CN102545201B - Method for establishing high-voltage direct-current small signal model - Google Patents

Method for establishing high-voltage direct-current small signal model Download PDF

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CN102545201B
CN102545201B CN201110446832.2A CN201110446832A CN102545201B CN 102545201 B CN102545201 B CN 102545201B CN 201110446832 A CN201110446832 A CN 201110446832A CN 102545201 B CN102545201 B CN 102545201B
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amp
delta
dc
current
dr
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CN102545201A (en
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陈陈
金小明
杨帆
彭波
金勇�
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上海交通大学
南方电网科学研究院有限责任公司
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    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60Arrangements for transfer of electric power between AC networks via a high-tension DC link, HVDC transmission

Abstract

The invention discloses a method for establishing a high-voltage direct-current small signal model. The method includes that (1), models are established in software SSAP (source service access point) which is object-oriented and modular, each direct-current power transmission project is independently packaged into a module, and each module and a corresponding synchronous generator model are equally connected into a total augmentation state equation of a system; (2), a direct-current power transmission system increases electric quantities of stable-state running balancing points on the basis of description of a quasi-stable-state equation of a convertor station including a rectifying station and a inversion station and a direct-current power transmission circuit differential equation, and a small signal linearization model is established; and (3) a main control system of the direct-current power transmission system includes fixed current control or fixed power control of the rectifying station and fixed arc quenching angle gamma control or fixed voltage control of the inversion station, and controllers are described by transfer functions. The scale of the system is not limited, and the method is suitable for analyzing electric system low-frequency oscillation also called small interference stability, and is applicable to searching measures for suppressing low-frequency oscillation.

Description

The method that high voltage direct current transmission small-signal model is set up

Technical field

The invention belongs to the modeling method that power system dynamic stability frequency domain method is analyzed.The spontaneous low-frequency oscillation of the large system of the interconnected electric power of ac/dc cannot normally move system, and this class small-signal stability is electromechanical oscillations in essence, should judge with system state equation linearisation and frequency domain method Eigenvalues analysis.The inearized model that the present invention relates to high voltage direct current transmission (HVDC) system (converting plant and master control system, Inverter Station and master control system and DC line) is set up.

Background technology

International and the domestic software that carries out low-frequency oscillation analysis have the SSAP of Shanghai Communications University, the Neva of DSA, German Siemens of Canadian Powertech Labs (PTL), the BPA of the SIMPOW of Sweden ABB and the China Power academy of sciences etc.Power system interconnection generator has reached more than thousand, and except SSAP, scale can be surrounded by DSA and BPA by suitable software, and wherein the tool direct current transportation HVDC of DSA institute and modeling of control system function introduction are as follows:

In DSA 8.0 softwares (in May, 2008 version) of Canada PTL company, SSAT is small-signal analysis instrument, refers to user's manual.Its DC transmission system model and transient stability analysis instrument TSAT are general, all DC transmission system are concentrated in " user defines control (UDC) " module, and P, Q Power Exchange are carried out in AC network connection.As shown in Figure 1.

HVDC model has detailed model; Functional mode (response, behavior etc.); And simplified model three classes.

Power System Interconnection scale is increasing, and stability analysis needs the detailed model of HVDC and control system and additional control system, to adopt the modulation of HVDC bilateral, and even coordinates to control the damping improving low-frequency oscillation.HVDC model in DSA software has following deficiency for small-signal stability analysis now:

1. all direct current transportation are concentrated on to converter region more than, the variable in model adopts total head (shown in Fig. 2).After initialization, system is separated separately, to reduce the scale of unit state equation.When the contained DC transmission engineering number of system is a lot of, may be restricted.

2. the conventional algebraic equation of simplified model represents, DC transmission line is simplified to resistance.And DC power transmission line reaches 1000-2000 kilometer, ignore inductance, flat ripple reactance and direct-to-ground capacitance and bring error.

3. even if set up the detailed model that comprises dynamic process, a lot of situations are also automatically converted into simplified model in computational process, near meritorious P remain unchanged (shown in Fig. 3) working point.And low-frequency oscillation belongs to electromechanical oscillations, should not ignore the variation of meritorious P.

Summary of the invention

The object of the invention is to for the deficiencies in the prior art, a kind of method that provides high voltage direct current transmission small-signal model to set up, can well solve the problem existing in above-mentioned background technology.

The method for building up of high voltage direct current transmission small-signal model of the present invention, comprises the following aspects:

(1) modeling in object-oriented and modular software SSAP, each DC transmission engineering individual packages becomes a module, and every synchro generator model total augmented state equation of connecting system coequally.Software and model expandability reach highest level.

(2) DC transmission system is with current conversion station (converting plant and Inverter Station) quasi-stable state equation and DC power transmission line differential equation.Increment to each electric weight of steady operation balance point, sets up small signal linearization model.

(3) DC transmission system master control system comprises: the rectification Current Control (or determine power control) of standing firm, the inversion extinguish angle γ that stands firm controls (or determining voltage control).Controller is all described with transfer function.

The method that direct current transportation small-signal model of the present invention is set up, specific implementation comprises the steps:

Step 1: during steady operation, the alternating current-direct current both sides electric weight fundamental relation formula of converter is as follows:

v d 0 = ( 3 2 / π ) BTV

V d=V d0cos(α)-(3/π)X CI dB

P=V dI d

I = ( 6 / π ) BTI d

Wherein V is change of current bus alternating voltage;

T is converter transformer turn ratio;

B is the rectifier bridge number of series connection;

X ccommutating reactance for every phase;

P, Q, I are respectively change of current bus and inject that the interchange of converter is meritorious, idle, electric current;

V d, I dfor direct voltage, electric current.

Above formula, in the place's linearisation of balance movement point, can be obtained to the small-signal linear relation of HVDC converter two ends alternating current-direct current variable, subscript x, y represents respectively x and the y axle component of AC variable in synchronous rotating frame.In formula, from a to m, each element is all the constant relevant with operational factor to ac and dc systems structural parameters.

Δ I x Δ I y ΔV d = a b c d e f g h i j k m ΔI d Δα ΔV x ΔV y - - - ( 2 )

Rectifier and inverter respectively modeling obtain two groups of linearisation algebraic equations;

Step 2: in the T-shaped equivalent electric circuit of DC line, R d, L d, C dbe respectively the lumped parameter of line resistance, inductance and direct-to-ground capacitance, wherein L dcomprise smoothing reactor.V dmfor circuit mid-point voltage.

The linearisation condition of small signal equation of DC line model is

Δ I · dr Δ V · dm Δ I · di = - R dr L dr - 1 L dr 0 1 C d 0 - 1 C d 0 1 L di - R di L di Δ I dr Δ V dm Δ I di + 1 L dr 0 0 0 0 - 1 L di Δ V dr Δ V di - - - ( 3 )

Δ I dr Δ I di = 1 0 0 0 0 1 Δ I dr Δ V dm Δ I di + 0 0 0 0 Δ V dr Δ V di

Wherein the r in subscript and i represent respectively rectification side and inversion side.

Step 3: DC controller structure is CIGRE DC reference model, rectification side adopts determines Current Control, and inversion side adopts determines the control of γ angle.Transfer function after simplification, can be converted to state space equation.

Step 4: the dynamical equation of the algebraic equation of both sides converter and DC control system and DC line is combined into the small signal linearization quasi steady state model of DC transmission system.

X · 0 = J A J B J C J D X V - - - ( 4 )

Retain state variable, the HVDC system state equation that is organized into augmentation is as follows:

X · = ( J A - J B J D - 1 J C ) X = AX - - - ( 5 )

With this equations of state, be packaged into independently small signal linearization model of each HVDC, as a sub-block in the augmented state equation of the large overall system of the interconnected electric power of alternating current-direct current.

After adopting technique scheme, beneficial effect of the present invention:

1. completely based on OOSE thought, the independent modeling of each high voltage direct current transmission project, directly accesses the total augmented state equation of the large system of the interconnected electric power of alternating current-direct current, and DC engineering number is unrestricted.

Other method is built high-voltage direct current model in a public module in, and scale may be restricted.

2. state equation linearisation modeling and the combination of frequency domain method signature analysis are the most applicable low-frequency oscillation of electric power system of generally acknowledging, the scheme of analysis on Small Disturbance Stability.Other modeling method normal and transient stability, large interference analysis share, but not low-frequency oscillation, little interference analysis special use.

3. because the large systems connection scale of the interconnected electric power of alternating current-direct current is increasing, low-frequency oscillation is easily to send out fault, all small-signal stability be to analyze planning, design, move each stage, system scale and the high voltage direct current transmission modeling method basis that is very important in detail and accurately taken into account.Other modeling method is described HVDC (High Voltage Direct Current) transmission system, comprises its master control system and additional control system, not and take into account the details of electric power system scale and direct current system, is not difficult to be applicable to explore the different braking measure of low-frequency oscillation.

Accompanying drawing explanation

Fig. 1 is background technology DSA 8.0 software users definition DC model structure block diagrams.

Fig. 2 is background technology line commutated converter model schematic diagram;

Fig. 3 is P and the Q characteristic schematic diagram of background technology line commutated converter simplified model;

Fig. 4 is that each DC transmission engineering individual packages of the embodiment of the present invention becomes a module frame chart;

Fig. 5 is the embodiment of the present invention 12 pulse conversion device stable state electric weight relations

Fig. 6 is the T-shaped equivalent circuit diagram of embodiment of the present invention DC line;

Fig. 7 is embodiment of the present invention DC controller transfer function schematic diagram;

Fig. 8 is that the meritorious measured waveform of rear two circuits occurs in embodiment of the present invention vibration;

Fig. 9 is that rear two circuit peak swing waveforms occur in embodiment of the present invention vibration.

Embodiment

Below embodiments of the invention are elaborated, the present embodiment be take technical solution of the present invention as prerequisite, provided detailed execution mode and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

As shown in Figure 1, the structure of the User Defined DC Model of mentioning in background technology, the Chinese of correspondence in figure: From DC is from direct current; From AC is from exchanging; Source Signal source signal; The control of all each the personal basic modules of direct current transportation of Controls of all DClinks Using Individual Basic Blocks; Loops and Bypass Paths are Allowed has allowed loop and bypass; Converter#1-#N rectifier bridge (station) 1-N; y c1-y cNcan be Trigger Angle, extinguish angle, direct current or direct voltage; Cond situation or condition, can be to lose, bypass or locking; DC Network Connecting All Converters connects the DC network of all converting plants; AC Network Interface AC network interface.

As shown in Figure 2, line commutated rectifier bridge (station) model of mentioning in background technology, in figure: DC Bus DC bus; Rec. converting plant; Inv. Inverter Station; Tap load tap changer; AC Bus ac bus.

As shown in Figure 4, in the present embodiment, it is guidance that object-oriented and modular soft project thought are take in software SSAP modeling.Each DC transmission engineering individual packages becomes a module, and every synchro generator model augmented state equation of connecting system coequally.The expandability of software and model is highest level.

As shown in Figure 5.In the present embodiment, system variable is got near increment operating point, by the linearisation of quasi-stable state equation, sets up direct current system small signal linearization model.

v d 0 = ( 3 2 / π ) BTV

V d=V d0cos(α)-(3/π)X CI dB

P=V dI d

I = ( 6 / π ) BTI d

Wherein V is change of current bus alternating voltage;

T is converter transformer turn ratio;

B is the bridge number of series connection;

X ccommutating reactance for every phase;

P, Q, I are respectively change of current bus and inject that the interchange of converter is meritorious, idle, electric current;

V d, I dfor direct voltage, electric current.

V d0output dc voltage, i.e. ideal rectifier voltage during for the full conducting zero load of rectifier bridge;

α is the Trigger Angle of rectifier bridge thyristor;

θ vfor AC voltage phase angle;

θ ifor ac-side current phase angle.

Equilibrium establishment operating point place lienarized equation on above formula basis, i.e. the small-signal linear relation of HVDC converter two ends alternating current-direct current variable, subscript x, y represents respectively x and the y axle component of AC variable in synchronous rotating frame.In formula, from a to m, each element is all the constant (mathematical derivation be omitted) relevant with operational factor to ac and dc systems structural parameters.

Δ I x Δ I y ΔV d = a b c d e f g h i j k m ΔI d Δα ΔV x ΔV y - - - ( 2 )

Rectifier and inverter respectively modeling obtain two groups of linearisation algebraic equations;

As shown in Figure 6, be the T-shaped equivalent electric circuit of DC line, R d, L d, C dbe respectively the lumped parameter of line resistance, inductance and direct-to-ground capacitance, wherein L dcomprise smoothing reactor.V dmfor circuit mid-point voltage.

The linearisation condition of small signal equation of DC line model is

Δ I · dr Δ V · dm Δ I · di = - R dr L dr - 1 L dr 0 1 C d 0 - 1 C d 0 1 L di - R di L di Δ I dr Δ V dm Δ I di + 1 L dr 0 0 0 0 - 1 L di Δ V dr Δ V di - - - ( 3 )

Δ I dr Δ I di = 1 0 0 0 0 1 Δ I dr Δ V dm Δ I di + 0 0 0 0 Δ V dr Δ V di

DC controller structure is CIGRE DC reference model, and rectification side adopts determines Current Control, and inversion side adopts determines the control of γ angle.Transfer function block diagram after simplification as shown in Figure 7, can be converted to state space equation.

The dynamical equation of the algebraic equation of both sides converter and DC control system and DC line is combined into the small signal linearization quasi steady state model of DC transmission system.

X · 0 = J A J B J C J D X V - - - ( 4 )

Only retain state variable, the HVDC system state equation that is organized into augmentation is as follows:

X · = ( J A - J B J D - 1 J C ) X = AX - - - ( 5 )

With this equations of state, be packaged into independently small signal linearization model of each HVDC, as a sub-block in the large overall system state equation of the interconnected electric power of alternating current-direct current.

Application example: south electric network low-frequency oscillation generation example and the contrast of SSAP software analysis result coincide.

Once, there is power oscillation in the main interconnection of south electric network, the about 175MW of I line hunting power wherein, the about 233MW of II line hunting power.There is the meritorious measured waveform (7 minutes and 59 seconds writing time) of rear two circuits as Figure 8-9 in vibration.This subsystem frequency of oscillation is 0.64Hz by analysis.

The low frequency oscillation mode that adopts SSAP to calculate is as shown in the table.

By SSAP and DC Model thereof, calculate the low-frequency oscillation Main Patterns of electrical network

Pattern numbering Eigenvalue λ=(σ ± j ω) Frequency f (Hz) Dampingratioζ ??1 ??-0.171135±j4.191494 ??0.667097 ??0.040795 ??2 ??-0.284789±j3.751613 ??0.597088 ??0.094772

Result in analytical table is known, and oscillation mode 1 is corresponding better with the oscillation mode of actual measurement gained, and oscillation mode meets, and frequency of oscillation is close, description be same physical phenomenon.

2.SSAP and direct current transportation model thereof calculate the large system small-signal stability of the interconnected electric power of alternating current-direct current for certain electrical network of China and analyze (calculating of linearized system characteristic root), be Low Frequency Oscillation Analysis: comprise 513, generator, 2639 of electrical network nodes, four DC transmission engineering such as extra-high voltage direct-current.Credible result.

Although content of the present invention has been done detailed introduction by above preferred embodiment, will be appreciated that above-mentioned description should not be considered to limitation of the present invention.Those skilled in the art, read after foregoing, for multiple modification of the present invention with to substitute will be all apparent.Therefore, protection scope of the present invention should be limited to the appended claims.

Claims (1)

1. the method that high voltage direct current transmission small-signal model is set up, is characterized in that:
(1) modeling in object-oriented and modular software SSAP, each DC transmission engineering individual packages becomes a module, and every synchro generator model total augmented state equation of connecting system coequally;
(2) DC transmission system is with current conversion station quasi-stable state equation and DC power transmission line differential equation, and the increment to each electric weight of steady operation balance point, sets up small signal linearization model;
(3) DC transmission system master control system comprises: stand firm Current Control or determine power and control of rectification, and the inversion extinguish angle γ that stands firm controls or determines voltage control, and controller is all described with transfer function;
Described method specific implementation comprises the steps:
Step 1: during steady operation, the alternating current-direct current both sides electric weight fundamental relation formula of converter is as follows:
V d 0 = ( 3 2 / π ) BTV
V d=V d0cos(α)-(3/π)X CI dB
I = ( 6 / π ) BTI d
Wherein V is change of current bus alternating voltage;
T is converter transformer turn ratio;
B is the rectifier bridge number of series connection;
X cfor the commutating reactance of every phase, often take the short-circuit impedance of convertor transformer;
P, Q, I are respectively change of current bus and inject that the interchange of converter is meritorious, idle, electric current;
V d, I dfor direct voltage, electric current;
V d0output dc voltage, i.e. ideal rectifier voltage during for the full conducting zero load of rectifier bridge;
α is the Trigger Angle of rectifier bridge thyristor;
θ vfor AC voltage-phase;
θ ifor ac-side current phase place;
By above formula in the place's linearisation of balance movement point, obtain the small-signal linear relation of HVDC converter two ends alternating current-direct current variable, subscript x, y represents respectively x and the y axle component of AC variable in synchronous rotating frame, and in formula, from a to m, each element is all the constant relevant with operational factor to ac and dc systems structural parameters;
Δ I x Δ I y Δ V d = a b c d e f g h i j k m Δ I d Δα Δ V x Δ V y
Rectifier and inverter respectively modeling obtain two groups of linearisation algebraic equations;
Step 2: in the T-shaped equivalent electric circuit of DC line, R d, L d, C dbe respectively the lumped parameter of line resistance, inductance and direct-to-ground capacitance, wherein L dcomprise smoothing reactor, V dmfor circuit mid-point voltage;
The linearisation condition of small signal equation of DC line model is
Δ I · dr Δ V · dm Δ I · di = - R dr L dr - 1 L dr 0 1 C d 0 - 1 C d 0 1 L di - R di L di Δ I dr Δ V dm Δ I di + 1 L dr 0 0 0 0 - 1 L di Δ V dr Δ V di
Δ I dr Δ I di = 1 0 0 0 0 1 Δ I dr Δ V dm Δ I di + 0 0 0 0 Δ V dr Δ V di
Wherein the r in subscript and i represent respectively rectification side and inversion side;
Step 3: DC controller structure is CIGRE DC reference model, rectification side adopts determines Current Control, and inversion side adopts determines the control of γ angle, and the transfer function after simplification, is converted to state space equation;
Step 4: the dynamical equation of the algebraic equation of both sides converter and DC control system and DC line is combined into the small signal linearization quasi steady state model of DC transmission system:
X · 0 = J A J B J C J D X V
Retain state variable, the HVDC system state equation that is organized into augmentation is as follows:
X · = ( J A - J B J D - 1 J C ) X = AX
With this equations of state, be packaged into independently small signal linearization model of each HVDC, as a sub-block in the augmented state equation of the large overall system of the interconnected electric power of alternating current-direct current.
CN201110446832.2A 2011-12-27 2011-12-27 Method for establishing high-voltage direct-current small signal model CN102545201B (en)

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