CC BY
15system allows you to comprehensively evaluate the design and technological solution and choose the best.
The method of estimating of the set of technical for thermomodernizate the building as a whole is developed. This method is allowed to determine the most technically, energy and cost-effective options for complex thermomodernization.
REFERENCES:
1. Law of Ukraine "On Energy Efficiency of Buildings" of 22.06.2017 No. 2118-VIII. URL: https://zakon.rada.gov.ua/laws/show/2118-19.
2. DSTU-N B V.3.2-3:2014 (2015) Nastanova z vykonannia termomodernizatsii zhytlovykh budynkiv K.: DP «Arkhbudinform».
3. DSTU-N B A.2.2-13:2015 —Energy efficiency of buildings. Guidelines for the energy assessment of buildings. URL: https://thermomodernisation.org/wp-content/uploads/2017/11/1783_-_.2.2-13_2015.pdf.
4. DBN B.2.6 - 31:2016 "Thermo insulation of buildings" (2017), Minregionbud, Kyiv.
5. Enerhoefektyvnist v munitsypalnomu sektori. Navchalnyi posibnyk dlia posadovykh osib mistsevoho samovriaduvannia (2015) / Maksymov A.S. ets. -AMU, USAID.
6. Bielienkova O.Iu., Tsyfra T.Iu., Matsapura O.V. & Ostapenko I.O. (2018) Ekonomichna otsinka zakhodiv z pidvyshchennia enerhoefektyvnosti. Shliakhy pidvyshchennia efektyvnosti budivnytstva v umovakh formuvannia rynkovykh vidnosyn. 36.78-82.
7. Menejliuk O.I., Cherepaschuk L.A., Olijnyk
N.V. Analysis of new constructive solutions of energy efficient heating constructions. Molodyj vchenyj, issue 1 (53), 2018. - pp.435-439
8. Ratushniak H. S, Ratushniak O. H. (2009) Up-ravlinnia enerhozberihaiuchymy proektamy ter-morenovatsiii budivel'. Navchal'nyj posibnyk.[Man-agement of energy-saving projects of thermo renovation of buildings. Tutorial.] UNIVERSUM, Ukraine, Vinnytsia.
9. Bielienkova, O.Yu., Ostapenko, I.O. (2013) Ekonomichna otsinka zakhodiv z pidvyshchennia enerhoefektyvnosti. Budivelne vyrobnytstvo. 55. 28 -31.
10. Systems with rigid fixing of a heater in a wall. Electronic resource: Access mode:
[http ://www. aspectplus. com.ua/con-tent/view/82/60/lang,ua/]
11. Aleksandrov A. V. «StrojPROFYl'» № 4-05. Electronic resource: Access mode: [http://stroypro-file.com/archive/1704]
12. Zvit pro naukovo-doslidnu robotu «Proveden-nia analitychnykh doslidzhen ta rozrobka pryntsypovykh budivelno-tekhnichnykh rishen shchodo provedennia kompleksnoi termomodernizatsii budynkiv zahalnoosvitnikh shkil biudzhetnoho utry-mannia (na prykladi 6 proektiv) z obgruntuvanniam dotsilnosti dlia povtornoho zastosuvannia» (2013).-K.:DP NDIBV.
13. Tormosov, R.Iu., Romaniuk, O.P., Safiulina, K.R. (2015) Pidhotovka proektnykh propozytsii iz chystoi enerhii: praktychnyi posibnyk. - K..:TOV «Polihraf plius».
USING THE FOURIER TRANSFORM OF THE HALF-CYCLE TO ENHANCE THE APPLICATION
OF THE PMU
Revyakin V.
Master degree Klimova T.
Candidate of Sciences in Technology, Associate Professor University «MPEI», Department "Relay protection and automation of power supply systems", Moscow,
Russia
Abstract
In this report it is offered modified discrete Fourier transform giving fast (observation window 10 ms), precise and simple for realization the algorithm of receiving estimations of parameters of sinusoidal oscillation, according to the IEEE Standard C37.118 requirements.
Keywords: PMU complexes in distributed power systems, PMU algorithms, the discrete Fourier transform, FCDFT, HCDFT, SDFT, noise and measurement errors. The possibility of using the algorithm in power distribution systems in special implementations of PMU(microPMU), requiring fast estimation at the presence of noise, is analyzed. In this article there are results of modeling various situations.
INTRODUCTION
Historically, power distribution systems did not require elaborate monitoring schemes. With radial topology and one-way power flow, it was only necessary to evaluate peak loads or fault currents, rather than continually observe the operating state. But the growth of distributed energy resources, such as renewable generation, electric vehicles, and demand response programs, introduces more short-term and unpredicted
fluctuations and disturbances [1]. This demands the need for more accurate and quicker measurements, judging from increasing changeability and uncertainty and the presence of a higher level of narrowband and broadband interference and measurement noises.
In order to expand the possibilities of using PMU devices, firstly it needs to perfect the technologies of PMU devices. For improving the characteristics of
PMU, the literature suggests various methods of modifying the discrete Fourier transform. For example, Smart Discrete Fourier Transform (SDFT) was proposed [3]. This method is based on a mathematical approach, that efficiently solves limitations of the standard DFT method and allows obtaining some increase in the accuracy of estimates of the parameters of the sinusoidal oscillation when the frequency of the observed signal deviates from the nominal value.
In this report it is offered one more modified discrete Fourier transform giving fast (observation window 10 ms), precise and simple for realization the algorithm of receiving estimations of parameters of sinusoidal oscillation, according to the IEEE Standard C37.11 and CNJ 59012820.29.020.011-2016 [4, 5] requirements. The comparison of several variants of the discrete Fourier Transform is on, which estimates the parameters of sinusoidal oscillation at the presence of noise. The presented below results of the offered algorithm confirm effective improving accuracy estimation of the required parameters for a given period of time at the presence of constantly changing dynamic parameters of the power system.
MAIN PART
Nowadays, in the dispatch centers of the System operator, 24-hour monitoring of the operating parameters processed by the SCADA software package is carried out in a constant mode. SCADA provides RMS measurements of current and voltage once a second. As a result, the SCADA system sees a lot, but not everything of all the information that is needed to analyze constantly changing dynamic conditions of the power system. But analysis and observation of transient phenomena require faster calculations.
In connection with this fact Wide Area Measurement System (WAMS) has been developed. This system is being actively implemented, assuming the use of special devices - Phasor Measurement Units (PMU). The PMU devices determine vectors (i.e., RMS values and phase angles) of voltage and current, they are used to calculate powers, and other operating parameters of the power system. Also, PMU must measure the frequency for each phase, the rate of change of frequency and all parameters of the positive sequence of electrical parameters. All the measurements are synchronized in time using the global positioning system (GPS) or GLONASS with a synchronization accuracy of at least 1 ^s. Thus, in comparison with SCADA, WAMS systems provide global static and dynamic observation of
The main algorithms for evaluating the
the vectors of the operating parameters of power systems, synchronized in time, with the possibility of automated processing of results.
The main criteria for selecting installation locations were the voltage and capacity of stations and substations, as a rule they were: turbine generators of nuclear power plants and thermal power plants with the capacity of 200 MW and more; hydrogenerators for hydroelectric power plants 100 MW and more; autotransformers installed in the controlled section (from the side of the highest voltage class); power lines of the highest voltage class of 220 kV and even above.
The quality and dynamics of the information received with the help of PMU arouses attention in their application at other voltage levels, in distribution networks, as well as in distributed power generation, i.e. when producing energy at the level of the distribution network or on the side of the consumer connected to the network. But in order to realize the advantages the distributed electricity generation brings, it is necessary to ensure the stability of operation, regulation and maintenance of normal operating condition, etc. Accordingly, new problems may appear in the planning, monitoring, control, management and protection of the distribution network, which will require constant analysis of electrical parameters in conditions of increased dynamic variability of the system [2]. It is also shown that these information problems can be solved by using PMU. In foreign literature, you can find the term for the PMU devices installed in distribution networks - a mi-croPMU (^PMU).
The main innovation in comparison with traditional PMU is a higher accuracy of phase angle (±0.01°). Firstly, this difference is explained by the presence of higher levels of harmonics in comparison with high voltage networks [2]. And then smaller power flows, respectively, and shorter transmission lines along which these power flows. The traditional PMU with an estimation error of ± 1° cannot provide the required accuracy for assessing the operation state for distributed power generation. Also requirements are imposed on the microPMU with increased noise immunity in comparison with a high-voltage PMU. For widespread use in distribution networks, microPMUs should be significantly cheaper than traditional ones.
In [9], the most frequently mentioned algorithms used in PMU implementation are listed in the literature.
Table 1.
1 Modified zero-crossing method
2 Prony analysis
3 Newton method
4 Kalman filter
5 Discrete Fourier transform, full-cycle DFT - FCDFT
6 Smart discrete Fourier transform SDFT
7 Wavelet approach
There is also another algorithm - TEO(Teager Energy Operator [10-13]). The calculation algorithm is based on the properties of a sinusoidal oscillation, using three consecutive samples:
Ek = x\ + xk+1xk-1 = A2sin2(ti) « A2a2, (1)
where xk = ^cos(Hk +0) - analyzed signal; xk+1 — csignal at sampling time k + 1; xk-1-- signal at sampling time k - 1.
All the algorithms that use the estimation of vector parameters according to formulas 1 and 2 give an accurate and fast result if there is no noise in the input signal. An example is shown in Fig. 1.
Fig. 1. Error in frequency estimation by the TEO method
In fig. 1, you can see that the TEO algorithm requires only three samples to estimate the frequency of the test signal when the amplitude varies step-by-step. The value of changes is shown in relative units in this scheme.
The speed and accuracy of the estimation is provided for all operating parameters with all options of their changes.
The verification of using the algorithms shows that algorithms based on the estimation of operating parameters by formulae (for example, 1, 2, TEO, ...) are sensitive to the presence of noise in test signals.
Fig. 2. Illustration offrequency calculation based on the intersection of the zero-level sinusoidal voltage (ua0)
and using the Fourier transform (uaF).
Comparison of noise immunity of the algorithms for calculating estimations of operating parameters
Figure 2 shows the results of using the zero-crossing and DFT methods when the frequency of the test signal is estimated in the ideal situation and at the presence of noise. The frequency varies step-by-step from 45 up to 55 Hz with a step of 1 Hz [4, 5], when the amplitude is equal to the nominal value.
Fig. 2 shows the frequency measurement error. The standard signal is subtracted from the measured frequency values. The transient measurement phenomenon defines a boundary between different frequency values, when the frequency swing occurs. This is well illustrated in Figure 2.a). The figure shows that the zero-crossing method (ua0) practically does not have any frequency measurement error compared to the DFT algorithm (uaF), in which the frequency measurement error increases when the measured frequency deviates from the nominal value of 50 Hz.
As far as it is necessary to verify the measurement devices of frequency under conditions similar to the real power system, fluctuations in the local frequency and voltage of the power system are added to the standard frequency changes. Figure 2 shows the essential worsening of the frequency estimation made by the
zero-crossing method of the sinusoidal voltage. Due to the fluctuation of the test signal the position of the zero-crossing point varies too. It leads to essential errors (up to units kHertz). The virtual measurement based on the Fourier algorithm gives a great deal less errors (fig. 2b).
Figure 3 shows the errors of the frequency and amplitude at the presence of the white noise obtained by the TEO method and the modified half-cycle discrete Fourier transform (MH_DFT) proposed below. The amplitude of the white noise varies within one percent of the amplitude of the test signal.
The dashed line in all the graphs in Fig. 3 marks the given change of the operating parameter, in this case the amplitude of the test signal. The change is shown in the right axes. In the left axes the estimation error of the frequency and amplitude of the test signal are illustrated.
Fig. 3.
Influence of interference on the parameters estimation in the TEO (green curves) and DFT methods (red curves)
In both examples (fig. 1, 2) the DFT algorithm is shown. It is more stable to the various interference, therefore its use in the modern PMU is widespread. It will be discussed below.
Smart discrete Fourier transform (SDFT), using the basic DFT method, is fully described in [14,15]. In this article, only the frequency estimation is considered, which is calculated according to the SDTF formulae:
where N is the number of components in the Fourier filter formula,
xk, Xk-1, Xk-2 - the output signals of the Fourier filter at sequential time moments.
Though in the less degree, but the SDFT algorithm is also sensitive to the noise in the input signal, because the estimation of operating parameters is produced by
using trigonometric formulae for separate components of the DFT main sum [16].
Testing of the sampling rate influence
Figure 4 shows the frequency estimation error when it varies step-by-step from 45 up to 55 Hz at different sampling rates.
An increase in the sampling rate is proposed for a more accurate calculation of synchronized vectors of inprt(:sigHa£)/ift-fle;tworks with distributed generation [8]. But its realization depends on using algorithms and it needs to be checked. Figure 4 shows the increase of the frequency estimation error with increasing the sampling rate of the test signal when the frequency of the test signal at the presence of noise varies step-by-step from 50 up to 45 Hz. This fact is explained that the informational change in the signal is equal to the decrease in the ratio of the signal power to the interference power with a constant sampling interval at the decrease in the sampling interval with a constant noise.
Fig. 4. Influence of the sampling rate on the operation of the SDFT algorithm (smart discrete Fourier transform)
for one and the same noisy input signal.
Next, several variants of the implementation of discrete Fourier transform algorithms are compared: the classical DFT algorithm [6], with a window function with a duration of one power-frequency period (full-cycle DFT - FCDFT) and a half-cycle DFT, i.e. with a window function with a duration of half-cycle DFT (HCDFT) [17-19].
Characteristics of the proposed algorithm
The modified DFT algorithm was developed with the possibility of using it in distributed power generation, i.e. the algorithm should provide maximum accuracy and speed.
To accelerate the speed of the algorithm it is logical to use the half-cycle DFT algorithm. In literature we come across the facts of the DFT using with a window function of half-cycle period of nominal frequency.
Fig. 5. Algorithm structure in the DFT methods of full-and half-periodic processing Windows data [17].
Compared with FCDFT, HCDFT shows worse filtering properties, especially for the constant component, interharmonics and harmonic interference effect. The main feature of the known DFT algorithms with any window function is shown in Fig. 5: after the frequency estimation of the input signal, the sampling rate is adjusted. It introduces some additional delay in estimation the operating parameters of the network.
The proposed modified DFT of the half-cycle (MH_DFT) doesn't require adjustment of the sampling
rate and provides suppression of the aperiodic component.
Figure 6 is a block diagram explaining all the actions necessary in estimating the input signal parameters at any input signal frequency values. It's necessary to keep in mind because the non-nominal frequency is the cause of the largest errors in the parameter estimation.
Fig. 6. Block diagram of the proposed modified half-period DFT algorithm (MH_DFT) with a window function
with duration of half standard frequency period.
Suppression of the aperiodic component occurs by using of various functions for estimating the value of the constant component or by differentiation of the input signal.
Some tasks require suppression of the constant component. For this purpose, the parameters of the aperiodic component are estimated in any way. Then these parameters are used in the future. Or the aperiodic component is removed at differentiation of the input signal, block 1.
At point 2 of the block "Preliminary assessment of frequency" when the frequency of the input signal deviates from the nominal value, used in the Fourier filter, oscillatory changes are observed. Then the adjustment of the sampling rate usually occurs (fig. 5). It is proposed to estimate the number of components in the Fourier filter formula by using the obtained frequency estimation, that is, to determine the number of signal samples corresponding to half of the period of the input signal frequency. "The frequency correction, calculating the period" is realized in the block.
There are three various methods for estimation of frequency correction: theoretical, empirical and the methods of optimal approximation of functions.
The theoretical method supposes using Window Discrete Fourier Transform to obtain exact values of corrective coefficients. In this situation the length of the window fixed and equal to 0.02s. The values of phase, frequency and amplitude are estimated for the input sinusoidal signal with the frequency that differs from the nominal value. The estimation formulae produce the
corresponding corrective coefficient formulae for the necessary parameters of the input signal. The method is complicated. Besides, it can also be shown, that the measurement error significantly increases when we use exact formulae for processing the noisy input signal.
The empirical method is based on consideration of the properties of experimentally obtained primary estimations for the necessary parameters of the input signal. According to [4,5], one of the scenarios for main tests PMU, class M inder static conditions is simulation of algorithm operation, when the frequency varies from 45 up to 55 Hz. For example, fig 7, a) shows the primary estimations of the frequency for phase voltages, when this parameter varies swinging from 50 up to 45 Hz and when the half-cycle DFT without additional correction is used (window length is equal to half cycle of the standard frequency). There are sinusoidal oscillations around the frequency equal to 45 Hz (constant shift) with the amplitude of 5 Hz, the frequency of 2 * 45 Hz and the corresponding phases (fa, fb, fc, Fig. 7, a)). Summation of the frequency estimations of three phases allows to obtain with a high accuracy the primary frequency estimation for voltage of the positive sequence f1. It has an oscillatory measurement error that is lower than 0.02 Hz across 0.01 s (half period) after the frequency of the input signal changes swings. The obtained frequency estimation makes it possible to define the number of discrete samples, corresponding to the period of the new frequency value of the input oscillation.
Fig. 7. The MHDFT possibilities when the frequency estimation of the positive sequence. Here and then the "s"
index in variables means smoothing fluctuations.
Averaging (smoothing) the oscillatory error over the period of its oscillations makes it possible to obtain a high accuracy of estimations of f1s (fig. 7, c)). The final measurement error is also oscillatory error with amplitude less than 0.0002 Hz, obtained approximately 0.02 s (one period) after the start of the disturbance. This error is significantly less and the result is obtained faster, whereby the Standard [4, 5] requires for any class of PMU.
The primary estimations of amplitude and phase for the input signal have the same properties, which described above.
The corrective coefficients are formed depending on the corrected frequency estimation. Multiplication the current amplitude (red curve, fig. 8, a) estimation (sample ii) by the coefficient kfa(ii)=fo/fas(ii) (ii is current estimation sample) significantly increases the accuracy the obtained estimation of the amplitude. The more accurately the frequency was determined, the more accurately the amplitude value was obtained (fig. 8, a).This regularity can be traced the phase estimation is occurred, too (fig. 8, b).
When the frequency of the input signal is equal to the nominal value of the standard frequency (Fourier filter setting), these coefficients are ones.
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Fig. 8. Comparison of accuracy of FCDFT algorithms (blue characteristics), HCDFT (red full lines) and MHDFT (red dotted lines) when the test signal frequency changes from 45 up to 55 Hz.
The dashed line in all graphs in Fig. 8 marks the specified change in the operating parameter - the frequency of the test signal, the change is shown in the right axes. The blue characteristics in both figures are based on amplitude estimation by the DFT algorithm with a window function with duration of one standard frequency period. The red characteristics are related to the amplitude and phase estimations by HCDFT with duration of window function is half cycle of standard frequency. The dotty red characteristics are obtained by correction of estimations with considering of the preliminary frequency estimation of the input signal by MH_DFT.
The standard [4,5] requires a comprehensive illustration of the parameter's estimations of the input signal
in all range of variation these parameters. An example of this illustration is shown in fig. 8. Fig 8 shows the amplitude and phase estimation measurement errors of the synchronized voltage vector (fig. 8 a), b)), when the test signal is supplied. These separate errors allow to estimate the total vector error (TVE) is the value, that characterized the amplitude and phase deviation of the measured vector from their specified values in the aggregate.
The accuracy of received estimations of the numerical parameters of the test signals can be estimated when it is provided a comparison of these signals with the reconstructed signals by the corresponding estimation errors (fig 9). Step-by -step variation from 50 to 45 Hz and from 55 to 50 Hz are considered.
Fig. 9. Illustration the accuracy of the definition of the estimation by the FCDFT algorithm (blue curves) and the MHDFT algorithm (red curves) in the recovery of input sinusoid oscillations according to the estimated numerical characteristics of the sinusoid at two frequency swings, the values of which are shows in the right axis.
In both situations the reconstructed signal by MH_DFT estimations (the red curves) practically always equal to the test signal (the black curves) after 0.01 s. The reconstructed signal by FCDFT estimations (the blue curves) always has a phase shift and the amplitude error, when the frequency is non-nominal. It agreed with the results showed in fig. 8.
The situation is much more complicated when evaluating the parameters of phase oscillations, which are considered separately, without taking into account other phases. Therefore, in this case it is considered the
possibilities and methods of optimal approximation of functions (fig. 10).
The method of optimal approximation uses the supposed functional dependency for estimation of the parameters, defined this dependency. This is the constant shift (45 Hz), the amplitude (5 Hz), the frequency (2*45 Hz) and the initial phase, that depended on initial disturbance. The method requires maximal processing powers and additional time no less than a period of the measured sinusoidal oscillation.
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Fig. 10. The MHDFT possibilities when the estimation voltage frequency of any phase
Figs 10 a), b), c) d) show the using two methods (empirical and optimal approximation) for the frequency estimation of phase voltages, when the frequency of the input signal changes from 50 up to 45 Hz. The curves (1) (3) show the constant smoothing of the oscillatory error: 0,05 per period (fas, the single smoothing), less than 0,001 Hz for one and a half period (fass, the double smoothing), and, as result, up to error of 0,00001 Hz for two periods of the nominal frequency (fasss, the triple frequency). The curve (4) (fa-opt)
shows the frequency estimation obtained by optimal approximation method.
It is interesting to combine the offered algorithm with the using the SDFT recommendations. The result is shown in fig. 11. Without the presence of noise, when the SDFT calculations added, the FCDFT algorithm provides the high frequency estimation accuracy of phase voltages after 22 ms. And non-modified half-cycle HCDFT gives the same result after 12 ms (fig. 11, b).
Fig. 11. The HCDFT and FCDFT algorithms at the presence of noise before SDFT processing (nand □ curves, respectively) and after the using of the SDFT processing (□ and □) curves); curve □- standard frequency change
By changing the scale (fig. 11, b), it is possible to observe the high accuracy of the frequency estimation under ideal signal processing conditions.
Fig. 12.
Effect of noise in the input signal on the accuracy of the MHDFT algorithm with window length is 10 ms
Fig. 12 shows: the curve 1 - the standard frequency variation, the curve 2 - the using of the half-cycle Fourier algorithm without correction and SDFT application. The group of curves 3 shows the application result of SDFT estimations to the HCDFT algorithm without the presence of noise in the input signal
(thin black curve) and at the presence of noise (red dotted curve). It observed significant value of the frequency measurement error. Further smoothing (averaging) of the obtained estimation per period of the oscillatory error allows to essential increase the accuracy of estimations. The result is the black dotted curve (3). By
changing the scale (fig. 12, b), the error of the final estimation is visible. The full curve 4 was obtained the using of the MH_DFT algorithm with single smoothing without application SDFT formulae. The using double
smoothing (the dashed curve 4) provides the frequency estimation error of phase voltage less than 0,001 Hz already after 30 ms.
Fig. 13. Effect of noise in the input signal on the accuracy of the FCDFT algorithm with window length is 20 ms
Fig. 13 shows: the curve 1 - the standard frequency variation, the curve 2 - the frequency estimation of the input signal obtained by the FCDFT algorithm without correction and application the SDFT formulae. The dotted blue curve 3 (the application result of the SDFT algorithm at the presence of noise) is laid over the thin black curve, that corresponded to the frequency estimation by the SDFT algorithm without the presence of noise. The using of noise is suppressed by smoothing (averaging) of the obtained estimation during the calculated duration of oscillations. The result is the black dotted curve (3). By changing the scale (fig. 13, b), the error of the final estimation is visible. The full curve 4 was obtained the using of the FCDFT algorithm with single smoothing without application SDFT formulae. The using double smoothing (the dashed curve 4) provides the frequency estimation uniform error of phase voltage less than 0,001 Hz already after 60 ms.
CONCLUSION
1. PMU, that applicated in power distributed systems, must provide high accuracy of the obtained estimations for characteristics of the operating parameters and have increased noisy immunity.
2. The work of two PMU algorithms is compared at the presence of white noise, when the frequency estimation is occurred. It shows, that the PMU algorithms, based on estimation of the sinusoidal oscillation parameters according to exacts trigonometric formulae, have large measurement errors, when the input signals are noisy. The PMU algorithms, based on different variants of DFT, have essential lower errors at the same compared conditions.
3. It shows the SDFT application for two algorithms with window length is 10 ms and 20 ms. Without
the presence of noise, when the SDFT calculations added, the FCDFT algorithm provides the high frequency estimation accuracy of phase voltages after 22 ms. The MH_DFT algorithm gives the same result after 12 ms (fig 12, b).
4. At the presence of noise in the input signals the using of double smoothing in MH_DFT with window length is equal to 10 ms (fig. 12, b) provides the frequency measurement error of phases voltages less than 0,001 Hz already after 30 ms. The double smoothing using in the FCDFT algorithm with window length is equal to 20 ms gives the similar measurement frequency error of phase voltages less than 0,001 Hz after 60 ms. The SDFT algorithm has significantly larger error in this situation even after smoothing.
5. The developed algorithm proposes available PMU decision to expand the capabilities of observation and control the power system.
REFERENCES:
1. Jason Sexauer, Pirooz Javanbakht, Salman Mohagheghi. Phasor Measurement Units for the Distribution Grid: Necessity and Benefits // Ref. 2013 IEEE PES Innovative Smart Grid Technologies Conference (ISGT) pp 1-6;
2. Alexandra von Meier [and others]. Precision Micro-Synchrophasors for Distribution Systems: A Summary of Applications // Ref. IEEE TRANSACTIONS ON SMART GRID, vol. 8, no. 6, november 2017
3. Dinesh Rangana Gurusinghe [and others]. Implementation of Smart DFT-based PMU Model in the Real-Time Digital Simulator // Conference: The International Conference on Power Systems Transients (IPST) At: Seoul, Republic of Korea June 2017
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5. IEEE Std C37.118.2-2011 - IEEE Standard for Synchrophasor Measurements for Power Systems.
6. Phadke, A. G. and Thorp, J. S. Synchronized Phasor Measurements and Their Applications, Springer, 2008.
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8. Alexandra von Meier, Reza Arghandeh. Every Moment Counts: Synchrophasors for Distribution Networks with Variable Resources // California Institute for Energy and Environment, University of California, Berkeley
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15. Smart DFT Based PMU Prototype, Isidora Radevic, Matija Naglic, Omar Mansour, Dennis Bi-jwaard, Marjan Popov, - 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA)
16. Modified DFT-Based Phasor Estimation Algorithms for Numerical Relaying Applications, K. M. Silva , F. A. O. Nascimento, IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 33, NO. 3, JUNE 2018
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18. An Improved Algorithm to Remove DC Offsets From Fault Current Signals, S.A. Gopalan, IEEE, Y.Mishra, V.Sreeram, H.Ho-Ching Iu, - IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 32, NO. 2, APRIL 2017
УДК 614.8.07/08:614.876 TOPICAL PROBLEMS OF MODELING MANAGEMENT SOLUTIONS IN EMERGENCY
SITUATIONS
Tikhonov M.
candidate of technical sciences, associate professor,
Sokolova A. master of technical sciences, Sokolova S. Doctor of Philosophy Ministry of Emergency Situations of the Republic of Belarus
Minsk
АКТУАЛЬНЫЕ ПРОБЛЕМЫ МОДЕЛИРОВАНИЯ УПРАВЛЕНЧЕСКИХ РЕШЕНИЙ В
ЧРЕЗВЫЧАЙНЫХ СИТУАЦИЯХ
Тихонов М.М.
кандидат технических наук, доцент Соколова А.А. магистр технических наук, Соколова С.Н.
доктор философии
Университет гражданской защиты МЧС Республики Беларусь
г. Минск
Abstract
In the article, the authors pay special attention to the issues of algorithmicization and modeling of management decisions, as well as a software product, which is necessary for training specialists of the Ministry of Emergency Situations in the field of protecting the population and territories from natural and synthetic emergencies through the introduction of innovative educational technologies.
