Microgrid power distribution system and power flow asymmetrical fault analysis method therefor

1. A microgrid distribution (MGD) system, comprising:

a smart apparatus, having a programmable device for executing a fault analysis method for a three-phase and single-phase mixed power distribution system by selecting at least one of single line-to-ground (SLG) fault analysis, double line-to-ground (DLG) fault analysis, open-conductor fault analysis, line-to-line (LL) fault analysis, and microturbine generation (MTG) fault analysis to solve a fault current, and for various types of faults of the microgrid distribution system, and obtaining appropriate boundary conditions to calculate a variety of different types of single or simultaneous fault currents of load points; and

a plurality of buses, at least one of which is connected to the smart apparatus;

wherein the programmable device executing the SLG, DLG, LL, open-conductor fault analysis, and MTG fault analysis method by using main relation matrix Z MGD ; and

wherein the main relation matrix Z MGD =Z V-BC B I in which Z V-BC is a first relation matrix while B I is a second relation matrix between a bus injection current and a branch current, and the relation matrix between the bus injection current [I] and the branch current [B] is denoted as [B]=[B I ][I], and the matrix B I is an upper triangular matrix only comprising values of 0 and 1.

2. The microgrid distribution system according to claim 1 , wherein the first relation matrix Z V-BC is an inter-bus impedance and is a lower triangular matrix, and the first relation matrix between the branch current and a bus voltage difference matrix [ΔV], and the main relation matrix Z MGD between the injection current and the bus voltage difference matrix [ΔV] are respectively denoted as:

[Δ V]=[Z V-BC ][B]=[Z MGD ][I].

3. The microgrid distribution system according to claim 1 , wherein the programmable device executes the SLG fault analysis step through an impedance Z f , an SLG fault occurs in a phase a of a Bus i, which represents one of the buses that has a fault and boundary conditions are denoted as:

I i,f a =I i a +I i,slg a ,I i,f b =I i b ,I i,f c =I i c ; and

V i,f a =Z f I i,slg a ;

wherein I i,f a , I i,f b and I i,f c are equivalent currents occurring in fault locations of the phase a, a phase b and a phase c and flowing into the Bus i, I a i , I b i and I c i are pre-fault currents, and V i,0 a and V i,f a are respectively a pre-fault voltage and a post-fault voltage;

and if an SLG fault occurs in the phase a of the Bus i, a fault current flows to the ground, a bus voltage of the phase a is changed from V a i,0 to Z f I a i,slg , and after the fault, the change amount of the bus current is denoted as:

Δ I i,f a =I i,slg a ,ΔI i,f b =0,Δ I i,f c =0;

and through iteration, a fault voltage iterative formula is denoted as follows:

Δ

⁢

⁢

V

i

,

f

a

=

V

i

,

0

a

-

Z

f

⁢

I

i

,

slg

a

Δ

⁢

⁢

I

i

,

f

a

=

V

i

,

0

a

-

Δ

⁢

⁢

V

i

,

f

a

Z

f

;

 wherein the variations of the branch currents generated by the fault current in MGD can be expressed as

[Δ B f a ]=[B I ][0 . . . Δ I i,f a 0 . . . ] T ;

where B I is the bus injection to a pre-fault of a branch current matrix having a general form expressed as

[ B f ]=[B MGD ]+[ΔB f a ];

where a bus mismatch voltages caused by the fault branch currents ΔB f can be rewritten as

[Δ V f ]=[Z V-BC ][B f ]=[Z MGD ][I f ];

so that after a single-line-to-ground fault occurs, the branch mismatch currents and bus mismatch voltages caused by the single-line-to-ground fault can be calculated directly and the solution for MGD power flow can be expressed as

[Δ V f i ]=[Z MGD,f ][I f i ];

and a post-fault voltage of each bus is calculated by use of the following formula:

[ V f ]=[V 0 ]−[ΔV f ];

wherein V 0 is a no-load voltage or bus reference voltage.

4. The microgrid distribution system according to claim 1 , wherein when the programmable device executes the DLG fault analysis, a DLG fault occurs in a phase a and a phase b of a Bus i, representing one of the buses that has a fault, through an impedance Z f , and boundary conditions are denoted as:

Δ I i,f a =I i,dlg a ,ΔI i,f b =I i,dlg b ,ΔI i,f c =0;

V i,f a =V i,f b =Z f (Δ I i,f a +ΔI i,f b );

wherein the variations of the branch currents generated by the fault currents in MGD can be expressed as

[Δ B f ab ]=[B I ][0 . . . ΔI i,f a ΔI i,f b 0 . . . ] T ;

and, in MGD, the fault branch currents B f caused by the fault currents can be rewritten as

[ B f ]=[B MGD ]+[ΔB f a ];

so that the bus mismatch voltages caused by the fault branch currents B f can be rewritten as

[Δ V f ]=[Z V-BC ][B f ]=[Z MGD ][I f ];

whereby the fault currents and bus mismatch voltages caused by the double line-to-ground fault can be calculated directly and the solution for MGD power flow.

5. The microgrid distribution system according to claim 1 , wherein when the programmable device executes the LL fault analysis, for an LL fault through an impedance Z f , a phase a and a phase b of the Bus i, representing one of the buses that has a fault, are regarded as the LL fault, and boundary conditions of a fault point need to satisfy:

I i,f a =I i a +I i,ll a ,I i,f b =I i b −I i,ll ab ,I i,f c =I i c ; and

V i,f a −V i,f b =Z f I i,ll ab ; and

wherein a fault current iterative formula thereof is denoted as follows:

Δ

⁢

⁢

I

i

,

f

ab

=

V

i

,

f

a

-

V

i

,

f

b

Z

f

;

,

 and a pre-fault load flow voltage solution is used as an initial condition so that a fault point branch current generated by a fault is denoted as:

[

B

f

]

=

[

B

I

,

origin

col

·

(

B

i

a

-

B

i

b

)

0

1

]

⁡

[

I

origin

Δ

⁢

⁢

I

i

,

f

ab

]

;

where the new column is column phase a minus column phase b of Bus i of B I,origin , and the new row is filled with “0” in B I,origin a and, finally, “1” is filled to the end of the diagonal;

and a bus voltage difference matrix caused by the fault branch current ΔB f is denoted as:

[Δ V f i ]=[Z V-BC,f ][B f ]=[Z MGD,f ][ΔI f i ];

in which the Z V-BC,f matrix is

[

Z

V

-

BC

,

f

]

=

[

Z

V

-

BC

,

origin

0

row

·

(

Z

i

a

-

Z

i

b

)

Z

f

]

;

where the new row is row phase a minus row phase b of Bus i of Z V-BC,origin , and Z f is filled to the position of the off-diagonal.

6. The microgrid distribution system according to claim 1 , wherein when the programmable device executes the open-conductor fault analysis step, a negative branch current of a fault point generated by an open-conductor fault is a boundary condition of the open-conductor fault, which is denoted as:

[

Δ

⁢

⁢

B

f

,

OC

]

=

[

0

…

∏

MG

⁢

⁢

fault

⁢

⁢

area

-

B

ij

a

0

…

]

T

;

where the whole branch current of the system is rewritten as:

[ B f ]=[B]+[ΔB f,OC ];

and a bus voltage difference matrix caused by a fault branch current ΔB f is denoted as:

[Δ V f,OC ]=[Z V-BC,f ][B f,OC ].

7. The microgrid distribution system according to claim 1 , wherein when the programmable device executes the MTG fault analysis step, boundary conditions of a fault point need to satisfy stand-alone mode and a grid-connected mode.

8. The microgrid distribution system according to claim 7 , wherein, in stand-alone mode, the MTG serves as an independent voltage source for supplying power to loads, and internal voltage V 0 — MT is constant at the instant of the fault so that the boundary conditions can be written as

Δ V 0 — MT,f abc =0

V g,f abc =V f ;

and a sensitivity matrix is used to calculate the injection current needed to keep the MTG's internal voltage constant, wherein relationships of voltage variations after a fault can be expressed as

[ V 0 — MT,f ]−[V f ]=[Z 0 — MT ][I g — n,f ]; and

[ V 0 — MT,0 −ΔV 0 — MT,f ]−[V f,0 −ΔV f ]=[Z 0 — MT ][I g — n,f ]

whereby the MGT terminal bus correction voltages after the fault occurred can be expressed as

[

Δ

⁢

⁢

V

f

i

]

=

[

Z

0

⁢

_

⁢

MT

,

f

]

⁡

[

I

g_n

,

f

i

]

-

[

V

0

⁢

_MT

,

0

-

V

f

,

0

]

I

g

,

f

=

∑

n

=

1

N

⁢

I

g_n

,

f

where N is the number of connected power modules, and n is the nth module in MTG.

9. The microgrid distribution system according to claim 7 , wherein, in grid-connected mode, in grid-connected mode, the MTG can operate as a power conditioner for the grid-connected mode to improve the microgrid quality of supplying power or sever as an emergency generator from the grid, and being based on the control strategy of grid-connected concept, the MTG terminal fault current can be written as

[

I

g_n

,

f

]

=

[

I

0

⁢

_

⁢

MT

]

-

[

Y

0

⁢

_

⁢

MT

]

⁡

[

V

g

,

f

]

I

g

,

f

=

∑

n

=

1

N

⁢

I

g_n

,

f

;

wherein the admittance matrix Y 0 — MT and the MTG internal balanced current source I 0 — MT are held constant in faults analysis, and the load flow voltage solution by iterative process is written as

[Δ V f i ]=[Z MGD,f ][I g,f i ].