# Δ-Σ Methods for Frequency Deviation Measurement of a Known Nominal Frequency Value

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## Abstract

Telecommunication and electric power systems are the two manmade dynamic systems. Reliability of these systems is of great importance to the security and economic well-being of modern society. These systems extend over thousands of kilometers, and their protection and stable operation require enormous investment. To ensure stable and reliable operations many system parameters have to be monitored. One of the most important parameters in power systems is the frequency. Frequency variation can affect system operation considerably. In power systems the supply and demand must be in balance. The frequency of the power source is related to the current drawn by different loads of the grid. Both effects, overload and underload, are undesirable. Thus, it is very important that the frequency of a power system is maintained very close to its nominal frequency. There are several methods proposed in the past for frequency deviation monitoring in power systems. In reference [1] the authors proposed a frequency computation technique suitable for single- or three-phase voltage signals. This method uses a level crossing detector which yields several estimates of the frequency within one cycle. In reference [2], the authors proposed a method for the precise measurement of the difference between two low frequencies. The method is based on multiplying the two incoming frequencies by a large factor. They offer a simple and inexpensive solution for a frequency difference meter. The authors of reference [3] offer three novel techniques for frequency measurement in power networks in the presence of harmonics. All three algorithms—zero crossing, DFT method, and phase-demodulation methods—were tested and verified by simulations. A relatively simple method for measuring and display of the line frequency deviation from its nominal value is proposed in reference [4]. This counting method is based on multiplication of the reference and measured signals. The zero-crossing technique for the purpose of frequency determination of a power signal is presented in reference [5]. The Fourier algorithm is used for digital filtering. The verification of the proposed algorithm is done using a DAQ device in conjunction with LabVIEW. S. J. Arif [6] proposed the use of a zero-crossing detector to produce a pulse train which is combined digitally with a clock of 10 KHz and then passed through a decade counter to give the unique contribution of pulses which are encoded and displayed. This method offers a resolution of 0.5 Hz. The use of a two-arm bridge for frequency deviation measurement is proposed in reference [7]. It is an analog implementation, which uses the principle of orthogonality. This system is sensitive to input amplitude variation and additive noise as well. The use of the two-arm bridge, based on the use of Δ-Σ modulation, is proposed in reference [8]. Orthogonality is based on the use of an analog integrator. Thus, this system is sensitive to input amplitude variation. A DSP technique is proposed in reference [9]. It uses a microcomputer and data acquisition card. It offers an accurate estimate of the order of 0.02 Hz for nominal, near-nominal, and off-nominal frequencies. A ROM-based frequency deviation meter is proposed in reference [10]. It consists of two look-up tables and complex timing and control circuits. It offers near 1 mHz resolution for indoor installation with near constant temperature. The experimental circuit discussed in [11] uses PLL for multiplication of 50 or 60 Hz frequencies by 100. It has a resolution of 0.01 Hz. A programmable frequency meter for low frequencies with known nominal value is proposed in [12]. The percentage of error is 0.174% for 50 Hz. A flexible programmable circuit for generation of a radio frequency signal for transmission is proposed in US Patent No: 2006/011595 A1. This digital modulation scheme uses the well-known principle of carrier orthogonality. It is known in theory and practice as a quadrature modulation. A proposed delta-sigma transmitter consists of a quadrature digital clock generator, two delta modulators, a pair of commutators (multipliers), analog summing amplifier, band-pass filter (BPF), and antenna. Input to the system is N-bit digital word generated by a controller (micro-processor). One-bit commutator is implemented using exclusive OR (XOR) gate. The quadrature clock generator is implemented using master–slave “D” flip-flop (or a four-stage ring oscillator). A 90-degree phase difference needs only to be approximately 90-degrees. A clock frequency of a phase generator must be greater than 1 MHz (even order of GHz) to shift an information in desired radio frequency bandwidth. A transmitted signal is arbitrary, and knowledge of frequency of a source is not required. Thus, this invention is meant for the transmission of information, not for instrumentation, i.e., detection of deviation of a known nominal frequency value. The first essential component for linear processing of a Δ-Σ bit-stream is a delta adder (DA) proposed by Kouvaras [13]. A DA adder is, in fact, a binary adder with interchanged roles of sum and carry-out terminals. The second vital component, used in this chapter, is a rectifying encoder (RE) [14], which can serve as a squaring circuit operator as well [15] [US Patent 9,141,339 B2]. Implementation of the proposed methods is based on the addition and squaring operation on an orthogonal Δ-Σ modulated bit-stream. Thus, operation of these circuits is based on linear and nonlinear operations on orthogonal Δ-Σ bit-streams, in order to detect violation of the orthogonality law when a signal of known nominal frequency value changes.

## References

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