RU2379812C1 - Method to control static stabilised ac voltage sources operated in parallel to common load - Google Patents

Abstract

FIELD: electrical engineering.

SUBSTANCE: invention relates to electrical engineering and can be used in constructing electric power generation or uninterrupted power supply systems. Proposed method comprises amplitude comparison signal is shaped by integration of the difference between amplitude reference signal and that of total signal corresponding to difference between current reactive components. Note that aforesaid difference voltages of active and reactive current components are formed as the difference between appropriate current components of only two sources, namely the difference between current components of the given and the other source, or the difference between current components of the other sources. Note here also that every difference in forming appropriate total signals is used only one time.

EFFECT: higher stability of voltage phase and amplitude on common load, uniform distribution of load current component between sources in static mode.

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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 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 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 [A.S. 1310974 USSR, 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 converters operating in parallel by summing the signals proportional to the currents of the converters form a signal for setting the current fraction of each converter 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 the given converter to the rated current of the load, 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 they form a control signal for each converter by summing the negative feedback signals for current, voltage, and a fractional reference signal ka.

This control method implements proportional control, both by the instantaneous values of the 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 [A.S. 966841 USSR, Н02Р 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 a prototype of the present invention, and consists in the fact that for each source built on the basis of a static frequency converter, instantaneous values of the output voltage and current are measured, an amplitude reference signal is generated, a phase reference signal is generated, signals proportional to the amplitude are generated and the phase of the output voltage of the source, measure the active and reactive components of the currents of the source and load, for each component form differential voltages proportional to the respective the differences between the active and reactive components of the load and source currents, the difference voltage of the active components of the currents are summed with a signal proportional to the amplitude of the output voltage of the source, the amplitude comparison signal is generated by comparing the reference amplitude signal and the total signal corresponding to the active components of the currents, the amplitude is proportional to the comparison signal control voltage, the differential voltage of the reactive components is summed with the signal, proportional In the phase of the output voltage of the source, the phase reference signal is compared with the total signal corresponding to the reactive components of the currents, proportionally to the result of the comparison, the phase of the control voltage is measured, the instantaneous value of the load current is measured and a correction signal equal to the difference of the load currents and the source is generated, the control signal is generated by summing the control voltage and 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, when generating differential voltages for the active and reactive components of the converter currents and the load, the difference between the active and reactive components of the converter currents and the load 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 in terms of current parameters decreases, and the uniformity of the loading of sources by the components of the load current decreases.

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, consisting in the fact that for each source, instantaneous values of the output voltage and current are measured, an amplitude reference signal is generated, a phase reference signal is generated, signals are generated, proportional to the amplitude and phase of the output voltage of the source, measure the active and reactive components of the currents of the sources, for each component form a differential voltage the voltage, the differential voltage of the active components of the currents are summed with a signal proportional to the amplitude of the output voltage of the source, an amplitude comparison signal is generated proportionally to which the amplitude of the control voltage is generated, the differential voltage of the reactive components of the currents is added to the signal proportional to the phase of the output voltage of the source, the phase comparison signal is proportional to which form the phase of the control voltage, the amplitude comparison signal is formed by integrating the differences of the reference phase signal and the total signal corresponding to the difference of the reactive components of the currents, and the indicated difference voltages of the active and reactive components of the currents form as the difference of the corresponding components of the currents only two sources, namely the difference between the components of the currents of this and other sources or the difference of the components of the current in other sources, and each difference of the component currents in the formation of the corresponding total signals is used only once.

(блок 6) и источник эталонного сигнала фазы выходного напряжения

(блок 7), которые соединены с первыми входами сумматоров (блоки 8 и 9). Вторые входы сумматоров (блоки 8 и 9) соединены с выходами пропорциональных звеньев сигналов, пропорциональных амплитуде и фазе выходного напряжения

и

(блоки 10 и 11). Третьи входы сумматоров (блоки 8 и 9) соединены с выходами пропорциональных звеньев разностей активных и реактивных составляющих токов источников R^A _i и R^Ф _i (блоки 12, 13). Выходы сумматоров (блоки 8 и 9) соединены с входами интеграторов И^A _i и И^Ф _i  (блоки 14, 15). Выход интегратора фазы И^Ф _i (блок 14) соединен с первым входом преобразователя П_i (блок 16), а второй вход преобразователя соединен с выходом задающего генератора ЗГ₀ (блок 5). Выход интегратора амплитуды И^A _i (блок 15) соединен со вторым входом генератора модулирующего напряжения ГMН_i (блок 17). Первый вход генератора модулирующего напряжения ГМН_i (блок 17) соединен с выходом преобразователя П_i (блок 15). Выход генератора модулирующего напряжения ГМН_i (блок 17) соединен с первым входом системы импульсно-фазового управления СИФУ_i (блок 17), а второй синхронизирующий вход системы импульсно-фазового управления соединен с выходом источника нестабильного напряжения U_ci (блок 19). Выход системы импульсно-фазового управления СИФУ_i (блок 17) соединен с первым управляющим входом силовой схемы статического преобразователя частоты СС_i (блок 20), второй силовой вход которого соединен с выходом источника нестабильного напряжения CФ_i (блок 19). Выход силовой схемы статического преобразователя частоты СС, (блок 20) через силовой фильтр СФ_i (блок 21) и датчик мгновенного значения тока источника ДТ_i (блок 22) соединен с общей нагрузкой Н (блок 4). Общая нагрузка Н (блок 4) соединена с входами фазового детектора ФД_i (блок 23), выпрямителя В_i (блок 24) и вторыми входами схем измерения активной I^a _i (блок 25) и реактивной I^p _i (блок 26) составляющих токов источников. Второй вход фазового детектора ФД_i (блок 23) соединен с выходом задающего генератора ЗГ₀ (блок 5). Выход фазового детектора ФД_i (блок 23) соединен с входом пропорционального звена фазы b_i ^Ф, а выход выпрямителя В_i (блок 24) соединен с входом пропорционального звена амплитуды b^A _i. Вторые входы схем измерения активной I^a _i (блок 25) и реактивной I^p _i (блок 26) составляющих токов источников соединены с выходом датчика мгновенного значения тока источника ДT_i (блок 22). Выходы схем измерения активной I^a _i (блок 25) и реактивной I^p _i (блок 26) составляющих токов источников соединены с выходами соответствующих схем вычитания СВ^a _i (блоки 27, 29, 31) и СВ^p _i (блоки 28, 30, 32) соответственно. Выходы схем вычитания соединены с входами пропорциональных звеньев разностей активных и реактивных составляющих токов источников R^A _i и R^Ф _i (блоки 12, 13).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 each output phase N of static stabilized AC voltage sources IST ₁ ... IST _N (blocks 1 ... 3) operating on a total load N (block 4). The sources are synchronized from a common master generator ЗГ ₀ (block 5). Each source includes an output voltage amplitude reference signal source.

(block 6) and the source signal of the phase output voltage

(block 7), which are connected to the first inputs of the adders (blocks 8 and 9). The second inputs of the adders (blocks 8 and 9) are connected to the outputs of the proportional parts of the signals proportional to the amplitude and phase of the output voltage

and

(blocks 10 and 11). The third inputs of the adders (blocks 8 and 9) are connected to the outputs of the proportional links of the differences of the active and reactive components of the currents of the sources R ^A _i and R ^Ф _i (blocks 12, 13). The outputs of the adders (blocks 8 and 9) are connected to the inputs of the integrators And ^A _i and And ^f _i (blocks 14, 15). The output of the phase integrator And ^Ф _i (block 14) is connected to the first input of the converter П _i (block 16), and the second input of the converter is connected to the output of the master generator ЗГ ₀ (block 5). The output of the amplitude integrator And ^A _i (block 15) is connected to the second input of the modulating voltage generator GMN _i (block 17). The first input of the modulating voltage generator GMN _i (block 17) is connected to the output of the converter P _i (block 15). The output of the modulating voltage generator GMN _i (block 17) is connected to the first input of the SIPU _i -phase pulse control system (block 17), and the second clock input of the pulse-phase control system is connected to the output of the unstable voltage source U _ci (block 19). The output of the pulse-phase control system SIFU _i (block 17) is connected to the first control input of the power circuit of the static frequency converter CC _i (block 20), the second power input of which is connected to the output of the unstable voltage source CF _i (block 19). The output of the power circuit of the static frequency converter SS, (block 20) through the power filter SF _i (block 21) and the sensor of the instantaneous value of the current source DT _i (block 22) is connected to the total load N (block 4). The total load N (block 4) is connected to the inputs of the phase detector PD _i (block 23), rectifier B _i (block 24) and the second inputs of the measuring circuits of active I ^a _i (block 25) and reactive I ^p _i (block 26) of the component currents sources. The second input of the phase detector PD _i (block 23) is connected to the output of the master oscillator ZG ₀ (block 5). The output of the phase detector PD _i (block 23) is connected to the input of the proportional phase link b _i ^Ф , and the output of the rectifier B _i (block 24) is connected to the input of the proportional link amplitude b ^A _i . The second inputs of the measuring circuits of active I ^a _i (block 25) and reactive I ^p _i (block 26) of the component currents of the sources are connected to the output of the sensor of the instantaneous value of the current source DT _i (block 22). The outputs of the measuring circuits of active I ^a _i (block 25) and reactive I ^p _i (block 26) of the component currents of the sources are connected to the outputs of the corresponding subtraction circuits CB ^a _i (blocks 27, 29, 31) and CB ^p _i (blocks 28, 30, 32) respectively. The outputs of the subtraction circuits are connected to the inputs of the proportional links of the differences of the active and reactive components of the currents of the sources R ^A _i and R ^Ф _i (blocks 12, 13).

The load H (block 4) may be a resistor or series or parallel connection of a resistor and inductor. The master oscillator ЗГ ₀ is a highly stable quartz oscillator according to any of the known schemes (Reference on quartz resonators / Androsova V.G., Banks V.N., Dikiji A.N. et al. Edited by P.G. Pozdnyakov. - M .: Communication, 1978.- 288 p.).

Sources of reference signals of the amplitude (block 6) and phase (block 7) of the output voltage are parametric stabilizers (see Sources of power supply of electronic equipment: Reference / Edited by G.S. Naivelt. - M .: Radio and communication, 1986). Adders (blocks 8 and 9), proportional links (blocks 10-13), integrators (blocks 14, 15) and subtraction schemes (blocks 27-32) are typical elementary links 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).

Converter П _i (block 16) is a circuit that implements the principle of vertical control based on a comparison of a reference sawtooth signal of a double frequency with respect to a synchronizing signal ЗГ ₀ and a constant voltage, followed by dividing the frequency of the received comparison signal by half (see BCRudenko, V. I. Senko, I. M. Chizhenko. Fundamentals of transformative technology. - M.: Higher school, 1980. - 424 p.). The GMN modulating voltage generator _i (block 17) is an analog multiplier of two signals (see Timoneev V.N., Velichko L.M., Tkachenko V.A. Analog signal multipliers in electronic equipment. - M.: Radio and communication, 1982 . - 112 p.). The system of pulse-phase control SIFU _i (block 17) is a standard system of pulse-phase control that implements the vertical control principle (see BC Rudenko, V. I. Senko, I. M. Chizhenko. Fundamentals of converting technology. - M.: Higher. School, 1980).

Static AC power source voltage SS _i (block 20), the scheme may be a frequency converter or the direct series connection of a rectifier and an inverter, or the inverter (see BCRudenko, V.I.Senko, Fundamentals I.M.Chizhenko converter technology -... M. : High School, 1980). The unstable voltage source U _ci (block 19) is an industrial network or a synchronous generator with a variable rotor speed or a battery. The power filter SF _i (block 21), for example, is a single-link LC filter in each output phase or a C filter in each output phase. The sensor of the instantaneous value of the output current of the source DT _i (block 22), for example, is a current transformer.

The phase detector PD _i (block 23) is made according to one of the standard schemes (see Shagildyan V.V., Lyakhovkin A.A. Phase locked loop systems. - M .: Communication, 1972. - 447 p.). Rectifier В _i (block 24) is a single-phase rectifier circuit (see BCRudenko, V.I.Senko, I.M. Chizhenko. Fundamentals of converting technology. - M.: Higher school, 1980).

The measurement schemes of active I ^a _i (block 25) and reactive I ^p _i (block 26) of the component currents of the sources are standard schemes of multipliers of analog signals (see Timoneev V.N., Velichko L.M., Tkachenko V.A. signal multipliers in electronic equipment. - M.: Radio and Communications, 1982. - 112 p.).

The control method is as follows. The amplitude amplitude signals U ^A _ETi and phases U ^Ф _ETi (blocks 6 and 7) are formed, which are constant voltages for the stabilized amplitudes and phases of the output voltage of the sources, which are supplied to the first inputs of the respective adders (blocks 8 and 9) with a positive sign. The voltage of the total load is supplied to the rectifier In _i (block 24) and the phase detector PD _i (block 23). At the output of the rectifier B _i , a voltage is formed whose constant component is proportional to the amplitude of the voltage of the total load. From the output of the rectifier, the voltage through the proportional link b ^A _i (block 11) is supplied to the second input of the amplitude adder (block 8) with a negative sign. At the output of the phase detector PD _i (block 23), a voltage is formed whose constant component is proportional to the phase of the voltage of the total load relative to the voltage phase of the master oscillator ZG ₀ (block 5). This voltage is supplied through the proportional link b ^Ф _i to the second input of the phase adder (block 9) with a negative sign.

Measurement schemes of the active I ^a _i (block 25) and reactive I ^p _i (block 26) component source currents multiply the instantaneous value of the source current measured by the DT _i sensor (block 22) and the instantaneous value of the source voltage when measuring the active component of current I ^a _i (block 25) or the instantaneous value of the output voltage of the source with a 90-degree phase shift in the output frequency when measuring the reactive component of the current I ^p _i (block 26). The output voltages of the measuring circuits of the active I ^a _i (block 25) and reactive I ^p _i (block 26) of the component currents of the sources are supplied to the corresponding circuit of subtracting the active component of the currents CB ^a _i (blocks 27, 29, 31) and the circuit of subtracting the reactive component of the currents CB ^p _i (blocks 28, 30, 32). The output voltages of the subtraction circuits through the corresponding proportional links R ^A _i and R ^Ф _i (blocks 12,13) are supplied to the third inputs of the adders (blocks 8, 9) with a negative sign.

At the outputs of the adders (blocks 8 and 9), the difference between the reference voltage of the amplitude and the total signal corresponding to the difference of the active components of the source currents (block 8), and the difference of the reference voltage of the phase and the total signal corresponding to the difference of the reactive components of the source currents (block 9) are formed. The output signals of the adders are integrated respectively by the integrator of the amplitude circuit And ^A _i (block 14) and the integrator of the phase circuit And ^f _i (block 15). The output signal of the integrator of the phase circuit AND ^Ф _i (block 15) is supplied to the converter П _i (block 16), which implements the vertical principle of forming an alternating output voltage synchronized by the signal of the master oscillator ЗГ ₀ (block 5) and having an adjustable phase relative to the phase of the signal of the master generator ZG ₀ (block 5) by the signal of the integrator of the phase circuit And ^f _i (block 15). The output voltage-regulated constant voltage of the amplitude integrator And ^A _i (block 14), and the variable, phase-controlled output voltage of the converter П _i (block 16), are fed to the inputs of the modulating voltage generator GMN _i (block 17), in which multiplication is implemented these signals. As a result, at the output of the generator of the modulating voltage GMN _i (block 17), an alternating sinusoidal voltage, which is supplied to the control input of the pulse-phase control system of SIFU _i (block 17), is formed, which is regulated in amplitude and phase as a function of the corresponding output voltages of the integrators. The SIPU _i -phase pulse-phase control system (block 17) implements a vertical control method, in which the sawtooth voltage is synchronized by the voltage of the unstable voltage source U _ci (block 19) and modulated pulse signals are generated to control the semiconductor switches of the power circuit CC _i (block 20) . In the power circuit CC _i (block 20), the energy of the primary source with unstable voltage parameters U _ci (block 19) is converted to the output energy with the specified voltage parameters (amplitude and phase). The power filter SF _i (block 21) reduces the amplitudes of the high-frequency components of the spectrum of the output voltage of the source, providing a sinusoidal shape of the output voltage.

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:

Where

- given relative reference signals, respectively, of the amplitude and phase of the output voltage;

- relative values

voltages proportional to the amplitude and phase of the output voltage;

- the relative active and reactive components of the source currents;

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

U _Hnom , I _Hnom , Z _Hnom - nominal effective values of the voltage and current of the load and the module of the nominal value of the load resistance;

f ^a _i (...), f ^p _i (...) - in the general case, nonlinear functions of the active and reactive components of the source currents that determine 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 component currents of the sources proposed in the method as the formation of differences of component currents of only two different sources and the use of each difference of component currents only once leads to the fulfillment of the conditions:

Then summing up all the equations for the active or reactive components in the expression (2), we obtain:

With the same values of the rated power of the sources and

respectively the same proportionality coefficients

и

выражения (4) преобразуются к виду:

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 amplitude and phase 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 amplitude and phase of the voltage at the total load are determined by the averaged values of the corresponding reference signals, due to which the stability of the voltage parameters at the total load can be increased while compensating for the spread of the reference signals of different signs, and do not depend on the magnitude of the load.

Thus, the stability of the amplitude and phase of the voltage at the total load in the proposed method is increased in comparison with the prototype method.

Determine the increase in the uniformity of the distribution of the components of the load current between the sources in static mode in the proposed 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:

Where

- a column vector of the active component currents of the sources;

- column vector of reactive components

source currents;

;

;

- 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;

;

;

- 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).

Using in the formation of the current functions f ^a _i (...) and f ^p _i (...) the 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 kind of matrices F ^A and F ^Ф , called circulants, in which each the next line is obtained by cyclic shift of the previous line:

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.

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 go from the values of the source currents to the difference of the component currents of the sources relative to any, for example, the 1st source. To do this, subtract and add the components of the 1st current -a ^A ₀ · I ^p _l + а ^Ф ₀ · I ^p _l or-а ^Ф ₀ · I ^p _l + а ^Ф ₀ · I ^p to the left side of each equation (8) _l . 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 1st current are excluded from the system of equations (the first zero column is formed in the coefficient matrix), and the transformed 1st equation becomes linearly dependent on 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 1-го столбца и 1-ой строки;Where

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

- векторы-столбцы размерности N-1, получаемые из соответствующих аналогичных векторов-столбцов правых частей исходной системы уравнений (3.12) вычеркиванием 1-ой 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 first row;

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

- a column vector of dimension N-1 of the difference of the reactive components of the source currents for each i-th and one 1st sources;

- differences of the corresponding current components of the i-th and 1st 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 the components between any k-th and m-th sources:

Then, according to expressions (6), the sums of squares of the differences of the component currents are found and the values of the coefficients of the matrices F ^A and F ^{Φ are} determined by the criterion of the minimum of these sums.

Let us explain the definition of the optimal coefficients of the matrices F ^A ₃ and F ^Ф ₃ for the case of parallel operation of three converters. We represent these matrices in the form:

Each element of the matrices (11) is represented by the difference of the maximum diagonal element and some increment a ^A _i = a ^A ₀ -Δa ^A _i or a ^Ф _i = а ^Ф ₀ -Δа ^Ф _i . 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 current components of the third source of the system of equations (10), they will take the following form:

Having solved the system of equations (13) for the active and reactive components of the differences of the currents and determined by (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 the increments of the matrix 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.

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 take Δa ^A ₁ = 0; Δа ^Ф ₁ = 0 and consider Δа ^A ₂ = а ^A ₀ ; Δа ^Ф ₂ = а ^Ф ₀ (or Δа ^A ₃ = а ^A ₀ ; Δа ^Ф ₃ = а ^Ф ₀ ), then according to expressions (12) we obtain Δа ^A ₃ = 0; Δа ^Ф ₃ = 0 (or Δа ^A ₂ = 0; Δа ^Ф ₂ = 0). Then the matrices F ^A ₃ and F ^Ф ₃ take the form:

If we take Δa ^A ₁ = a ^A ₀ ; Δа ^Ф ₁ = а ^Ф ₀ and consider Δа ^A ₂ = 0; Δа ^Ф ₂ = 0 (or Δа ^A ₃ = 0; Δа ^Ф ₃ = 0), then according to expressions (12) we obtain Δа ^A ₃ = 2а ^A ₀ ; Δа ^Ф ₃ = 2а ^Ф ₀ (or Δа ^A ₂ = 2а ^A ₀ ; Δа ^Ф ₂ = а ^Ф ₀ ). Then the matrices F ^A ₃ and F ^Ф ₃ take the form:

The resulting matrix structures show that structures using the difference between the active and reactive 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 in the formation of the corresponding total signals used only once.

For the prototype method, the values of the corresponding increments of the matrix coefficients have the values Δa ^A ₁ = (1/3) and ^A ₀ ; Δa ^A ₂ = (2/3) a ^A ₀ ; Δa ^A ₃ = (2/3) a ^A ₀ ; Δа ^Ф ₁ = (1/3) and ^Ф ₀ ; Δа ^Ф ₂ = (2/3) а ^Ф ₀ ; Δа ^Ф ₃ = (2/3) and ^Ф ₀ .

The table below compares the prototype method, in which the difference signal in terms of 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 parallel sources .

With the parallel operation of two sources, the effectiveness of the proposed method (comparing the values of S ^A _i and S ^Ф _i ) is 4 times higher than in the prototype method, three times with three sources, and with four sources in parallel, two (the first terms) up 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 the differences of the component currents in each source, which eliminates the reduction in the efficiency of regulation by the current parameters as a result of mutual compensation of the differences of 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 uniformity of the distribution of current components between parallel working sources in comparison with the prototype method.

Claims (1)

A method of controlling static stabilized AC voltage sources operating in parallel for a common load, which consists in measuring instantaneous values of the output voltage and current for each source, generating an amplitude reference signal, generating a phase reference signal, and generating signals proportional to the amplitude and phase of the source voltage output , measure the active and reactive components of the source currents, for each component form the differential voltage, the differential voltage of the active components of the currents are summed with a signal proportional to the amplitude of the output voltage of the source, an amplitude comparison signal is generated proportionally to which the amplitude of the control voltage is generated, the differential voltage of the reactive components of the currents is added to a signal proportional to the phase of the source voltage, a phase comparison signal is proportional to which the control voltage phase is formed characterized in that the amplitude comparison signal is formed by integrating the difference of the reference of the amplitude signal and the total signal corresponding to the difference of the active components of the currents, the phase comparison signal is formed by integrating the difference of the reference phase signal and the total signal corresponding to the difference of the reactive components of the currents, and the indicated difference voltages of the active and reactive components of the currents are formed as the difference of the corresponding components of the currents of only two sources, namely, the difference of the component currents of this and another sources or the difference of the component currents of other sources k, and each difference in the formation of the corresponding summed signals is used only once.