CN101674023A - Harmonic resolution method of alternating-current/direct-current interconnection system - Google Patents

Abstract

The invention discloses a harmonic resolution method of an alternating-current/direct-current interconnection system. The method comprises the following steps: calculating the actual triggering angle,the phase transformation angle and the delay conduction angle of each current transformation valve in a current transformer according to the interphase fundamental-frequency voltage of current transformation buses and the direct-current component of direct current and the triggering angle command of a direct-current control system; calculating a three-phase voltage switching function and a three-phase current switching function and transforming the three-phase voltage switching function switching function and the three-phase current switching function into positive-sequence and negative-sequence components; establishing a sequence component model of the current transformer by the positive-sequence and negative-sequence current switching function and the positive-sequence and negative-sequence voltage switching function; and combining the model and an equivalent harmonic network of the alternating-current/direct-current system and carrying out simultaneous resolution on the total system, thereby calculating each subharmonic voltage and current of both sides of alternating current and direct current of the current transformer. The method realizes the harmonic resolution of the alternating-current/direct-current system under a condition that an asymmetric fault occurs in an alternating-current system, lowers the calculation quantity, has higher calculation accuracy and can be applied to the harmonic analysis of the alternating-current/direct-current interconnection system under various normal operation working conditions and faults.

Description

A kind of harmonic resolution method of alternating-current/direct-current interconnection system

Technical field

The present invention relates to the harmonic resolution method in the field of power, specifically be meant a kind of harmonic resolution method of alternating-current/direct-current interconnection system that is applicable under various operating conditions and the failure condition.

Background technology

For satisfying the electricity needs of following sustainable growth, realize wider most optimum distribution of resources, high voltage direct current (HVDC) transmission system obtains increasingly extensive application.To the end of the year 2007, existing area, 4 times high power DC transmission system feed-in Guangdong carries direct current power to reach 10800MW altogether.The area, Guangdong has become maximum in the world many feed-ins alternating current-direct current hybrid system.When AC system generation unbalanced fault, the safe and stable operation that each time feature that ac and dc systems produces and uncharacteristic harmonics might influence system.Therefore be necessary to set up the ac and dc systems harmonic resolution method that is applicable under the AC system unbalanced fault condition.

Existing at present unified first-harmonic and the uncharacteristic harmonics trend method that is applied to the ac and dc systems harmonic analysis, it sets up the converter dynamic model to carry out harmonic resolution based on the differential equation, is difficult to from its alternating current-direct current both sides harmonic wave generation of mechanism research, transmission and interactional mechanism.This method depends on system-wide Model in Time Domain based on the differential equation, and need carry out iterative, so its calculating is larger, is difficult to use in extensive ac and dc systems.And existing harmonic analysis method based on switch function, it is by the voltage and current switch function of structure reflection converter switch motion, describe converter alternating current-direct current both sides voltage and current relation with this, and calculate the harmonic voltage and the harmonic current of converter alternating current-direct current both sides.Yet when AC system generation unbalanced fault, converter is in the asymmetric operating state.The actual conducting of converter valve will be offset constantly this moment, and the three-phase angle of overlap no longer is equal to each other.In addition, have humorous wave interaction between the AC and DC system: the each harmonic electric current that direct current system is injected to AC system will produce each time background harmonics voltage, and it will react on the HVDC system, influence the harmonic current that direct current system produces.Have the humorous wave interaction of not considering ac and dc systems based on the harmonic analysis method of switch function now, also do not consider the asymmetric operating state of converter under the AC system unbalanced fault.

Summary of the invention

The objective of the invention is to overcome the shortcoming and defect of prior art, a kind of harmonic resolution method of alternating-current/direct-current interconnection system that is applicable under various operating conditions and the failure condition is provided.This method need not iteration, according to of the influence of asymmetric three-phase commutation voltage to the converter switch motion, it is unequal to comprise that the converter valve conducting is offset constantly with the three-phase angle of overlap, three-phase voltage current switch function and converter preface component switch function model have been set up based on fundametal component, correction component and commutation component, and carry out the harmonic resolution of ac and dc systems in conjunction with the equivalent harmonic wave network of ac and dc systems, significantly reduced the calculating scale, satisfied engineering and used required.

Purpose of the present invention is achieved through the following technical solutions: a kind of harmonic resolution method of alternating-current/direct-current interconnection system may further comprise the steps:

(1) data processing:, calculate corresponding line voltage fundamental component according to the fundamental component of known converter AC side phase voltage;

(2) phase deviation of calculating synchronizing voltage: the fundamental component of three line voltages is converted to α component and β component, and, calculates the phase place of DC control system synchronizing voltage respectively according to the amplitude and the phase place of α component and β component

By the phase place of the fundamental component of three line voltages, and calculate

Calculate the phase deviation of synchronizing voltage respectively

With

Wherein subscript ab, bc and ca represent that respectively above-mentioned angular deflection is a benchmark with the phase place of ab, bc and ca line voltage fundamental component, set mark mn=ab, bc, ca; A, b, c represent the phase in the three-phase respectively;

(3) calculate converter valve turn on delay angle and actual trigger angle: calculate resulting synchronizing voltage phase deviation in trigger angle command value that more known DC control system provides and the step (2), calculate converter valve turn on delay angle θ _Ab, θ _BcAnd θ _Ca, and actual trigger angle α _Ab, α _BcAnd α _Ca, wherein subscript ab, bc and ca represent that respectively above-mentioned angle is corresponding to ab, bc and the commutation of ca two-phase;

(4) calculate angle of overlap: according to the fundamental component of the line voltage that calculates in the step (1) with by the actual trigger angle of step (3) gained, and known equivalence is to the converter transformer leakage reactance X of valve side _r, converter DC side electric current DC component I _{D (0)}, the angle of overlap μ when calculating ab, bc and the commutation of ca two-phase _Ab, μ _BcAnd μ _Ca

(5) the q order harmonic components of compute switch function: the turn on delay angle, actual trigger angle and the angle of overlap that calculate by step (3) and step (4), calculate the q order harmonic components of three-phase current switch function, and calculate the q order harmonic components of positive sequence and negative-sequence current switch function thus, wherein q is any nonzero integer; Turn on delay angle, actual trigger angle and angle of overlap by step (3) and step (4) calculate calculate the q order harmonic components of three-phase voltage switch function, and calculate the q order harmonic components of positive sequence and negative sequence voltage switch function thus;

(6) find the solution the each harmonic voltage and current of AC/DC interconnected system: the preface component model of structure converter, and calculate the equivalent harmonic impedance Z of each time that sees into from the converter DC side toward DC network according to existing method _{D (k)}, calculate the equivalent positive sequence harmonic impedance Z of seeing into from the converter AC side toward AC network of each time _(k) ⁺With the equivalent negative phase-sequence harmonic impedance of each time Z _(k) ^-Thereby, find the solution the each harmonic voltage and current of AC/DC interconnected system.

To better implement the present invention, described step (1) data processing specifically is meant: according to the fundamental component U of known converter AC side three-phase voltage _{A (1)}, U _{B (1)}, U _{C (1)}, subscript " 1 " expression first harmonic component wherein, i.e. fundamental component, calculate corresponding line voltage fundamental component by following formula:

U _ab(1)＝U _b(1)-U _a(1)

U _bc(1)＝U _c(1)-U _b(1)

U _ca(1)＝U _a(1)-U _c(1)

Wherein, U _{Ca (1)}Fundamental component for change of current bus ca line voltage; U _{Ab (1)}Fundamental component for change of current bus ab line voltage; U _{Bc (1)}Fundamental component for change of current bus bc line voltage.

Described step (2) is calculated the skew of synchronizing voltage phase place, specifically is meant: establish

With Represent the α component and the β component of commutation voltage respectively, it is calculated by following formula:

$\left[\begin{array}{c}{\stackrel{\·}{U}}_{\mathrm{\α}}\\ {\stackrel{\·}{U}}_{\mathrm{\β}}\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{ca}\left(1\right)}\\ U_{\mathrm{ab}\left(1\right)}\\ U_{\mathrm{bc}\left(1\right)}\end{array}\right]$

Utilize the α component of commutation voltage

β component with commutation voltage

Calculate the phase place of DC control system synchronizing voltage by following formula

In the formula, U _αAnd U _βBe respectively the amplitude of the α component and the β component of commutation voltage;

With

Be respectively the α component of commutation voltage and the phase angle of β component;

According to U _{Ca (1)}Phase place

The phase place of Uab (1)

U _{Bc (1)}Phase place

Calculate the phase deviation of synchronizing voltage respectively

Wherein

Phase deviation for the alternate synchronizing voltage of ca;

Phase deviation for the alternate synchronizing voltage of ab;

Phase deviation for the alternate synchronizing voltage of bc.

Described step (3) is calculated converter valve turn on delay angle and actual trigger angle, specifically is meant: according to the trigger angle instruction α of DC control system _o, calculate converter valve turn on delay angle θ _MnWith actual trigger angle α _Mn:

In the following formula, all angles are all to lag behind to just, and are leading for negative.

Described step (4) is calculated angle of overlap, specifically is meant: establish μ _MnAngle of overlap during for the commutation of mn two-phase, and according to the DC component I of known converter DC side electric current _{D (0)}(being the zero degree harmonic component), equivalent converter transformer leakage reactance X to the valve side _r, actual trigger angle α _Mn, and the amplitude of change of current bus line voltage fundamental component | U _{Mn (1)}|, the following formula of substitution calculates angle of overlap μ _Mn:

μ _mn＝cos ^-1(cosα _mn-2X _rI _d(0)/|U _mn(1)|)-α _mn

The q order harmonic components of described step (5) compute switch function specifically is meant:

5.1 calculate the q order harmonic components S of switch function fundametal component by the following formula formula _{B (q)}Q order harmonic components S with switch function correction component _{Fab (q)}, S _{Fbc (q)}, S _{Fca (q)}:

$S_{b\left(q\right)}=\frac{1}{\mathrm{q\π}}[\sin \frac{\mathrm{q\π}}{3}+j(\cos \mathrm{q\π}+\cos \frac{2\mathrm{q\π}}{3})]$

$S_{\mathrm{fab}\left(q\right)}=\frac{j}{2\mathrm{q\π}}\left[e^{-j{\mathrm{\θ}}_{\mathrm{ab}}}(e^{-\mathrm{jq\π}}-1)(e^{-\mathrm{jq}{\mathrm{\θ}}_{\mathrm{ab}}}-1)\right]$

$S_{\mathrm{fbc}\left(q\right)}=\frac{j}{2\mathrm{q\π}}\left[e^{-j{\mathrm{\θ}}_{\mathrm{bc}}}(e^{-\mathrm{jq\π}}-1)(e^{-\mathrm{jq}{\mathrm{\θ}}_{\mathrm{bc}}}-1)\right]$

$S_{\mathrm{fca}\left(q\right)}=\frac{j}{2\mathrm{q\π}}\left[e^{-j{\mathrm{\θ}}_{\mathrm{ca}}}(e^{-\mathrm{jq\π}}-1)(e^{-\mathrm{jq}{\mathrm{\θ}}_{\mathrm{ca}}}-1)\right]$

Wherein, q is any nonzero integer; E is the truth of a matter of natural logrithm; J is an imaginary unit;

5.2 q order harmonic components S by following formula calculating voltage switch function commutation component _{U μ ab (q)}, S _{U μ bc (q)}, S _{U μ ca (q)}Q order harmonic components S with current switch function commutation component _{I μ ab (q)}, S _{I μ bc (q)}, S _{I μ ca (q)}:

$S_{\mathrm{u\μab}\left(q\right)}=\frac{j}{4\mathrm{q\π}}\left[e^{-j{\mathrm{\μ}}_{\mathrm{ab}}}(e^{-\mathrm{jq\π}}-1)(e^{-\mathrm{jq}{\mathrm{\μ}}_{\mathrm{ab}}}-1)\right]$

$S_{\mathrm{u\μbc}\left(q\right)}=\frac{j}{4\mathrm{q\π}}\left[e^{-j{\mathrm{\μ}}_{\mathrm{bc}}}(e^{-\mathrm{jq\π}}-1)(e^{-\mathrm{jq}{\mathrm{\μ}}_{\mathrm{bc}}}-1)\right]$

$S_{\mathrm{u\μca}\left(q\right)}=\frac{j}{4\mathrm{q\π}}\left[e^{-j{\mathrm{\μ}}_{\mathrm{ca}}}(e^{-\mathrm{jq\π}}-1)(e^{-\mathrm{jq}{\mathrm{\μ}}_{\mathrm{ca}}}-1)\right]$

$S_{\mathrm{i\μab}\left(q\right)}={\∫}_{-\mathrm{\π}}^{-\mathrm{\π}+{\mathrm{\μ}}_{\mathrm{ab}}}[\frac{\left|U_{\mathrm{ab}\left(1\right)}\right|(\cos {\mathrm{\α}}_{\mathrm{ab}}+\cos ({\mathrm{\α}}_{\mathrm{ab}}+\mathrm{\ωt}))}{2X_r{I}_{d\left(0\right)}}-1]e^{-\mathrm{jq\ωt}}\mathrm{d\ωt}$

$+{\∫}_0^{{\mathrm{\μ}}_{\mathrm{ab}}}[1-\frac{\left|U_{\mathrm{ab}\left(1\right)}\right|(\cos {\mathrm{\α}}_{\mathrm{ab}}-\cos ({\mathrm{\α}}_{\mathrm{ab}}+\mathrm{\ωt}))}{2X_r{I}_{d\left(0\right)}}]e^{-\mathrm{jq\ωt}}\mathrm{d\ωt}$

$S_{\mathrm{i\μbc}\left(q\right)}={\∫}_{-\mathrm{\π}}^{-\mathrm{\π}+{\mathrm{\μ}}_{\mathrm{bc}}}[\frac{\left|U_{\mathrm{bc}\left(1\right)}\right|(\cos {\mathrm{\α}}_{\mathrm{bc}}+\cos ({\mathrm{\α}}_{\mathrm{bc}}+\mathrm{\ωt}))}{2X_r{I}_{d\left(0\right)}}-1]e^{-\mathrm{jq\ωt}}\mathrm{d\ωt}$

$+{\∫}_0^{{\mathrm{\μ}}_{\mathrm{bc}}}[1-\frac{\left|U_{\mathrm{bc}\left(1\right)}\right|(\cos {\mathrm{\α}}_{\mathrm{bc}}-\cos ({\mathrm{\α}}_{\mathrm{bc}}+\mathrm{\ωt}))}{2X_r{I}_{d\left(0\right)}}]e^{-\mathrm{jq\ωt}}\mathrm{d\ωt}$

$S_{\mathrm{i\μca}\left(q\right)}={\∫}_{-\mathrm{\π}}^{-\mathrm{\π}+{\mathrm{\μ}}_{\mathrm{ca}}}[\frac{\left|U_{\mathrm{ca}\left(1\right)}\right|(\cos {\mathrm{\α}}_{\mathrm{ca}}+\cos ({\mathrm{\α}}_{\mathrm{ca}}+\mathrm{\ωt}))}{2X_r{I}_{d\left(0\right)}}-1]e^{-\mathrm{jq\ωt}}\mathrm{d\ωt}$

$+{\∫}_0^{{\mathrm{\μ}}_{\mathrm{ca}}}[1-\frac{\left|U_{\mathrm{ca}\left(1\right)}\right|(\cos {\mathrm{\α}}_{\mathrm{ca}}-\cos ({\mathrm{\α}}_{\mathrm{ca}}+\mathrm{\ωt}))}{2X_r{I}_{d\left(0\right)}}]e^{-\mathrm{jq\ωt}}\mathrm{d\ωt}$

In the formula, | U _{Mn (1)}| be U _{Mn (1)}Amplitude, α _MnBe actual trigger angle;

5.3 calculate the q order harmonic components S of three-phase voltage switch function _{Ua (q)}, S _{Ub (q)}, S _{Uc (q)}Q order harmonic components S with the three-phase current switch function _{Ia (q)}, S _{Ib (q)}, S _{Ic (q)}:

$\left\{\begin{array}{c}{S}_{\mathrm{ua}\left(q\right)}=S_{b\left(q\right)}+S_{\mathrm{u\μA}\left(q\right)}+S_{\mathrm{fA}\left(q\right)}\\ S_{\mathrm{ub}\left(q\right)}=S_{b\left(q\right)}{e}^{-j2\mathrm{q\π}/3}+S_{\mathrm{u\μB}\left(q\right)}+S_{\mathrm{fB}\left(q\right)}\\ S_{\mathrm{uc}\left(q\right)}=S_{b\left(q\right)}{e}^{j2\mathrm{q\π}/3}+S_{\mathrm{u\μC}\left(q\right)}+S_{\mathrm{fC}\left(q\right)}\end{array}\right.$

$\left\{\begin{array}{c}{S}_{\mathrm{ia}\left(q\right)}=S_{b\left(q\right)}+S_{\mathrm{i\μA}\left(q\right)}+S_{\mathrm{fA}\left(q\right)}\\ S_{\mathrm{ib}\left(q\right)}=S_{b\left(q\right)}{e}^{-j2\mathrm{q\π}/3}+S_{\mathrm{i\μB}\left(q\right)}+S_{\mathrm{fB}\left(q\right)}\\ S_{\mathrm{ic}\left(q\right)}=S_{b\left(q\right)}{e}^{j2\mathrm{q\π}/3}+S_{\mathrm{i\μC}\left(q\right)}+S_{\mathrm{fC}\left(q\right)}\end{array}\right.$

In the formula,

$S_{\mathrm{u\μA}\left(q\right)}=S_{\mathrm{u\μab}\left(q\right)}{e}^{-\mathrm{jq}(\mathrm{\π}/3+{\mathrm{\θ}}_{\mathrm{ab}})}-S_{\mathrm{u\μca}\left(q\right)}{e}^{\mathrm{jq}(\mathrm{\π}/3-{\mathrm{\θ}}_{\mathrm{ca}})};$

$S_{\mathrm{u\μB}\left(q\right)}={-S}_{\mathrm{u\μbc}\left(q\right)}{e}^{-\mathrm{jq}(\mathrm{\π}/3+{\mathrm{\θ}}_{\mathrm{bc}})}-S_{\mathrm{u\μab}\left(q\right)}{e}^{-\mathrm{jq}(\mathrm{\π}/3+{\mathrm{\θ}}_{\mathrm{ab}})}$

$S_{\mathrm{u\μC}\left(q\right)}=S_{\mathrm{u\μca}\left(q\right)}{e}^{\mathrm{jq}(\mathrm{\π}/3-{\mathrm{\θ}}_{\mathrm{ca}})}+S_{\mathrm{u\μbc}\left(q\right)}{e}^{-\mathrm{jq}(\mathrm{\π}/3+{\mathrm{\θ}}_{\mathrm{bc}})};$

S _fA(q)＝S _fab(q)e ^-jqπ/3-S _fca(q)e ^jqπ/3；

S _fB(q)＝S _fbc(q)-S _fab(q)e ^-jqπ/3；

S _fC(q)＝S _fca(q)e ^jqπ/3-S _fbc(q)；

$S_{\mathrm{i\μA}\left(q\right)}=S_{\mathrm{i\μab}\left(q\right)}{e}^{-\mathrm{jq}({\mathrm{\θ}}_{\mathrm{ab}}+\mathrm{\π}/3)}-S_{\mathrm{i\μca}\left(q\right)}{e}^{\mathrm{jq}(\mathrm{\π}/3-{\mathrm{\θ}}_{\mathrm{ca}})};$

$S_{\mathrm{i\μB}\left(q\right)}={-S}_{\mathrm{i\μbc}\left(q\right)}{e}^{-\mathrm{jq}({\mathrm{\θ}}_{\mathrm{bc}}+\mathrm{\π}/3)}-S_{\mathrm{i\μab}\left(q\right)}{e}^{-\mathrm{jq}(\mathrm{\π}/3+{\mathrm{\θ}}_{\mathrm{ab}})};$

$S_{\mathrm{i\μC}\left(q\right)}=S_{\mathrm{i\μca}\left(q\right)}{e}^{\mathrm{jq}(\mathrm{\π}/3-{\mathrm{\θ}}_{\mathrm{ca}})}+S_{\mathrm{i\μbc}\left(q\right)}{e}^{-\mathrm{jq}(\mathrm{\π}/3+{\mathrm{\θ}}_{\mathrm{bc}})};$

Wherein, θ _Ab, θ _BcAnd θ _CaConverter valve turn on delay angle when being respectively ab, bc and the commutation of ca two-phase; μ _Ab, μ _BcAnd μ _CaAngle of overlap when being respectively ab, bc and the commutation of ca two-phase;

5.4 respectively by S _{Ua (q)}, S _{Ub (q)}, S _{Uc (q)}And S _{Ia (q)}, S _{Ib (q)}, S _{Ic (q)}, calculate corresponding positive sequence and negative sequence voltage switch function, and positive sequence and negative-sequence current switch function:

$\left[\begin{array}{c}{S}_{u\left(q\right)}^{+}\\ S_{u\left(q\right)}^{-}\end{array}\right]=\left[\begin{array}{ccc}{S}_{\mathrm{ua}\left(q\right)}& S_{\mathrm{ub}\left(q\right)}& S_{\mathrm{uc}\left(q\right)}\end{array}\right]\left[\begin{array}{cc}1& 1\\ a^2& a\\ a& a^2\end{array}\right]$

$\left[\begin{array}{c}{S}_{i\left(q\right)}^{+}\\ S_{i\left(q\right)}^{-}\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& a^2& a\\ 1& a& a^2\end{array}\right]\left[\begin{array}{c}{S}_{\mathrm{ia}\left(q\right)}\\ S_{\mathrm{ib}\left(q\right)}\\ S_{\mathrm{ic}\left(q\right)}\end{array}\right]$

In the formula, a=e ^{J2 π/3}, S _{I (q)} ⁺Q order harmonic components for the forward-order current switch function; S _{I (q)} ^-Q order harmonic components for the negative-sequence current switch function; S _{U (q)} ⁺Q order harmonic components for the positive sequence voltage switch function; S _{U (q)} ^-Q order harmonic components for the negative sequence voltage switch function.

Described step (6) is found the solution the each harmonic voltage and current of AC/DC interconnected system, specifically is meant:

6.1 the preface component model of structure converter:

Calculate the q order harmonic components of the three-phase voltage switch function of gained according to step (5), set up the equation of the quantitative relationship of expression converter DC side 2 subharmonic voltages and AC side fundamental frequency and 3 subharmonic voltages:

$U_{d\left(2\right)}=\underset{p=-\mathrm{1,1}}{\mathrm{\Σ}}\left[\begin{array}{cc}{S}_{u\left(p\right)}^{+}& S_{u\left(p\right)}^{-}\end{array}\right]\left[\begin{array}{c}{U}_{(2-p)}^{+}\\ U_{(2-p)}^{-}\end{array}\right]---\left(1\right)$

In the formula, U _(2-p) ⁺And U _(2-p) ^-Be respectively (2-p) order harmonic components of positive sequence and negative phase-sequence alternating voltage, wherein p gets 1 or-1, U _{D (2)}2 order harmonic components for the converter dc voltage;

Calculate the q order harmonic components of the three-phase current switch function of gained according to step (5), set up expression converter DC side electric current 0 time, 2 times and the equation of-2 order harmonic components and AC side k subharmonic current quantitative relationship;

$\left[\begin{array}{c}{I}_{\left(k\right)}^{+}\\ I_{\left(k\right)}^{-}\end{array}\right]=\left[\begin{array}{c}{S}_{i(k-2)}^{+}\\ S_{i(k-2)}^{-}\end{array}\right]I_{d\left(2\right)}+\left[\begin{array}{c}{S}_{i(k+2)}^{+}\\ S_{i(k+2)}^{-}\end{array}\right]I_{d(-2)}+\left[\begin{array}{c}{S}_{i\left(k\right)}^{+}\\ S_{i\left(k\right)}^{-}\end{array}\right]I_{d\left(0\right)}---\left(2\right)$

In the formula, I _(k) ⁺And I _(k) ^-Be respectively positive sequence and negative phase-sequence alternating current k order harmonic components, I _{D (2)}, I _{D (2)}And I _{D (0)}2 times ,-2 times and 0 order harmonic components for converter DC side electric current;

6.2, calculate the equivalent harmonic wave resistance of each time of seeing into from the converter DC side toward DC network Z according to existing method _{D (k)}, calculate the equivalent positive sequence harmonic impedance Z of seeing into from the converter AC side toward AC network of each time _(k) ⁺With the equivalent negative phase-sequence harmonic impedance of each time Z _(k) ^-, wherein subscript " k " is represented harmonic number, k is any nonzero integer;

6.3 calculate the Z of gained according to step (6.2) _(k) ⁺And Z _(k) ^-, set up the equation that reflects converter AC side harmonic voltage and harmonic current quantitative relationship:

$U_{\left(k\right)}^{+}=Z_{\left(k\right)}^{+}{I}_{\left(k\right)}^{+},k\≠1---\left(3\right)$

$U_{\left(k\right)}^{-}=Z_{\left(k\right)}^{-}{I}_{\left(k\right)}^{-},k\≠1---\left(4\right)$

6.4 calculate the equivalent k subharmonic impedance Z of seeing into to DC network from the converter DC side according to step (6.2) _{D (k)}, set up the equation that reflects converter DC side harmonic voltage and harmonic current quantitative relationship:

U _d(k)＝Z _d(k)I _d(k) (5)

6.5 simultaneous solution equation (1)～(5), thereby obtain converter alternating current-direct current both sides each harmonic voltage and current.

The present invention compared with prior art has following advantage and beneficial effect:

(1) existing unified system first-harmonic and uncharacteristic harmonics trend method, its converter dynamic model of setting up based on the differential equation carries out harmonic resolution, is difficult to from its alternating current-direct current both sides harmonic wave generation of mechanism research, transmission and interactional mechanism.This method depends on system-wide Model in Time Domain based on the differential equation, and need carry out iterative, so its calculating is larger, is difficult to use in extensive ac and dc systems.The invention provides a kind of iteration that need not, be applicable under various normal operating conditions and the failure condition ac and dc systems harmonic resolution method.This method is described converter alternating current-direct current both sides voltage and current relation with this by being configured to reflect the voltage and current switch function of converter switch motion, its clear physics conception, and computational process is simple and higher precision arranged.

(2) in view of when the AC system generation unbalanced fault, converter is in the asymmetric operating state.The actual conducting of converter valve will be offset constantly this moment, and the three-phase angle of overlap no longer is equal to each other.In addition, have humorous wave interaction between the AC and DC system: the each harmonic electric current that direct current system is injected to AC system will produce each time background harmonics voltage, and it will react on the HVDC system, influence the harmonic current that direct current system produces.Have the humorous wave interaction of not considering ac and dc systems based on the harmonic analysis method of switch function now, also do not consider the asymmetric operating state of converter under the AC system unbalanced fault.Be meant that specifically its switch function of constructing has supposed that the switch motion of converter under various disturbance situations is unaffected, has promptly supposed the three-phase alternating voltage symmetry, and the switch motion of each valve keeps symmetry in the converter.Therefore its switch function of constructing is the constant periodic function of waveform.Ac and dc systems harmonic resolution method provided by the present invention, set up based on fundametal component, revise the three-phase voltage current switch function of component and commutation component, can reflect the various operating conditions and the asymmetric operating state of converter all sidedly.In addition, institute of the present invention extracting method carries out simultaneous solution in conjunction with the equivalent harmonic wave impedance of ac and dc systems, has fully reflected to have humorous wave interaction between the AC and DC system.

(3) effectively reduced the calculating scale.The harmonic resolution method that the present invention carried need not iteration, does not rely on the Model in Time Domain of system, thereby has realized the simplification of finding the solution, and effectively reduces the calculating scale.

Description of drawings

Fig. 1 is the structural representation of converter in the HVDC (High Voltage Direct Current) transmission system of the present invention.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited thereto.

1. the structure of converter is utilized fundamental component (converting to the valve side) U of known three-phase change of current busbar voltage as shown in Figure 1 in the HVDC (High Voltage Direct Current) transmission system of the present invention _{A (1)}, U _{B (1)}And U _{C (1)}, as:

Calculate corresponding line voltage fundamental component:

2. with U _{Ab (1)}, U _{Bc (1)}And U _{Ca (1)}Be converted to the α component With the β component

$=\frac{2}{3}\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{ca}\left(1\right)}\\ U_{\mathrm{ab}\left(1\right)}\\ U_{\mathrm{bc}\left(1\right)}\end{array}\right]$

By With

Calculate the phase place of DC control system synchronizing voltage

According to

With And

Calculate the phase deviation of synchronizing voltage

Trigger angle instruction α according to DC control system _o, as α _o=19.77 °, calculate converter valve turn on delay angle θ _Ab, θ _BcAnd θ _Ca:

θ _ab＝22.11°；

θ _bc＝0°；

θ _ca＝0°；

With actual trigger angle α _Ab, α _BcAnd α _Ca:

α _ab＝0°；

α _bc＝60.24°；

α _ca＝17.85°；

According to the DC component of known converter DC side electric current (as I _{D (0)}=1.28kA), equivalent converter transformer leakage reactance X to the valve side _r(X _r=13.58 ohm), actual trigger angle α _MnWith | U _{Mn (1)}|, calculate angle of overlap:

5. turn on delay angle, actual trigger angle and the angle of overlap that is calculated by step (3) and step (4) calculates the q order harmonic components S of a, b and c phase voltage switch function respectively _{Ua (q)}, S _{Ub (q)}And S _{Uc (q)}, and the q order harmonic components S of a, b and c phase current switch function _{Ia (q)}, S _{Ib (q)}And S _{Ic (q)}, be example with wherein first harmonic component respectively:

S _b(1)＝0.1726+j0.5236

S _fA(1)＝0.1221+j0.0015

S _fB(1)＝-0.1221-j0.0015

S _fC(1)＝0

S _uμA(1)＝0.1172-j0.0896

S _uμB(1)＝-0.1082+j0.0223

S _uμC(1)＝-0.0090+j0.0672

S _iμA(1)＝0.1251-j0.0776

S _iμB(1)＝-0.1134+j0.0109

S _iμC(1)＝-0.0117+j0.0667

Then:

$\left\{\begin{array}{c}{S}_{\mathrm{ua}\left(1\right)}=S_{b\left(1\right)}+S_{\mathrm{u\μA}\left(1\right)}+S_{\mathrm{fA}\left(1\right)}=0.4120+j0.4355\\ S_{\mathrm{ub}\left(1\right)}=S_{b\left(1\right)}{e}^{-j2\mathrm{\π}/3}+S_{\mathrm{u\μB}\left(1\right)}+S_{\mathrm{fB}\left(1\right)}=0.1368-j0.3905\\ S_{\mathrm{uc}\left(1\right)}=S_{b\left(1\right)}{e}^{j2\mathrm{\π}/3}+S_{\mathrm{u\μC}\left(1\right)}+S_{\mathrm{fC}\left(1\right)}=-0.5488-j0.0451\end{array}\right.$

$\left\{\begin{array}{c}{S}_{\mathrm{ia}\left(1\right)}=S_{b\left(1\right)}+S_{\mathrm{i\μA}\left(1\right)}+S_{\mathrm{fA}\left(1\right)}=0.4199+j0.4475\\ S_{\mathrm{ib}\left(1\right)}=S_{b\left(1\right)}{e}^{-j2\mathrm{\π}/3}+S_{\mathrm{i\μB}\left(1\right)}+S_{\mathrm{fB}\left(1\right)}=0.1316-j0.4019\\ S_{\mathrm{ic}\left(1\right)}=S_{b\left(1\right)}{e}^{j2\mathrm{\π}/3}+S_{\mathrm{i\μC}\left(1\right)}+S_{\mathrm{fC}\left(1\right)}=-0.5515-j0.0456\end{array}\right.$

Calculate the q order harmonic components S of forward-order current switch function _{I (q)} ⁺, the q order harmonic components S of negative-sequence current switch function _{I (q)} ^-, the positive sequence voltage switch function q order harmonic components S _{U (q)} ⁺, the negative sequence voltage switch function q order harmonic components S _{U (q)} ^-, be example with wherein 1 order harmonic components respectively:

$\left[\begin{array}{c}{S}_{u\left(1\right)}^{+}\\ S_{u\left(1\right)}^{-}\end{array}\right]=\left[\begin{array}{ccc}{S}_{\mathrm{ua}\left(1\right)}& S_{\mathrm{ub}\left(1\right)}& S_{\mathrm{uc}\left(1\right)}\end{array}\right]\left[\begin{array}{cc}1& 1\\ a^2& a\\ a& a^2\end{array}\right]\left[\begin{array}{c}0.32+j0.06\\ 0.92+j1.25\end{array}\right]$

$\left[\begin{array}{c}{S}_{i\left(1\right)}^{+}\\ S_{i\left(1\right)}^{-}\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& a^2& a\\ 1& a& a^2\end{array}\right]\left[\begin{array}{c}{S}_{\mathrm{ia}\left(1\right)}\\ S_{\mathrm{ib}\left(1\right)}\\ S_{\mathrm{ic}\left(1\right)}\end{array}\right]=\left[\begin{array}{c}0.31+j0.42\\ 0.11+j0.03\end{array}\right]$

In the formula, a=e ^{J2 π/3}

6. according to existing method, calculate the equivalent harmonic impedance Z of each time that sees into from the converter DC side toward DC network _{D (k)}, be example with 2 subharmonic impedances wherein, Z is arranged _{D (2)}=6.93+j304.82 Ω; And the equivalent positive sequence harmonic impedance Z of seeing into from the converter AC side toward AC network _(k) ⁺With negative phase-sequence harmonic impedance Z _(k) ^-, be example with wherein 3 subharmonic impedances respectively, have $Z_{\left(3\right)}^{+}=-39.30+j93.59\mathrm{\Ω},$ $Z_{\left(3\right)}^{-}=-34.98+j134.17\mathrm{\Ω};$

7. simultaneous solution equation (1)～(5), thus the each harmonic voltage and current of converter AC side and DC side obtained, be example with DC side 2 subharmonic voltages and AC side 3 subharmonic currents, have:

U _d(2)＝136.31+j4.69kV

$I_{\left(3\right)}^{+}=0.33+j0.24\mathrm{kA}$

$I_{\left(3\right)}^{-}=0.13-j0.02\mathrm{kA}$

With rectification side change of current bus generation Single Phase Metal fault is example, apply the present invention to the Harmonics Calculation that the expensive wide II of CIGREHVDC modular system and south electric network returns the HVDC transmission system, and compare with the simulation result that carries out the Digital Simulation gained based on PSCAD/EMTDC.Considered in emulation that under the situation that does not cause converter generation commutation failure the unbalanced fault of different situations takes place separately for rectification side and inversion top-cross stream bus.

Return in the HVDC system detailed model at CIGRE HVDC system's detailed model and expensive wide II, converter adopts detailed electro-magnetic transient model, reflection data variation that can be real-time.And obtain generally acknowledging in the industry based on the correctness of the result of calculation of PSCAD/EMTDC gained, so the harmonic resolution method that other proposed is all by coming detection accuracy in contrast.

Table 1～3 are the emulation and the result of calculation of part, and wherein simulation value and calculated value are the value of humorous wave amplitude maximal phase in the abc three-phase.

The calculating and the simulation result of each harmonic when table 1 is rectification side Single Phase Metal fault:

Table 2 returns the Harmonics Calculation result and the emulation knot of HVDC system detailed model for expensive wide II:

Table 3 is the Harmonics Calculation result and the simulation result of CIGRE HVDC system detailed model:

The foregoing description is a preferred implementation of the present invention; but embodiments of the present invention are not limited by the examples; other any do not deviate from change, the modification done under spirit of the present invention and the principle, substitutes, combination, simplify; all should be the substitute mode of equivalence, be included within protection scope of the present invention.

Claims (8)

1, a kind of harmonic resolution method of alternating-current/direct-current interconnection system is characterized in that: specifically may further comprise the steps:

(1) data processing:, calculate corresponding line voltage fundamental component according to the fundamental component of known converter AC side phase voltage;

(2) phase deviation of calculating synchronizing voltage: the fundamental component of three line voltages is converted to α component and β component, and, calculates the phase place of DC control system synchronizing voltage respectively according to the amplitude and the phase place of α component and β component By the phase place of the fundamental component of three line voltages, and calculate

Calculate the phase deviation of synchronizing voltage respectively

With

Wherein subscript ab, bc and ca represent that respectively above-mentioned angular deflection is a benchmark with the phase place of ab, bc and ca line voltage fundamental component, set mark mn=ab, bc, ca; A, b, c represent the phase in the three-phase respectively;

(3) calculate converter valve turn on delay angle and actual trigger angle: calculate resulting synchronizing voltage phase deviation in trigger angle command value that more known DC control system provides and the step (2), calculate converter valve turn on delay angle θ _Ab, θ _BcAnd θ _Ca, and actual trigger angle α _Ab, α _BcAnd α _Ca, wherein subscript ab, bc and ca represent that respectively above-mentioned angle is corresponding to ab, bc and the commutation of ca two-phase;

(4) calculate angle of overlap: according to the fundamental component of the line voltage that calculates in the step (1) with by the actual trigger angle of step (3) gained, and known equivalence is to the converter transformer leakage reactance X of valve side _r, converter DC side electric current DC component I _{D (0)}Angle of overlap μ when calculating ab, bc and the commutation of ca two-phase _Ab, μ _BcAnd μ _Ca

(5) the q order harmonic components of compute switch function: the turn on delay angle, actual trigger angle and the angle of overlap that calculate by step (3) and step (4), calculate the q order harmonic components of three-phase current switch function, and calculate the q order harmonic components of positive sequence and negative-sequence current switch function thus, wherein q is any nonzero integer; Turn on delay angle, actual trigger angle and angle of overlap by step (3) and step (4) calculate calculate the q order harmonic components of three-phase voltage switch function, and calculate the q order harmonic components of positive sequence and negative sequence voltage switch function thus;

(6) find the solution the each harmonic voltage and current of AC/DC interconnected system: the preface component model of structure converter, and calculate the equivalent harmonic impedance Z of each time that sees into from the converter DC side toward DC network according to existing method _{D (k)}, calculate the equivalent positive sequence harmonic impedance Z of seeing into from the converter AC side toward AC network of each time _(k) ⁺With the equivalent negative phase-sequence harmonic impedance of each time Z _(k) ^-Thereby, find the solution the each harmonic voltage and current of AC/DC interconnected system.

2, a kind of harmonic resolution method of alternating-current/direct-current interconnection system according to claim 1 is characterized in that: described step (1) data processing specifically is meant: according to the fundamental component U of known converter AC side three-phase voltage _{A (1)}, U _{B (1)}, U _{C (1)}, subscript " 1 " expression first harmonic component wherein, i.e. fundamental component, calculate corresponding line voltage fundamental component by following formula:

U _ab(1)＝U _b(1)-U _a(1)

U _bc(1)＝U _c(1)-U _b(1)

U _ca(1)＝U _a(1)-U _c(1)

Wherein, U _{Ca (1)}Fundamental component for change of current bus ca line voltage; U _{Ab (1)}Fundamental component for change of current bus ab line voltage; U _{Bc (1)}Fundamental component for change of current bus bc line voltage.

3, a kind of harmonic resolution method of alternating-current/direct-current interconnection system according to claim 1 is characterized in that: described step (2) is calculated the skew of synchronizing voltage phase place, specifically is meant: establish

With

Represent the α component and the β component of commutation voltage respectively, it is calculated by following formula:

$\left[\begin{array}{c}{\stackrel{.}{U}}_{\mathrm{\α}}\\ {\stackrel{.}{U}}_{\mathrm{\β}}\end{array}\right.3=\frac{2}{3}\left[\begin{array}{ccc}1& -1/2& -1/2\\ 0& \sqrt{3}/2& -\sqrt{3}/2\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{ca}\left(1\right)}\\ U_{\mathrm{ab}\left(1\right)}\\ U_{\mathrm{bc}\left(1\right)}\end{array}\right]$

Utilize the α component of commutation voltage

β component with commutation voltage

Calculate the phase place of DC control system synchronizing voltage by following formula

In the formula, U _αAnd U _βBe respectively the amplitude of the α component and the β component of commutation voltage;

With

Be respectively the α component of commutation voltage and the phase angle of β component;

According to U _{Ca (1)}Phase place

U _{Ab (1)}Phase place

U _{Bc (1)}Phase place Calculate the phase deviation of synchronizing voltage respectively

Wherein Phase deviation for the alternate synchronizing voltage of ca;

Phase deviation for the alternate synchronizing voltage of ab;

Phase deviation for the alternate synchronizing voltage of bc.

4, a kind of harmonic resolution method of alternating-current/direct-current interconnection system according to claim 1 is characterized in that: described step (3) is calculated converter valve turn on delay angle and actual trigger angle, specifically is meant: according to the trigger angle instruction α of DC control system _o, calculate converter valve turn on delay angle θ _MnWith actual trigger angle α _Mn:

In the following formula, all angles are all to lag behind to just, and are leading for negative.

5, a kind of harmonic resolution method of alternating-current/direct-current interconnection system according to claim 1 is characterized in that: described step (4) is calculated angle of overlap, specifically is meant: establish μ _MnAngle of overlap during for the commutation of mn two-phase, and according to the DC component I of known converter DC side electric current _{D (0)}, i.e. zero degree harmonic component, equivalent converter transformer leakage reactance X to the valve side _r, actual trigger angle α _Mn, and the amplitude of change of current bus line voltage fundamental component | U _{Mn (1)}|, the following formula of substitution calculates angle of overlap μ _Mn:

μ _mn＝cos ^-1(cosα _mn-2X _rI _d(0)/|U _mn(1)|)-α _mn

6, a kind of harmonic resolution method of alternating-current/direct-current interconnection system according to claim 1 is characterized in that: the q order harmonic components of described step (5) compute switch function specifically is meant:

5.1 calculate the q order harmonic components S of switch function fundametal component by the following formula formula _{B (q)}Q order harmonic components S with switch function correction component _{Fab (q)}, S _{Fbc (q)}, S _{Fca (q)}:

$S_{b\left(q\right)}=\frac{1}{\mathrm{q\π}}[\sin \frac{\mathrm{q\π}}{3}+j(\cos \mathrm{q\π}+\cos \frac{2\mathrm{q\π}}{3})]$

$S_{\mathrm{fab}\left(q\right)}=\frac{j}{2\mathrm{q\π}}\left[e^{-j{\mathrm{\θ}}_{\mathrm{ab}}}(e^{-\mathrm{jq\π}}-1)(e^{-\mathrm{jq}{\mathrm{\θ}}_{\mathrm{ab}}}-1)\right]$

$S_{\mathrm{fbc}\left(q\right)}=\frac{j}{2\mathrm{q\π}}\left[e^{-j{\mathrm{\θ}}_{\mathrm{bc}}}(e^{-\mathrm{jq\π}}-1)(e^{-\mathrm{jq}{\mathrm{\θ}}_{\mathrm{bc}}}-1)\right]$

$S_{\mathrm{fca}\left(q\right)}=\frac{j}{2\mathrm{q\π}}\left[e^{-j{\mathrm{\θ}}_{\mathrm{ca}}}(e^{-\mathrm{jq\π}}-1)(e^{-\mathrm{jq}{\mathrm{\θ}}_{\mathrm{ca}}}-1)\right]$

Wherein, q is any nonzero integer; E is the truth of a matter of natural logrithm; J is an imaginary unit;

5.2 q order harmonic components S by following formula calculating voltage switch function commutation component _{U μ ab (q)}, S _{U μ bc (q)}, S _{U μ ca (q)}Q order harmonic components S with current switch function commutation component _{I μ ab (q)}, S _{I μ bc (q)}, S _{I μ ca (q)}:

$S_{\mathrm{u\μab}\left(q\right)}=\frac{j}{4\mathrm{q\π}}\left[e^{-j{\mathrm{\μ}}_{\mathrm{ab}}}(e^{-\mathrm{jq\π}}-1)(e^{-\mathrm{jq}{\mathrm{\μ}}_{\mathrm{ab}}}-1)\right]$

$S_{\mathrm{u\μbc}\left(q\right)}=\frac{j}{4\mathrm{q\π}}\left[e^{-j{\mathrm{\μ}}_{\mathrm{bc}}}(e^{-\mathrm{jq\π}}-1)(e^{-\mathrm{jq}{\mathrm{\μ}}_{\mathrm{bc}}}-1)\right]$

$S_{\mathrm{u\μca}\left(q\right)}=\frac{j}{4\mathrm{q\π}}\left[e^{-j{\mathrm{\μ}}_{\mathrm{ca}}}(e^{-\mathrm{jq\π}}-1)(e^{-\mathrm{jq}{\mathrm{\μ}}_{\mathrm{ca}}}-1)\right]$

$S_{\mathrm{i\μab}\left(q\right)}={\∫}_{-\mathrm{\π}}^{-\mathrm{\π}+{\mathrm{\μ}}_{\mathrm{ab}}}[\frac{\left|U_{\mathrm{ab}\left(1\right)}\right|(\cos {\mathrm{\α}}_{\mathrm{ab}}+\cos ({\mathrm{\α}}_{\mathrm{ab}}+\mathrm{\ωt}))}{2X_r{I}_{d\left(0\right)}}-1]e^{-\mathrm{jq\ωt}}\mathrm{d\ωt}$

$+{\∫}_0^{{\mathrm{\μ}}_{\mathrm{ab}}}[1-\frac{\left|U_{\mathrm{ab}\left(1\right)}\right|(\cos {\mathrm{\α}}_{\mathrm{ab}}-\cos ({\mathrm{\α}}_{\mathrm{ab}}+\mathrm{\ωt}))}{2X_r{I}_{d\left(0\right)}}]e^{-\mathrm{jq\ωt}}\mathrm{d\ωt}$

$S_{\mathrm{i\μbc}\left(q\right)}={\∫}_{-\mathrm{\π}}^{-\mathrm{\π}+{\mathrm{\μ}}_{\mathrm{bc}}}[\frac{\left|U_{\mathrm{bc}\left(1\right)}\right|(\cos {\mathrm{\α}}_{\mathrm{bc}}+\cos ({\mathrm{\α}}_{\mathrm{bc}}+\mathrm{\ωt}))}{2X_r{I}_{d\left(0\right)}}-1]e^{-\mathrm{jq\ωt}}\mathrm{d\ωt}$

$+{\∫}_0^{{\mathrm{\μ}}_{\mathrm{bc}}}[1-\frac{\left|U_{\mathrm{bc}\left(1\right)}\right|(\cos {\mathrm{\α}}_{\mathrm{bc}}-\cos ({\mathrm{\α}}_{\mathrm{bc}}+\mathrm{\ωt}))}{2X_r{I}_{d\left(0\right)}}]e^{-\mathrm{jq\ωt}}\mathrm{d\ωt}$

$S_{\mathrm{i\μca}\left(q\right)}={\∫}_{-\mathrm{\π}}^{-\mathrm{\π}+{\mathrm{\μ}}_{\mathrm{ca}}}[\frac{\left|U_{\mathrm{ca}\left(1\right)}\right|(\cos {\mathrm{\α}}_{\mathrm{ca}}+\cos ({\mathrm{\α}}_{\mathrm{ca}}+\mathrm{\ωt}))}{2X_r{I}_{d\left(0\right)}}-1]e^{-\mathrm{jq\ωt}}\mathrm{d\ωt}$

$+{\∫}_0^{{\mathrm{\μ}}_{\mathrm{ca}}}[1-\frac{\left|U_{\mathrm{ca}\left(1\right)}\right|(\cos {\mathrm{\α}}_{\mathrm{ca}}-\cos ({\mathrm{\α}}_{\mathrm{ca}}+\mathrm{\ωt}))}{2X_r{I}_{d\left(0\right)}}]e^{-\mathrm{jq\ωt}}\mathrm{d\ωt}$

In the formula, | U _{Mn (1)}| be U _{Mn (1)}Amplitude, α _MnBe actual trigger angle;

5.3 calculate the q order harmonic components S of three-phase voltage switch function _{Ua (q)}, S _{Ub (q)}, S _{Uc (q)}Q order harmonic components S with the three-phase current switch function _{Ia (q)}, S _{Ib (q)}, S _{Ic (q)}:

$\left\{\begin{array}{c}{S}_{\mathrm{ua}\left(q\right)}=S_{b\left(q\right)}+S_{\mathrm{u\μA}\left(q\right)}+S_{\mathrm{fA}\left(q\right)}\\ S_{\mathrm{ub}\left(q\right)}=S_{b\left(q\right)}{e}^{-j2\mathrm{q\π}/3}+S_{\mathrm{u\μB}\left(q\right)}+S_{\mathrm{fB}\left(q\right)}\\ S_{\mathrm{uc}\left(q\right)}=S_{b\left(q\right)}{e}^{j2\mathrm{q\π}/3}+S_{\mathrm{u\μC}\left(q\right)}+S_{\mathrm{fC}\left(q\right)}\end{array}\right.$

$\left\{\begin{array}{c}{S}_{\mathrm{ia}\left(q\right)}=S_{b\left(q\right)}+S_{\mathrm{i\μA}\left(q\right)}+S_{\mathrm{fA}\left(q\right)}\\ S_{\mathrm{ib}\left(q\right)}=S_{b\left(q\right)}{e}^{-j2\mathrm{q\π}/3}+S_{\mathrm{i\μB}\left(q\right)}+S_{\mathrm{fB}\left(q\right)}\\ S_{\mathrm{ic}\left(q\right)}=S_{b\left(q\right)}{e}^{j2\mathrm{q\π}/3}+S_{\mathrm{i\μC}\left(q\right)}+S_{\mathrm{fC}\left(q\right)}\end{array}\right.$

In the formula,

$S_{\mathrm{u\μA}\left(q\right)}=S_{\mathrm{u\μab}\left(q\right)}{e}^{-\mathrm{jq}(\mathrm{\π}/3+{\mathrm{\θ}}_{\mathrm{ab}})}-S_{\mathrm{u\μca}\left(q\right)}{e}^{\mathrm{jq}(\mathrm{\π}/3-{\mathrm{\θ}}_{\mathrm{ca}})};$

$S_{\mathrm{u\μB}\left(q\right)}=S_{\mathrm{u\μbc}\left(q\right)}{e}^{-\mathrm{jq}(\mathrm{\π}/3+{\mathrm{\θ}}_{\mathrm{bc}})}-S_{\mathrm{u\μab}\left(q\right)}{e}^{-\mathrm{jq}(\mathrm{\π}/3-{\mathrm{\θ}}_{\mathrm{ab}})}$

$S_{\mathrm{u\μC}\left(q\right)}=S_{\mathrm{u\μca}\left(q\right)}{e}^{-\mathrm{jq}(\mathrm{\π}/3+{\mathrm{\θ}}_{\mathrm{ca}})}-S_{\mathrm{u\μbc}\left(q\right)}{e}^{-\mathrm{jq}(\mathrm{\π}/3-{\mathrm{\θ}}_{\mathrm{bc}})};$

$S_{\mathrm{fA}\left(q\right)}=S_{\mathrm{fab}\left(q\right)}{e}^{-\mathrm{jq\π}/3}-S_{\mathrm{fca}\left(q\right)}{e}^{\mathrm{jq\π}/3};$

$S_{\mathrm{fB}\left(q\right)}=S_{\mathrm{fbc}\left(q\right)}-S_{\mathrm{fab}\left(q\right)}{e}^{\mathrm{jq\π}/3};$

$S_{\mathrm{fC}\left(q\right)}=S_{\mathrm{fca}\left(q\right)}{e}^{\mathrm{jq\π}/3}-S_{\mathrm{fbc}\left(q\right)};$

$S_{\mathrm{i\μA}\left(q\right)}=S_{\mathrm{i\μab}\left(q\right)}{e}^{-\mathrm{jq}({\mathrm{\θ}}_{\mathrm{ab}}+\mathrm{\π}/3)}-S_{\mathrm{i\μca}\left(q\right)}{e}^{\mathrm{jq}(\mathrm{\π}/3-{\mathrm{\θ}}_{\mathrm{ca}})};$

$S_{\mathrm{i\μB}\left(q\right)}=S_{\mathrm{i\μbc}\left(q\right)}{e}^{-\mathrm{jq}({\mathrm{\θ}}_{\mathrm{bc}}+\mathrm{\π}/3)}-S_{\mathrm{i\μab}\left(q\right)}{e}^{-\mathrm{jq}(\mathrm{\π}/3+{\mathrm{\θ}}_{\mathrm{ab}})};$

$S_{\mathrm{i\μC}\left(q\right)}=S_{\mathrm{i\μca}\left(q\right)}{e}^{\mathrm{jq}\left({\mathrm{\π}/3-\mathrm{\θ}}_{\mathrm{ca}}\right)}-S_{\mathrm{i\μbc}\left(q\right)}{e}^{-\mathrm{jq}(\mathrm{\π}/3+{\mathrm{\θ}}_{\mathrm{bc}})};$

Wherein, θ _Ab, θ _BcAnd θ _CaConverter valve turn on delay angle when being respectively ab, bc and the commutation of ca two-phase; μ _Ab, μ _BcAnd μ _CaAngle of overlap when being respectively ab, bc and the commutation of ca two-phase;

5.4 respectively by S _{Ua (q)}, S _{Ub (q)}, S _{Uc (q)}And S _{Ia (q)}, S _{Ib (q)}, S _{Ic (q)}Calculate positive sequence and negative sequence voltage switch function, and positive sequence and negative-sequence current switch function:

$\left[\begin{array}{c}{S}_{u\left(q\right)}^{+}\\ S_{u\left(q\right)}^{-}\end{array}\right]=\left[\begin{array}{ccc}{S}_{\mathrm{ua}\left(q\right)}& S_{\mathrm{ub}\left(q\right)}& S_{\mathrm{uc}\left(q\right)}\end{array}\right]\left[\begin{array}{cc}1& 1\\ a^2& a\\ a& a^2\end{array}\right]$

$\left[\begin{array}{c}{S}_{i\left(q\right)}^{+}\\ S_{i\left(q\right)}^{-}\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& a^2& a\\ 1& a& a^2\end{array}\right]\left[\begin{array}{c}{S}_{\mathrm{ia}\left(q\right)}\\ s_{\mathrm{ib}\left(q\right)}\\ S_{\mathrm{ic}\left(q\right)}\end{array}\right]$

In the formula, a=e ^{J2 π/3}, S _{I (q)} ⁺Q order harmonic components for the forward-order current switch function; S _{I (q)} ^-Q order harmonic components for the negative-sequence current switch function; S _{U (q)} ⁺Q order harmonic components for the positive sequence voltage switch function; S _{U (q)} ^-Q order harmonic components for the negative sequence voltage switch function.

7, a kind of harmonic resolution method of alternating-current/direct-current interconnection system according to claim 1 is characterized in that: described step (6) is found the solution the each harmonic voltage and current of AC/DC interconnected system, specifically is meant:

6.1 the preface component model of structure converter:

Calculate the q order harmonic components of the three-phase voltage switch function of gained according to step (5), set up the equation of the quantitative relationship of expression converter DC side 2 subharmonic voltages and AC side fundamental frequency and 3 subharmonic voltages:

$U_{d\left(2\right)}=\underset{p=-\mathrm{1,1}}{\mathrm{\Σ}}\left[\begin{array}{cc}{S}_{u\left(p\right)}^{+}& S_{u\left(p\right)}^{-}\end{array}\right]\left[\begin{array}{c}{U}_{(2-p)}^{+}\\ U_{(2-p)}^{-}\end{array}\right]---\left(1\right)$

In the formula, U _(2-p) ⁺And U _(2-p) ^-Be respectively (2-p) order harmonic components of positive sequence and negative phase-sequence alternating voltage, wherein p gets 1 or-1, U _{D (2)}2 order harmonic components for the converter dc voltage;

Calculate the q order harmonic components of the three-phase current switch function of gained according to step (5), set up expression converter DC side electric current 0 time, 2 times and the equation of-2 order harmonic components and AC side k subharmonic current quantitative relationship;

$\left[\begin{array}{c}{I}_{\left(k\right)}^{+}\\ I_k^{-}\end{array}\right]=\left[\begin{array}{c}{S}_{i(k-2)}^{+}\\ S_{i(k-2)}^{-}\end{array}\right]I_{d\left(2\right)}+\left[\begin{array}{c}{S}_{i(k+2)}^{+}\\ S_{i(k+2)}^{-}\end{array}\right]I_{d(-2)}+\left[\begin{array}{c}{S}_{i\left(k\right)}^{+}\\ S_{i\left(k\right)}^{-}\end{array}\right]I_{d\left(0\right)}---\left(2\right)$

In the formula, I _(k) ⁺And I _(k) ^-Be respectively the k order harmonic components of positive sequence and negative phase-sequence alternating current, I _{D (2)}, I _{D (2)}And I _{D (0)}2 times ,-2 times and 0 order harmonic components for converter DC side electric current;

6.2, calculate the equivalent harmonic wave resistance of each time of seeing into from the converter DC side toward DC network Z according to existing method _{D (k)}, calculate the equivalent positive sequence harmonic impedance Z of seeing into from the converter AC side toward AC network of each time _(k) ⁺With the equivalent negative phase-sequence harmonic impedance of each time Z _(k) ^-, wherein subscript " k " is represented harmonic number, k is any nonzero integer;

6.3 calculate the Z of gained according to step (6.2) _(k) ⁺And Z _(k) ^-, set up the equation that reflects converter AC side harmonic voltage and harmonic current quantitative relationship:

$U_{\left(k\right)}^{+}=Z_{\left(k\right)}^{+}{I}_{\left(k\right)}^{+},k\≠1---\left(3\right)$

$U_{\left(k\right)}^{-}=Z_{\left(k\right)}^{-}{I}_{\left(k\right)}^{-},k\≠1---\left(4\right)$

6.4 calculate the equivalent k subharmonic impedance Z of seeing into to DC network from the converter DC side according to step (6.2) _{D (k)}, set up the equation that reflects converter DC side harmonic voltage and harmonic current quantitative relationship:

U _d(k)＝Z _d(k)I _d(k) (5)

6.5 simultaneous solution equation (1)～(5), thereby obtain converter alternating current-direct current both sides each harmonic voltage and current.

Images