Energy measurement Energy is one of the most

Energy measurement Energy is one of the most important physical quantities in any branch of science and engineering and especially in electrical engineering. Energy exchange processes lead to the study of electrical networks from the physical point of view and allow an in-depth knowledge of power transfer within the electrical world and between electric and other forms of energy. The definitions of energy and power represent the starting point for any successive study. 1. Energy is the amount of work that the system is capable of doing. 2. Power is the time rate of doing work. Energy can be mathematically defined as the definite integral of the power over a given time interval. The power available in a two-terminal section of a generic electric circuit is given by the product of the voltage across the terminals and the current flowing through the section itself (p = vi). The electric energy (E) flowing through the same section is defined by the integral of the power over the observation interval

Electrodynamic DC - meter Dc electric engine, without metal Aluminium disc with permanent magnet

Ac induction energy meter

Electronic energy metres

preamplifiers

Completely digital energy metres Analog filter

Frequency and Periodic Time measurement T (sec)

Measuring frequency Resonance method: -mechanical -AC RLC circuits measured current Resonance at f_0 frequency

Frequency conversion method Effective U of the pulse signal proportional to frequency of the sinus signal

Digital frequency measurement Reference nown frequency, 10 hz F_r Divided frequency, 1 hz F_r/N T_k = 1/(F_R/N)=N/F_R N_x=F_x*T_k

Error curves, relative error comes from relative error of the ref oscillator (h_x) and relative error of the counting 1/N_x

Extention of the range

Measuring of the periodic time Gate is controlled by the measured signal.

Measuring time – intervall between to pulses Comparator cirquits are give start and stop signal to the gate.

Measuring phase shift from time-intervall What is phase, what is phase shift?

Digital phase-shift measurement