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Original article / Оригинальная статья
DOI: http://dx.doi.org/10.21285/1814-3520-2020-3-649-662
State estimation of a three-phase four-wire secondary distribution network
Yana I. Kuzkina*'**, Irina I. Golub**, Evgeniy V. Boloev**
*Irkutskenergo Engineering Center LLC,, Irkutsk, Russia **Melentiev Energy Systems Institute SB RAS, Irkutsk, Russia
Abstract: A state estimation algorithm for assessing the state of a power delivery network according to the measurement information performed by smart meters is proposed and its efficient use in a real low-voltage three-phase four-wire secondary distribution network demonstrated. Nonlinear state estimation is performed by a method of simple iterations, at each step of which an overdetermined system of linear equations of measurements is solved by the method of weighted least squares. State estimation is performed independently for each phase and the neutral wire; phase voltage estimates relative to the neutral wire are determined according to estimates of the phase wire voltages and the neutral wire relative to the ground. Testing of the method is carried out on the example of a real 11-node main feeder, on the poles of which MIR S-04, MIR S-05 and MIR S-07 single-phase and three-phase meters of Russian production are installed. For the state estimation, information was used on the hourly average power of loads and voltage modules for 576 measurement sections taken from the protocols of an automated commercial electricity accounting system. The high accuracy of the obtained estimates is confirmed by no more than 1.2 V residues between the measured values of the variables and their estimates. Two methods for determining energy losses by estimating voltages - with respect to earth and a neutral wire, respectively - are presented. The possibility of balancing loads by moving single-phase loads of the most loaded phase to a less loaded phase is demonstrated. The calculations performed for a real network show the proximity of variables measured by smart meters to their estimates, confirming the effectiveness of the presented algorithm for assessing the state of the secondary distribution network with explicit consideration of the neutral wire.
Keywords: state estimation, three-phase four-wire secondary distribution network, simple iteration method, neutral wire, voltage phase wire (neutral wire) - earth, voltage phase wire - neutral wire
Acknowledgements: The research was carried out under State Assignment III.17.4.2 (reg. number АААА-А117030310438-1) of the Fundamental Researches of the SB RAS. The authors express gratitude to the regional state unitary energy enterprise Oblkom-munenergo for the information provided for the study.
Information about the article: Received March 03, 2020; accepted for publication May 05, 2020; available online June 30, 2020.
For citation: Kuzkina YaI, Golub II, Boloev EV. State estimation of three phase four wire secondary distribution network. Vestnik Irkutskogo gosudarstvennogo tehnicheskogo universiteta = Proceedings of Irkutsk State Technical University. 2020;24(3):649-662. https://doi.org/10.21285/1814-3520-2020-3-649-662
УДК 621.311
Оценивание состояния трехфазной четырехпроводной вторичной распределительной сети
© Я.И. Кузькина***, И.И. Голуб**, Е.В. Болоев**
*ООО «Инженерный центр «Иркутскэнерго», г. Иркутск, Россия
**Институт систем энергетики им. Л.А. Мелентьева СО РАН, г. Иркутск, Россия
Резюме: Цель - показать эффективность использования в реальной трехфазной четырехпроводной вторичной распределительной сети низкого напряжения предлагаемого в работе алгоритма оценивания состояния сети по информации об измерениях, выполняемых интеллектуальными счетчиками. Нелинейное оценивание состояния производится методом простых итераций, на каждом шаге которого переопределенная система линейных уравнений измерений решается методом взвешенных наименьших квадратов. Оценивание состояния выполняется для каждой фазы и нейтрального провода независимо, оценки фазных напряжений относительно нейтрального провода определяются по оценкам напряжений фазных проводов и нейтрального провода относительно земли. Тестирование метода проводится на примере реального 11 -узлового магистрального фидера, на опорах которого
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):649-662
установлены однофазные и трехфазные счетчики МИР С-04, МИР С-05 и МИР С-07 российского производства. Для оценивания состояния использовалась информация о среднечасовых мощностях нагрузок и модулей напряжений для 576 срезов измерений, взятая из протоколов автоматизированной системы коммерческого учета электроэнергии. Высокую точность полученных оценок подтверждают не превышающие 1,2 В остатки между измеренными значениями переменных и их оценками. Представлены способы определения потерь энергии по оценкам напряжений как относительно земли, так и относительно нейтрального провода. Показана возможность симметрирования фазных нагрузок перемещением однофазных нагрузок наиболее нагруженной фазы в менее нагруженную. Проведенные для реальной сети расчеты показывают близость измеренных интеллектуальными счетчиками значений переменных к их оценкам, что подтверждает эффективность представленного алгоритма оценивания состояния вторичной распределительной сети с явным учетом нейтрального провода.
Ключевые слова: оценивание состояния, трехфазная четырехпроводная вторичная распределительная сеть, метод простых итераций, нейтральный провод, напряжение фазный провод (нейтральный провод) - земля, напряжение фазный провод - нейтральный провод
Благодарности: Работа выполнена в рамках государственного задания 111.17.4.2 (рег. № АААА-А17-117030310438-1) фундаментальных исследований СО РАН. Авто-ры выражают благодарность ОГУЭП «Облком-мунэнерго» за предоставленную для исследования информацию.
Информация о статье: Дата поступления 03 марта 2020 г.; дата принятия к печати 05 мая 2020 г.; дата он-лайн-размещения 30 июня 2020 г.
Для цитирования: Кузькина Я.И., Голуб И.И., Болоев Е.В. Оценивание состояния трехфазной четырехпроводной вторичной распределительной сети. Вестник Иркутского государственного технического университета. 2020. Т. 24. № 3. С. 649-662. https://doi.org/10.21285/1814-3520-2020-3-649-662
1. INTRODUCTION
In recent years, there have been many works aimed at solving the problem of state estimation (SE) of primary distribution networks (DNs) of medium voltage, as well as secondary low voltage DNs, illustrated by examples of test networks. Such examples of three-phase four-wire primary and secondary DNs, containing information on the network topology, including equivalent circuit element and loads parameters, are given in [1]. Although four-wire primary DNs are widely used in contemporary electricity distribution systems worldwide, Russian electricity networks rarely use a four-wire configuration. Test information about the secondary network parameters is important when developing programs for state estimation, calculating flow distribution and analysing DN modes.
The effectiveness of the developed algorithms can be proved by testing them on real networks combining network parameter information with carried-out measurements. In the present work, the SE of a real secondary three-phase four-wire DN according to smart meter measurements is illustrated by the example of a main feeder (Fig. 1), whose phases are connected to 24 private houses with single-phase and three-phase loads. The ac-
counting of domestic energy consumption at the properties is carried out by means of MIR S-04 and MIR S-05 smart three-phase and single-phase meters installed on the feeder poles, with the total energy entering the feeder measured by a MIR S-07 balanced three-phase meter [2]. In Fig. 1 the phases of connecting loads, determined according to the results of a special study, are indicated next to the house numbers [3-5]. In addition to energy measurements, MIR meters allow interval measurements of average active and reactive power values, as well as average values of voltage modules, to be carried out. The work used information obtained from the protocol of an automated system for commercial accounting of power consumption (ASCAPC) on hourly average measurements of capacities and voltage modules in the phases of the main feeder over a period of 24 days.
In contradistinction to high voltage networks, the most important distinguishing characteristics of a DN are as follows: operation of the network in radial mode; asymmetry due to imbalance of phase loads, which can be single-phase, two-phase and three-phase; excess of inductive resistances by active resistances of communication lines; equal degree of voltage dependence, both on active and reactive power. In order to take into ac-
650
ISSN 1814-3520
count the asymmetry of the secondary DN characteristics, a three-phase four-wire model is required.
One of the most complete models of a three-phase four-wire DN, referred to by many researchers, is presented in [6]: in addition to phase wires, this model includes an earth, a neutral wire and its grounding. The forward-backward method [7] used in [6] to calculate the flow distribution in such a network consists in calculating the mode when moving along the network graph, first from the hanging load nodes to the root power node of the network, and then from the root node in the direction of the hanging nodes. While this method is relatively easy to program and provides transpar-
ent results, the most significant limitation of the method is associated with the presence of contours in the network. A number of alternative methods have been proposed for calculating the load flow and SE of four-wire networks [8-10] that allow this limitation [7] to be overcome. The main drawback of these methods is the assumption of the presence of grounding in all nodes of the neutral wire, as a consequence of which the voltage in the neutral wire relative to earth is zero, allowing a four-wire network to be simulated as a three-wire equivalent. The simple iteration approach, used in [11] to calculate load flow in a test three-wire network, also pertains to such methods.
Fig. 1. Main feeder of the secondary distribution network with branches to the houses Рис. 1. Магистральный фидер вторичной распределительной сети с ответвлениями к домам
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):649-662
Fig. 2. Current modules in sections of phase conductors a, b, c and neutral wire n of the 11-node main feeder: 1 and 2 - first and second modes; 3 and 4 - first and second stages of load balancing Рис. 2. Модули токов в секциях фазных проводов a, b, с и нейтрального провода n 11-узлового магистрального фидера: (1) и (2) - первый и второй режимы, (3) и (4) - первый и второй этапы симметрирования нагрузок
In practice, the grounding impedances installed in the load nodes provide non-zero voltage values in the neutral wire. In [6, 12], it is shown that not only the grounding impedances, but also the earth resistance, affects the voltage in the neutral wire, and, consequently, the voltage in the phase wires relative to the neutral wire.
The effect of the imbalance of phase loads on currents and voltages in the neutral wire is illustrated by the example of a three-phase four-wire feeder with a neutral wire, grounded only at the power supply unit. The graphics in Fig. 2, 1 and 2, based on the calculation of the flow distribution for the two modes of the 11-node three-phase four-wire feeder [5], show that the current modules in the neutral wire will increase if the asymmetry of the respective currents rises in phases. The current module in the neutral wire can be equal to and greater than the currents in the phase wires that require its control.
In order to calculate the load flow in the network, a minimal set of measurements was used, including measurements of the active
and reactive power of the loads in phases and measurements of voltages that did not coincide in modules in the phases of the power supply unit; such voltage asymmetry, as follows from [13], arises with an asymmetric phase load in the «star-star with neutral terminal» transformers.
For the first mode, as evidenced by the lower value of the current in the neutral wire, the current asymmetry in the feeder section 18 is less than for the second mode. The large current in the neutral wire in the second mode is determined by the phase current s, which is comparable with the total phase current a and b. For both modes, an increase in current in the final three sections of the neutral wire is associated with a sharp decrease in the phase current b in them.
An obvious way to equalise phase currents is therefore either to move a singlephase load from a more loaded phase to a less loaded one, or to change it using the same principle of connecting a three-phase load to the phases. On the example of the second mode, it is demonstrated that load bal-
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):649-662
ancing leads to a decrease in the current in the neutral wire. In Fig. 2, 3 shows the currents obtained by load balancing when connecting single-phase loads of 10 and 11 houses instead of phase c, for phases b and a; Fig. 2, 4 shows currents following a further reduction in the load of phase c when switching the single-phase load of 23 houses from phase c to phase b.
Fig. 3 shows a vector diagram of currents and voltages for one of the nodes of the four-wire feeder; for simplicity of illustration, the phase voltage vectors relative to the ground and the phase node current vectors are shown to coincide with axes A, B, C of the diagram. Since the sum of phase current vectors that are not coincident in mode is equal to the nodal current I of the neutral wire, the
n '
voltage in the neutral wire relative to the ground Un0 can be calculated on this basis.
By analogy with the illustration in [14] , the difference between the voltage vectors in phases relative to earth UM, Ub0, Uc0 and the voltage vector in the neutral wire relative to
earth U„0 is equal to the voltage in the phase
wires Uan,Ubn,Uc„ relative to the neutral wire
n. From the diagram it follows that phases a and b correspond to voltage modules with respect to the neutral wire smaller than the voltage modules relative to earth, while phase c, which has a minimal current, corresponds to a voltage exceeding the voltage relative to earth.
Fig. 4 presents graphs of voltage modules in phases for an 11-node feeder, comprising a neutral wire relative to earth and voltages in phases relative to the neutral wire. Particular attention is drawn to the behaviour of the voltage in phase b with respect to the neutral wire, increasing in the section 9-11 of the feeder, which is associated with a decrease in the phase current in this section, see Fig. 2. The load balancing discussed above, mainly due to an increase in the load of the phase b, allows not only the current in the neutral wire to be reduced, but also the voltage, see Fig. 4, and allowed us to approximate the voltage in phase b relative to the neutral wire to the voltage relative to earth, as shown in Fig. 4, 5 .
Fig. 3. Vector diagram of nodal currents and three-phase voltages of a four-wire network Рис. 3. Векторная диаграмма узловых токов и напряжений трехфазной четырехпроводной сети
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):649-662
Fig. 4. Voltages in phases relative to earth Ua0, Ub0, Uc0 in phases relative to the neutral wire Uan, Ubn and Ucn, as
well as in the neutral wire Un0 in relation to the earth (1-6) Рис. 4. Напряжения в фазах относительно земли Ua0, Ub0, Uc0, в фазах относительно нейтрального провода Uan, Ubn, Ucn и в нейтральном проводе Un0 относительно земли
The monitoring of special cases of the behaviour of the three-phase four-wire DN mode variables can be carried out based on the measurements of power consumption and voltages coming from smart meters and stored in the ASCAPC protocols using SE programs.
Recently, a number of works have appeared [15-18] related to the SE of a primary three-phase four-wire DN operating system. A significant difference between the simulation of such a network and that of a secondary network, both when explicitly taking into account the neutral wire and its grounding, as well as in three-phase modelling, is the need to take into account the intrinsic and mutual resistances between the phase conductors, between the neutral wire and earth, as well as
the conductivities of the earth itself. The secondary network SE algorithm proposed below, which takes into account neither mutual resistances nor ground conductivities, allows the SE DN procedure to be performed for each phase and neutral wire independently.
2. STATE ESTIMATION OF A THREE-PHASE FOUR-WIRE DISTRIBUTION NETWORK
Here we consider the main stages of the SE procedure of a three-phase four-wire network using information on the network topology, parameters of the elements of its equivalent circuit, as well as measurements carried out by smart meters, including active
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):649-662
zapb-c and reactive z"-'
a-b-c
node power and voltage modules z
In each phase, the same number of nodes is specified, but the number of load nodes in the phases can differ; in transit nodes, zero values of active and reactive node powers are set.
We will write the SE task of a three-phase four-wire network similarly to [6], but without taking into account the current flow in the ground, which is true under the assumption that the neutral wire is grounded only at the power node; the system of measurement equations will be solved by simple iteration [11] consisting of two iteratively repeating steps.
At the first step of the first iteration k = 1, in the nodes i of each phase a, b, c and the neutral wire n according to the meas-
ured values of the active z'
and reactive
za ,c load capacities and the initial voltage values Ua,b,c equal to the rated voltage at the first iteration, [6] pseudo-measurements of
ZjaAcn = zabc,n + jza:b,c,n node currents are
*Jpt
determined:
f~a
Ja i
+ Jz. + ß.
Jpi
Jpi
J + Jz.
Jpi
(1)
'Jk
zn + izn
"Jai J Jpi J ^
( zp — jzQ )/ ua ( % - fzQ )/ u
( zP - i% )/u
-(ZJa + zJb ■ a2 + zJc ■ al) where
al = —1/2+jV^/2 ;
a 2 = —1/2—jylï/2.
When writing equations (1), the capacitive conductivities of the phase wires and the neutral wires to the earth are assumed to be zero.
At the second step of each iteration, a
system of linear measurement equations is solved (2), whose coefficient matrix elements are gaAc and ba,b,c - under the matrices of active and reactive nodal conductivities; Ia,b,c and 0a,b,c - single and zero submatrices; the vector of unknowns, called the state vector, is formed by the longitudinal u\a-b'c,u'tn and
transverse u"aAc, u"n vector components of
phase voltages and voltages in the neutral wire. The right-hand sides of the equations comprise the pseudo-measurements of the nodal currents and the longitudinal components of the nodal stresses, set at the first iteration to be equal to the measurements of the voltage modules.
The mutual resistance between the phase wires and the neutral wire is assumed to be zero, which is true for low-voltage networks, allowing equations (3) to be solved at iterations for each phase and neutral wire separately.
f
a-b-c-n gi ъa
a-b-c-n ga
a-b-c-n 0a
Л
(2)
a b c n
u
V U
a b c n
Jk
Jai —a-b - c - n ZJpi
U i
Jk
In general, system (2), which includes all DN nodes, can be represented in the form of four systems of linear equations written for each of the three phases and the neutral wire:
i Кb-c )
-12
a b c a b c
i r"-b-c )
12 -
a
Z
HU = z; .
;; (3)
(4)
Since systems (3) are overdetermined, they are multiplied by weight coefficients in order to smooth out errors in individual measurements ( ^ b c )—l2.
Although there is no classical solution for overdetermined systems, the solution vec-
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):649-662
tor Uakb,ccan be calculated, allowing the distance between the vectors of the right and left sides to be minimised (3) using the criterion
Г/Т ja,b,c\ r rj a,b,c тта,Ъ,ст ja,b,c\T J (Uk ) = (Zk -H Uk ) x
(r>a,b,c\ 1 / r^a,b,c тта,Ъ,ст та,Ъ,с \ Rv ) (Zk - H Uk )■
(5)
This method is referred to as the method of weighted least squares; the solution Ua'b'c of the minimisation problem can be obtained from the normal system of equations (6) with a square matrix by means of the Gauss method.
b,c\ 1 j ja,b,c \ t ja,b,c _
Uk =
l( zra,b,c\T ( T>a,b,c\ 1 тт a,b,c\
((H ) I Ra ) H )
= (Ha,b,c )T (Rab,c )-1 Z
(6)
Solution Uakb-c provides estimates of
the nodal stress vectors in each phase relative to the ground. The values of the nodal stress vectors in the neutral wire relative to the ground un can also be obtained using the
Gauss method from a system of linear equations with a square matrix (4). An important advantage of this method, which significantly speeds up the SE procedure, is the constancy at the iterations of the structure and values of the elements of the normalised matrix used to determine the stress estimates of all phases.
Estimates of the nodal stress vectors in the phase wires relative to the neutral wire (7) can be defined as the difference between the voltage vectors in the phase wires relative to the ground and the nodal stress vectors in the neutral wire relative to the ground, as illustrated in Fig. 3, 4.
ul = uaa - un
Uh = Ukb - un ■ a1;
Uh = Ul - Un ■ a2.
(7)
The iterative process ends when the maximum difference between the state variables obtained at adjacent iterations does not
exceed the predetermined accuracy of the calculation. Let us designate the estimates of the nodal voltage vectors in the phases and the neutral wire relative to earth as calculated according to UM,Ub0,Uc0,Un0, and the estimates of the voltages in the phase wires relative to the neutral wire as Uan,Ubn,Un.
It should be noted that, for the equality to zero of the estimated currents in the transit nodes below, instead of minimising (5) when calculating vectors of nodal voltages in phases relative to the earth Uakb-c, the SE of the real
network is minimised by the Lagrangian function [19], including criterion (5), written for the pseudomeasurement of currents, and limits [20] at zero currents.
3. ILLUSTRATION OF THE EFFECTIVENESS OF THE PROPOSED METHOD FOR STATE ESTIMATION
We illustrate the SE of the DN using the example of a real 11-node main feeder, in all phases of which node 1 is the supply and node 2 is the transit; in phases a and b, the transit nodes are 6 and 7. Thus, phases a and b each contain 7, while phase C contains 9 load nodes. Three counters are installed on poles 3-5 and 9-11 of the main feeder, two on each of poles 6 and 7, and four counters on pole 8; one three-phase meter is installed on poles 8, 10, 11 and two on pole 3; the remaining counters are single-phase (see Fig. 1). For meters installed in the same node, the average phase measurement values of active and reactive powers and voltage modules are calculated on an hourly basis.
Defined in this way in the 7 load nodes of phases a and b and the 9 nodes of phase c, 576 measurement sections of the hourly average values of the active power of the loads and voltage modules for 24 days, are shown on Fig. 5 and Fig. 6. Measurements of the hourly average reactive power of the loads not presented in the form of graphs are not large, as evidenced by the average power factor for the three phases equal to 0.934.
>
Ol 02 03 04 06 06 07 OS 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
hour
hour
Fig. 5. Measurements of the hourly average load capacities in the 7 nodes of phases a and b, as well as the 9
nodes of phase c for a 24-day period Рис. 5. Измерения среднечасовых мощностей нагрузок в 7-ми узлах фаз а и b, и 9-ти узлах фазы с за 24-дневный период
225
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
hour
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
hour
Fig. 6. Measurements of the hourly average values of stress modules in the 7 load nodes of phases a and b, and the 9 nodes of phase c, carried out over 24 days Рис. 6. Измерения среднечасовых значений модулей напряжений в 7-ми нагрузочных узлах фаз а и b, и 9 узлах фазы с, выполненные в течение 24 сут
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):649-662
Fig. 7. Evaluation of voltage modules Uan, Ubn, Ucn (a - c) with respect to the neutral
wire in 11 nodes of the main feeder for 576 measurement sections Рис. 7. Оценки модулей напряжений Uan, Ubn, Ucn относительно нейтрального провода в 11-ти узлах магистрального фидера для 576 срезов измерений
The limits of change in average total values were determined by analysing the phase load graphs in Fig. 5; for phases a, b and c, these are 4.49-16.44 kW, 6.054-17.48 kW, 9.11-28.0 kW, respectively.
Fig. 7 shows the estimates of voltage modules with respect to the neutral wire Uan,Ubn,Ucn in 11 nodes of the main feeder,
obtained for 576 measurement sections in accordance with the three-phase four-wire network SE algorithm (1)-(7) and taking into account the restrictions on zero currents [20]. On average, for one SE measurement slice, 8 iterations were required for a given accuracy of
the estimates of stresses at adjacent iterations equal to 10-3 V.
The high accuracy of the estimates is confirmed by not exceeding 1.2 V maximum absolute values of residuals equal to the difference between the estimated Ûan,Ûbn,Ûcn and measured U ,U ,U values of the
an' bn' cn
phase voltage modules relative to the neutral
max lU -U , t/, -U, ,\U -U
an an\> bn bn\> cn ci
shown in Fig. 8.
, (8)
Fig. 8. Maximum absolute values of the residues for the three phases Рис. 8. Максимальные абсолютные значения остатков для трех фаз
The SE results were used to determine the load energy losses in the phases and the neutral wire for each of the 576 modes, along with a comparison of two methods for determining the losses. According to the first method AP1, when calculating for each mode currents and power losses (energy losses per hour) in the feeder sections, voltage estimates relative to earth Ua0 ,Ub0 ,Uc0 ,Un0, were used,
while the second method AP2 used voltage estimates for the neutral wire to determine currents and power losses Unn,Ubn, Unn .
The total losses for 576 modes, calculated by the first method, as the sum of the losses in the phase wires and the neutral wire, coincide with the losses obtained in the second way, as the sum of the losses in the phase wires:
AP1 = APa 1 + APb 1 + APc 1 + APn 1 =
=259.364 + 125.506 + 395.899 + 86193 = = 866.962 kW ■ h;
AP2 =APa 2 +APb 2 +APc 2 = = 236.079 + 108.3H + 522.506 = = 866.962 kW ■ h.
Another confirmation of the coincidence of the results of determining the hourly losses in two ways is shown in the Fig. 9 diagrams of areas having accumulation, which for each hour of the day demonstrate the contribution of both individual components of hourly energy losses, as well as their sum. As follows from Fig. 9, the upper graphs of both diagrams, which correspond to the total values of hourly energy losses, match exactly.
T-4-T-4-T-T-4-T-T-4-CMCMCMf\|CM
hour 2
Fig. 9. Results of determining hourly energy losses over the course of a day: 1 - AP1; 2 - AP2 Рис. 9. Результаты определения часовых потерь энергии в течение суток: 1 - AP1; 2 - AP2
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):649-662
4. CONCLUSION
A solution to the SE problem of a real secondary DN using hourly average measurements of loads and voltage modules over the course of 24 days is presented. Despite the forced averaging of measurements of the load powers and voltage modules over several meters, the high quality of the estimates obtained is confirmed by the residuals of the phase voltage estimates relative
to the neutral wire not exceeding 1.2 V.
It is shown that an effective way of balancing the loads, leading to a decrease in the current in the neutral wire and allowing the phase voltage to be estimated relative to the neutral wire to the phase voltage relative to the ground, is to move a single-phase load of the most loaded phase to a less loaded phase.
Two approaches to the determination of electrical energy losses in the secondary RS, giving the same results, are proposed.
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Authorship criteria
Kuzkina Ya.I., Golub I.I., Boloev E.V. declare equal participation in obtaining and formali-zation of scientific results and bear equal responsibility for plagiarism.
Conflict of interests
The authors declare that there is no conflict of interests regarding the publication of this article.
The final manuscript has been read and approved by all the co-authors.
INFORMATION ABOUT THE AUTHORS
Yana I. Kuzkina,
First Category Engineer of the Design Sector, Relay Protection and Automation Service, Irkutskenergo Engineering Center LLC, 67, Ryabikov Blvd., Irkutsk 664043, Russia; Postgraduate Student,
Melentiev Energy Systems Institute SB RAS, 130, Lermontov St., Irkutsk 664033, Russia; e-mail: yaigk@yandex.ru
Irina I. Golub,
Dr. Sci. (Eng.), Professor, Leading Researcher,
Melentiev Energy Systems Institute SB RAS, 130, Lermontov St., Irkutsk 664033, Russia; H e-mail: golub@isem.irk.ru
Evgeniy V. Boloev,
Cand. Sci. (Eng.), Senior Researcher,
Melentiev Energy Systems Institute SB RAS, 130, Lermontov St., Irkutsk 664033, Russia; e-mail: boloev@isem.irk.ru
19. Aschmoneit F.C., Peterson N.M., Adrian E.C. State estimation with equality constraints // 10th Power Industry Computer Application: Conference Proceedings. May 1977, Toronto. Toronto, 1977. P. 427-430.
20. Golub I., Boloev E. Methods of linear and nonlinear state estimation of distribution net-work // Rudenko International Conference on Methodological Problems in Reliability Study of Large Energy Systems: E3S International Web of Conferences. 2018. Vol. 58. 5 р. [Электронный ресурс]. URL:
https://www.e3s-conferences.org/articles/e3sconf/abs/
2018/33/e3sconf_rses2018_03010/e3sconf_rses2018_
03010.html (03.02.2020).
https://doi.org/10.1051/e3sconf/20185803010
Критерии авторства
Кузькина Я.И., Голуб И.И., Болоев Е.В. заявляют о равном участии в получении и оформлении научных результатов и в равной мере несут ответственность за плагиат.
Конфликт интересов
Авторы заявляют об отсутствии конфликта интересов.
Все авторы прочитали и одобрили окончательный вариант рукописи.
СВЕДЕНИЯ ОБ АВТОРАХ
Кузькина Яна Игоревна,
инженер 1 категории сектора проектирования, Служба релейной защиты и автоматики, ООО «Инженерный центр «Иркутскэнерго», 664043, г. Иркутск, бул. Рябикова, 67, Россия; аспирант,
Институт систем энергетики
им. Л.А. Мелентьева СО РАН,
664033, г. Иркутск, ул. Лермонтова, 130, Россия;
e-mail: yaigk@yandex.ru
Голуб Ирина Ивановна,
доктор технических наук, профессор,
ведущий научный сотрудник,
Институт систем энергетики
им. Л.А. Мелентьева СО РАН,
664033, г. Иркутск, ул. Лермонтова, 130, Россия,
Н e-mail: golub@isem.irk.ru
Болоев Евгений Викторович,
кандидат технических наук,
старший научный сотрудник,
Институт систем энергетики
им. Л.А. Мелентьева СО РАН,
664033, г. Иркутск, ул. Лермонтова, 130, Россия,
e-mail: boloev@isem.irk.ru
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):649-662
