# Organization of Control of the Generalized Power Quality Parameter Using Wald’s Sequential Analysis Procedure

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## Abstract

**:**

## 1. Introduction

_{2}emissions per unit of output. The need for this is due to the 2023 introduction of the carbon tax in the European Union, with goods exported to the EU from countries with high levels of atmospheric CO

_{2}emissions subject to the tax. Thus, the more visible the carbon footprint of an industrial enterprise, the less attractive it will be to consumers and investors.

- THDi < 0.1—normal situation, with no faults in the operation of electrical equipment;
- 0.1 < THDi < 0.5—significant pollution of the EPDN by harmonic components, with the danger of increasing the temperature of electrical equipment, which necessitates the transition to larger cross-sections of cable lines, as well as the use of GUs of DG facilities and backup power supply sources of higher capacity;
- THDi > 0.5—a large degree of pollution of the EPDN by harmonic components, which can lead to failures and shutdowns of electrical equipment due to overheating; requires the installation of filtering and compensation devices.

_{rated}within one or two periods of the utility frequency [14].

- Voltage sags (less than 90% of U
_{rated}in at least one phase); - Voltage interruptions (less than 5% of U
_{rated}phase voltage in all phases); - Overvoltages and surge voltages (switching and atmospheric overvoltages).

- To keep the mix and values of regulated PQPs up to date based on periodic review of regulatory requirements and accumulated statistical data, as well as requirements for the efficiency of manufacturing processes and the quality of manufactured products;
- To determine the current operating conditions of the EPDN on-line;
- To carry out continuous automated data collection and processing, analysis, and reporting on PQP deviations from their standard values;
- To create a statistical database on PQPs for information support of the operation of electric power quality management systems;
- To identify critical areas of the EPDN, where deviations of PQPs are the most significant and occur quite often, which requires the arrangement of their continuous monitoring and control;
- To identify (and contain) sources of current and voltage distortions that may cause significant damage, in order to implement measures to change their operating state or power distribution circuit to mitigate the negative impact;
- To make recommendations addressed to duty officers on the implementation of organizational and engineering measures to bring the PQPs to their standard values;
- To determine the most effective ways of load balancing to compensate harmonic components in currents and voltages generated by a nonlinear load with power electronic components;

^{2}R. These two factors accelerate the processes of reducing the rotation speed and the values of free currents in the rotors of IMs [24].

- Centralized data processing, as a rule, requires a large bandwidth of data transmission channels and significant computing power of the central computing device [28].

## 2. Materials and Methods

- The hypergeometric distribution determines the numerical value of deviations of PQPs that made it to the aggregate sample, while taking into account the decision-making during monitoring on deviations, as governed by the “acceptable/not acceptable” principle. The hypergeometric distribution from the outset assumes the process of sampling and the execution of the monitoring procedure;
- The binomial distribution is used when estimating the aggregate timed sample of a PQP (a composite parameter) when each instantaneous value has a probabilistic nature and may or may not correspond to the established standard values. The sampling-based monitoring procedure in the analysis of the binary “conform/fails to conform” relationship is modeled by the binomial distribution;
- Poisson distribution can be applied when investigating the distribution of non-conformities, including those of individual PQPs at certain time intervals. The use of this distribution to analyze the results of sampling-based monitoring of PQPs is implemented in order to mathematically simplify the relations of hypergeometric and binomial models of monitoring procedures;
- The normal distribution, as a rule, describes the cumulative result of monitoring with respect to alternative PQPs, as well as modeling the distribution of quantitative PQPs as a source of continuous random variables [27].

- Positive $(\rho >0)$, when $\left({\sigma}^{2}\left[D\right]/\left\{M\left[D\right]\times \left(1-M\left[D\right]/N\right)\right\}\right)>1$, or ${\sigma}^{2}\left[D\right]>\left\{M\left[D\right]\times \left(1-M\left[D\right]/N\right)\right\}$;
- Negative $(\rho <0)$, when $\left({\sigma}^{2}\left[D\right]/\left\{M\left[D\right]\times \left(1-M\left[D\right]/N\right)\right\}\right)<1$, or ${\sigma}^{2}\left[D\right]<\left\{M\left[D\right]\times \left(1-M\left[D\right]/N\right)\right\}$;
- Equal to zero $\left(\rho =0\right)$, when $\left({\sigma}^{2}\left[D\right]/\left\{M\left[D\right]\times \left(1-M\left[D\right]/N\right)\right\}\right)=1$, or ${\sigma}^{2}\left[D\right]=\left\{M\left[D\right]\times \left(1-M\left[D\right]/N\right)\right\}$.

## 3. Results

- To form a generalized PQP, which can be used to estimate the comprehensive impact of a set of deviations of individual PQPs on the operation of electrical loads of a particular consumer;
- To determine the ranges of acceptable deviations of the generalized PQP, within which no damage occurs to specific consumers. This problem can be solved using simulation data for various circuit/operating state situations and the operating conditions of a particular consumer, including in the main maintenance circuits of the external distribution network;
- To develop a procedure for sampling-based monitoring of PQPs on the basis of the generalized PQP for subsequent decision-making on the implementation of organizational and technical measures to bring the generalized PQP into the acceptable range.

_{j}is binary and takes the value of 1—under unacceptable PQP deviation with respect to the j-th index—or 0—under acceptable PQP deviation.

_{j}for a particular EPDN can be obtained from the results of simulation or monitoring of PQPs in various conditions of EPDN operation over a long time interval as related to its circuit and operation.

**m**is distributed as governed by the binomial distribution with the probability independent of n, the random variable $\xi $, as a linear combination of asymptotically normal quantities ${m}_{j}$ (j = 1, 2, …, k), also has an asymptotically normal distribution with the expected value ${m}_{\xi}$ and variance ${\sigma}_{\xi}^{2}$:

_{ξ}

_{set}.

_{ξ}is the true mean value, is defined by the following equality:

## 4. Discussion

_{1}… I

_{M}); a comparison unit, including comparison circuits (CC

_{1}… CC

_{N}) for each of the PCIs; a multiplication unit, consisting of N multiplication units for each of the PCIs; a group adder unit; a sequential analysis unit; and a memory unit.

_{i}are fed to the input of the sequential analysis unit. The other input of the sequential analysis unit receives arrays of acceptance a(m) and rejection b(m) numbers, whose components correspond to the setpoint values for each step of the sequential analysis procedure. Figure 3 illustrates the decision-making process in the sequential analysis aided by a generalized PQP, where the sequential analysis process ends with assuming the hypothesis of an unacceptable deviation of the generalized PQP from the standard value.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

PQP | Power quality parameter |

EPDN | Electric power distribution network |

GU | Generating unit |

DG | Distributed generation |

RES | Renewable energy source |

ESS | Electricity storage system |

THDi | Total harmonic current distortion |

IM | Induction motor |

DSP | Digital signal processor |

FPGA | Field-programmable gate array |

ASIC | Application-specific integrated circuit |

PQMS | Power quality monitoring system |

SCADA | Supervisory control and data acquisition |

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**Figure 1.**A transient in the EPDN of an industrial enterprise during a near-to-generator three-phase short circuit in the external distribution network.

**Figure 3.**The process of sequential decision-making regarding the deviations of the generalized PQP.

**Figure 4.**Structural diagram of the device that implements the sampling-based monitoring procedure of the generalized PQP.

**Table 1.**Values of the variables used in the sequential decision-making procedure regarding the deviations of the generalized PQP.

m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

ξ | 149 | 151 | 154 | 155 | 148 | 160 | 156 | 154 | 150 |

${\displaystyle \sum}_{i=1}^{m}}{\xi}_{i$ | 149 | 300 | 454 | 609 | 757 | 917 | 1123 | 1287 | 1437 |

a(m) | 55 | 197.5 | 340 | 482.5 | 625 | 767.5 | 910 | 1052.5 | 1195 |

b(m) | 256.9 | 399.4 | 541.9 | 684.4 | 826.9 | 969.4 | 1111.9 | 1254.4 | 1396.9 |

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**MDPI and ACS Style**

Kulikov, A.; Ilyushin, P.; Suslov, K.; Filippov, S.
Organization of Control of the Generalized Power Quality Parameter Using Wald’s Sequential Analysis Procedure. *Inventions* **2023**, *8*, 17.
https://doi.org/10.3390/inventions8010017

**AMA Style**

Kulikov A, Ilyushin P, Suslov K, Filippov S.
Organization of Control of the Generalized Power Quality Parameter Using Wald’s Sequential Analysis Procedure. *Inventions*. 2023; 8(1):17.
https://doi.org/10.3390/inventions8010017

**Chicago/Turabian Style**

Kulikov, Aleksandr, Pavel Ilyushin, Konstantin Suslov, and Sergey Filippov.
2023. "Organization of Control of the Generalized Power Quality Parameter Using Wald’s Sequential Analysis Procedure" *Inventions* 8, no. 1: 17.
https://doi.org/10.3390/inventions8010017