CN107623341B - VSC inverter station mathematical model for supplying power to passive network and internal model controller - Google Patents

VSC inverter station mathematical model for supplying power to passive network and internal model controller Download PDF

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CN107623341B
CN107623341B CN201710980721.7A CN201710980721A CN107623341B CN 107623341 B CN107623341 B CN 107623341B CN 201710980721 A CN201710980721 A CN 201710980721A CN 107623341 B CN107623341 B CN 107623341B
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余瑜
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Hubei University of Technology
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Abstract

The invention relates to a VSC inverter station global small signal mathematical model and an internal model controller for supplying power to a passive network. And then, comprehensively considering the dynamic performance index ISE and the robust performance index M value function of the control system, and selecting a proper low-pass filter bandwidth. And finally, deducing the structure and parameters of the internal model controller of the VSC inverter station according to an internal model principle, wherein the controlled quantity is the components of d and q axes of the voltage of the common node at the AC side of the VSC inverter station. In conclusion, the designed VSC inverter station internal model controller can realize constant alternating voltage control, can provide stable alternating voltage for a passive network under the working conditions of load fluctuation, controlled quantity set value change, parameter perturbation and the like, and has good electric energy quality.

Description

VSC inverter station mathematical model for supplying power to passive network and internal model controller
Technical Field
The invention belongs to the technical field of electric power engineering. In particular to a method for designing an internal model controller of a VSC (voltage source type converter based on a fully-controlled power electronic device) inversion station for supplying power to a passive network.
Background
The VSC is independently controllable in active and reactive power, the current of the VSC can be automatically turned off, no additional reversing voltage is needed, and the electric energy quality is good. Therefore, the VSC is widely used in high-voltage direct-current transmission systems such as flexible direct-current transmission systems, hybrid direct-current transmission systems, and multi-terminal direct-current transmission systems, and when the VSC is used as an inverter station, the VSC can supply power to passive networks such as drilling platforms, remote islands, and large cities or industrial centers that cannot use overhead line corridors. However, the VSC inverter station is frequently disturbed due to changes of system power flow, load fluctuation, short-time faults and the like, certain errors exist in the model due to simplification during VSC converter mathematical modeling, in addition, model mismatch is also caused due to changes of component parameters along with time environment, and higher requirements are provided for closed-loop dynamic performance and robust stability of a VSC inverter station control system.
Disclosure of Invention
Aiming at the problems, the invention provides a method for designing an internal model controller of a VSC inverter station for supplying power to a passive network according to an internal model control principle, so that a control system has good robust stability under the condition of meeting a certain dynamic performance requirement, and can provide stable alternating voltage for the passive network when the load fluctuates or the parameters of a main circuit perturb.
The technical scheme provided by the invention is as follows:
a design method of an internal model controller of a VSC inverter station for supplying power to a passive network is characterized by comprising the following steps:
1. and establishing an equivalent main circuit topological graph according to the VSC inverter station structure.
2. And deducing a small signal mathematical model according to the topological graph of the VSC inverter station main circuit.
3. And (3) completing the design of the internal model controller of the VSC inverter station according to an internal model control principle, the derived small signal model (internal model) and a low-pass filter (considering system performance index ISE and robust performance index M to select a proper filter time constant) for the robust characteristic.
The method comprises the following steps:
the utility model provides a to numerical model of VSC contravariant station of passive network power supply, its characterized in that, to the VSC contravariant station main circuit topology of passive network power supply, accomplish the contravariant by the VSC transverter in this main circuit topology, set up steady voltage electric capacity C in order to stabilize DC voltage at VSC transverter DC side, set up low pass filter in order to filter high frequency harmonic at VSC transverter AC side. The alternating current side of the VSC converter is connected with a reactor and a transformer, and finally connected with a passive load; the global small signal mathematical model comprises:
model is simplified to VSC transverter: simplify VSC transverter for inertia link, VSC transverter's small-signal mathematical model is formula (1). Switching delay τ ═ 1.5T, ucd、ucqIs a d-axis component, a q-axis component, u, of a fundamental frequency phase voltage of an AC side of the convertercd*、ucqAnd the reference values of d-axis components and q-axis components of the SPWM modulated wave voltage are set.
Figure GDA0002210703690000021
Connecting a reactor and a transformer to simplify a model: the coupling reactor and transformer equivalent impedance is R, L. The mathematical model of the small signal connecting the reactor and the transformer is formula (2).
Wherein isd、isqD-axis and q-axis components of AC side fundamental frequency phase current of the converter; u. ofsd、usqThe fundamental frequency phase voltage d and q-axis components of the PCC point on the AC side of the converter.
Figure GDA0002210703690000031
Passive load simplified model: the equivalent impedance of the passive load is represented by RL、LLAnd (4) equivalence. The passive load small signal mathematical model is formula (3).
Figure GDA0002210703690000032
The states of the VSC inversion station and the output equation are obtained through the joint type (1), (2) and (3) as formulas (4) and (5). Wherein the state variable x ═ Δ isdΔisqΔucdΔucq]TThe VSC converter station is a two-input and two-output system, and an input variable u is ═ delta ucd*Δucq*]TOutput variable y ═ Δ usdΔusq]T. The system matrix a is a 4 × 4 square matrix, see equation (7). The input matrix B is a 4 × 2 matrix, see equation (8). The output matrix C is a 2 × 4 matrix, see equation (9). The direct transfer matrix D is a 2 × 1 matrix, see equation (10).
VSC contravariant station global small signal mathematical model: VSC inversion station global small signal mathematical model G(s) is shown in formula (6).
Figure GDA0002210703690000033
y＝Cx+Du (5)
Figure GDA0002210703690000035
Figure GDA0002210703690000041
Figure GDA0002210703690000042
D＝[0 0](10)
An internal model controller of a VSC inverter station supplying power to a passive network based on a VSC inverter station mathematical model supplying power to the passive network is characterized by comprising the following steps:
step 1: the method comprises the following steps of (1) factorizing a VSC inversion station global small signal mathematical model (an object model) in a formula (11):
Figure GDA0002210703690000043
whereinThe transfer function of the all-pass filter, including all time lags and the right half-plane zero,
Figure GDA0002210703690000045
is a transfer function with minimal phase characteristics, stable and contains no prediction terms.
Step 2: the low pass filter filters a selection of time constants or bandwidths. The dynamic performance index ISE and the robust performance index M value function of the control system are comprehensively considered and are respectively shown in formulas (12) and (13). Where e is the error and η is the complementary sensitivity. The larger the bandwidth is, although the response to the external disturbance is not obvious, the weaker the capability of suppressing the high-frequency noise is, in this example, the bandwidth is equal to 500rad/s, and the order is 1.
Figure GDA0002210703690000046
Figure GDA0002210703690000047
And step 3: VSC internal model controller GC(S is shown in formula (14), wherein F (S) is a low-pass filter diagonal matrix shown in formula (15)fIs the filter time constant, α is the filter bandwidth, and r is the filter order.
Figure GDA0002210703690000051
And 4, step 4: internal model equivalent controller G of inverter stationeq(s) is shown in formula (16). MATLAB-based calculation of VSC inverter equivalent controller Geq(s), reducing the order to a proper order based on a Hankel optimal model, and designing to obtain the VSC inverter internal model equivalent controller GeqThe parameter(s) is shown in formula (17).
Figure GDA0002210703690000054
And the design of the internal model equivalent controller of the VSC inverter station for supplying power to the passive network is completed.
Therefore, the invention has the following advantages:
1. the closed loop dynamic performance of the designed VSC internal model control system is good: when the alternating voltage command value changes, the alternating voltage command value can change along with the change of the command value quickly; the alternating voltage can be well controlled to keep stable when the load fluctuates, and the quality of the electric energy for supplying power to the passive network is improved.
2. The designed VSC internal model control system also has certain robustness to model mismatch: the harmonic wave generated by perturbation of circuit parameters can be effectively filtered.
Drawings
Fig. 1 is a topology diagram of a main circuit of a VSC inverter station according to the present invention.
Fig. 2 is a simplified model of the VSC converter according to the present invention.
Fig. 3 is a block diagram of an internal model controller of the VSC inverter according to the present invention.
Detailed Description
The internal model controller of the VSC inverter station for supplying power to the passive network has a specific design flow which is roughly divided into five steps:
the method comprises the following steps: a topological diagram of a VSC inverter station main circuit is shown in figure 1.
The VSC converter completes inversion, a voltage stabilizing capacitor C is connected in parallel on the DC side of the VSC converter to stabilize DC voltage and filter out partial harmonic, a filter is connected in parallel on the AC side of the VSC converter to filter out high-frequency harmonic, R, L is equivalent impedance of a connecting reactor and a transformer, and when a passive network is connected, a passive load is formed by RL、LLAnd (4) equivalence.
Step two: and deriving a VSC inverter station small signal model. The object model comprises three parts: (1) equivalent model (2) of VSC converter connects equivalent resistance and inductance R, L model (3) of reactor and transformer and load equivalent resistance and inductance RL、LLAnd (4) modeling. The VSC converter is simplified into an inertia link, and the inertia link is shown in figure 2. Taking switch delay tau as 1.5T, ucd、ucqIs a d-axis component, a q-axis component, u, of a fundamental frequency phase voltage of an AC side of the convertercd*、ucqEquation (1) describes a simplified model of the VSC converter, wherein the reference values are d-axis component and q-axis component of the SPWM modulated wave voltage.
Figure GDA0002210703690000061
The VSC converter station inversion side connection reactor, the transformer and the connected alternating current load small signal model are expressed as formulas (2) and (3). i.e. isd、isqD-axis and q-axis components of AC side fundamental frequency phase current of the converter; u. ofsd、usqThe fundamental frequency phase voltage d and q-axis components of the PCC point on the AC side of the converter.
Figure GDA0002210703690000062
The forms of the state equation and the output equation of the VSC inversion station obtained in the joint type (1), (2) and (3) are shown in the formulas (5) and (6)
Figure GDA0002210703690000071
y＝Cx+Du (6)
Wherein the state variable x ═ Δ isdΔisqΔucdΔucq]TThe VSC converter station is a two-input and two-output system, and an input variable u is ═ delta ucd*Δucq*]TOutput variable y ═ Δ usdΔusq]T. The VSC converter station transfer function (internal model) g(s) is shown in equation (7).
Step three: factorization of the internal model is shown in formula (8):
Figure GDA0002210703690000073
wherein
Figure GDA0002210703690000074
The transfer function of the all-pass filter, including all time lags and the right half-plane zero,
Figure GDA0002210703690000075
is a transfer function with minimal phase characteristics, stable and contains no prediction terms.
Internal model controller GC(S) is represented by the formula (9). Wherein F (S) is a low-pass filter diagonal matrix (10), TfIs the filter time constant, α is the filter bandwidth, and r is the filter order. A formula of an internal model controller of the VSC converter is shown in a formula (11).
Figure GDA0002210703690000076
Figure GDA0002210703690000077
Figure GDA0002210703690000078
The selection of the filter time constant or bandwidth needs to comprehensively consider the dynamic performance index ISE and the robust performance index M value function of the control system, which are respectively shown in formulas (12) and (13). Where e is the error and η is the complementary sensitivity. The larger the bandwidth is, the less the response to external disturbance is, but the weaker the ability to suppress high-frequency noise is, so in this example, the bandwidth is set to 500rad/s, and the order is set to 2.
Figure GDA0002210703690000079
Calculating VSC inverter equivalent controller G by using MATLAB simulation softwareeqReducing the order to a proper order based on the Hankel optimal model to obtain the VSC inverter internal model controller GeqParameter see formula (14), internal model controller GeqThe structure is shown in fig. 3.
Figure GDA0002210703690000082
And the internal model controller of the VSC inverter station for supplying power to the passive network is designed.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (1)

1. The internal model controller of the VSC inverter station for supplying power to the passive network is based on a VSC inverter station mathematical model for supplying power to the passive network, and is characterized in that the VSC inverter station mathematical model for supplying power to the passive network comprises a VSC inverter station main circuit topology for supplying power to the passive network, wherein inversion is completed by a VSC converter in the main circuit topology, a voltage stabilizing capacitor C is arranged on the direct current side of the VSC converter to stabilize direct current voltage, and a low-pass filter is arranged on the alternating current side of the VSC converter to filter high-frequency harmonics; the alternating current side of the VSC converter is connected with a reactor and a transformer, and finally connected with a passive load; the global small signal mathematical model comprises:
model is simplified to VSC transverter: simplifying the VSC into an inertia link, wherein a small-signal mathematical model of the VSC is an expression (1); switching delay τ ═ 1.5T, ucd、ucqIs a d-axis component, a q-axis component, u, of a fundamental frequency phase voltage of an AC side of the convertercd*、ucqThe reference values of d and q axis components of the SPWM modulated wave voltage are shown;
Figure FDA0002232777830000011
connecting a reactor and a transformer to simplify a model: the equivalent impedance of the connecting reactor and the transformer is R1、L1(ii) a The mathematical model of the small signal connecting the reactor and the transformer is an expression (2);
wherein isd、isqD-axis and q-axis components of AC side fundamental frequency phase current of the converter; u. ofsd、usqFundamental frequency phase voltage d and q-axis components of a PCC point on the AC side of the converter;
Figure FDA0002232777830000012
passive load simplified model: the equivalent impedance of the passive load is represented by RL、LLEquivalence is carried out; the passive load small signal mathematical model is formula (3);
Figure FDA0002232777830000021
the VSC inversion station state equation and the output equation are obtained in the joint type (1), (2) and (3) according to the formulas (4) and (5); wherein the state variable x ═ Δ isdΔisqΔucdΔucq]TThe VSC converter station is a two-input and two-output system, and an input variable u is ═ delta ucd*Δucq*]TOutput variable y ═ Δ usdΔusq]T(ii) a The system matrix A is a 4 × 4 square matrix, see formula (7); the input matrix B is a 4 × 2 matrix, see equation (8); the output matrix C is a 2 × 4 matrix, see equation (9); the direct transfer matrix D is a 2 × 1 matrix, see equation (10);
a VSC inversion station global small signal mathematical model G(s) is shown in a formula (6);
y＝Cx+Du (5)
Figure FDA0002232777830000023
Figure FDA0002232777830000024
Figure FDA0002232777830000025
Figure FDA0002232777830000026
D＝[0 0](10)；
the method comprises the following steps:
step 1: the method comprises the following steps of (1) factorizing a VSC inversion station global small signal mathematical model, wherein the mathematical model is shown in a formula (11):
Figure FDA0002232777830000031
wherein
Figure FDA0002232777830000032
The transfer function of the all-pass filter, including all time lags and the right half-plane zero,
Figure FDA0002232777830000033
is a transfer function with minimum phase characteristics, is stable and does not contain a prediction term;
step 2: selection of a low-pass filter filtering time constant or bandwidth; comprehensively considering dynamic performance index ISE of the control system and a robust performance index M value function, respectively see formulas (12) and (13); wherein e is the error and η is the complementary sensitivity; the larger the bandwidth is, although the response to external disturbance is not obvious, the weaker the capability of suppressing high-frequency noise is, the bandwidth of the embodiment is taken as alpha being 500rad/s, and the order is taken as 1;
Figure FDA0002232777830000034
Figure FDA0002232777830000035
and step 3: VSC internal model controller GC(S) see formula (14); wherein F (S) is a low-pass filter diagonal matrix see (15); t isfIs the filter time constant, α is the filter bandwidth, r is the filter order;
Figure FDA0002232777830000036
Figure FDA0002232777830000037
and 4, step 4: internal model equivalent controller G of inverter stationeq(s) see formula (16); MATLAB-based calculation of VSC inverter equivalent controller Geq(s), reducing the order to a proper order based on a Hankel optimal model, and designing the VSC inverterModulus equivalent controller Geq(s) see formula (17);
Figure FDA0002232777830000038
Figure FDA0002232777830000041
and the design of the internal model equivalent controller of the VSC inverter station for supplying power to the passive network is completed.
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