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Network-centric technologies for control of three-phase network operation modes.

Introduction and problem definition. System processes of intellectualization of Ukrainian electric power system are based on the introduction of Smart Grid technologies. The value of this technological transformation is to redistribute the demand for electric power at the moments of maximum load, to reduce additional investments in the reorganization of the power system in order to increase its productivity [1], Multilevel development of the control system of the operation modes of a three-phase network implies the use of the principle of network-centricity--the control of heterogeneous objects of the energy system infrastructure in a single information and communication management space due to the formation and maintenance of a single integrated contextual information environment for all tiers [2].

The concept of network-centric control of the modes of operation of a three-phase network implies the formation and maintenance in the actual state of a single image of the real state in the most understandable and simple form for the whole system. One of the ways to achieve these management objectives is to introduce into the system of operational maintenance of the power system [1], in addition to the distributed subsystem of digital measuring modules, a group of unmanned aerial vehicles (UAV) for monitoring the state of a three-phase network [3], Multi-agent technologies for the collection and transmission of information using UAVs ensure the continuity of acquisition and the relevance of the contextual information image of the three-phase network.

Reactivity, asymmetry and nonlinearity of load in a three-phase system lead to the presence of inactive components of the total power and causes not only additional losses of electricity, but also causes the appearance of pulsations of instantaneous power (IP) the energy non-equilibrium of the system. This causes a decrease in the efficiency, it contributes to the occurrence of dangerous resonance phenomena during the operation of the equipment.

Analysis of recent investigations and publications. The efficiency of the use of electric energy is determined mainly by the creation of such conditions for its consumption, under which the required quality of electric energy supply is provided with minimal losses [4, 5], The quality of electricity supply can significantly affect the power consumption, reliability of the power supply system [6], Exceed of the quality indicators of electric energy above the permissible leads to a reduction in the service life of the equipment, a decrease in its efficiency and a violation of the technological process. Minimization of losses in the 3-phase system is significantly associated with the possibility of reducing additional losses that are caused by consumption nodes with asymmetric and non-linear loads [7].

The goal of investigations is the development of methods for compensating the inactive component of instantaneous power in the presence of an asymmetric load under conditions of network-centric control of the operating modes of a three-phase network.

Main materials of investigations. A 3-wire circuit is a special case of the 4-wire circuit. The introduced definitions of unbalanced (balanced, really balanced) and unbalanced (balanced) modes remain valid for the 3-wire scheme. However, IP of O-balanced processes are used to classify modes.

In a 3-wire circuit:

- the active instantaneous power is fully determined by O-balanced current and voltage processes

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

- the vector IP coincides with its 0-component

q(t) = [q.sub.0](t) = [q.sub.0](t)[e.sub.0]

and is fully determined by [q.sub.0] = [q.sub.0](t) = [[i x u].sup.*] [e.sub.0] algebraic projection of the vector IP onto the unit vector [e.sub.0] which we call a scalar inactive IP.

The decomposition of instantaneous powers into constant and variable components for:

- active IP:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)

where [tau] [greater than or equal to] 0 is the arbitrary number;

- inactive (scalar) IP:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)

classify processes in a 3-wire circuit.

If active IP has no variable (pulsed) component [[??].sub.!](t) [equivalent to] = 0. then mode is balanced. In the general caseB [TEXT NOT REPRODUCIBLE IN ASCII] [??] = p(t) - [bar.p] [not equal to] O and the mode is unbalanced.

As q(t) = [q.sub.0](t) = [q.sub.0](t)[e.sub.0], then the mode:

--at which inactive IP has no variable component [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is balanced;

--at which the inactive IP is identically equal to zero [q.sub.0] (t) [equivalent to] 0 is really balanced.

Note that the symmetric sinusoidal mode is balanced and balanced, but it is really unbalanced if the standard reactive power is not zero.

Decomposition of current in a 4-wire network with the isolation of zero sequence (ZS). For a 4-wire circuit, the decomposition of the current i=[i.sub.0]+[i.sub.!] is valid The basis curves [w.sub.1](t), [w.sub.2](t) of processes in 3-wire circuit which are used for the decomposition of the current components, are complemented by the unit vector of the ZS.

The voltage vector u (measured with respect to an arbitrary reference point) defines two orthogonal O-balanced vectors:

- the vector of phase voltages (using a projector matrix [u.sub.!] = [D.sub.!] x u) and

- the vector of phase-to-phase voltages (using a skew-symmetric matrix [u.sub.[parallel]] = [K.sup.*] x [u.sub.!]).

At each moment of time, the triple of vectors: [w.sub.1](t), [w.sub.2](t) [e.sub.0] forms an orthononnal basis of the space [S.sup.(3)] since the following orthononnality condition is valid:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3)

The orthogonal current decomposition is valid:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)

because i + [i.sub.!] + [i.sub.0], and [i.sub.0][perpendicular to][u.sub.!]; [i.sub.0][perpendicular to][u.sub.[parallel]] then for the decomposition (4) coefficients is valid the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; (5)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; (6)

[i.sub.0](t) = [i.sup.*][e.sub.0]. (7)

Therefore, the decomposition (4) is obtained from the decomposition for the 3-wire circuit

[i.sub.0] = [i.sub.1] + [i.sub.2] = [p.sub.!](t)/[u.sub.!] [w.sub.!] + [q.sub.0](t)/[u.sub.!] [w.sub.[parallel]], (8)

by additional term (7). This gives decomposition of the current for a 4-wire circuit (Fig. 1) in vector-matrix form:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (9)

Decomposition is valid at any voltage [u.sub.0](t) of O-sequence.

As [p.sub.0]=[u.sub.0] x [i.sub.0] then compensation of current of 0-sequence always compensate power of 0-sequence ([i.sub.0]=0 [??] [p.sub.0]=0). The converse is not true. In addition, the part of the vector IP is also compensated.

The proposed basis method expands the vector method [8, 9] for any ZS voltage [u.sub.0](t) and shows that the different theories of the IP of the 3-wire circuit are due to the choice of basis in the 2-dimensional subspace [L.sup.2.sub.!].

Features of compensation by the method of basis functions. Before the compensation, the current in the load network is equal to the current of the source [i.sub.S](t)=[i.sub.L](i)=i(t) and can contain the O-sequence current regardless of the presence ([u.sub.0][not equal to] 0) or the absence ([u.sub.0] = 0) of the voltage displacement.

Compensation of the current of the 0-sequence [i.sub.0] excludes from the source circuit:

- the active IP of the 0-sequence (both its constant and the variable components at any 0-sequence voltage);

- the vector IP component due to the ZS.

Moreover, this procedure is performed without delay in time, since it does not require integration. Integration and compensation of the 0-balanced current component [i.sub.2] (collinear phase-to-phase voltage) which determines the inactive IP, due to 0-balanced current and voltage processes, does not require integration. Compensation of currents [i.sub.0](i) and [i.sub.2](t) is equivalent to compensation of the vector IP and 0-component of active power (if [u.sub.0] [not equal to] 0) and is carried out without delay in time. Compensation of active current:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

is associated with the pulsating component of the active IP and will require integration. In addition, the expansion coefficients determine the connection of the current vector in the [alpha][beta] coordinates of the orthononnal basis in the 2-dimensional subspace and instantaneous powers and can be found without intermediate calculations directly using the measured instantaneous currents i(t) and instantaneous stress values u(t).

Algorithm and implementation of the current decomposition program

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

ss determined by the following procedures:

- calculation of 0-balanced vector of phase and phase-to-phase voltage:

[u.sub.i](t) = [D.sub.!]u(t), [u.sub.[parallel]](t) = [K.sup.*]u(t): (12)

- calculation of active IP and inactive IP of 0-balanced mode:

[p.sub.!](t) = [i.sup.*] [u.sub.!] = [i.sup.*] [D.sub.!] u, (13)

[q.sub.0](t) = [i.sup.*] [u.sub.[parallel]] = [i.sup.*] [K.sup.*] u. (14)

By the Simulink visual programming method the program in the Matlab package is implements. The Matlab package constructs a block diagram of the program using a palette of mathematical model components of various specified electrical power devices. The developed program also implements the current decomposition (15), the first component of which provides power supply with constant power:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (15)

- The simulation results (Fig. 2-5) represent qualitatively the energy processes in the 4-wire circuit of power supply, in particular, confirm (Fig. 2) the theoretical known behavior of the active and inactive current of pq-theory in the sine-wave mode with symmetrical voltage: the active current realizing the active IP and the reactive current realizing the vector IP (second and third pallets from above) contain a harmonic of the 3-order.

The active current which realizes the integral active power:

[i.sub.S] = [u.sub.!] (P/[u.sup.2.sub.!]), (16)

(Fig. 5, bottom pallet) and provides a mode of consumption with current in the source circuit at which:

- current is 0-balanced [i.sub.0](t)[equivalent to]0 [??] q'(t) [equivalent to]0 (middle pallet in Fig. 5);

- the mode is really balanced [q.sub.0](t)[equivalent to]0 (top pallet in Fig. 5);

- the mode is balanced [p.sub.!](t) [equivalent to] [[bar.p].sub.!] = [P.sub.!] (bottom pallet in Fig. 5).

Conclusions. Network-centric technologies for controlling the operating modes of a three-phase network using multi-agent methods for collecting and transmitting information using UAVs ensure the continuity of acquisition and the relevance of the contextual information image of the state of the power system.

The case of the decomposition of instantaneous powers into a constant and a variable component for a 3-wire system is considered. The peculiarities of the power balance for different modes of its functioning are singled out. It should be noted that the symmetric sinusoidal mode is balanced, but it is really unbalanced if the standard reactive power is not zero.

The zero sequence current compensation procedure excludes from the source circuit both the active component of the instantaneous power of the zero sequence and the vector component caused by the zero sequence current. This procedure is performed without delay in time, since it does not require integration.

To solve the compensation problem, it is enough to know the total value of the inactive components of the total power (the value of inactive power) without its detailed elaboration. The creation of a measurement and accounting methodology will require knowledge of the values of each inactive component separately, which necessitates the development of a unified approach to measuring and compensating inactive components of full power and developing a generalized theory of power. Only in a 3-wire system with symmetrical voltage, the elimination of pulsations and the symmetrization of phase conductivities are equivalent problems (the power of pulsations and the power of asymmetry of phase conductivities are equal). With unbalanced voltage these powers are different, their analysis for electrical systems requires the creation of a vector mathematical model of the energy processes of asymmetric regimes of 3-phase systems.

Unbalanced loads, which, in addition to additional losses, lead to asymmetry in the voltage and pulsation of the energy flow, cause much greater harm to the power supply than the symmetry of the reactive phase conductivities (reactive power).

doi: 10.20998/2074-272X.2017.3.10

Received 25.04.2017

UDC 621.311

REFERENCES

[1.] Sokol Y.I., Gryb O.G., Shvets S.V. The structural and parametrical organization of elements of a power supply system in the conditions of network centrism. Electrical engineering & electromechanics, 2016, no.2, pp. 61-64. (Rus). doi: 10.20998/2074-272X.2016.2.11.

[2.] Sokol Y.I., Gryb O.G., Shvets S.V. Network centrism optimization of expeditious service of elements of the power supply system. Electrical engineering & electromechanics, 2016, no.3, pp. 67-72. (Rus). doi: 10.20998/2074272X.2016.3.11.

[3.] Shvets S.V., Voropai U. G. Mariechantal aspects of the use of unmanned aerial vehicles. Bulletin of Kharkiv Petro Vasylenko National Technical University of Agriculture, 2016, no.176, pp. 33-34. (Ukr).

[4.] Denisyuk S.P. Optimization of power consumption for energy saving in systems with converters. Problems of energy saving, 1994, no.2-3, pp. 81-88. (Rus).

[5.] Prakhovnik A.V. Energy saving: unconventional look and a different strategy. Energetic and electrification, 2008, no.4, pp. 30-33. (Rus).

[6.] Shidlovsky A.K., Kuznetsov V.G. Povyshenie kachestva elektroenergii v elektricheskikh setiakh [Increase the power quality in electric networks]. Kyiv, Naukova Dumka Publ., 1985. 286 p. (Rus).

[7.] Zhezhelenko I.V., Saenko Yu.L. Voprosy kachestva elektroenergii v elektroustanovkakh [Issues of power quality in electrical installations]. Mariupol, PSTU Publ., 1996. 173 p. (Rus).

[8.] Tenti P., Mattavelli P., Tedeschi E. Compensation techniques based on reactive power conservation. 7th Int. Workshop on Power Definitionsand Measurements under Non -Sinusoidal Conditions, Cagliari, Italy, July 2006, pp. 84-90.

[9.] Sirotin Yu.A. Unbalanced current and the pulsating current at asymmetrical voltage. Tekhnichna elektrodynamika, 2012, no.2, pp. 42-43.

Y.I. Sokol (1), Doctor of Technical Science, Professor, Corresponding Member of the National Academy of Science of Ukraine,

YuA. Sirotin (1), Doctor of Technical Science, Professor,

T.S. Iierusalimova (1), Candidate of Technical Science,

O.G. Gryb (1), Doctor of Technical Science, Professor,

S.V. Shvets (1), Candidate of Technical Science, Associate Professor,

D.A. Gapon (1), Candidate of Technical Science, Associate Professor,

(1) National Technical University <<Kharkiv Polytechnic Institute>>, 2, Kyrpychova Str., Kharkiv, 61002, Ukraine, phone +38 057 7076551, e-mail: Ierusalimovat@mail.ru, dima12345ml@mail.ru, se_sx@bk.ru

Caption: Fig. 1. Current and voltage decomposition in the 4-wire system ([u.sub.0][parallel][e.sub.0])

Caption: Fig. 2. Oscillograms of total current decomposition onto components

Caption: Fig 3. Oscillograms of vector and scalar IP decomposition onto components

Caption: Fig. 4. Oscillograms of scalar IP and components of vector IP before compensation

Caption: Fig. 5. Oscillograms of scalar IP and components of vector IP after compensation
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Author:Sokol, Y.I.; Sirotin, Yu.A.; Iierusalimova, T.S.; Gryb, O.G.; Shvets, S.V.; Gapon, D.A.
Publication:Electrical Engineering & Electromechanics
Article Type:Report
Date:May 1, 2017
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