CN105162346A - MMC mathematical model analysis method based on virtual potential method - Google Patents

Abstract

The invention discloses an MMC mathematical model analysis method based on a virtual potential method. The MMC mathematical model analysis method is characterized by comprising the following: step SS1, KCL and KVL equations of an MMC phase unit are listed according to an MMC equivalent circuit; step SS2, a virtual zero potential point is defined, and then the virtual potential method is adopted to determine electrical quantity; step SS3, the electrical quantity determined in the step SS2 serves as a substrate, the KCL and KVL equations of an MMC are substituted into the substrate to determine an MMC mathematical model and describe operation control characteristics of the MMC. The MMC mathematical model analysis method is used for simplifying the KVL equation of the MMC and establishing and describing the MMC mathematical model by defining the virtual zero potential point of the MMC and utilizing the virtual zero potential point to define and understand the correlated electrical quantity. In addition, the meaning of the defined correlated electrical quantity and the influence on the MMC operation characteristics of the correlated electrical quantity can be visually interpreted, and accordingly the MMC mathematical model is clearly described and has important significance on understanding of the MMC operation characteristics.

Description

Based on the MMC mathematics model analysis method of virtual voltage potential method

Technical field

The present invention relates to a kind of MMC mathematics model analysis method based on virtual voltage potential method, belong to operation and control of electric power system technical field.

Background technology

Current flexible DC power transmission engineering adopts the VSC of two level or three level mostly, and the series connection of switching device can cause the dynamic voltage balancing problem of device, the stability that influential system runs.MMC reaches higher voltage by submodule voltage superposition and exports, and advantages such as having Modular Structure Design, be easy to expansion, switching loss is low, harmonic wave of output voltage content is little, improves redundancy and the reliability of system greatly.As a kind of emerging technology being applied to flexible direct-current transmission field, there is the advantage of its uniqueness, but also shorter for the search time of MMC both at home and abroad, the application experience of Practical Project is also less, is thus of great significance for the research tool carrying out system modelling and control strategy aspect.

Current MMC Mathematical Modeling writes on the basis of MMC facies unit KCL and KVL equation at row, by defining complicated physical quantity, simplifying KVL equation, setting up MMC Mathematical Modeling.But when defining complicated physical quantity, few or not directly perceived to the com-parison and analysis of its process and physical significance, there is very large obstacle for understanding MMC operation characteristic.In the present invention, virtual voltage potential method is applied to MMC mathematics model analysis, can visual interpretation define the meaning of physical quantity and it is on the impact of MMC operation characteristic, significant to grasp MMC Mathematical Modeling, contribute to understanding MMC operation characteristic.

Summary of the invention

The object of the invention is the defect overcoming prior art existence, propose a kind of MMC mathematics model analysis method based on virtual voltage potential method, for understanding and setting up MMC Mathematical Modeling, simultaneously for the modeling and simulating of MMC provides basis.

The present invention adopts following technical scheme: based on the MMC mathematics model analysis method of virtual voltage potential method, it is characterized in that, comprise the steps:

Step SS1 is according to MMC equivalent electric circuit, and row write MMC facies unit KCL and KVL equation;

Step SS2 defining virtual zero potential point, then utilizes virtual voltage potential method determination electric parameters, and determines electric parameters physical meaning;

Step SS3 passes through, using the electric parameters in step SS2 as substrate, to substitute into KCL, KVL equation of MMC, determine MMC Mathematical Modeling, and utilizes the determined electric parameters physical meaning of described step SS2 to describe MMC operation control characteristic.

Preferably, described step SS1 specifically comprises: utilize KVL and KCL law to arrange and separate electric parameters relation equation:

Upper mesh equation: $U_{dc}/2-u_{pj}-u_{vj}=L\frac{{\mathrm{di}}_{pj}}{dt}+R_0{i}_{pj}---\left(1\right)$

Lower mesh equation: $U_{dc}/2-u_{nj}+u_{vj}=L\frac{{\mathrm{di}}_{nj}}{dt}+R_0{i}_{nj}---\left(2\right)$

Node current equation: i _vj=i _pj-i _nj(3)

(1), (2) add and subtract mutually, then have:

U _dc-(u _nj+u _pj)＝R ₀(i _nj+i _pj)+Ld(i _nj+i _pj)/dt(4)

(u _nj-u _pj)-2u _vj＝R ₀(i _pj-i _nj)+Ld(i _pj-i _nj)/dt(5)

Wherein, converter exchanges the phase voltage of outlet side, line current is respectively u _vj, i _vj(j=a, b, c), footnote p, n represent upper and lower bridge arm respectively, and the voltage vector of described upper and lower bridge arm can with 6 controlled voltage source u _pj, u _nj(j=a, b, c) equivalence, corresponding bridge arm current is i _pj, i _nj, L ₀for the inductance value of brachium pontis series reactance, resistance R ₀be used for the loss of equivalent brachium pontis, direct voltage is ± U _dc/ 2.

Preferably, described step SS2 specifically comprises: establish the voltage magnitude of MMC both positive and negative polarity DC line A, B point equal and reverse, and virtual voltage potential zero point is u _0j, vectorial l _p, l _nrepresent upper and lower bridge arm voltage respectively, vector length is directly proportional to voltage magnitude, virtual voltage potential u at zero point _0jbe positioned at upper and lower bridge arm voltage vector sum mid point.

Preferably, described step SS2 specifically also comprises: establish facies unit jth phase unbalance voltage to be set to ucirj, facies unit internal emf e _j, then:

2u _cirj＝U _dc-(u _nj+u _pj)(6)

2e _j＝u _nj-u _pj(7)

With vectorial l _p, l _n, l _dcrepresent upper and lower bridge arm voltage and DC voltage respectively, vector length is directly proportional to voltage magnitude; By u _cirjwith virtual point position u at zero point _0jmake comparisons, vector superposition can obtain its voltage vector;

L _cirj=l _dc/ 2-(l _nj+ l _pj)/2 (8) utilize virtual voltage potential method, through l _p, l _nsuperposition can synthesize u ₀, e _jcorresponding vectorial l ₀, l _ej, be easy to get:

l _ej＝(l _n-l _p)/2＝l _n-(l _p+l _n)/2(9)

U _cirjdue to upper and lower bridge arm voltage sum and direct voltage is unequal causes, e _jproduce due to facies unit upper and lower bridge arm Voltage unbalance.

Preferably, described step SS3 specifically comprises: bring formula (3), formula (7) into formula (4), can obtain:

u _vj＝e _j-R ₀i _vj/2-Ldi _vj/2dt(10)

Formula (10) describes the dynamic characteristic of converter outside, gives MMC regulates the outside input current of MMC mathematic(al) representation by the output voltage changing upper and lower brachium pontis sub-series module group;

Formula (6) is substituted into formula (5), has:

u _cirj＝R ₀i _cirj+L ₀di _cirjdt(11)

i _cirj＝(i _nj+i _pj)/2(12)

I in formula _cirjfor flowing through the inverter inside electric current of upper and lower brachium pontis simultaneously, be called jth phase unsymmetrical current; Formula (10) and formula (11) are the Mathematical Modeling of MMC, and two equations respectively describe outside and the internal dynamics of MMC.

The beneficial effect that the present invention reaches: the present invention, by defining MMC virtual voltage potential zero point, utilizes define and understand related electric amount virtual zero point, for simplifying the KVL equation of MMC, setting up and describing MMC Mathematical Modeling; Simultaneously can visual interpretation define the meaning of related electric amount and it is on the impact of MMC operation characteristic, thus clear description MMC Mathematical Modeling, to understanding, MMC operation characteristic is significant.

Accompanying drawing explanation

Fig. 1 is the fundamental diagram of MMC of the present invention.

Fig. 2 is the equivalent circuit diagram of MMC of the present invention.

Fig. 3 is the schematic diagram at virtual voltage potential of the present invention zero point.

Fig. 4 is u of the present invention _cirjvirtual voltage potential figure.

Fig. 5 is e of the present invention _jvirtual voltage potential figure.

Fig. 6 is that MMC AC of the present invention simplifies equivalent circuit diagram.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.Following examples only for technical scheme of the present invention is clearly described, and can not limit the scope of the invention with this.

The present invention proposes a kind of MMC mathematics model analysis method based on virtual voltage potential method, it is characterized in that, comprises following 3 steps.

Step SS1 is according to MMC equivalent electric circuit, and row write MMC facies unit KCL and KVL equation, and Fig. 2 is the equivalent circuit diagram of MMC of the present invention; Specifically comprise: utilize KVL and KCL law to arrange and separate electric parameters relation equation:

Upper mesh equation: $U_{dc}/2-u_{pj}-u_{vj}=L\frac{{\mathrm{di}}_{pj}}{dt}+R_0{i}_{pj}---\left(1\right)$

Lower mesh equation: $U_{dc}/2-u_{nj}+u_{vj}=L\frac{{\mathrm{di}}_{nj}}{dt}+R_0{i}_{nj}---\left(2\right)$

Node current equation: i _vj=i _pj-i _nj(3)

(1), (2) add and subtract mutually, then have:

U _dc-(u _nj+u _pj)＝R ₀(i _nj+i _pj)+Ld(i _nj+i _pj)/dt(4)

(u _nj-u _pj)-2u _vj＝R ₀(i _pj-i _nj)+Ld(i _pj-i _nj)/dt(5)

Wherein, Fig. 1 is the fundamental diagram of MMC of the present invention, and in figure, v point represents that converter exchanges the phase voltage of outlet side, line current is respectively u _vj, i _vj(j=a, b, c), footnote p, n represent upper and lower bridge arm respectively, and the voltage vector of described upper and lower bridge arm can with 6 controlled voltage source u _pj, u _nj(j=a, b, c) equivalence, corresponding bridge arm current is i _pj, i _nj, L ₀for the inductance value of brachium pontis series reactance, resistance R ₀be used for the loss of equivalent brachium pontis, direct voltage is ± U _dc/ 2.

Step SS2 defining virtual point position zero point, then utilize virtual voltage potential method determination electric parameters, and determine electric parameters physical meaning; Specifically comprise: establish the voltage magnitude of MMC both positive and negative polarity DC line A, B point equal and reverse, virtual voltage potential zero point is u _0j, vectorial l _p, l _nrepresent upper and lower bridge arm voltage respectively, vector length is directly proportional to voltage magnitude, and Fig. 3 is the schematic diagram at virtual voltage potential of the present invention zero point, virtual voltage potential u at zero point _0jbe positioned at upper and lower bridge arm voltage vector sum mid point.

Step SS2 specifically also comprises: establish facies unit jth phase unbalance voltage to be set to u _cirj, facies unit internal emf e _j, then:

2u _cirj＝U _dc-(u _nj+u _pj)(6)

2e _j＝u _nj-u _pj(7)

With vectorial l _p, l _n, l _dcrepresent upper and lower bridge arm voltage and DC voltage respectively, vector length is directly proportional to voltage magnitude; By u _cirjwith virtual point position u at zero point _0jmake comparisons, vector superposition can obtain its voltage vector, and Fig. 4 is u of the present invention _cirjvirtual voltage potential figure;

l _cirj＝l _dc/2-(l _nj+l _pj)/2(8)

Fig. 5 is e of the present invention _jvirtual voltage potential figure, utilizes virtual voltage potential method, through l _p, l _nsuperposition can synthesize u ₀, vectorial l that ej is corresponding ₀, l _ej, be easy to get:

l _ej＝(l _n-l _p)/2＝l _n-(l _p+l _n)/2(9)

By Fig. 4, Fig. 5 easy understand, u _cirjdue to upper and lower bridge arm voltage sum and direct voltage is unequal causes, e _jproduce due to facies unit upper and lower bridge arm Voltage unbalance.

Step SS3 passes through, using the electric parameters in step SS2 as substrate, to substitute into KCL, KVL equation of MMC, determine MMC Mathematical Modeling, and utilizes the determined electric parameters physical meaning of step SS2 to describe MMC operation control characteristic; Specifically comprise: bring formula (3), formula (7) into formula (4), can obtain:

u _vj＝e _j-R ₀i _vj/2-Ldi _vj/2dt(10)

Formula (10) describes the dynamic characteristic of converter outside, gives MMC regulates the outside input current of MMC mathematic(al) representation by the output voltage changing upper and lower brachium pontis sub-series module group.Accordingly, can obtain MMC AC of the present invention and simplify equivalent circuit as Fig. 6, converter is connected with external communication system with substitutional resistance by one group of equivalent inductance.

When three-phase alternating current system balancing, total direct current of converter is divided equally substantially between three facies units.According to formula (4), the alternating current component in facies unit circulation is mainly by (the i.e. u of wave component on the left of equation _cirj) cause.Because the alternating current component in facies unit circulation does not appear in formula (10), therefore can think that exchanging Circulation Components does not affect substantially on converter external behavior and power delivery under normal operating conditions.

Formula (6) is substituted into formula (5), has:

u _cirj＝R ₀i _cirj+L ₀di _cirjdt(11)

i _cirj＝(i _nj+i _pj)/2(12)

I in formula _cirjfor flowing through the inverter inside electric current of upper and lower brachium pontis simultaneously, be called jth phase unsymmetrical current; Formula (10) and formula (11) are the Mathematical Modeling of MMC, and two equations respectively describe outside and the internal dynamics of MMC.

In the Mathematical Modeling of MMC, external system to the effect of UPFC by voltage source u _vjchange reflect; And u _cirjobtained by change of current inhibitor, e _jobtained by the output of system-level controller, both can be used for the voltage and current that control MMC exports, and then control meritorious, reactive power and corresponding DC bus-bar voltage etc.

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the prerequisite not departing from the technology of the present invention principle; can also make some improvement and distortion, these improve and distortion also should be considered as protection scope of the present invention.

Claims (5)

1., based on the MMC mathematics model analysis method of virtual voltage potential method, it is characterized in that, comprise the steps:

Step SS1 is according to MMC equivalent electric circuit, and row write MMC facies unit KCL and KVL equation;

Step SS2 defining virtual zero potential point, then utilizes virtual voltage potential method determination electric parameters, and determines electric parameters physical meaning;

Step SS3 passes through, using the electric parameters in step SS2 as substrate, to substitute into KCL, KVL equation of MMC, determine MMC Mathematical Modeling, and electric parameters physical meaning describes MMC and runs control characteristic to utilize step SS2 to determine.

2. the MMC mathematics model analysis method based on virtual voltage potential method according to claim 1, it is characterized in that, described step SS1 specifically comprises: utilize KVL and KCL law to arrange and separate electric parameters relation equation:

Upper mesh equation: $U_{dc}/2-u_{pj}-u_{vj}=L\frac{{\mathrm{di}}_{pj}}{dt}+R_0{i}_{pj}---\left(1\right)$

Lower mesh equation: $U_{dc}/2-u_{nj}+u_{vj}=L\frac{{\mathrm{di}}_{nj}}{dt}+R_0{i}_{nj}---\left(2\right)$

Node current equation: i _vj=i _pj-i _nj(3)

(1), (2) add and subtract mutually, then have:

U _dc-(u _nj+u _pj)＝R ₀(i _nj+i _pj)+Ld(i _nj+i _pj)/dt(4)

(u _nj-u _pj)-2u _vj＝R ₀(i _pj-i _nj)+Ld(i _pj-i _nj)/dt(5)

Wherein, converter exchanges the phase voltage of outlet side, line current is respectively u _vj, i _vj(j=a, b, c), footnote p, n represent upper and lower bridge arm respectively, and the voltage vector of described upper and lower bridge arm can with 6 controlled voltage source u _pj, u _nj(j=a, b, c) equivalence, corresponding bridge arm current is i _pj, i _nj, L ₀for the inductance value of brachium pontis series reactance, resistance R ₀be used for the loss of equivalent brachium pontis, direct voltage is ± U _dc/ 2.

3. the MMC mathematics model analysis method based on virtual voltage potential method according to claim 1, it is characterized in that, described step SS2 specifically comprises: establish the voltage magnitude of MMC both positive and negative polarity DC line A, B point equal and reverse, and virtual voltage potential zero point is u _0j, vectorial l _p, l _nrepresent upper and lower bridge arm voltage respectively, vector length is directly proportional to voltage magnitude, virtual voltage potential u at zero point _0jbe positioned at upper and lower bridge arm voltage vector sum mid point.

4. the MMC mathematics model analysis method based on virtual voltage potential method according to claim 3, it is characterized in that, described step SS2 specifically also comprises: establish facies unit jth phase unbalance voltage to be set to u _cirj, facies unit internal emf e _j, then:

2u _cirj＝U _dc-(u _nj+u _pj)(6)

2e _j＝u _nj-u _pj(7)

With vectorial l _p, l _n, l _dcrepresent upper and lower bridge arm voltage and DC voltage respectively, vector length is directly proportional to voltage magnitude; By u _cirjwith virtual point position u at zero point _0jmake comparisons, vector superposition can obtain its voltage vector;

l _cirj＝l _dc/2-(l _nj+l _pj)/2(8)

Utilize virtual voltage potential method, through l _p, l _nsuperposition can synthesize u ₀, e _jcorresponding vectorial l ₀, l _ej, be easy to get:

l _ej＝(l _n-l _p)/2＝l _n-(l _p+l _n)/2(9)

U _cirjdue to upper and lower bridge arm voltage sum and direct voltage is unequal causes, represent this phase internal current i _cirjresist and the voltage drop on equivalent resistance, if facies unit internal emf e a brachium pontis series connection _j, e _jproduce due to facies unit upper and lower bridge arm Voltage unbalance.

5. the MMC mathematics model analysis method based on virtual voltage potential method according to claim 1, it is characterized in that, described step SS3 specifically comprises: bring formula (3), formula (7) into formula (4), can obtain:

u _vj＝e _j-R ₀i _vj/2-Ldi _vj/2dt(10)

Formula (10) describes the dynamic characteristic of converter outside, gives MMC regulates the outside input current of MMC mathematic(al) representation by the output voltage changing upper and lower brachium pontis sub-series module group;

Formula (6) is substituted into formula (5), has:

u _cirj＝R ₀i _cirj+L ₀di _cirjdt(11)

i _cirj＝(i _nj+i _pj)/2(12)

I in formula _cirjfor flowing through the inverter inside electric current of upper and lower brachium pontis simultaneously, be called jth phase unsymmetrical current; Formula (10) and formula (11) are the Mathematical Modeling of MMC, and two equations respectively describe outside and the internal dynamics of MMC.