CN111697634B - Modeling method for direct-current voltage control small signal based on alternating-current and direct-current side instantaneous power - Google Patents
Modeling method for direct-current voltage control small signal based on alternating-current and direct-current side instantaneous power Download PDFInfo
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Abstract
The application provides a modeling method of a direct-current voltage control small signal based on alternating-current and direct-current side instantaneous power, which comprises the following steps: s1: constructing a small signal model of a power balance equation of an alternating current side of an inverter in a direct current distribution network; s2: constructing a small signal model of a power balance equation at the direct current side of the converter in the direct current distribution network; s3: constructing a direct-current voltage control small signal model according to the power balance relation between the alternating-current side and the direct-current side of the converter in the direct-current distribution network; the S1 further includes: s11: determining a power balance equation of an alternating current side of an inverter in a direct current distribution network; the S2 further includes: s21: determining the voltage-current relationship of the direct current side of the converter after adding the LC filter according to the positive and negative of the power value; s22: and determining a power balance equation of the direct current side of the converter in the direct current distribution network. According to the modeling method provided by the invention, on the basis of considering the power loss of the converter and the switching device, the influence of the converter AC/DC side energy storage element on the DC voltage control effect in the running process of the system is considered, and the accuracy of the DC voltage control small signal model is improved.
Description
Technical Field
The invention relates to the technical field of operation control of a direct current distribution network system, in particular to a modeling method of a direct current voltage control small signal based on alternating current-direct current side instantaneous power.
Background
In recent years, direct current distribution networks have been receiving attention because of having efficient distributed energy access capability and being capable of being connected with a traditional alternating current power grid to form a multi-terminal power grid, and converters are core equipment with the most complex functions of the direct current power grid. The energy storage unit at the alternating current side of the voltage source type converter can bring internal instantaneous power flow change, and the small-signal dynamic response of the direct current bus voltage can be changed from a minimum system in an inversion running state to a non-minimum phase system in a rectification running state, so that the stability of direct current voltage control is affected. In the case of the dc-side energy storage unit, when the power thereof is taken into account in the dc voltage input/output equation, the zero point distribution of the transfer function is likewise changed due to the different operating states of the converter, so that the bus voltage is influenced. With the expansion of the scale of the direct current power grid, the stability and the working efficiency of the power system after grid connection are important points of attention. However, the current research is less, the degree of cutting refinement is not high, and the following 2 point defects exist: (1) taking into account the power loss P of the converter and the switching devices loss However, the corresponding current i is not taken into consideration when defining the direct-current-side direct current loss The method comprises the steps of carrying out a first treatment on the surface of the (2) When considering the instantaneous power of the DC side capacitor, the voltage drop caused by the newly added DC side inductor is not considered, and the DC side voltage V of the converter is calculated dc As capacitor voltage
Therefore, a method for precisely modeling a small signal model of direct-current voltage control considering the instantaneous power of the direct-current power distribution network voltage source converter on the alternating-current side is needed to overcome the defects of the prior art.
Disclosure of Invention
In view of the above, the invention provides a modeling method for a direct-current voltage control small signal based on the instantaneous power of an alternating-current and direct-current side.
The invention provides a modeling method of a direct-current voltage control small signal based on alternating-current and direct-current side instantaneous power, which is characterized by comprising the following steps of: the method comprises the following steps:
s1: constructing a small signal model of a power balance equation of an alternating current side of an inverter in a direct current distribution network;
s2: constructing a small signal model of a power balance equation at the direct current side of the converter in the direct current distribution network;
s3: constructing a direct-current voltage control small signal model according to the equal relation between an alternating-current side small signal model and a direct-current side small signal model of an inverter in a direct-current distribution network;
the step S1 further includes:
s11: determining a power balance equation of an alternating current side of an inverter in a direct current distribution network;
the step S2 further includes:
s21: determining the voltage-current relationship of the direct current side of the converter after adding the LC filter according to the positive and negative of the power value;
s22: and determining a power balance equation of the direct current side of the converter in the direct current distribution network.
Further, the ac side power balance equation is determined by the following method:
1.5VsdId-DWL-PR-Pt＝0(1)
wherein Vsd represents d-axis component of the AC side network side voltage of the converter under dq coordinate system, I d Representing current space vector in dq coordinate system
D represents a differentiation factor with respect to time, dx=d (x)/dt, W L Representing the energy of the equivalent inductance of the AC side, P R Represents the equivalent resistance R (R) s And r on Sum) of power, P t Representing the ac side power of the inverter.
Further, the small signal model of the alternating current side power balance equation is determined by the following method:
ΔP t ＝1.5I d0 ΔV sd +(-1.5L s I d0 s+1.5V sd0 -3RI d0 )ΔI d -(1.5L s I q0 s+3RI q0 )ΔI q (2)
wherein DeltaP t Representing AC side small signal quantity, I d0 Representing steady state operating point I d Corresponding value V sd Representing d-axis component of the AC side network side voltage of the converter under the dq coordinate system, ls representing the sum of equivalent inductance of a connecting transformer and a reactor and leakage inductance of the transformer, s representing Laplacian, V sd0 Representing d-axis component steady-state operating point of converter AC side network side voltage under dq coordinate system, R representing equivalent resistance of connecting transformer and reactor, I d Representing current space vector in dq coordinate system
Active term, I q0 Representing steady state operating point I q Corresponding steady state value, I q The q-axis component in the grid-side current dq coordinate system of the ac side of the inverter is represented.
Further, the relation between the voltage and the current is determined by the following method:
wherein i is Leq Indicating inductor current, I dc Representing the direct current at the outlet of the direct current line connected with the direct current side of the converter, P loss Representing power loss due to reverse recovery of the switch and tracking current process, V dc Representing the DC voltage at the DC side of the converter connected to the DC line outlet, V Ceq Representing the capacitance voltage, L eq Represents the dc side equivalent inductance, D represents the differential factor over time, dx=d (x)/dt.
Further, the power balance equation of the alternating current side of the converter in the direct current distribution network is determined by adopting the following method:
wherein Pdc represents the transmission power of the DC side of the converter, D represents the differential factor with respect to time, dx=d (x)/dt, C eq Representing the equivalent capacitance of the DC side, V Ceq Representing the capacitance voltage, L eq Representing the equivalent inductance of the DC side, i Leq Representing inductor current, P loss Indicating power loss due to reverse recovery of the switch and tracking current process, I dc Representing the DC current at the DC side of the converter connected with the DC line outlet, V dc Representing the dc voltage at the dc link outlet of the dc link at the dc side of the converter.
Further, the small signal model of the direct current side power balance equation is determined by the following method:
wherein DeltaP dc Representing DC side small signal quantity, C eq Represents the equivalent capacitance of the direct current side, L eq Represents the equivalent inductance of the direct current side, P loss0 Representing steady state value of power loss, V dc0 Indicating the corresponding value of the DC voltage at the outlet of the converter at the steady-state operating point, I dc0 Representing the corresponding value of the DC current at the outlet of the converter at the steady-state operating point, S represents the Laplacian, and P loss Representing the power loss due to the reverse recovery of the switch and the tracking current process.
Further, step S3 further includes: and combining the double-loop control structure of the converter to obtain a direct-current voltage control small-signal model.
The beneficial technical effects of the invention are as follows: according to the modeling method provided by the invention, on the basis of considering the power loss of the converter and the switching device, the influence of the converter AC/DC side energy storage element on the DC voltage control effect in the running process of the system is considered, and the accuracy of the DC voltage control small signal model is improved.
Drawings
The invention is further described below with reference to the accompanying drawings and examples:
fig. 1 is a topology structure diagram of a three-terminal dc power distribution network according to the present application.
Fig. 2 is a topological structure diagram of a dc-to-dc distribution network voltage source converter according to the present application.
Fig. 3 is a dual-loop control structure diagram of the dc distribution network voltage source converter of the present application.
Fig. 4 is a small signal model of dc voltage control of the dc distribution network voltage source converter.
Detailed Description
The invention is further described below with reference to the accompanying drawings of the specification:
the invention provides a modeling method of a direct-current voltage control small signal based on alternating-current and direct-current side instantaneous power, which is characterized by comprising the following steps of: the method comprises the following steps:
s1: constructing a small signal model of a power balance equation of an alternating current side of an inverter in a direct current distribution network;
s2: constructing a small signal model of a power balance equation at the direct current side of the converter in the direct current distribution network;
s3: constructing a direct-current voltage control small signal model according to the power balance relation between the alternating-current side and the direct-current side of the converter in the direct-current distribution network;
the step S1 further includes:
s11: determining a power balance equation of an alternating current side of an inverter in a direct current distribution network;
the step S2 further includes:
s21: determining the voltage-current relationship of the direct current side of the converter after adding the LC filter according to the positive and negative of the power value;
s22: and determining a power balance equation of the direct current side of the converter in the direct current distribution network.
In this embodiment, the ac side power balance equation is determined by the following method:
1.5V sd I d -DW L -P R -P t ＝0 (1)
wherein V is sd Representation, I d Representing current space vector in dq coordinate system
D represents a differentiation factor with respect to time, dx=d (x)/dt, W L Representing the energy of the equivalent inductance of the AC side, P R Represents the equivalent resistance R (R) s And r on Sum) of power, P t Representing the ac side power of the inverter.
Since the inverter adopts current vector control, each term should use current space vector in dq coordinate system
Representation, including active term I d And reactive term I q . While the instantaneous power transmitted on the ac side can be expressed as:
wherein P is ac3-3 Representing the instantaneous power transmitted on the ac side,
space vector representing ac side voltage, +.>
Space vectors representing ac side currents are then:
wherein P is R Represents the equivalent resistance R (R) s And r on Sum), R represents an ac side equivalent resistance,
space vector representing ac side voltage, +.>
Space vector representing alternating side current, active term I d Representing dq coordinatesCurrent space vector under the system->
Active term, I q Representing the current space vector in dq coordinate system +.>
Is not included in the reactive term.
For an ac side three-phase inductor, the stored energy is:
wherein W is L Representing the energy of the equivalent inductance on the AC side, L S Representation, i a Representing the current of phase A, i in three-phase power on alternating current side b Representing B-phase current, i in three-phase power at AC side c Representing the C-phase current in the ac side three-phase power,
wherein, the three-phase current of the alternating current side can be expressed as:
wherein i is a Representing the current of phase A, i in three-phase power on alternating current side b Representing B-phase current, i in three-phase power at AC side c Representing C-phase current in three-phase power on alternating current side, wherein I is space vector
Amplitude of>
For the corresponding phase angle, it is therefore possible to obtain:
wherein i is a Representing the current of phase A, i in three-phase power on alternating current side b Representing B-phase current, i in three-phase power at AC side c Representing C-phase current in three-phase power on alternating current side, wherein I is space vector
Is a function of the magnitude of (a).
Thus, it is possible to obtain:
wherein W is L Representing the energy of the equivalent inductance on the AC side, L S Representing I as a space vector
Amplitude, I of (2) d Representing the current space vector in dq coordinate system +.>
Active term, I q Representing the current space vector in dq coordinate system +.>
Is not included in the reactive term.
In this embodiment, the small signal model of the ac side power balance equation is determined by the following method:
ΔP t ＝1.5I d0 ΔV sd +(-1.5L s I d0 s+1.5V sd0 -3RI d0 )ΔI d -(1.5L s I q0 s+3RI q0 )ΔI q (2)
wherein DeltaP t Representing AC side small signal quantity, I d0 Representing steady state operating point I d Corresponding value V sd Representing d-axis component of the AC side network side voltage of the converter under the dq coordinate system, ls represents the sum s of equivalent inductance of a connecting transformer and a reactor and leakage inductance of the transformer represents Laplacian, and V sd0 Represents V sd R represents equivalent resistance of the connecting transformer and the reactor, I q0 Representing steady state operating point I q Corresponding toValue of I q The q-axis component of the current dq on the ac side of the inverter is represented by the coordinate system, s is represented by the laplace operator, and R is represented by the equivalent resistance on the ac side.
Aiming at the nonlinear equation of the power balance equation of the alternating current side of the converter obtained in the step S1, the power balance equation is unfolded by utilizing the Taylor series, and the specific calculation process is as follows:
the function F:
wherein V is sd Representing d-axis component of AC side network side voltage of converter under dq coordinate system, I d Representing current space vector in dq coordinate system
Ls represents the sum of the equivalent inductance of the coupling transformer and the reactor and the leakage inductance of the transformer, I q Representing the current space vector in dq coordinate system +.>
D represents a differential factor with respect to time, dx=d (x)/dt, P t Representing the ac side power of the inverter.
Deployment is performed at steady state operating point:
wherein DeltaP t Is a small signal quantity, (H.O.T) is a higher-order term generated during expansion, and is ignored here, V sd Representation, I d Representing current space vector in dq coordinate system
Is represented by Ls, I q Representing current space vector in dq coordinate system
D represents a differential factor with respect to time, dx=d (x)/dt, P t Representing the ac side power of the inverter.
The system steady state operating point may be expressed as:
(E.P.)＝(V sd-0 ,I d-0 ,DI d-0 ,I q-0 ,DI q-0 ,P t-0 )＝(V sd0 ,I d0 ,0,I q0 ,0,P t0 )(2-3)
wherein V is sd0 Representation, I d0 Representation, I q0 Representation, P t0 Representation of
The following steps are obtained:
ΔP t ＝1.5I d0 ΔV sd +1.5V sd0 ΔI d -1.5L s I d0 Δ(DI d )-1.5L s I q0 Δ(DI q )-3RI d0 ΔI d -3RI q0 ΔI q (2-4)
wherein DeltaP t Representing AC side small signal quantity, I d0 Representation, I d Is expressed as V sd Is expressed as V sd0 Representation, I q0 Representation, I q Ls and R represent equivalent resistances on the ac side.
Laplace transform on the above is available (Laplace operator s is omitted):
ΔP t ＝1.5I d0 ΔV sd +(-1.5L s I d0 s+1.5V sd0 -3RI d0 )ΔI d -(1.5L s I q0 s+3RI q0 )ΔI q (2)
wherein DeltaP t Representing AC side small signal quantity, I d0 Representation, I d Is expressed as V sd Is expressed as V sd0 Representation, I q0 Representation, I q Denoted Ls, R denotes an ac side equivalent resistance, and S denotes a laplace operator.
In this embodiment, the relationship between the voltage and the current is determined by the following method:
wherein i is Leq Indicating inductor current, I dc Representing the direct current at the outlet of the direct current line connected with the direct current side of the converter, P loss Representing power loss due to reverse recovery of the switch and tracking current process, V dc Representing the DC voltage at the DC side of the converter connected to the DC line outlet, V Ceq Representing the capacitance voltage, L eq Represents the dc side equivalent inductance, D represents the differential factor over time, dx=d (x)/dt.
In this embodiment, the power balance equation of the ac side of the converter in the dc distribution network is determined by the following method:
wherein Pdc represents the transmission power of the DC side of the converter, D represents the differential factor with respect to time, dx=d (x)/dt, C eq Representing the equivalent capacitance of the DC side, V Ceq Representing the capacitance voltage, L eq Representing the equivalent inductance of the DC side, i Leq Representing inductor current, P loss Indicating power loss due to reverse recovery of the switch and tracking current process, I dc Representing the DC current at the DC side of the converter connected with the DC line outlet, V dc Representing the dc voltage at the dc link outlet of the dc link at the dc side of the converter.
In this embodiment, the small signal model of the dc side power balance equation is determined by the following method:
wherein DeltaP t Representing small signal quantity, C eq Represents the equivalent capacitance of the direct current side, L eq Represents the equivalent inductance of the direct current side, P loss0 Is expressed as V dc0 Representation, I dc0 Represented by S, P loss Indicating that it is due to a switchReverse recovery and tracking current process.
Consider the invariable P of AC/DC power t ＝P dc At the time, can be obtained:
wherein D represents a differential factor over time, dx=d (x)/dt, C eq Representing the equivalent capacitance of the DC side, V dc Representing the DC voltage V at the DC side of the converter connected to the DC line outlet Ceq Representing the capacitance voltage, L eq Representing the equivalent inductance of the DC side, i Leq Representing inductor current, P loss Indicating power loss due to reverse recovery of the switch and tracking current process, I dc Representing the direct current at the outlet of the direct current line connected with the direct current side of the converter, P t Representing the ac side power of the inverter.
The above method is developed as follows:
wherein D represents a differential factor over time, dx=d (x)/dt, C eq Representing the equivalent capacitance of the DC side, V dc Representing the DC voltage V at the DC side of the converter connected to the DC line outlet Ceq Representing the capacitance voltage, L eq Representing the equivalent inductance of the DC side, i Leq Representing inductor current, P loss Indicating power loss due to reverse recovery of the switch and tracking current process, I dc Representing the direct current at the outlet of the direct current line connected with the direct current side of the converter, P t Representing the ac side power of the inverter.
The following steps are obtained:
wherein D represents a differentiation factor with respect to time, dx=d (x)/(x)dt，C eq Representing the equivalent capacitance of the DC side, V dc Representing the DC voltage V at the DC side of the converter connected to the DC line outlet Ceq Representing the capacitance voltage, L eq Representing the equivalent inductance of the DC side, i Leq Representing inductor current, P loss Indicating power loss due to reverse recovery of the switch and tracking current process, I dc Representing the direct current at the outlet of the direct current line connected with the direct current side of the converter, P t Representing the ac side power of the inverter.
Will be described above as variable V dc ,DV dc ,D 2 V dc ,I dc ,DI dc ,D 2 I dc ,P loss ,DP loss ,D 2 P loss ,P t Expressed as dynamic equation G:
wherein,,
wherein D represents a differential factor over time, dx=d (x)/dt, C eq Representing the equivalent capacitance of the DC side, V dc Representing the DC voltage V at the DC side of the converter connected to the DC line outlet Ceq Representing the capacitance voltage, L eq Representing the equivalent inductance of the DC side, i Leq Representing inductor current, P loss Indicating power loss due to reverse recovery of the switch and tracking current process, I dc Representing the direct current at the outlet of the direct current line connected with the direct current side of the converter, P t Representing the ac side power of the inverter.
Expanding the dynamic equation G at a steady-state operating point by using a Taylor series:
and the system steady state operating point may be expressed as:
(E.P.)＝(V dc-0 ,DV dc-0 ,D 2 V dc-0 ,I dc-0 ,DI dc-0 ,D 2 I dc-0 ,P loss-0 ,DP loss-0 ,D 2 P loss-0 ,P t-0 )
＝(V dc0 ,0,0,I dc0 ,0,0,P loss0 ,0,0,P t0 )(5-6)
wherein P is t0 Representation, P loss0 Representation, I dc0 Is expressed as V dc0 The representation is made of a combination of a first and a second color,
and then the linear small signal dynamic equation of the direct current side of the converter can be obtained:
wherein P is t0 Representation, P loss0 Representation, I dc0 Is expressed as V dc0 D represents a differential factor over time, dx=d (x)/dt, C eq Representing the equivalent capacitance of the DC side, V dc Representing the DC voltage V at the DC side of the converter connected to the DC line outlet Ceq Representing the capacitance voltage, L eq Representing the equivalent inductance of the DC side, i Leq Representing inductor current, P loss Indicating power loss due to reverse recovery of the switch and tracking current process, I dc Representing the direct current at the outlet of the direct current line connected to the direct current side of the converterFlow, P t Representing the ac side power of the inverter.
Laplace transform on the above is available (Laplace operator s is omitted):
from the ac-dc side power balance of the converters obtained in S11 and S22, respectively, it is possible to obtain:
wherein DeltaP t Representing AC side small signal quantity, I d0 Representing steady state operating point I d Corresponding value, I d Active term representing current space vector I in dq coordinate system, R representing ac side equivalent resistance, S representing laplace operator, D representing differential factor with respect to time, dx=d (x)/dt, C eq Representing the equivalent capacitance of the DC side, V dc Representing the DC voltage V at the DC side of the converter connected to the DC line outlet Ceq Representing the capacitance voltage, L eq Representing the equivalent inductance of the DC side, i Leq Representing inductor current, P loss Indicating power loss due to reverse recovery of the switch and tracking current process, I dc Representing the direct current at the outlet of the direct current line connected with the direct current side of the converter, P t Representing the ac side power of the inverter.
In this embodiment, step S3 further includes: and combining the double-loop control structure of the converter to obtain a direct-current voltage control small-signal model.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the technical solution of the present invention, which is intended to be covered by the scope of the claims of the present invention.
Claims (2)
1. A modeling method of a direct-current voltage control small signal based on alternating-current and direct-current side instantaneous power is characterized by comprising the following steps of: the method comprises the following steps:
s1: constructing a small signal model of a power balance equation of an alternating current side of an inverter in a direct current distribution network;
the small signal model of the alternating current side power balance equation is determined by adopting the following method:
ΔP t ＝1.5I d0 ΔV sd +(-1.5L s I d0 s+1.5V sd0 -3RI d0 )ΔI d -(1.5L s I q0 s+3RI q0 )ΔI q (2)
wherein DeltaP t Representing AC side small signal quantity, I d0 Representing steady state operating point I d Corresponding value V sd Representing d-axis component of the AC side network side voltage of the converter under the dq coordinate system, ls representing the sum of equivalent inductance of a connecting transformer and a reactor and leakage inductance of the transformer, s representing Laplacian, V sd0 Representing d-axis component steady-state operating point of converter AC side network side voltage under dq coordinate system, R representing equivalent resistance of connecting transformer and reactor, I d Representing current space vector in dq coordinate system
Active term, I q0 Representing steady state operating point I q Corresponding steady state value, I q Representing q-axis components of the current dq coordinate system of the alternating current side network side of the converter;
the alternating current side power balance equation is determined by the following method:
1.5V sd I d -DW L -P R -P t ＝0 (1)
wherein Vsd represents d-axis component of the AC side network side voltage of the converter under dq coordinate system, I d Representing current space vector in dq coordinate system
Active term of (2)D represents a differentiation factor over time, dx=d (x)/dt, W L Representing the energy of the equivalent inductance of the AC side, P R Represents the power of the equivalent resistance R on the AC side, R represents R s And r on Sum, P t Representing the ac side power of the inverter;
s2: constructing a small signal model of a power balance equation at the direct current side of the converter in the direct current distribution network;
the small signal model of the direct current side power balance equation is determined by adopting the following method:
wherein DeltaP dc Representing DC side small signal quantity, C eq Represents the equivalent capacitance of the direct current side, L eq Represents the equivalent inductance of the direct current side, P loss0 Representing steady state value of power loss, V dc0 Indicating the corresponding value of the DC voltage at the outlet of the converter at the steady-state operating point, I dc0 Representing the corresponding value of the DC current at the outlet of the converter at the steady-state operating point, S represents the Laplacian, and P loss Representing power loss due to reverse recovery of the switch and tracking current process;
s3: constructing a direct-current voltage control small signal model according to the equal relation between an alternating-current side small signal model and a direct-current side small signal model of an inverter in a direct-current distribution network;
the step S1 further includes:
s11: determining a power balance equation of an alternating current side of an inverter in a direct current distribution network;
the power balance equation of the alternating current side of the converter in the direct current distribution network is determined by adopting the following method:
wherein Pdc represents the transmission power of the direct current side of the inverter, D represents the differentiation factor with respect to time,
Dx＝d(x)/dt，C eq indicating DC side, etcEffective capacitance, V Ceq Representing the capacitance voltage, L eq Representing the equivalent inductance of the DC side, i Leq Representing inductor current, P loss Indicating power loss due to reverse recovery of the switch and tracking current process, I dc Representing the DC current at the DC side of the converter connected with the DC line outlet, V dc Representing the direct current voltage at the position where the direct current side of the converter is connected with the outlet of the direct current line; the step S2 further includes:
s21: determining the voltage-current relationship of the direct current side of the converter after adding the LC filter according to the positive and negative of the power value;
the relation of the voltage and the current is determined by adopting the following method:
wherein i is Leq Indicating inductor current, I dc Representing the direct current at the outlet of the direct current line connected with the direct current side of the converter, P loss Representing power loss due to reverse recovery of the switch and tracking current process, V dc Representing the DC voltage at the DC side of the converter connected to the DC line outlet, V Ceq Representing the capacitance voltage, L eq Represents the dc side equivalent inductance, D represents the differential factor over time, dx=d (x)/dt;
s22: and determining a power balance equation of the direct current side of the converter in the direct current distribution network.
2. The modeling method of a direct current voltage control small signal based on alternating current-direct current side instantaneous power according to claim 1, wherein the modeling method is characterized by comprising the following steps: step S3 further includes: and combining the double-loop control structure of the converter to obtain a direct-current voltage control small-signal model.
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