CN108280271A - THE UPFC equivalent modeling method based on switch periods average principle - Google Patents
THE UPFC equivalent modeling method based on switch periods average principle Download PDFInfo
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Abstract
The present invention relates to power system modeling and analysis technical field, especially a kind of THE UPFC UPFC equivalent modeling methods based on switch periods average principle, including：It is made of static synchronous series compensator SSSC and static synchronous compensator STATCOM in parallel based on the THE UPFC UPFC models of modularization multi-level converter MMC, in conjunction with switch periods average equivalent principle, static synchronous compensator STATCOM exchange side is established respectively, DC side equivalent controlled source model, then synchronous series compensator SSSC exchange side is established respectively, DC side equivalent controlled source model, parallel equivalent capacitance on DC bus between synchronous series compensator SSSC and static synchronous compensator STATCOM, realize the side in parallel of UPFC, the joint Equivalent Modeling and simulation calculation of series side.The present invention can accurately reflect UPFC in subsynchronous oscillation of electrical power system, the dynamic characteristic of low-frequency oscillation, simplify UPFC models, accelerate calculating speed, and disclosure satisfy that the required precision of Power System Stability Analysis and control.
Description
Technical Field
The invention relates to the technical field of modeling and analysis of power systems, in particular to an equivalent modeling method of a unified power flow controller based on a switching period averaging principle.
Background
Unified Power Flow Controller (UPFC) based on Modular Multilevel Converter (MMC) has advantages such as harmonic characteristics is good, easy modularized design, compact size and do not need device direct series connection, is applicable to the transmission of electricity field of high pressure large capacity, can improve circuit transmission capacity, improves system transient stability, optimizes the trend and reduces the network loss, consequently receives attention.
The establishment of the MMC-UPFC simulation model suitable for different application needs is the basis for simulation analysis of the application of the MMC-UPFC in the power system, and the accurate establishment of the electromagnetic transient model reflecting the actual sub-model and the mutual connection of the sub-model has large scale and extremely low simulation speed. If the first MMC Project (TBC) in the world has the rated capacity of 400MW, the direct-current voltage is +/-200 kV, a single bridge arm comprises 216 submodule pieces, the whole MMC device has 12551 submodule pieces in total, the electromagnetic transient model which accurately reflects the submodule pieces and the connection relation of the submodule pieces is large in scale, if the simulation step length is 20us, the simulation time length is 5s, and each simulation needs more than 3000h (125d) through simulation test and estimation, the adjustment and optimization of control parameters and subsequent research work cannot be carried out.
Therefore, some researchers have proposed different simplified speed-up modeling methods, and some documents have proposed an MMC simulation speed-up model in which each submodule of the MMC is separately modeled and then connected in series by using a controlled current source, and the model adopts a plurality of separate submodules, so that the simulation speed of the MMC can be increased to a certain extent. There is a literature that proposes an MMC fast electromagnetic transient simulation model that solves the dynamic characteristics of each sub-module by using a user-defined numerical calculation module and models the bridge arm output voltage in cooperation with a controlled voltage source, and the simulation model can obtain a simulation result basically consistent with a detailed switch model, but the modeling method is still complex.
Disclosure of Invention
Aiming at the problems, the invention provides an equivalent modeling method of a unified power flow controller based on a switching period averaging principle, which comprises the following steps:
step 1: respectively establishing an alternating current side equivalent model and a direct current side equivalent model of the static synchronous compensator STATCOM by combining a switching period average equivalent principle, wherein the alternating current side of the static synchronous compensator STATCOM is equivalent by using a three-phase controlled voltage source, and the direct current side of the static synchronous compensator STATCOM is equivalent by using a controlled current source;
step 2: respectively establishing an alternating current side equivalent model and a direct current side equivalent model of a synchronous series compensator SSSC (synchronous series compensator) by combining a switching period average equivalent principle, wherein an alternating current side equivalent model circuit of the synchronous series compensator SSSC is equivalent by a three-phase controlled voltage source, and a direct current side controlled current source of the synchronous series compensator SSSC is equivalent by a controlled current source;
and step 3: establishing a direct-current side parallel equivalent capacitor circuit of a synchronous series compensator SSSC and a static synchronous compensator STATCOM, connecting an equivalent capacitor in parallel on a direct-current bus between the synchronous series compensator SSSC and the parallel side STATCOM, and establishing a direct-current side equivalent circuit to realize the combined simulation calculation of the parallel side and the serial side of the UPFC.
The step 2 specifically comprises:
the unified power flow controller UPFC is composed of a static synchronous series compensator SSSC and a static synchronous compensator STATCOM which are connected in parallel, the static synchronous series compensator SSSC and the static synchronous compensator STATCOM are both composed of MMC type current converters, each phase of each three-phase MMC type current converter is composed of an upper bridge arm and a lower bridge arm, each bridge arm is composed of a plurality of half-bridge sub-module current converters with the same structure which are connected in series and then connected in series with a reactor L,
the relation between the average voltage and the average current of each half-bridge submodule in the MMC over a switching cycle is:
wherein D represents the duty ratio of the half-bridge submodule power switch converter;the average voltage is output by an alternating current side port of the half-bridge submodule;the direct current voltage is the direct current voltage of a direct current side capacitor of the half-bridge submodule;the average current of an alternating current side port of the half-bridge submodule is obtained;is the average current of the half-bridge submodule DC side capacitor.
The modular multilevel converter MMC adopts a carrier phase-shifting sine pulse width modulation strategy to perform pulse width modulation on N sub-module converters in each bridge arm, and the pulse width modulation strategy is characterized in that the pulse width modulation strategy comprises the following steps of:
wherein u is1.totalThe alternating-current side phase voltage is output by the modular multilevel converter MMC; n is the number of sub-module converters in each bridge arm;the average voltage of the switching period output by the sub-module converter,step 2.2: establishing an equivalent model of an alternating current side of the static synchronous compensator STATCOM, wherein the alternating current side of the static synchronous compensator STATCOM is represented by a three-phase controlled voltage source as follows:
wherein v isSTATCOM.fga、vSTATCOM.fgb、vSTATCOM.fgcRespectively providing three-phase equivalent controlled voltage source voltages of an abc at the AC side of the STATCOM; n is a radical ofstatcomFor the number of submodules in series on each bridge arm, vc.statcomIs a sub-module DC capacitor voltage, Vdc.statcomThe voltage of the STATCOM direct current side of the static synchronous compensator is obtained; dTstatcom.a、dTstatcom.b、dTstatcom.cRespectively, the equivalent transformation coefficients of three phases abc,
the equivalent transformation coefficients of three abc phases of the static synchronous compensator STATCOM are respectively as follows:
wherein v isstatcom.aref、vstatcom.bref、vstatcom.crefThe voltage is an abc three-phase reference voltage of a static synchronous compensator STATCOM; kstatcomFor the ac-dc equivalent coefficient of the static synchronous compensator STATCOM,
wherein u isa.statcomFor the ac-side phase voltage effective value of the static synchronous compensator STATCOM,
step 2.3: establishing a direct-current side equivalent model of the static synchronous compensator STATCOM, wherein the direct-current side of the static synchronous compensator STATCOM is equivalent to a controlled current source, and the controlled current source is as follows:
iSTATCOM.fgg＝dTstatcom.a·iSa1+dTstatcom.b·iSb1+dTstatcom.c·iSc1(8)
wherein iSa1、iSb1、iSc1The three-phase current is the three-phase current on the alternating current side of the STATCOM of the static synchronous compensator.
The step 3 specifically includes:
step 3.1, establishing an alternating current side equivalent model of the synchronous series compensator SSSC,
wherein v isSSSC.fga、vSSSC.fgb、vSSSC.fgcThree-phase equivalent controlled voltage source voltages at the alternating current side of the synchronous series compensator SSSC are respectively provided; n is a radical ofssscThe number of the sub-modules connected in series on each bridge arm of the synchronous series compensator SSSC is equal to the number of the sub-modules connected in series on each bridge arm of the synchronous series compensator SSSC; v. ofc.ssscIs the submodule direct current capacitor voltage; vdc.ssscThe direct-current side voltage of the synchronous series compensator SSSC; dTsssc.a、dTsssc.b、dTsssc.cThe equivalent transformation coefficients of the three abc phases are respectively:
wherein v issssc.aref、vsssc.bref、vsssc.crefThe abc three-phase reference voltages are respectively generated by a control part on the SSSC side of the synchronous series compensator; kssscIs the ac-dc equivalent coefficient of the synchronous series compensator SSSC:
wherein u isa.ssscFor the effective value of the voltage of the alternating-current side phase of the synchronous series compensator SSSC,
step 3.2: establishing a direct-current side equivalent model of the SSSC, wherein the direct-current side equivalent of the SSSC is a controlled current source:
iSSSC.fgs＝dTsssc.a×iSa2+dTsssc.b×iSb2+dTsssc.c×iSc2(14)
wherein iSa2、iSb2、iSc2The synchronous series compensator SSSC alternating-current side three-phase current.
The step 4 specifically includes: by adopting the equivalent principle of periodic average value, an equivalent capacitor C is connected in parallel on a direct current bus between a synchronous series compensator SSSC and a parallel-side static synchronous compensator STATCOMdcFor simulating the dynamic course of the capacitance in each submodule,
DC equivalent capacitor CdcComprises the following steps:
wherein N isstatcomThe number of the sub-module converters cascaded in the STATCOM is the number of the sub-module converters cascaded in the STATCOM; cstatcomThe direct-current capacitance value of a submodule converter connected in series in the static synchronous compensator STATCOM is obtained; n is a radical ofssscFor commutating submodules connected in series in synchronous series compensator SSSCThe number of devices; cssscThe direct current capacitance value of the submodule converter in the synchronous series compensator SSSC.
Advantageous effects
The invention provides a united equivalent modeling method of a static synchronous series compensator SSSC (static synchronous series compensator) at the series side and a static synchronous compensator STATCOM at the parallel side of a unified power flow controller based on an average period equivalent model aiming at the specific requirements of stable analysis and control of a UPFC (unified power flow controller) after the UPFC is accessed into a power system.
Drawings
FIG. 1 is an electrical relationship diagram of a UPFC and an access grid;
FIG. 2 is a structure diagram of an MMC-UPFC parallel side STATCOM and series side SSSC converter;
FIG. 3 is a control structure diagram of a STATCOM of a UPFC parallel side static synchronous compensator;
FIG. 4 is a control structure diagram of a static synchronous compensator SSSC on the UPFC series side;
FIG. 5 is a schematic diagram of MMC-STATCOM principle;
FIG. 6 is a schematic diagram of a half-bridge sub-module configuration;
FIG. 7 is a schematic diagram of static synchronous compensator STATCOM equivalent modeling;
FIG. 8 is a schematic diagram of SSSC equivalent modeling of a static synchronous series compensator;
FIG. 9 is a circuit diagram of an equivalent model of the DC side of the STATCOM;
FIG. 10 is a circuit diagram of an AC-side equivalent model of the STATCOM;
FIG. 11 is a circuit diagram of an SSSC period average equivalent model of a static synchronous series compensator;
fig. 12 is a waveform of an active power transient calculation result under disturbance based on establishment of a unified power flow controller UPFC joint equivalent model.
Detailed Description
The embodiments are described in detail below with reference to the accompanying drawings.
The equivalent modeling method of the unified power flow controller based on the switching period average principle comprises the following steps:
as shown in fig. 1 below, the unified power flow controller UPFC includes two parts: a static synchronous series compensator SSSC and a parallel static synchronous compensator STATCOM. A static synchronous series compensator SSSC in a unified power flow controller UPFC injects an alternating voltage with controllable amplitude and phase angle on a transmission line, the voltage can be regarded as a voltage source synchronous with the system fundamental frequency, and the power flow on the line can be changed, so that the main function of the unified power flow controller UPFC is realized; the basic function of the MMC converter of the static synchronous compensator STATCOM is to provide or absorb active power according to the demand on the dc bus, it can also emit or absorb reactive power, and it can provide parallel reactive compensation for the lines alone.
As shown in fig. 2, in the unified power flow controller UPFC, converters of the static synchronous compensator STATCOM and the static synchronous compensator SSSC both adopt an MMC structure. The bridge arm of each MMC current converter is formed by connecting a plurality of half-bridge sub-module current converters in series, and the number of the series sub-module current converters is large, so that the simulation calculation speed is greatly reduced.
The voltage dq axis control strategy of the parallel-side static synchronous compensator STATCOM is shown in fig. 3, and the dq axis reference voltage is:
wherein u isCa(t)、uCb(t)、uCc(t) three-phase voltage at a static synchronous compensator STATCOM bus C is converted to a dq axis to obtain uCd(t)、uCq(t) representing d and q axis components, respectively; i.e. iEa(t)、iEb(t)、iEc(t) three-phase currents flowing into a bus C of the STATCOM are respectively converted to dq axes to obtain iEd(t)、iEq(t); r is an equivalent value of total loss of the connecting reactor and the bridge arm;
u1d(t) is the d-axis control voltage component, u, of the STATCOM output1q(t) is a q-axis control voltage component output by the static synchronous compensator STATCOM; ω is synchronous angular velocity of rotation, ω -2 π f0Wherein f is0＝50Hz；LEThe total equivalent inductance of a static synchronous compensator STATCOM machine end series reactor and a step-down transformer ET,
the expression of the differential equation of the voltage on the parallel side is discretized,andthe parallel side current reference value representing the next sampling moment is given by the direct current capacitor voltage control module; sampling value u at the present timesd(k) And usq(k) Is the quantity obtained by voltage measurement and park transformation, i at the current momentEd(k) And iEq(k) Is the quantity obtained by current measurement and park transformation.
Comparing the actually measured voltage and current values with the reference value, and adjusting by a PI link to obtain the voltage control quantity of the next momentAndthe current transformer output always tracks the given current as the input control quantity of the current transformer trigger control link.
Voltage dq axis control strategy of synchronous series compensator SSSC control architecture as shown in fig. 4, the main function of the converter of a static synchronous compensator SSSC is to string an active voltage of a certain amplitude and phase angle on the transmission line under the voltage support of a dc capacitor to maintain the active and reactive power transmitted on the transmission line consistent with reference values. Direct-axis component and quadrature-axis component reference value of output current at alternating current side of synchronous series compensator SSSCAndthe expression of (a) is:
wherein u isBa、uBb、uBcRespectively converting three-phase voltage at a bus B at the mounting position of the synchronous series compensator SSSC to a dq axis to be uBd、uBq；ia、ib、icThree-phase current at a bus C of the SSSC of the synchronous series compensator is converted to a dq axis and then is id、iq；P*、Q*Respectively set reference active power and reactive power.
The dq-axis reference voltage of the synchronous series compensator SSSC is:
wherein u is2d(t) is a d-axis control voltage component output by the SSSC; u. of2q(t) is a static synchronous series compensatorQ-axis control voltage component of the SSSC output; u. ofBd(t) is a voltage component of converting three-phase voltage at a bus B of the SSSC of the static synchronous series compensator to a d axis; u. ofBq(t) is a voltage component of three-phase voltage at a bus b of the static synchronous series compensator SSSC converted to a q axis; i.e. id(t) is a current component of a three-phase current of the static synchronous series compensator SSSC flowing into the bus B and converted to the d axis; i.e. iq(t) converting three-phase current flowing into a bus B by the SSSC into a current component of a q axis;
ω is synchronous angular velocity of rotation, ω -2 π f0Wherein f is0＝50Hz；LBThe total equivalent inductance of a reactor and a series coupling transformer BT are connected in series at the SSSC terminal of the static synchronous series compensator.
Discretizing the expression, (k) representing the current moment, (k +1) representing the next moment, wherein the variable of the next moment is an output reference value, calculating a power outer loop to make a difference between active power and reactive power measured on a line and the power reference value, and obtaining a current reference value under a dq coordinate system by the obtained difference through a PI linkAndthe measured current is subtracted from the current reference value through the current inner loop, and the voltage reference value of the series current converter is obtained through the PI linkAndthe obtained voltage reference value is used as an input signal of the trigger control module of the series current converter, so that a PWM control signal of the current converter is generated, and the output current of the alternating current side of the series current converter always tracks the effective value of the current.
1. Establishing equivalent model of STATCOM (static synchronous compensator) of UPFC (unified power flow controller) parallel side
Fig. 5 shows a single-phase structure diagram of the static synchronous compensator STATCOM, each phase is composed of an upper bridge arm and a lower bridge arm, and each bridge arm is formed by connecting a plurality of submodules SM with the same structure in series and then connecting a reactor L in series. For the purposes of modular design and manufacturing, the three-phase 6 bridge arms have symmetry and identical parameters, the leakage resistance of a capacitor is neglected, and the sum of the loss of the sub-module SM, the loss of a connecting reactor and a transformer of an access system and the loss of a STATCOM device of the static synchronous compensator is represented by R; the three-phase voltages at the alternating current side of the STATCOM of the static synchronous compensator are respectively va.statcom、vb.statcom、vc.statcomThe three-phase current on the AC side is iSa1、iSb1、iSc1；Vdc.statcomThe direct current voltage of the static synchronous compensator STATCOM direct current side is obtained; i isdc.statcomIs direct current side current; n is a radical ofstatcomThe number of the submodules on each bridge arm in series connection is; vc.statcomIs the submodule direct current capacitor voltage; l is a connecting reactor; u. ofacIs the supply voltage of the ac network.
An equivalent diagram of each submodule in a bridge arm is shown in fig. 6, the converter MMC obtains an output voltage waveform with high waveform quality at a low switching frequency, switching loss of the converter and filter capacity are reduced, and efficiency and economy of the converter are improved.
For the MMC, each phase circuit is composed of a plurality of half-bridge submodules, if a detailed bridge arm and converter model containing a plurality of half-bridge submodules is established, the problems of complex modeling and extremely low simulation speed are caused, and the invention adopts the switching period average equivalent principle to establish the converter simplified model of the STATCOM.
In the switching inverter circuit, a model of an average value in one switching period, that is, a switching period average equivalent model, is:
wherein x (T) is a state variable in the inverter, TsIs one switching cycle. Obtaining a switching period average operator when performing switching period average operation on state variables such as voltage and currentThe average value retains the low-frequency component of the state variable, and ignores the high-frequency component part and the harmonic component and the frequency conversion component of the switching frequency.
A mathematical model of the half-bridge sub-modules is established using a switching function, the switching function being:
wherein k is a, b, c, each of a, b, c; t1, T2 are switching cells in the half bridge sub-modules.
The method specifically comprises the step of replacing a state equation established in different time periods in one period by a continuous state equation with the average state of one period as a solution quantity. As shown in fig. 6, the relationship between the average voltage and current over the switching period is:
wherein D represents the duty cycle of the power switching converter;the average voltage is output by an alternating current side port of the half-bridge submodule;the direct current voltage is the direct current voltage of a direct current side capacitor of the half-bridge submodule;the average current of an alternating current side port of the half-bridge submodule is obtained;is the average current of the half-bridge submodule DC side capacitor.
The MMC adopts a Carrier phase-shifted sinusoidal pulse width modulation strategy (CPS-SPWM) to perform pulse width modulation on N sub-modules in each bridge arm by adopting a lower switching frequency, so that triangular carriers are sequentially shifted by 2 pi/N phase angles, and the N sub-modules are respectively controlled to determine whether each sub-module is switched on or switched off. For fundamental and low frequency components:
wherein u is1.totalThe alternating-current side phase voltage is output by the MMC; n is the number of the sub-modules in each bridge arm;the average voltage of the switching period output by the sub-module,
the MMC outputs fundamental component voltage which is N times of average periodic voltage of a single submodule and is the same as modulation wave, and the fundamental component voltage is obtained by the formula (7).
The switching period average equivalent principle is adopted, the switching period average equivalent circuit is used for replacing an MMC current converter of the STATCOM, and the electric quantity of the direct current side and the alternating current side is guaranteed to be consistent near or below the fundamental frequency.
1) Alternating current side equivalent model of static synchronous compensator STATCOM
Static synchronous compensator STATCOM converter equivalent circuit diagram as shown in fig. 7, the ac side of the STATCOM is represented by a three-phase controlled voltage source:
wherein v isSTATCOM.fga、vSTATCOM.fgb、vSTATCOM.fgcRespectively providing three-phase equivalent controlled voltage source voltages of an abc at the AC side of the STATCOM; n is a radical ofstatcomFor the number of submodules in series on each bridge arm, vc.statcomIs a sub-module DC capacitor voltage, Vdc.statcomThe voltage of the STATCOM direct current side of the static synchronous compensator is obtained; dTstatcom.a、dTstatcom.b、dTstatcom.cRespectively, the equivalent transformation coefficients of three phases abc,
the equivalent transformation coefficients of three abc phases of the static synchronous compensator STATCOM are respectively as follows:
wherein v isstatcom.aref、vstatcom.bref、vstatcom.crefFor the abc three-phase reference voltage of the static synchronous compensator STATCOM, the dq-axis reference voltage u in equation (1)1d、u1qTransforming to an abc phase coordinate system; kstatcomFor the ac-dc equivalent coefficient of the static synchronous compensator STATCOM,
wherein,ua.statcomfor the ac-side phase voltage effective value of the static synchronous compensator STATCOM,
2) direct-current side equivalent model of STATCOM (static synchronous compensator)
In the switching period average value equivalent model, the direct current side of the static synchronous compensator STATCOM is replaced by a controlled current source, the controlled current source is related to the three-phase current of the alternating current side, and the formula of the controlled current source is as follows:
iSTATCOM.fgg＝dTstatcom.a·iSa1+dTstatcom.b·iSb1+dTstatcom.c·iSc1(13)
wherein iSa1、iSb1、iSc1The three-phase current is the three-phase current on the alternating current side of the STATCOM of the static synchronous compensator.
2. Equivalent model of static synchronous series compensator SSSC
The MMC static synchronous series compensator SSSC is a series FACTS device, and its schematic structure is shown in fig. 8. The static synchronous series compensator SSSC is mainly composed of a voltage source type converter VSC, a direct current bus capacitor series coupling transformer and the like. The novel series compensation device based on the VSC can simulate inductance or capacitance by injecting a series controllable voltage vertical to the line current to the line, so that the operation parameters on the line are changed, and the effect of adjusting the line transmission power and inhibiting power oscillation is achieved.
The equivalent modeling principle of the static synchronous series compensator SSSC on the series side is similar to that of the parallel side STATCOM, and the equivalent modeling is still carried out on the MMC converter part of the static synchronous series compensator SSSC. In the period average value equivalent model, the direct current side controlled current source is still related to the alternating current side three-phase current, and the coefficient can be obtained by calculation according to the average period principle. The switching devices and diodes of each bridge arm are entirely replaced by controlled voltage sources, and similarly, the controlled voltage is also related to direct current voltage. At this time, the electrical connection between the ac side and the dc side can be directly replaced by a controlled source, and an equivalent circuit based on the principle of average value of the switching period is shown in fig. 9, and the equivalent circuit can separate the ac side and the dc side.
1) Alternating-current side equivalent model of static synchronous series compensator SSSC
The three-phase equivalent controlled voltage source voltage at the alternating current side of the static synchronous series compensator SSSC is as follows:
wherein v isSSSC.fga、vSSSC.fgb、vSSSC.fgcThree-phase equivalent controlled voltage source voltages at the alternating current side of the synchronous series compensator SSSC are respectively provided; n is a radical ofssscThe number of the sub-modules connected in series on each bridge arm of the synchronous series compensator SSSC is equal to the number of the sub-modules connected in series on each bridge arm of the synchronous series compensator SSSC; v. ofc.ssscIs the submodule direct current capacitor voltage; vdc.ssscThe direct-current side voltage of the synchronous series compensator SSSC; dTsssc.a、dTsssc.b、dTsssc.cThe equivalent transformation coefficients of the three abc phases are respectively:
wherein v issssc.aref、vsssc.bref、vsssc.crefReference voltages u of dq axis in equation (3) for abc three phases respectively generated by a control section on the SSSC side of the synchronous series compensator2d、u2qTransforming to an abc phase coordinate system; kssscIs the ac-dc equivalent coefficient of the synchronous series compensator SSSC:
wherein u isa.ssscFor the effective value of the voltage of the alternating-current side phase of the synchronous series compensator SSSC,
2) direct-current side equivalent model of static synchronous series compensator SSSC
Direct current side controlled current source
iSSSC.fgs＝dTsssc.a×iSa2+dTsssc.b×iSb2+dTsssc.c×iSc2(19)
Wherein iSa2、iSb2、iSc2The synchronous series compensator SSSC alternating-current side three-phase current.
3. Direct-current side parallel equivalent capacitor circuit of static synchronous series compensator SSSC and static synchronous compensator STATCOM
The static synchronous series compensator SSSSSSSC at the series side of the UPFC is connected in parallel with the static synchronous compensator STATCOM at the parallel side, the direct current voltages are equal, namely Vdc.sssc＝Vdc.statcom. In the equivalent modeling of the static synchronous series compensator SSSC at the UPFC series side and the STATCOM at the parallel side, the dynamic process of a direct current capacitor in a series submodule is ignored, and the linear simulation of a periodic average value equivalent model is directly adopted, so that the equivalent capacitor C is connected in parallel on a direct current bus between the SSSC at the UPFC series side and the STATCOM at the parallel sidedcAnd is used for simulating the dynamic process of the capacitor in each submodule.
DC equivalent capacitor Cdc：
Wherein N isstatcomFor cascaded submodules in static synchronous compensator STATCOMThe number of converters; cstatcomThe direct-current capacitance value of a submodule converter connected in series in the static synchronous compensator STATCOM is obtained; n is a radical ofssscThe number of the sub-module converters connected in series in the synchronous series compensator SSSC is equal to the number of the sub-module converters connected in series in the synchronous series compensator SSSC; cssscThe direct current capacitance value of the submodule converter in the synchronous series compensator SSSC.
According to the method, the parallel capacitance values of the STATCOM direct current side and the SSSC direct current side are obtained through calculation, and a direct current side equivalent circuit is established to realize the combined simulation calculation of the parallel side and the serial side of the UPFC.
Example 1
In order to verify the correctness of the UPFC equivalent model, the UPFC equivalent model is established in PSCAD/EMTDC according to the method, and the UPFC parallel side STATCOM equivalent model, the UPFC static synchronous series compensator SSSC equivalent model and the DC side equivalent capacitor C are respectively establisheddcAnd joint simulation calculation of the UPFC is realized.
The established MMC-UPFC comprises two parts: a static synchronous series compensator SSSC and a parallel static synchronous compensator STATCOM. The total capacity of the UPFC converter is 3 multiplied by 250MVA, wherein 2 groups of converters are connected in series, and the capacity is 2 multiplied by 250 MVA; the parallel converter 1 group with the capacity of 250MVA has a UPFC structure shown in figure 1.
Each group of MMC transverter parameters:
a: the number of modules: n is a radical ofstatcom112+11 (redundant);
b: module voltage: u shapestatcom.c＝1607V
c, module current: the parallel side: 837A, tandem side: 890A (effective value);
d: module capacitance value: 11000 uF;
e: bridge arm reactor: 36 mH;
f: rated dc voltage: 90 kV.
1) Establishing equivalent model of STATCOM (static synchronous compensator)
Based on the above principle, a parallel side STATCOM equivalent model is established on a power system electromagnetic transient simulation program PSCAD/EMTDC software platform, as shown in fig. 9-10.
In FIGS. 9 to 10, iSTATCOM.fggFor a direct current side controlled current source, vSTATCOM.fga、vSTATCOM.fgb、vSTATCOM.fgcFor an alternating-current side three-phase controlled voltage source, a basic control system based on a switching period average equivalent principle is the same as an STATCOM original control system, only control circuits of the controlled voltage source and the controlled current source are added, a duty ratio generating circuit and a gate trigger signal generating circuit are omitted, and the rest are basically the same. And the control circuit of the newly added controlled voltage source and controlled current source is calculated according to the formulas (8) to (13).
2) Establishing equivalent model of static synchronous series compensator SSSC
Similarly, an equivalent model of the static synchronous series compensation SSSC on the series side is established, as shown in fig. 11.
The basic control system based on the switching period average value equivalent principle is the same as the SSSC original control system, only control circuits of a controlled voltage source and a controlled current source are added, a duty ratio generating circuit and a gate trigger signal generating circuit are omitted, and the rest are basically the same. The control circuits of the added controlled voltage source and controlled current source can be calculated according to the formulas (14) - (19).
3) Direct-current side parallel equivalent capacitor circuit for establishing static synchronous series compensator SSSC and static synchronous compensator STATCOM
The static synchronous series compensator SSSC is the same as the MMC current converter of the parallel static synchronous compensator STATCOM in structure and parameters, and the number N of series sub-modules of each current converterstatcom112, the capacitance value of each sub-module is 11000uF, and the parallel equivalent capacitance value C can be calculated by the formula (20)dc196.4uF, substitute calculation model.
Finally, a joint equivalent model of the static synchronous series compensator SSSC of the UPFC and the static synchronous compensator STATCOM connected in parallel can be established in the PSCAD/EMTDC, and transient process simulation under various working conditions and disturbances can be realized on the model, and the result is shown in FIG. 12.
The calculation results of the established UPFC combined equivalent model and the original switch model are compared on the PSCAD/EMTDC, and the waveform curves of the calculation results of the two models are basically consistent. The calculation time of 18 seconds on a computer with a main frequency of 3.33GHz and a CPU model of Intel Core i5 needs 30 seconds based on a UPFC combined equivalent model, the calculation time of an original switch model needs 40 minutes, the calculation speed is improved by 80 times, and the effect of greatly improving the calculation speed on the basis of ensuring that the transient stability analysis requirement of a power system is met is achieved.
The present invention is not limited to the above embodiments, and any changes or substitutions that can be easily made by those skilled in the art within the technical scope of the present invention are also within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (4)
1. The equivalent modeling method of the unified power flow controller based on the switching period average principle is characterized by comprising the following steps of:
step 1: respectively establishing an alternating current side equivalent model and a direct current side equivalent model of the static synchronous compensator STATCOM by combining a switching period average equivalent principle, wherein the alternating current side of the static synchronous compensator STATCOM is equivalent by using a three-phase controlled voltage source, and the direct current side of the static synchronous compensator STATCOM is equivalent by using a controlled current source;
step 2: respectively establishing an alternating current side equivalent model and a direct current side equivalent model of a synchronous series compensator SSSC (synchronous series compensator) by combining a switching period average equivalent principle, wherein an alternating current side equivalent model circuit of the synchronous series compensator SSSC is equivalent by a three-phase controlled voltage source, and a direct current side controlled current source of the synchronous series compensator SSSC is equivalent by a controlled current source;
and step 3: establishing a direct-current side parallel equivalent capacitor circuit of the synchronous series compensator SSSC and the static synchronous compensator STATCOM, and connecting an equivalent capacitor in parallel on a direct-current bus between the synchronous series compensator SSSC and the static synchronous compensator STATCOM, so as to realize the combined simulation calculation of the parallel side and the serial side of the unified power flow controller UPFC.
2. The equivalent modeling method for the unified power flow controller based on the switching cycle averaging principle according to claim 1, wherein the step 1 specifically comprises: the unified power flow controller UPFC is composed of a static synchronous series compensator SSSC and a static synchronous compensator STATCOM which are connected in parallel, the static synchronous series compensator SSSC and the static synchronous compensator STATCOM are both composed of MMC type current converters, each phase of each three-phase MMC type current converter is composed of an upper bridge arm and a lower bridge arm, each bridge arm is composed of a plurality of half-bridge sub-module current converters with the same structure which are connected in series and then connected in series with a reactor L,
the relation between the average voltage and the average current of each half-bridge submodule in the MMC over a switching cycle is:
d is the duty ratio of the half-bridge submodule power switch converter;the average voltage is output by an alternating current side port of the half-bridge submodule;the direct current voltage is the direct current voltage of a direct current side capacitor of the half-bridge submodule;the average current of an alternating current side port of the half-bridge submodule is obtained;is the average current of the half-bridge submodule DC side capacitance,
the modular multilevel converter MMC adopts a carrier phase-shifting sine pulse width modulation strategy to perform pulse width modulation on N sub-module converters in each bridge arm, and the pulse width modulation strategy is characterized in that the pulse width modulation strategy comprises the following steps of:
wherein u is1.totalThe alternating-current side phase voltage is output by the modular multilevel converter MMC; n is the number of sub-module converters in each bridge arm;the average voltage of the switching period output by the sub-module converter,step 2.2: establishing an equivalent model of an alternating current side of the static synchronous compensator STATCOM, wherein the alternating current side of the static synchronous compensator STATCOM is represented by a three-phase controlled voltage source as follows:
wherein v isSTATCOM.fga、vSTATCOM.fgb、vSTATCOM.fgcRespectively providing three-phase equivalent controlled voltage source voltages of an abc at the AC side of the STATCOM; n is a radical ofstatcomThe number of the submodules connected in series on each bridge arm is; v. ofc.statcomIs the submodule direct current capacitor voltage; vdc.statcomThe voltage of the STATCOM direct current side of the static synchronous compensator is obtained; dTstatcom.a、dTstatcom.b、dTstatcom.cEquivalent transformation of three phases abc respectivelyThe number of the conversion coefficients is changed,
the equivalent transformation coefficients of three abc phases of the static synchronous compensator STATCOM are respectively as follows:
wherein v isstatcom.aref、vstatcom.bref、vstatcom.crefThe voltage is an abc three-phase reference voltage of a static synchronous compensator STATCOM; kstatcomFor the ac-dc equivalent coefficient of the static synchronous compensator STATCOM,
wherein u isa.statcomFor the ac-side phase voltage effective value of the static synchronous compensator STATCOM,
step 2.3: establishing a direct-current side equivalent model of the static synchronous compensator STATCOM, wherein the direct-current side of the static synchronous compensator STATCOM is equivalent to a controlled current source, and the controlled current source is as follows:
iSTATCOM.fgg＝dTstatcom.a·iSa1+dTstatcom.b·iSb1+dTstatcom.c·iSc1(8)
wherein iSa1、iSb1、iSc1The three-phase current is the three-phase current on the alternating current side of the STATCOM of the static synchronous compensator.
3. The equivalent modeling method for the unified power flow controller based on the switching cycle averaging principle according to claim 1, wherein the step 3 specifically comprises:
step 3.1, establishing an alternating current side equivalent model of the synchronous series compensator SSSC,
wherein v isSSSC.fga、vSSSC.fgb、vSSSC.fgcThree-phase equivalent controlled voltage source voltages at the alternating current side of the synchronous series compensator SSSC are respectively provided; n is a radical ofssscThe number of the sub-modules connected in series on each bridge arm of the synchronous series compensator SSSC is equal to the number of the sub-modules connected in series on each bridge arm of the synchronous series compensator SSSC; v. ofc.ssscIs the submodule direct current capacitor voltage; vdc.ssscThe direct-current side voltage of the synchronous series compensator SSSC; dTsssc.a、dTsssc.b、dTsssc.cThe equivalent transformation coefficients of the three abc phases are respectively:
wherein v issssc.aref、vsssc.bref、vsssc.crefThe abc three-phase reference voltages are respectively generated by a control part on the SSSC side of the synchronous series compensator; kssscIs the ac-dc equivalent coefficient of the synchronous series compensator SSSC:
wherein u isa.ssscFor the effective value of the voltage of the alternating-current side phase of the synchronous series compensator SSSC,
step 3.2: establishing a direct-current side equivalent model of the SSSC, wherein the direct-current side equivalent of the SSSC is a controlled current source:
iSSSC.fgs＝dTsssc.a×iSa2+dTsssc.b×iSb2+dTsssc.c×iSc2(14)
wherein iSa2、iSb2、iSc2Three-phase current at the alternating current side of the synchronous series compensator SSSC is respectively.
4. The equivalent modeling method for the unified power flow controller based on the switching cycle averaging principle as claimed in claim 1, wherein the step 4 specifically comprises: by adopting the equivalent principle of periodic average value, an equivalent capacitor C is connected in parallel on a direct current bus between a synchronous series compensator SSSC and a parallel-side static synchronous compensator STATCOMdcFor simulating the dynamic course of the capacitance in each submodule,
DC equivalent capacitor CdcComprises the following steps:
wherein N isstatcomThe number of the sub-module converters cascaded in the STATCOM is the number of the sub-module converters cascaded in the STATCOM; cstatcomThe direct-current capacitance value of a submodule converter connected in series in the static synchronous compensator STATCOM is obtained; n is a radical ofssscThe number of the sub-module converters connected in series in the synchronous series compensator SSSC is equal to the number of the sub-module converters connected in series in the synchronous series compensator SSSC; cssscThe direct current capacitance value of the submodule converter in the synchronous series compensator SSSC.
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