CN110909518B - MMC reliability analysis method based on improved average value model - Google Patents

MMC reliability analysis method based on improved average value model Download PDF

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CN110909518B
CN110909518B CN201911076070.4A CN201911076070A CN110909518B CN 110909518 B CN110909518 B CN 110909518B CN 201911076070 A CN201911076070 A CN 201911076070A CN 110909518 B CN110909518 B CN 110909518B
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晁武杰
唐志军
林国栋
郭健生
胡文旺
李超
李智诚
林少真
翟博龙
刘龙辉
张志耿
林晨翔
吴翔宇
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Electric Power Research Institute of State Grid Fujian Electric Power Co Ltd
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Abstract

The invention relates to an MMC reliability analysis method based on an improved average value model, which comprises the following steps: s1, constructing an improved average value model capable of reflecting sub-module faults according to an expression of a sub-module average switching function in an MMC under the operation state with the sub-module faults; s2, solving output direct current voltage and current, alternating current voltage and current and internal circulation of a bridge arm of the MMC based on an improved average value model and in combination with the electrical characteristics and the circuit law of the power element to obtain the running state of the MMC under the sub-module fault; s3, constructing an MMC reliability index; and S4, evaluating the reliability of the MMC system according to the running state of the MMC under the sub-module fault and based on the reliability index of the MMC. According to the method, the influence of submodule faults on the average switching function is considered, and the reliability evaluation calculation result is more accurate.

Description

MMC reliability analysis method based on improved average value model
Technical Field
The invention belongs to the field of MMC reliability analysis, and particularly relates to an MMC reliability analysis method based on an improved average value model.
Background
Due to the development of power electronic technology, controllable turn-off devices and the emergence of pulse width modulation technology, the direct current transmission technology is a brand-new stage, namely flexible direct current transmission technology. Modular Multilevel Converters (MMC) have the advantages of high modularity, low switching frequency, good waveform quality, etc., so the flexible dc power transmission system based on MMC is the most studied and the most existing in actual engineering today. The system has good development and application prospects, so that reliability analysis on the MMC is very important.
The method for evaluating the reliability of the power system mainly comprises four parts, namely element reliability modeling, system state selection, system state analysis and reliability index calculation, and the MMC is different from the traditional power system in that a large number of power electronic devices and control technologies are applied, so that the MMC system analysis method is different from the traditional power system. The existing MMC system analysis method is based on an average value model for analysis, the calculation result is accurate in a normal operation state, but under the operation state with sub-module faults, the influence of the sub-module faults on an average switching function is not considered in the existing average value model, and the calculation result is inaccurate.
Disclosure of Invention
In view of this, the present invention provides an MMC reliability analysis method based on an improved average value model, which considers the influence of sub-module faults on an average switching function, and the reliability evaluation calculation result is more accurate.
In order to achieve the purpose, the invention adopts the following technical scheme:
an MMC reliability analysis method based on an improved average value model comprises the following steps:
s1, constructing an improved average value model capable of reflecting sub-module faults according to an expression of a sub-module average switch function in an MMC under the condition that the sub-module faults exist;
s2, solving output direct current voltage and current, alternating current voltage and current and internal circulation of a bridge arm of the MMC based on an improved average value model and in combination with the electrical characteristics and the circuit law of the power element to obtain the running state of the MMC under the sub-module fault;
s3, constructing an MMC reliability index;
and S4, evaluating the reliability of the MMC system according to the running state of the MMC under the sub-module fault and based on the reliability index of the MMC.
Further, the step S1 specifically includes:
step S11, obtaining u according to the voltage waveform at the x-phase alternating current outlet, wherein x = a, b and c vx_ref And u vx Respectively a modulated wave and an output wave at an x-phase alternating current outlet, the expressions are respectively
u vx_ref ＝U m sin(ωt) (1)
Figure BDA0002262495310000021
In formula (2), U m For modulating the amplitude of the wave, U C For each submodule operating voltage, s isThe maximum number of inputs of the sub-modules,
Figure BDA0002262495310000022
the phase angle of the modulation wave corresponding to the input of k submodules is expressed as follows
Figure BDA0002262495310000031
Figure BDA0002262495310000032
Figure BDA0002262495310000033
Wherein m is the modulation ratio, N is the number of sub-modules of a single bridge arm, and U dc To output a dc voltage value.
Reference voltage u of upper and lower bridge arms of each phase without adding circulating current suppression px_ref 、u nx_ref The expression is as follows:
Figure BDA0002262495310000034
s12, acquiring the number of submodules input by an upper bridge arm and a lower bridge arm of each phase according to the distribution map of the number of the submodules input by the upper bridge arm and the lower bridge arm under an NLM (non line of sight) modulation strategy;
step S13, setting X, X = a, b, c phase upper bridge arm to have X px The sub-modules are in fault, and an instantaneous expression of the number of the upper bridge arm input sub-modules reflecting the number of the fault sub-modules is obtained
Figure BDA0002262495310000035
Equation (7) is expressed as follows using a fourier series expansion:
Figure BDA0002262495310000041
wherein
Figure BDA0002262495310000042
/>
Figure BDA0002262495310000043
In formula (10)
Figure BDA0002262495310000044
γ x The phase angle difference between the phase voltage phase angle and the phase angle of the a phase voltage is 0, 120 degrees and-120 degrees corresponding to the a phase, the b phase and the c phase respectively;
step S14, supposing that the lower bridge arm has X nx If the sub-modules are in fault, obtaining the instantaneous expression of the number of the lower bridge arm input sub-modules reflecting the number of the fault sub-modules
Figure BDA0002262495310000045
Equation (12) is expressed as follows using a fourier series expansion:
Figure BDA0002262495310000051
wherein
Figure BDA0002262495310000052
Figure BDA0002262495310000053
By the formulae (8) and (13) can be obtainedImproved average switching function S of lower bridge arm px 、S nx
Figure BDA0002262495310000054
This is the improved mean model.
Further, the step S2 specifically includes:
s21, setting the upper and lower bridge arm current i of each phase px 、i nx By a direct current I dcpx 、I dcnx And the harmonic current of each order
Figure BDA0002262495310000055
The composition is shown as the following formula:
Figure BDA0002262495310000061
wherein n is the harmonic order, I pxn 、I nxn For each harmonic amplitude, θ pxn 、θ nxn The phase angle of each harmonic.
Step S22, ignoring third and higher harmonics and considering that the second harmonic is suppressed by the circulating current suppression strategy, equation (17) can be converted to
Figure BDA0002262495310000062
Aggregate average value i of upper and lower bridge arm capacitance currents C_px 、i C_nx As the product of the corresponding leg current and the average switching function,
Figure BDA0002262495310000071
step S23, when the system is in a stable operation state, the capacitor voltage is in a dynamic balance state, so that the DC component of the capacitor current is 0, namely
Figure BDA0002262495310000072
Formula (20) can be rewritten as
Figure BDA0002262495310000073
The average value of the capacitor voltage set of the upper bridge arm is
Figure BDA0002262495310000081
Wherein C is the sub-module capacitance value, so that the output voltage u of the upper bridge arm can be obtained px Is composed of
Figure BDA0002262495310000082
In the formula u px_0 、u px_1 、u px_2 、V px And the direct current component, the fundamental frequency component, the second harmonic component and the third and above higher harmonic components of the output voltage of the upper bridge arm are respectively represented.
Step S24, setting the power voltage of the alternating current system as u sx The bridge arm inductance is L, and kirchhoff voltage law is applied to the fundamental component of the upper bridge arm and the AC side path to obtain the fundamental component
Figure BDA0002262495310000083
If the AC system voltage phase angle is ahead of the voltage phase angle delta at the AC outlet of the MMC and the voltage at the AC outlet of the MMC is used as the reference value, the formula (24) can be converted into the following formula
Figure BDA0002262495310000084
The finishing formula (25) can be obtained
a 1 sinωt+a 2 cosωt＝0 (26)
In the formula
Figure BDA0002262495310000091
If the formula (26) is satisfied, then
Figure BDA0002262495310000092
Combined and arranged to obtain the product (21), (27), (28)
Figure BDA0002262495310000093
In the formula
Figure BDA0002262495310000094
Wherein
Figure BDA0002262495310000101
Can be obtained by solving formula (29)
Figure BDA0002262495310000102
From this, the amplitude of the base frequency current is obtained
Figure BDA0002262495310000103
Wherein
Figure BDA0002262495310000104
And S21, obtaining instantaneous expressions of the voltage and the current of each bridge arm and instantaneous expressions of the voltage and the current of each node according to the obtained amplitude of the fundamental frequency current, and obtaining the running state of the current system.
Further, the MMC reliability indexes comprise an expected direct-current voltage output by the MMC, an expected direct-current voltage ripple coefficient, an expected MMC transmission power shortage, an expected power shortage probability, an expected current harmonic content at an alternating-current outlet and an expected bridge arm circulating current content.
Further, the expectation of the MMC outputting the dc voltage is specifically:
MMC outputs direct current voltage U dc Is formed by connecting the output direct current voltages of three-phase bridge arms in parallel, so that U is formed dc Can be expressed as
U dc (t)＝max{u dca (t)，u dcb (t)，u dcc (t)} (35)
In the formula, max { } represents taking the maximum value;
to U dc Fourier decomposition is carried out to obtain
Figure BDA0002262495310000111
Wherein, U dc0 Is a direct current component, a k sin(kωt+δ k ) For each alternating current component.
So MMC outputs DC voltage expectation E (U) dc ) Is shown as
E(U dc )＝∑ X∈S U dc0 (X)p(X) (37)。
Wherein S is the set of all the states of the system, X is a system state, U dc0 (X) is the DC component on the DC bus in the X state, and p (X) is the probability of the X state (the same below).
Further, the dc voltage ripple coefficient is expected to be specifically:
by half the peak-to-peak value or by a table-type ripple of the effective value, the ripple magnitude U w The details are as follows
Figure BDA0002262495310000112
Wherein T is the power frequency period.
The ripple factor ε is the ratio of ripple to DC voltage, i.e.
Figure BDA0002262495310000113
Therefore, the expected ripple factor E (ε) of the MMC output DC voltage can be expressed as
E(ε)＝∑ X∈S ε(X)p(X) (40)。
Wherein epsilon (X) is the output direct current voltage ripple coefficient under the X state.
Further, the MMC transmission power shortage expectation and power shortage probability expectation specifically include:
the actual transmission power of the MMC can be expressed as a direct current bus voltage U dc With the direct bus current I dc Product of (2)
P＝U dc ·I dc (41)
The power deficit of the MMC may be expressed as the rated power P e Difference from actual power P, i.e.
P loss ＝P e -P (42)
MMC power deficit therefore expects E (P) loss ) Is shown as
E(P loss )＝∑ X∈S P loss (X)p(X) (43)
Probability of power deficit p loss Is shown as
Figure BDA0002262495310000121
Wherein, P loss (X) is the power deficit in the X state.
Further, the current harmonic content at the ac outlet is expected to be specifically:
Figure BDA0002262495310000131
in the formula I k Representing the current amplitude of the kth harmonic at the ac outlet.
Further, the expected bridge arm circulating current content is specifically as follows:
bridge arm circulating current content is expected to be expressed as follows
Figure BDA0002262495310000132
Wherein, I cxk Representing the k-times circulating amplitude, I, of the x-phase bridge arm dc A rated direct current value is set for the bridge arm;
comprehensively considering the circulating current content of the three-phase bridge arm, the final expected value is
E(TCD)＝max{E a (TCD)，E b (TCD)，E c (TCD)} (47)。
Compared with the prior art, the invention has the following beneficial effects:
1. according to the method, the influence of the submodule faults on the average switching function is considered, and the reliability evaluation calculation result is more accurate.
2. The invention utilizes an improved average value model to analyze the state of the MMC: based on an improved average value model, the output direct current voltage and current, the output alternating current voltage and current and the internal circulation of the bridge arm of the MMC are solved by combining the electrical characteristics of the power element and the circuit laws such as kirchhoff voltage and current, and the running state of the MMC under the sub-module fault can be obtained.
Drawings
FIG. 1 is an output voltage and its modulated wave at the a-phase AC outlet of the MMC system in an embodiment of the present invention;
FIG. 2 is a distribution diagram of the number of submodules thrown into the upper and lower arms in an embodiment of the present invention;
fig. 3 is a flow chart of a method in an embodiment of the invention.
Detailed Description
The invention is further explained by the following embodiments in conjunction with the drawings.
Referring to fig. 3, the present invention provides an improved mean value model-based MMC reliability analysis method, including the following steps:
s1, constructing an improved average value model capable of reflecting sub-module faults according to an expression of a sub-module average switching function in an MMC under the operation state with the sub-module faults;
s2, solving output direct current voltage and current, alternating current voltage and current and internal circulation of a bridge arm of the MMC based on the improved average value model and by combining the electrical characteristics of the power element and a circuit law to obtain the running state of the MMC under the sub-module fault;
s3, establishing an MMC reliability index;
and S4, evaluating the reliability of the MMC system according to the running state of the MMC under the sub-module fault and based on the reliability index of the MMC.
In this embodiment, the improved mean model is specifically constructed as follows:
taking phase a as an example, the voltage waveform at the a-phase AC outlet can be obtained as shown in FIG. 1,
in the figure, the voltage waveform at the x-phase ac outlet, where x = a, b, c, results in
u vx_ref And u vx Respectively a modulated wave and an output wave at an x-phase alternating current outlet, the expressions are respectively
u va_ref ＝U m sin(ωt) (1)
Figure BDA0002262495310000141
In the formula (2), m is a modulation ratio, U m For modulating the amplitude of the wave, U C For the operating voltage of each submodule, s is the maximum input number of submodules,
Figure BDA0002262495310000151
the phase angle of the modulation wave corresponding to the input of k submodules is expressed as follows
Figure BDA0002262495310000152
Figure BDA0002262495310000153
Figure BDA0002262495310000154
Wherein m is the modulation ratio, N is the number of sub-modules of the single bridge arm, U dc To output a dc voltage value.
Reference voltage u of upper and lower bridge arms of each phase without adding circulating current suppression px_ref 、u nx_ref The expression is as follows:
Figure BDA0002262495310000155
under the NLM modulation strategy, the number of submodules invested by upper and lower bridge arms of each phase can be represented by FIG. 2
To output a wave u va For the limit, the upper part is the number of upper bridge arm input submodules (the hatched part in the figure), the lower part is the number of lower bridge arm input submodules (the blank part in the figure), when the output wave is 0, the number of the upper and lower bridge arm input submodules is equal and is N/2, and as the output wave increases, every time one U rises, the output wave increases c The number of the submodules of the lower bridge arm in the input state is increased by 1, the number of the submodules of the upper bridge arm in the input state is decreased by 1, and the rest is repeated until the output wave rises to the wave crest; when the output wave is reduced from the wave crest, the number of the submodules of the upper bridge arm and the lower bridge arm in the input state is changed along with the output wave, and the change trend is opposite to the trend of increasing the output wave. It can be found that at the peak of the ac output wave, the upper bridge arm still has the sub-module in the on state, and the corresponding lower bridge arm has the sub-module in the off state, which is caused by the modulation ratio m.
Let X (X = a, b, c) phase upper arm have X px Failure of each sub-module can be reflectedInstantaneous expression of bridge arm input submodule quantity of barrier submodule quantity
Figure BDA0002262495310000161
Equation (7) is expressed as follows using a fourier series expansion:
Figure BDA0002262495310000162
wherein
Figure BDA0002262495310000163
Figure BDA0002262495310000164
In formula (10)
Figure BDA0002262495310000171
γ x The phase angle difference between the phase voltage phase angle and the phase angle of the phase voltage a corresponds to that the three phases a, b and c are respectively 0, 120 degrees and-120 degrees.
Similarly, suppose the lower arm has X nx If each sub-module fails, the following formula can be obtained
Figure BDA0002262495310000172
Equation (12) is expressed as follows using a fourier series expansion:
Figure BDA0002262495310000173
wherein
Figure BDA0002262495310000174
/>
Figure BDA0002262495310000175
The average switching function of the upper and lower arms obtained by the equations (8) and (13) is
Figure BDA0002262495310000181
In this embodiment, the MMC operating state solution is specifically as follows:
setting the upper and lower bridge arm current i of each phase px 、i nx By a direct current I dcpx 、I dcnx And the harmonic current of each order
Figure BDA0002262495310000182
The composition is shown as the following formula:
Figure BDA0002262495310000183
wherein n is the harmonic order, I pxn 、I nxn For each harmonic amplitude, θ pxn 、θ nxn The phase angle of each harmonic.
Ignoring third and higher harmonics and considering that the second harmonic is suppressed by the circulating current suppression strategy, equation (17) may be converted to
Figure BDA0002262495310000184
The collective average value of the capacitive currents being the product of the bridge arm current and the average switching function, i.e.
Figure BDA0002262495310000191
When the system is in a stable operation state, the capacitor voltage is in a dynamic balance state, so that the DC component of the capacitor current is 0, namely
Figure BDA0002262495310000192
Formula (20) can be rewritten as
Figure BDA0002262495310000193
The average value of the capacitor voltage set of the upper bridge arm is
Figure BDA0002262495310000201
Wherein C is the sub-module capacitance value, so that the output voltage u of the upper bridge arm can be obtained px Is composed of
Figure BDA0002262495310000202
In the formula u px_0 、u px_1 、u px_2 、V px And the direct current component, the fundamental frequency component, the second harmonic component and the third and above higher harmonic components of the output voltage of the upper bridge arm are respectively represented.
Let u be the supply voltage of the AC system sx The bridge arm inductance is L, and kirchhoff voltage law is applied to the fundamental component of the upper bridge arm and the AC side path to obtain the fundamental component
Figure BDA0002262495310000203
Assuming that the phase angle of the AC system voltage is ahead of the phase angle of the voltage at the AC outlet of the MMC as delta and the voltage at the AC outlet of the MMC is used as a reference value, the equation (24) can be converted to the following equation
Figure BDA0002262495310000204
The finishing formula (25) can be
a 1 sinωt+a 2 cosωt＝0 (26)
In the formula
Figure BDA0002262495310000211
/>
If the formula (26) is satisfied, then
Figure BDA0002262495310000212
Combined and vertical (21), (27) and (28) to obtain
Figure BDA0002262495310000213
In the formula
Figure BDA0002262495310000214
Wherein
Figure BDA0002262495310000221
Can be obtained by solving formula (29)
Figure BDA0002262495310000222
From this, the amplitude of the base frequency current is obtained
Figure BDA0002262495310000223
Wherein
Figure BDA0002262495310000224
Therefore, the fundamental frequency current amplitude is obtained through the relation of the current and the voltage in the MMC, the fundamental frequency current amplitudes of the a-phase lower bridge arm and the b-phase upper and lower bridge arms can be obtained in the same way, and the running state of the MMC can be further obtained. Substituting the obtained fundamental frequency current amplitude into the formula, the instantaneous expressions of the voltage and the current of each bridge arm and the instantaneous expressions of the voltage and the current of each node can be obtained, and the running state of the current system is also obtained.
In this embodiment, through the voltage-current expressions of the bridge arms and the nodes, it can be obtained that the sub-module fault affects the dc output voltage, the current at the ac outlet, and the circulating current on the bridge arms, and the following indexes are proposed for quantifying these influences:
1) MMC output DC voltage expectation
MMC outputs direct current voltage U dc The output voltage of the MMC sub-module is overlapped and supported, and the fault of the sub-module directly influences U dc ，U dc The variation of the MMC can lead to the variation of the transmission power, and the power transmission capability of the MMC is reduced, so that the output direct-current voltage of the MMC can be used as an index in the reliability evaluation of the MMC.
MMC outputs direct current voltage U dc Is formed by connecting the output direct current voltages of three-phase bridge arms in parallel, so that U is formed dc Can be expressed as
U dc (t)＝max{u dca (t)，u dcb (t)，u dcc (t)} (35)
In the formula, max { } represents taking the maximum value.
To U dc Fourier decomposition is carried out to obtain
Figure BDA0002262495310000231
Wherein, U dc0 Is a direct current component, a k sin(kωt+δ k ) Is divided into each timeAn alternating current component.
Therefore, the MMC outputs the DC voltage expectation E (U) dc ) Can be expressed as
E(U dc )＝∑ X∈S U dc0 (X)p(X) (37)
Wherein S is the set of all the states of the system, X is a system state, U dc0 (X) is the DC component on the DC bus in the X state, and p (X) is the probability of the X state (the same below).
2) DC voltage ripple factor expectation
The direct-current voltage ripple coefficient reflects the direct-current voltage fluctuation condition, the direct-current voltage fluctuation causes the fluctuation of transmission power, the electric energy quality of a direct-current side is affected, the loss of direct-current side equipment is aggravated, the service life of the direct-current side equipment is shortened, and therefore the direct-current voltage ripple coefficient expectation can be used as an index for evaluating the reliability of the MMC.
The representation of the ripple may be represented by a half of the peak-to-peak value, or an effective value, and is herein represented by a half of the peak-to-peak value. The ripple magnitude U w Is expressed as follows
Figure BDA0002262495310000241
Wherein T is the power frequency period.
The ripple factor ε is the ratio of ripple to DC voltage, i.e.
Figure BDA0002262495310000242
Therefore, the expected ripple factor E (epsilon) of the DC voltage output by the MMC can be expressed as
E(ε)＝∑ X∈S ε(X)p(X) (40)
Wherein epsilon (X) is the output direct current voltage ripple coefficient under the X state.
3) MMC transmission power deficit expectation and power deficit probability expectation
The MMC has the main functions of realizing AC-DC conversion and transmitting power, so the transmission power can also be used as an index for reliability evaluation of the MMC.
The actual transmission power of the MMC may be expressed as
P＝U dc ·I dc (41)
The power deficit of the MMC may be expressed as the difference between the rated power and the actual power, i.e. the power deficit is
P loss ＝P e -P (42)
MMC power deficit therefore expects E (P) loss ) Can be expressed as
E(P loss )＝∑ X∈S P loss (X)p(X) (43)
Probability of power deficit p loss Can be expressed as
Figure BDA0002262495310000253
/>
Wherein, P loss (X) is the power deficit in the X state.
4) Current harmonic content expectation at AC outlet
The influence of harmonic waves generated by MMC faults on a system is of great importance to an alternating current side system, and the reliability of the MMC can be reflected to a certain extent, so that the current harmonic content at an alternating current outlet can be expected to serve as an index of the reliability of the MMC.
Figure BDA0002262495310000251
In the formula I k Representing the current amplitude of the kth harmonic at the ac outlet.
(5) Bridge arm circulating current content expectation
Harmonic waves generated by MMC faults can only form circulating currents in the MMC, so that the circulating current content of a bridge arm can be expected to be used as an index of the reliability of the MMC.
Taking phase a as an example, the expected circulating current content of the bridge arm can be represented as follows
Figure BDA0002262495310000252
Wherein, I cak Representing the amplitude of the k-times loop current, I, of the a-phase bridge arm dc The rated direct current value of the bridge arm. The circulation content of the three-phase bridge arm is comprehensively considered, and the final expected value can be set as
E(TCD)＝max{E a (TCD)，E b (TCD)，E c (TCD)} (47)
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (8)

1. An MMC reliability analysis method based on an improved average value model is characterized by comprising the following steps:
s1, constructing an improved average value model capable of reflecting sub-module faults according to an expression of a sub-module average switching function in an MMC under the operation state with the sub-module faults;
s2, solving output direct current voltage and current, alternating current voltage and current and internal circulation of a bridge arm of the MMC based on the improved average value model and by combining the electrical characteristics of the power element and a circuit law to obtain the running state of the MMC under the sub-module fault;
s3, constructing an MMC reliability index;
s4, evaluating the reliability of the MMC system according to the running state of the MMC under the sub-module fault and based on the reliability index of the MMC;
the step S1 specifically includes:
step S11, obtaining u according to the voltage waveform at the x-phase alternating current outlet, wherein x = (a, b, c) vx_ref And u vx The modulation wave and the output wave at the outlet of the x-phase alternating current are respectively represented as follows:
u vx_ref ＝U m sin(ωt) (1)
Figure FDA0004019661980000011
in formula (2), U m For modulating the amplitude of the wave, U C The operating voltage of each submodule, s the maximum input number of submodules,
Figure FDA0004019661980000021
the expression is the phase angle of the modulation wave corresponding to the input of k submodules as follows:
Figure FDA0004019661980000022
Figure FDA0004019661980000023
Figure FDA0004019661980000024
wherein m is the modulation ratio, N is the number of sub-modules of the single bridge arm, U dc To output a DC voltage value;
reference voltage u of upper and lower bridge arms of each phase without adding circulating current suppression px_ref 、u nx_ref The expression is as follows:
Figure FDA0004019661980000025
s12, acquiring the number of submodules input by the upper bridge arm and the lower bridge arm of each phase according to the number distribution map of the submodules input by the upper bridge arm and the lower bridge arm under an NLM (line segment modulation) strategy;
s13, setting an X-phase upper bridge arm to have X px The sub-modules are in fault, and an instantaneous expression of the number of the upper bridge arm input sub-modules reflecting the number of the fault sub-modules is obtained
Figure FDA0004019661980000031
Equation (7) is expressed as follows using a fourier series expansion:
Figure FDA0004019661980000032
wherein
Figure FDA0004019661980000033
Figure FDA0004019661980000034
In formula (10)
Figure FDA0004019661980000035
γ x The phase angle difference between the phase voltage phase angle and the phase angle difference between the phase voltage a and the phase voltage a corresponds to the three phases a, b and c which are respectively 0, 120 degrees and-120 degrees;
step S14, supposing that the lower bridge arm has X nx If the sub-modules are in fault, obtaining the instantaneous expression of the number of the lower bridge arm input sub-modules reflecting the number of the fault sub-modules
Figure FDA0004019661980000041
Equation (12) is expressed as follows using a fourier series expansion:
Figure FDA0004019661980000042
wherein
Figure FDA0004019661980000043
Figure FDA0004019661980000044
The improved average switching function S of the upper and lower bridge arms can be obtained through the formulas (8) and (13) px 、S nx ；
Figure FDA0004019661980000051
This is an improved mean model.
2. The improved mean value model-based MMC reliability analysis method of claim 1, wherein the step S2 is specifically:
step S21, setting the upper and lower bridge arm current i of each phase px 、i nx By a direct current I dcpx 、I dcnx And the harmonic current of each order
Figure FDA0004019661980000052
The composition is shown as the following formula:
Figure FDA0004019661980000053
wherein n' is the harmonic order, I pxn 、I nxn For each harmonic amplitude, θ pxn 、θ nxn The phase angle of each harmonic;
step S22, ignoring third and higher harmonics and considering that the second harmonic is suppressed by the circulating current suppression strategy, equation (17) can be converted to
Figure FDA0004019661980000054
Aggregate average value i of upper and lower bridge arm capacitance currents C_px 、i C_nx As the product of the corresponding leg current and the average switching function,
Figure FDA0004019661980000061
step S23, when the system is in a stable operation state, the capacitor voltage is in a dynamic balance state, so that the DC component of the capacitor current is 0, namely
Figure FDA0004019661980000062
Formula (20) can be rewritten as
Figure FDA0004019661980000063
The average value of the capacitor voltage set of the upper bridge arm is
Figure FDA0004019661980000071
Wherein C is the sub-module capacitance value, so that the output voltage u of the upper bridge arm can be obtained px Is composed of
Figure FDA0004019661980000072
In the formula u px_0 、u px_1 、u px_2 、V px Respectively representing a direct current component, a fundamental frequency component, a second harmonic component and a third and above higher harmonic component of the output voltage of the upper bridge arm;
step S24, setting the power supply voltage of the alternating current system as u sx The bridge arm inductance is L, and kirchhoff voltage law is applied to the fundamental component of the upper bridge arm and the AC side path to obtain the fundamental component
Figure FDA0004019661980000073
If the AC system voltage phase angle is ahead of the voltage phase angle delta at the AC outlet of the MMC and the voltage at the AC outlet of the MMC is used as the reference value, the formula (24) can be converted into the following formula
Figure FDA0004019661980000074
The finishing formula (25) can be obtained
a 1 sinωt+a 2 cosωt＝0 (26)
In the formula
Figure FDA0004019661980000081
/>
To make equation (26) true, then
Figure FDA0004019661980000082
Combined and arranged to obtain the product (21), (27), (28)
Figure FDA0004019661980000083
In the formula
Figure FDA0004019661980000084
Wherein
Figure FDA0004019661980000091
Resolution of formula (29) gives
Figure FDA0004019661980000092
From this, the amplitude of the fundamental current is obtained
Figure FDA0004019661980000093
Wherein
Figure FDA0004019661980000094
And S21, obtaining instantaneous expressions of the voltage and the current of each bridge arm and instantaneous expressions of the voltage and the current of each node according to the obtained amplitude of the fundamental frequency current, and obtaining the running state of the current system.
3. The improved mean model-based MMC reliability analysis method of any of claims 1-2, characterized in that: the MMC reliability indexes comprise an expected direct-current voltage output by the MMC, an expected direct-current voltage ripple coefficient, an expected MMC transmission power shortage and power shortage probability, an expected current harmonic content at an alternating-current outlet and an expected bridge arm circulating current content.
4. The MMC reliability analysis method based on improved mean value model of claim 3, wherein the MMC outputs DC voltage expectation specifically is:
MMC (Modular multilevel converter) output direct-current voltage U dc Is formed by connecting the output direct current voltages of three-phase bridge arms in parallel, so that U is formed dc Can be expressed as
U dc (t)＝max{u dca (t)，u dcb (t)，u dcc (t)} (35)
Wherein max { } represents taking the maximum value;
to U dc Fourier decomposition is carried out to obtain
Figure FDA0004019661980000101
Wherein, U dc0 Is a direct current component, a k sin(kωt+δ k ) For each AC component;
so MMC outputs DC voltage expectation E (U) dc ) Is shown as
E(U dc )＝∑ X∈S U dc0 (X)p(X) (37)；
Wherein S is the set of all the states of the system, X is a system state, U dc0 And (X) is a direct current component on a direct current bus in an X state, and p (X) is the probability of the occurrence of the X state.
5. The MMC reliability analysis method based on the improved mean value model of claim 3, wherein the DC voltage ripple coefficient expectation is specifically:
by half the peak value or the effective value table ripple, the ripple magnitude U w The details are as follows
Figure FDA0004019661980000102
Wherein T is a power frequency period;
the ripple factor epsilon is the ratio of ripple to DC voltage, i.e.
Figure FDA0004019661980000103
Therefore, the expected ripple factor E (epsilon) of the DC voltage output by the MMC can be expressed as
E(ε)＝∑ X∈S ε(X)p(X) (40)；
Wherein epsilon (X) is the ripple coefficient of the output direct current voltage in the X state.
6. The MMC reliability analysis method of claim 3, wherein the MMC transmission power deficit expectation and power deficit probability expectation are specifically:
the actual transmission power of the MMC can be expressed as a direct current bus voltage U dc With the direct bus current I dc Product of (2)
P＝U dc ·I dc (41)
The power deficit of the MMC may be expressed as the rated power P e Difference from actual power P, i.e.
P loss ＝P e -P (42)
MMC power deficit expectation E (P) loss ) Is shown as
E(P loss )＝∑ X∈S P loss (X)p(X) (43)
Probability of power deficit P loss Is shown as
Figure FDA0004019661980000111
Wherein, P loss (X) is the power deficit in the X state.
7. The MMC reliability analysis method based on an improved mean value model of claim 3, wherein the current harmonic content at the AC outlet is expected to be specifically:
Figure FDA0004019661980000121
in the formula I k Representing the current amplitude of the kth harmonic at the ac outlet.
8. The MMC reliability analysis method based on the improved mean value model of claim 3, wherein the expected circulating current content of the bridge arm is specifically:
bridge arm circulating current content is expected to be expressed as follows
Figure FDA0004019661980000122
Wherein, I cxk Representing the k-order circulating amplitude, I, of the x-phase bridge arm dc A rated direct current value is set for the bridge arm;
comprehensively considering the circulating current content of the three-phase bridge arm, the final expected value is
E(TCD)＝max{E a (TCD)，E b (TCD)，E c (TCD)} (47)。
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