable signal magnitude estimation with a minimum error. Ways of filtering quality improvement concerned with the window functions are proposed. Thus, the joint usage of digital filter and Hamming window allows to achieve the zero value of the signal magnitude gain factor in high-frequency range and substantially suppress all spectral components above 100 Hz. The increasing of the signal magnitude settling time in this case can be reduced by choosing the most optimal parameters of the all components of the current measuring element.

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