RU2380820C1 - Method for control of static stabilised ac voltage sources, working in parallel for common load - Google Patents

Abstract

FIELD: electrical engineering.

SUBSTANCE: in control method, measured instantaneous voltage and current values of each source are transformed from three-phase abc-system of coordinates into two-phase dq-system of coordinates that rotates with constant frequency Ω. As reference signals, reference signals are used accordingly for d- and q-components of source output voltage. As current parametres, accordingly d- and q- components of source current are used. The first comparison signal is formed by integration of reference signal difference for d-component of source voltage and summary signal, which corresponds to difference of d-components in source currents. The second comparison signal is formed by integration of reference signal difference for q-component of source voltage and summary signal, which corresponds to difference of q-components in source currents. Specified differential voltages are formed, accordingly, as difference of d- or q-components of currents in just two sources. Each difference in formation of according summary signals is used just once. Formation of three-phase control voltage of source is carried out by reverse transformation of d- and q-components of comparison result from two-phase dq-system of coordinates into three-phase abc-system of coordinates.

EFFECT: improved stability of amplitude and voltage phase at common load and increased evenness of load current components distribution among sources in static mode.

1 dwg, 1 tbl

Description

The invention relates to the field of electrical engineering and can be used in the construction of electrical energy generation systems or guaranteed power supply systems, in which to achieve reliable power supply and increase the output power, static stabilized sources of electrical energy are connected in parallel to the total load. The primary sources with unstable input energy parameters in such systems can be an industrial frequency network or a synchronous generator with a variable shaft speed or a battery. The function of stabilizing the parameters of the alternating output voltage is assigned to a static frequency converter (direct frequency converter), which converts the voltage of one usually unstable frequency into the voltage of another, stable frequency, or to static converters that realize the formation of an alternating voltage of one frequency from an alternating voltage of another frequency through the DC link (rectifier-inverter), or to the inverter with the primary source of constant voltage. The required harmonic composition of the output voltage is achieved by turning on the low-pass filter source at the output.

A known method of controlling static stabilized voltage sources of direct or alternating current, operating in parallel to the total load [SU AS 1310974, H02M 7/48. A method for controlling static frequency converters operating in parallel for a common load // E.A. Podyakov, N.I. Borodin, V.V. Ivantsov, S.A. Kharitonov, Yu.E. Semenov, - publ. 05/15/87, bull. No. 18], which consists in generating a signal for setting the output voltage of the converters, measuring the voltage at the total load and generating a negative voltage feedback signal by subtracting the signal proportional to the voltage at the total load from the voltage setting signal, measuring the output current of each converter, forming the reference signal of the load current of the parallel-running converters by summing the signals proportional to the currents of the converters form a signal for setting the current fraction of each pre in the load current is proportional to the reference signal of the load current, with a proportionality coefficient equal to the ratio of the rated current of this converter to the rated load current, a negative current feedback signal is generated by subtracting the signal proportional to the current of this converter from the signal for setting the current fraction of this converter, and form a control signal for each converter by summing the negative feedback signals for current, voltage and a signal for setting a fraction of t ka.

This control method implements proportional control, both by the instantaneous values of currents and by the instantaneous value of the output voltage in each of the parallel sources, and therefore it has static errors in stabilizing the total voltage and the distribution of the load current between the sources when the load changes.

In addition, a known method of controlling static stabilized AC voltage sources operating in parallel to a common load [SU A.S. 966841, H02P 13/16. A method for controlling static frequency converters operating in parallel for a common load / N.I. Borodin, S.A. Kharitonov, - publ. 10/15/82, bull. No. 38], which is the prototype of the present invention and consists in the fact that for each source measure the instantaneous values of the output voltage and current, form the first reference signal - the reference amplitude signal, form the second reference signal - the reference phase signal, generate signals proportional to the first - the amplitude and the second phase stabilized parameters of the output voltage, measure the active and reactive components of the converter currents and loads, for each component form the first and second differential voltages proportional respectively to the difference between the active and reactive components of the load currents and the source, the first differential voltage of the active components is summed with a signal proportional to the first stabilized output voltage parameter - the voltage amplitude of the converter, the formation of the first comparison signal - amplitude comparison signal is carried out by comparing the first reference signal - the amplitude reference signal and the total signal corresponding to the active components, proportions the control voltage amplitude is formed ionically, the second differential voltage — the differential voltage of the reactive components — is summed with a signal proportional to the converter voltage phase, the second reference signal — the phase reference signal — is compared with the second total signal corresponding to the reactive components, and the control voltage phase is proportional to the comparison result, measure the instantaneous value of the load current and form a correction signal equal to the difference of the load currents and and the source, the control signal is formed by summing the control voltage and the correction signal.

This control method also implements proportional control, both by the instantaneous values of currents and by the instantaneous value of the output voltage in each of the parallel sources, and therefore it has static errors in stabilizing the total voltage and the distribution of the load current between the sources when the load changes.

In this control method, as in the previous one, in the formation of differential voltages for the active and reactive components of the converter power and the load, the difference between the active and reactive components of the converter current and the load current reduced to the converter current is used in each i-th source, i.e. divided by the number of converters:

From the expression (1) it is seen that the differences of the component currents can have opposite signs and due to this they can compensate each other. Therefore, the efficiency of regulation with respect to the current parameters decreases, and the uniformity of the loading of sources by the components of the load current deteriorates.

The objective of the invention is to increase the stability of the amplitude and phase of the voltage at the total load and increase the uniformity of the distribution of the components of the load current between the sources in static mode.

This is achieved by the fact that in the known method of controlling static stabilized AC voltage sources operating in parallel for a common load, namely, for each source, instantaneous values of the output voltage and current are measured, the first and second reference signals are generated for the first and second stabilized parameters, respectively output voltage, generate signals proportional to the first and second stabilized parameters of the output voltage, generate signals proportional to which are initial to the first and second parameters of the source currents, the first and second differential voltages are generated for each source, the first differential voltage is summed with a signal proportional to the first stabilized output voltage parameter, the second difference voltage is summed with a signal proportional to the second stabilized output voltage parameter, the first and second comparison signals, according to the result of the comparison, form the amplitude and phase of the control voltage, characterized in that the measured instant The voltage and current values of each source are converted from a three-phase abc coordinate system to a two-phase dq coordinate system rotating with a constant frequency Ω, and the first and second reference signals are respectively used reference signals for the d- and q-components of the source output voltage, in As the first and second current parameters, the d- and q-components of the source current are used respectively, the first comparison signal is formed by integrating the difference of the reference signal for the d-component of the voltage and point and the total signal corresponding to the difference of the d-component currents of the sources, the second comparison signal is formed by integrating the difference of the reference signal for the q-component of the source voltage and the total signal corresponding to the difference of the q-components of the source currents, the first and second difference voltages are formed respectively as the difference d- or q-component currents of only two sources, namely the difference of the component currents of this and other sources or the difference of the component currents of other sources accuracy, and each difference in the formation of the corresponding total signals is used only once, and the indicated formation of the three-phase control voltage of the source is performed by the inverse transformation of the d- and q-components of the comparison result from the two-phase dq-coordinate system to the three-phase abc-coordinate system.

(блок 5) и источник второго эталонного сигнала для q-составляющей выходного напряжения

(блок 6), которые соединены с первыми входами сумматоров (блоки 7 и 8). Вторые входы сумматоров (блоки 7 и 8) соединены с выходами пропорциональных звеньев для d- и q-составляющих выходного напряжения

и

(блоки 9, 10). Третьи входы сумматоров (блоки 7 и 8) соединены с выходами пропорциональных звеньев разностей d- и q-составляющих токов источников

и

(блоки 11, 12). Выходы сумматоров (блоки 7 и 8) соединены с входами интеграторов

и

(блоки 13, 14). Выходы интеграторов соединены с входами обратных преобразователей координат ПК^-1 (блок 15), выходы которых соединены с входами систем импульсно-фазового управления СИФУ_i (блок 16). Выходы систем импульсно-фазового управления соединены с силовыми схемами статических преобразователей частоты ПЧ (блок 17). На силовые схемы преобразователей так же поступают напряжения источников нестабильного напряжения Uc (блок 18). Выходы силовых схем через низкочастотные фильтры Ф_i (блок 19), датчики мгновенного значения фазного тока ДТа, ДТв, ДТс (блоки 20…22) соединены с общей нагрузкой Н (блок 4) и входами прямых преобразователей координат выходного напряжения ПК (блок 23). Выходы прямых преобразователей координат выходного напряжения ПК (блок 23) соединены с входами пропорциональных звеньев

, и

(блоки 9, 10). Выходы датчиков мгновенных значений фазных токов ДТа, ДТв, ДТс (блоки 20…22) соединены с входами прямых преобразователей координат выходных токов ПК (блок 24), выходы которых соединены с входами схем вычитания (блоки 25…30). Выходы схем вычитания (блоки 25…30) соединены с входами соответствующих пропорциональных звеньев

и

(блоки 11, 12).The drawing shows one of the possible structural schemes that implements the proposed method for controlling parallel sources. This block diagram implements the parallel operation of N three-phase static stabilized AC voltage sources IST ₁ ... IST _N (blocks 1 ... 3) operating at a total load N (block 4). Each source includes a source of the first reference signal - for the d-component of the output voltage

(block 5) and the source of the second reference signal for the q-component of the output voltage

(block 6), which are connected to the first inputs of the adders (blocks 7 and 8). The second inputs of the adders (blocks 7 and 8) are connected to the outputs of the proportional links for the d- and q-components of the output voltage

and

(blocks 9, 10). The third inputs of the adders (blocks 7 and 8) are connected to the outputs of the proportional links of the differences of the d- and q-component currents of the sources

and

(blocks 11, 12). The outputs of the adders (blocks 7 and 8) are connected to the inputs of the integrators

and

(blocks 13, 14). The outputs of the integrators are connected to the inputs of the inverse coordinate transformers PC ^-1 (block 15), the outputs of which are connected to the inputs of the pulse-phase control systems SIFU _i (block 16). The outputs of the pulse-phase control systems are connected to the power circuits of the inverter static frequency converters (block 17). The voltage circuits of the converters also receive the voltage of the unstable voltage sources Uc (block 18). The outputs of the power circuits through low-pass filters Ф _i (block 19), sensors of the instantaneous phase current value ДТа, ДТв, ДТс (blocks 20 ... 22) are connected to the common load N (block 4) and the inputs of the direct coordinate converters of the output voltage PC (block 23) . The outputs of the direct transducers of coordinates of the output voltage of the PC (block 23) are connected to the inputs of the proportional links

, and

(blocks 9, 10). The outputs of the sensors of instantaneous values of the phase currents DTa, DTv, DTs (blocks 20 ... 22) are connected to the inputs of the direct coordinate converters of the output currents of the PC (block 24), the outputs of which are connected to the inputs of the subtraction circuits (blocks 25 ... 30). The outputs of the subtraction circuits (blocks 25 ... 30) are connected to the inputs of the corresponding proportional links

and

(blocks 11, 12).

The load H (block 4) may be a resistor or series or parallel connection of a resistor and inductor. Sources of reference signals - for the d-component of the output voltage (block 5) and for the q-component of the output voltage (block 6), for example, parametric stabilizers (see Sources of power supply of electronic equipment: Reference / Edited by G.S. Naivelt. - M .: Radio and communication, 1986). Adders (blocks 7 and 8), proportional links (blocks 9, 10 and 11, 12), integrators (blocks 13, 14) are typical elementary links known from the theory of automatic control (see. Theory of automatic control. Part 1. Linear theory automatic control systems, Edited by A.A. Voronov, Textbook for Universities, Moscow: Higher School, 1977). The inverse coordinate converter PC ^-1 (block 15) implements the transformation of two dq-coordinates of a coordinate system rotating with a constant frequency Ω into a three-phase symmetric system with a constant frequency Ω abc, known from electromechanics and the theory of an automated electric drive (Vazhnov A.I. Transient processes in AC machines. - L.: Energy, Leningrad. Department, 1980) and is a multiplier of analog signals (Timoneev V.N., Velichko L.M., Tkachenko V.A. Analog signal multipliers in a radio electronic device re. - M.: Radio and Communications, - 1982. - 112 p.). SIFU _i (block 16) is a standard pulse-phase control system that implements the vertical control principle (see BCRudenko, V.I.Senko, I.M. Chizhenko. Fundamentals of converting technology. - M.: Higher school, 1980). The power circuit of a static frequency source of an alternating voltage of an inverter (block 17) can be a direct frequency converter or a series connection of a rectifier and an inverter or an inverter (see BC Rudenko, V. I. Senko, I. M. Chizhenko. Fundamentals of converter technology. High School, 1980). The unstable voltage source Uc (block 18) is an industrial network or a synchronous generator with a variable rotor speed or a battery. The power filter F (block 19) is, for example, a single-link LC filter in each output phase or a C filter in each output phase. The instantaneous phase current sensors (blocks 20 ... 22) are, for example, current transformers. Direct PC coordinate converters (blocks 23, 24) implement the conversion of three-phase quantities (currents and voltages) from the three-phase abc-coordinate system to the d- and q-components of the dq-coordinate system rotating at a constant frequency (known from electromechanics and the theory of an automated electric drive) (Vazhnov A.I. Transients in alternating current machines. - L .: Energy, Leningrad., 1980) and are multipliers of analog signals (Timoneev V.N., Velichko L.M., Tkachenko V.A. multipliers of signals in electronic ap Parature. - M.: Radio and Communications. - 1982. - 112 p.). Subtraction schemes (blocks 25 ... 30) are typical elementary units known from the theory of automatic control (see. Theory of automatic control. Part 1. Theory of linear systems of automatic control. Edited by A.A. Voronov. Textbook for universities. - M .: Higher school, 1977).

) и второй (

) эталонные сигналы, представляющие собой постоянные напряжения, для первого (d-составляющая) и второго (q-составляющая) стабилизируемых параметров выходного напряжения, которые поступают на первые входы соответствующих сумматоров (блоки 7 и 8) с положительным знаком. Преобразователи координат ПК (блоки 24 и 23) преобразуют трехфазные системы измеренных синусоидальных величин, соответственно выходных напряжений и токов (блоки 20…22) источников, во вращающуюся с постоянной частотой Ω систему двух d- и q-координат соответственно напряжений (

- первый параметр стабилизируемого напряжения, и

- второй параметр стабилизируемого напряжения) и токов (

- первый параметр токов,

- второй параметр токов), которые представляют собой сигналы постоянного тока. D- и q-составляющие выходного напряжения поступают через пропорциональные звенья (блоки 9 и 10) на вторые входы сумматоров (блоки 7 и 8) с отрицательным знаком. D- и q-составляющие токов источников поступают на входы схем вычитания своих источников с положительным знаком и на входы схем вычитания других источников с отрицательным знаком (блоки 25…30). Схемы вычитания (блоки 25…30) формируют первое (разность d-составляющих токов -

) и второе (разность q-составляющих токов -

) разностные напряжения, которые через пропорциональные звенья (блоки 11 и 12) поступают на третьи входы сумматоров (блоки 7 и 8) с отрицательным знаком. Сумматоры (блоки 7 и 8) формируют разность соответствующих эталонных сигналов и соответствующих суммарных сигналов. Так как все сигналы, поступающие на сумматоры - напряжения постоянного тока, то и формируемые сумматорами напряжения так же являются напряжениями постоянного тока. Эти напряжения поступают на интеграторы (блоки 13 и 14), которые формируют первый (блок 13) и второй (блок 14) сигналы сравнения путем интегрирования разности соответствующих эталонных и суммарных сигналов. Выходные напряжения интеграторов поступают на обратный преобразователь координат ПК^-1 (блок 15), который формирует трехфазную систему управляющих напряжений, амплитуда и фаза которых определяется входными сигналами ПК^-1 (блок 15), то есть результатами интегрирования. В системе импульсно-фазового регулирования (блок 16) управляющие напряжения преобразуются в последовательность модулированных импульсов, обеспечивающих коммутацию силовых ключей схем статического источника переменного напряжения ПЧ (блок 17), преобразующего энергию источника нестабильного напряжения Uc (блок 18) в переменное напряжение стабильной частоты Ω с параметрами, определяемыми управляющим напряжением СИФУ_i (блок 16). Силовой фильтр Ф (блок 19) в значительной мере исключает высокочастотные составляющие спектра выходного напряжения и тока источника, обеспечивая их синусоидальность.The operation of the circuit is as follows. Formed (blocks 5 and 6) the first (

) and the second (

) reference signals, which are constant voltages, for the first (d-component) and second (q-component) stabilized parameters of the output voltage, which are supplied to the first inputs of the respective adders (blocks 7 and 8) with a positive sign. PC coordinate converters (blocks 24 and 23) transform three-phase systems of measured sinusoidal values, respectively output voltages and currents (blocks 20 ... 22) of sources, into a system of two d- and q-coordinates, respectively, of voltages rotating at a constant frequency Ω (

- the first parameter of the stabilized voltage, and

is the second parameter of the stabilized voltage) and currents (

is the first parameter of the currents,

is the second parameter of currents), which are DC signals. D- and q-components of the output voltage are supplied through the proportional links (blocks 9 and 10) to the second inputs of the adders (blocks 7 and 8) with a negative sign. The D- and q-components of the source currents go to the inputs of the subtraction schemes of their sources with a positive sign and to the inputs of the subtraction schemes of other sources with a negative sign (blocks 25 ... 30). Subtraction schemes (blocks 25 ... 30) form the first (the difference of the d-component currents -

) and the second (the difference of q-component currents is

) differential voltages, which are transmitted through the proportional links (blocks 11 and 12) to the third inputs of the adders (blocks 7 and 8) with a negative sign. Adders (blocks 7 and 8) form the difference between the corresponding reference signals and the corresponding total signals. Since all the signals entering the adders are DC voltages, the voltages generated by the adders are also DC voltages. These voltages are supplied to integrators (blocks 13 and 14), which form the first (block 13) and second (block 14) comparison signals by integrating the difference of the corresponding reference and total signals. The output voltages of the integrators are fed to the inverse coordinate converter PC ^-1 (block 15), which forms a three-phase system of control voltages, the amplitude and phase of which is determined by the input signals PC ^-1 (block 15), that is, the results of integration. In the pulse-phase control system (block 16), the control voltages are converted into a sequence of modulated pulses that provide switching of the power keys of the circuits of a static source of an alternating voltage of the inverter (block 17), which converts the energy of an unstable voltage source Uc (block 18) into an alternating voltage of a stable frequency Ω s parameters determined by the control voltage SIFU _i (block 16). The power filter F (block 19) largely eliminates the high-frequency components of the spectrum of the output voltage and current of the source, ensuring their sinusoidality.

Thus, the stabilization of the voltage parameters at the total load and the distribution of the load current between the sources is carried out by regulating the amplitudes and phases of the control voltage of the sources as a function of the measured parameters of the total voltage and the differences in the parameters of the source currents.

The static mode during the parallel operation of N sources is described by the following system of equations, which is equal to zero the sum of the input currents of all integrators:

,

- приведенные относительные эталонные сигналы соответствующих параметров выходного напряжения;Where

,

- given relative reference signals of the corresponding parameters of the output voltage;

,

- относительные значения стабилизируемых параметров выходного напряжения;

,

- relative values of stabilized output voltage parameters;

,

- относительные составляющие токов источников;

,

- relative components of currents of sources;

,

- приведенные коэффициенты, характеризующие долю сигналов, распределяющих токи источников, в результирующем управляющем сигнале по отношению к сигналам, стабилизирующих параметры напряжения на нагрузке;

,

- given coefficients characterizing the proportion of signals distributing the currents of the sources in the resulting control signal with respect to the signals stabilizing the voltage parameters at the load;

,

,

- номинальные действующие значения напряжения и тока нагрузки и модуль номинального значения сопротивления нагрузки;

,

,

- nominal effective values of voltage and load current and module of the nominal value of the load resistance;

,

- в общем случае нелинейные функции от составляющих токов источников, определяющие распределение тока нагрузки между ними;

,

- in the general case, non-linear functions of the component currents of the sources, determining the distribution of the load current between them;

N is the number of sources working in parallel;

i = 1, 2, ..., N is the serial number of the source.

The formation of differences of the component currents of the sources proposed in the method as the formation of differences of the component currents of only two different sources leads to the fulfillment of the conditions:

;

;

Then summing up all the equations for the d- or q-components in expression (2), we obtain:

и

выражения (4) преобразуются к виду:With the same values of the rated power of the sources and, accordingly, the same proportionality coefficients

and

expressions (4) are converted to the form:

The last expressions (5) show that in the parallel operation of the sources, the reference signals of the stabilized parameters of the common voltage are averaged.

Increasing the stability of voltage parameters at a common load in a static mode occurs by integrating the algebraic sum of constant voltages and using the proposed combinations of differences in current parameters. In this case, the voltage parameters at the total load are determined by the averaged values of the reference signals, due to which the stability of the voltage parameters at the total load can be improved while compensating for the spread of the reference signals of different signs, and do not depend on the magnitude of the load.

Since the d- and q-components of the voltage at the total load are connected through linear conversion with phase instantaneous values of the voltage at the total load, the stability of the amplitude and phase of the voltage at the total load is also increased in comparison with the prototype.

Compare the uniformity of the load sources of the load current components in the proposed method and the prototype method. As a criterion for the uniformity of the load, we take the minimum of the sum of the squares of the differences of the component currents of all parallel sources:

As functions of the component currents of the sources, we take a linear combination of the differences of the component currents of all sources, each with its own coefficient.

Then equations (2) turn into systems of linear equations with respect to source currents:

;

;

- вектор-столбец d-составляющих токов источников;Where

- a column vector of d-component currents of sources;

- вектор-столбец q-составляющих токов источников;

- a column vector of q-component currents of sources;

;

; - квадратные матрицы размера N×N, элементами которых являются коэффициенты пропорциональности составляющих токов источников, наличие и значения которых влияют на точность распределения нагрузки между источниками;

;

; - N × N square matrices whose elements are the proportionality coefficients of the component currents of the sources, the presence and values of which affect the accuracy of the load distribution between the sources;

;

- векторы-столбцы правых частей линейных уравнений, каждый элемент которых представляет собой разность соответствующего i-го эталонного сигнала и параметров общего выходного напряжения согласно выражениям (4).

;

- column vectors of the right parts of linear equations, each element of which is the difference of the corresponding i-th reference signal and the parameters of the total output voltage according to expressions (4).

и

разностей составляющих токов и выполнение условий (3) при различных значениях составляющих токов источников приводит к особому виду матриц F^d и F^q, именуемых циркулянтами, в которых каждая последующая строка получается циклическим сдвигом предыдущей строки:Use in the formation of current functions

and

differences of the component currents and the fulfillment of conditions (3) for different values of the component current of the sources leads to a special form of the matrices F ^d and F ^q , called circulants, in which each subsequent row is obtained by cyclic shift of the previous row:

;

;

The diagonal elements of the resulting matrices have a positive sign, the maximum value of the absolute value and characterize the participation in the load distribution of the module's own currents. The off-diagonal matrix elements have a negative sign and characterize the participation in the load distribution of the currents of other modules.

или -

. Первое слагаемое объединим с составляющей тока собственного источника (диагональный элемент матрицы). Второе слагаемое разобьем на N-1 составляющих с коэффициентами, совпадающими по модулю с недиагональными элементами строки, и объединим их с составляющими токов других модулей. В результате составляющие l-го тока из системы уравнений исключаются (в матрице коэффициентов образуется l-й нулевой столбец), а преобразованное l-е уравнение становится линейно зависимым с другими уравнениями системы и его тоже следует из преобразованной системы уравнений исключить.The solution of the system of equations (8), taking into account the selected type of matrices (9) with respect to the component currents, is impossible because their principal determinants are identically equal to zero. Therefore, in the system of equations (8), we perform a change of variables and move from the values of the source currents to the difference of the component currents of the sources relative to any, for example, l-th source. To do this, subtract and add the components of the l-th current to the left side of each equation (8) -

or -

. Combine the first term with the current component of the source (diagonal matrix element). We divide the second term into N-1 components with coefficients that coincide modulo with off-diagonal elements of the string, and combine them with the current components of other modules. As a result, the components of the lth current are excluded from the system of equations (the lth zero column is formed in the coefficient matrix), and the transformed lth equation becomes linearly dependent with other equations of the system and should also be excluded from the transformed system of equations.

The initial system of equations transformed in this way (8) will take the following form:

,

- квадратные матрицы размерности N-1, получаемые из матриц (9) вычеркиванием l-го столбца и l-й строки;Where

,

- square matrices of dimension N-1, obtained from matrices (9) by deleting the lth column and lth row;

,

- вектора-столбцы размерности N-1, получаемые из соответствующих аналогичных векторов-столбцов правых частей исходной системы уравнений (3.12) вычеркиванием l-й строки;

,

- column vectors of dimension N-1, obtained from the corresponding similar column vectors of the right-hand sides of the original system of equations (3.12) by deleting the lth row;

- вектор-столбец размерности N-1 разности d-составляющих токов источников для каждого i-го и одного l-го источников;

- a column vector of dimension N-1 of the difference of the d-component currents of the sources for each i-th and one l-th sources;

- вектор-столбец размерности N-1 разности q-составляющих токов источников для каждого i-го и одного l-го источников;

- a column vector of dimension N-1 of the difference of q-component currents of sources for each i-th and one l-th sources;

;

- разности соответствующих составляющих токов i-го и l-го источников.

;

- differences of the corresponding current components of the i-th and l-th sources.

The main determinant of the systems of equations (10) is already identically non-zero, and the unknowns of these systems of equations of the difference of the component currents can be found. Knowing the differences of the component currents between each i-th and one l-th sources, you can always determine the difference of components between any k-th and m-th sources:

;

;

Then, using the expressions (6), the sums of the squared differences of the component currents are found and the values of the matrix coefficients F ^d and F ^{q are} determined by the criterion of the minimum of these sums.

и

для случая параллельной работы трех преобразователей. Представим эти матрицы в виде:Let us explain the definition of optimal matrix coefficients

and

for the case of parallel operation of three converters. We represent these matrices in the form:

или

. При этом, в соответствие с требованиями (3) и (7), должны выполняться условия равенства нулю сумм коэффициентов каждой строки и каждого столбца матриц:Each matrix element (11) is represented by the difference of the maximum diagonal element and some increment

or

. Moreover, in accordance with the requirements of (3) and (7), the conditions for equality to zero of the sums of the coefficients of each row and each column of the matrices must be satisfied:

Then, when passing from the values of the component currents of the sources to the differences of the component currents relative to the components of the current of the third source, the system of equations (10) will take the following form:

Having solved the system of equations (13) for the d- or q-components of the differences of the currents and determined from (11) the differences of the components of the second and third sources, from the expressions (6) we define:

The obtained analytical dependences of the sums of squared differences of the component currents of the sources contain in the numerator a combination of reference signals, the values of which cannot vary, and uniquely set the parameters of the output voltage during independent operation and vary slightly, and the denominator - a combination of changes in diagonal coefficients. These parameters can vary and determine the structure and parameters of the load-distributing current functions (2). To minimize the functions (14), their denominators should take maximum values.

;

и считать

;

(или

;

), то согласно выражениям (12), получим

;

(или

;

). Тогда матрицы

и

примут вид:An analysis of the behavior of the denominator functions (14), which are second-order functions of several arguments, shows that the maximum of the denominator and, accordingly, the minimum of functions (14) is achieved in the extreme ranges of variation of the increments of their arguments. Therefore, if we accept

;

and count

;

(or

;

), then according to expressions (12), we obtain

;

(or

;

) Then the matrices

and

will take the form:

or

;

и считать

;

(или

то согласно выражениям (12) получим

;

(или

;

). Тогда матрицы

и

примут вид:If accept

;

and count

;

(or

then according to expressions (12) we get

;

(or

;

) Then the matrices

and

will take the form:

or

The obtained matrix structures show that structures using the difference of the d- or q-components of the currents of only two sources have the maximum uniformity of loading of sources during parallel operation, namely, the difference of the component currents of this and other sources or the difference of the component currents of other sources, each difference being formed the corresponding summed signals are used only once.

;

;

;

;

;

.For the prototype method, the values of the corresponding increments of the coefficients of the matrices have values

;

;

;

;

;

.

Below is table No. 1, in which the prototype method is compared, in which the difference signal by the components of the source currents is the difference between the components of the output current of the source and the components of the load current divided by the number of parallel sources, and the proposed method for two, three and four in parallel working sources.

Table number 1 N The initial equations:
Prototype method
The proposed method

,

:
При способе-прототипе
При предлагаемом способеAmounts

,

:
With the prototype method
With the proposed method 2

3

four

и

) в 4 раза выше, чем в способе-прототипе, при работе трех источников - в три раза, а при параллельной работе четырех источников - от двух (первые слагаемые) до четырех (вторые слагаемые) раз.With the parallel operation of two sources, the effectiveness of the proposed method (comparison of values

and

) 4 times higher than in the prototype method, when three sources work, three times, and when four sources work in parallel, from two (first terms) to four (second terms) times.

An increase in the uniformity of the distribution of the load current between the sources is achieved through the use of only two sources of component current differences in each source, which eliminates a decrease in the regulation efficiency by current parameters as a result of mutual compensation of differences in the component currents of opposite signs.

Thus, the proposed vector method for controlling parallel working sources increases the stability of the amplitude and phase of the voltage at the total load and the uniform distribution of current components between parallel working sources.

Claims (1)

A method of controlling static stabilized AC voltage sources operating in parallel for a common load, which consists in measuring the instantaneous values of the output voltage and current for each source, generating the first and second reference signals for the first and second stabilized output voltage parameters, respectively, and generating proportional signals the first and second stabilized parameters of the output voltage, generate signals proportional to the first and second parameters of the currents sources, for each source the first and second difference voltages are generated, the first difference voltage is summed with a signal proportional to the first stabilized output voltage parameter, the second difference voltage is summed with a signal proportional to the second stabilized output voltage parameter, the first and second comparison signals are generated, according to the comparison result form the amplitude and phase of the control voltage, characterized in that the measured instantaneous values of voltage and current of each sources are converted from a three-phase abc coordinate system to a two-phase dq coordinate system rotating with a constant frequency Ω, the first and second reference signals are respectively the reference signals for the d and q components of the output voltage of the source, and the first and second current parameters are used accordingly, the d-and q-components of the source current, the first comparison signal is formed by integrating the difference of the reference signal for the d-component of the source voltage and the total signal corresponding to of the difference of the d-component currents of the sources, the second comparison signal is formed by integrating the difference of the reference signal for the q-component of the source voltage and the total signal corresponding to the difference of the q-component currents of the sources, the first and second difference voltages are formed respectively as the difference d- or q- component currents of only two sources, namely, the difference of the component currents of this and other sources or the difference of the component currents of other sources, each difference being Hovhan respective sum signals used only once, and said control formation of a three-phase voltage source is performed by reversely converting the d- and q-components of the comparison result of the two-phase dq-coordinate system in the three-phase abc-system coordinates.