# Power Quality Impact and Its Assessment: A Review and a Survey of Lithuanian Industrial Companies
## 2 Literature Review
### Economic Impact
Economical damage caused by harmonics can be calculated as follows:  
\[D=D_{w}+D_{a}, \tag{2}\]  
where \(D_{w}\)--operational costs associated with increased energy loss; \(D_{a}\)--ageing costs associated with the heating effects. The operating temperature of both motors supplied by non-sinusoidal waveform and transformers feeding non-linear loads is higher due to the increase in eddy currents [25], and the dissipated power is proportional to their frequency:  
\[P=\frac{\pi^{2}}{6 kD}\frac{{B_{p}}^{2}f^{2}d^{2}}{\rho}, \tag{3}\]  
where \(P\)--power lost per unit mass, W/kg; \(k\)--constant equal to 1 for a thin sheet and 2 for a thin wire; \(B_{p}\)--peak magnetic field flux density, T; \(f\)--frequency, Hz; \(d\)--thickness of the sheet or diameter of the wire, m; \(D\)--density of the material, kg/m\({}^{3}\); \(\rho\)--resistivity of the material, \(\Omega\)m [26; 27]. Reliable operation of both power grid and end-use equipment is a key factor in avoiding economic losses. For example, incorrect tripping of relay protection can be caused by either voltage sag (due to voltage drop not only in the network but also in the secondary circuits) or harmonics, which puts consumers at risk of experiencing a supply interruption and consequent outage. Also, as is seen from the results of the survey of Lithuanian industrial companies (Section 4), the failure of a single chain/device of a technological line in most cases causes the stoppage of the entire line: restarting an interrupted technological line is a hard and time-consuming task, as it is necessary to remove the remaining damaged products and materials which are no longer suitable for use. Obviously, sequential technological processes are more common and are more vulnerable than parallel. A sequential process stops if at least one of its elements fails, and a parallel process stops only if all of its elements fail. In mathematical terms, the reliability of a sequential process, which is composed of \(i\) elements and when all of them are dependent, is:  
\[P=\prod_{i}\left(1-P_{i}\right), \tag{4}\]  
while the reliability of a parallel process, when all elements are independent, is:  
\[P=1-\prod_{i}P_{i}, \tag{5}\]  
where \(P\)--probability of continuous process operation (reliability); \(P_{i}\)--failure probability of the process element with index \(i\). Although studies on the impact of PQ on the equipment and its severity assessment algorithms are very important and will have great practical significance (as a part of predictive maintenance and outage management), their execution is full of challenges at least due to the reasons mentioned in [1; 2; 8]--scientific immaturity of the PQ field, deficiency of PQ monitoring systems, hardly predictable nature of PQ phenomena, laboratories required for both artificial generation of PQ phenomena (voltage sags, impulses, etc.) and immunity testing, etc. The ageing process is natural for all equipment and worsens its characteristics (e.g., degrades the dielectric properties of insulation, LED devices experiences lumen deprecation and chromaticity shift, etc. ), and the main goal is to accurately quantify the negative impact of PQ phenomena and their contribution to the acceleration of the ageing processes. Such damage will depend on the type of device, operating conditions, type of PQ phenomenon, its parameters, quantity, exposure time, etc. : for example, in the case of insulation, the task is to evaluate the influence of the number of both voltage transients and swells, their parameters and shape as well as insulation operating conditions (temperature, humidity, mechanical stress, chemical environment, radiation, etc.) on such characteristics as breakdown voltage and loss angle, and in the case of harmonics--the influence of harmonic frequency, sequence, magnitude and exposure duration on vibration of rotating machines, thermal effect and, for instance, its impact on chemical reactions in LED materials.