CN104104102B - Voltage source converter type multi-terminal direct current transmission system steady operation point optimization method - Google Patents

Abstract

A kind of voltage source converter type multi-terminal direct current transmission system steady operation point optimization method, comprising: build DC network equation; Solve the direct voltage-current characteristics equation of each current conversion station; Suppose that each current conversion station all runs on normal condition, according to direct voltage-current characteristics equation and the DC network equation of each current conversion station, obtain characteristic equation group when system is normally run; Utilize Newton-Raphson solution by iterative method system performance equation group; Judge all solution I of above-mentioned characteristic equation group respectively _dciand U _dciwhether in normal range (NR).Direct voltage-electric current operation characteristic the equation group of the VSC-MTDC transmission system current conversion station that the present invention derives can react the DC side Steady of each current conversion station; Meanwhile, the control model modification method based on priority can select current conversion station control model exactly under different operating mode.

Description

Voltage source converter type multi-terminal direct current transmission system steady operation point optimization method

Technical field

The present invention relates to DC transmission system field, particularly relate to a kind of voltage source converter type multi-terminal direct current transmission system steady operation point optimization method.

Background technology

Voltage source converter type high voltage direct current (voltagesourceconverterbasedhighvoltagedc, VSC-HVDC) the technology of transmission of electricity advantage that cannot match in excellence or beauty because adopting full-controlled switch device and pulse modulation technology to make it have multiple Traditional DC, along with the develop rapidly of renewable energy power generation and the growing tension in transmission of electricity corridor, VSC-HVDC technology of transmission of electricity has become one of optimal selection ensureing transmission of electricity safety and reliability, and be applied to renewable energy source power in the world, urban electricity supply, the asynchronous interconnected and field such as power market transaction and multi-terminal HVDC transmission of AC system.

Wherein, extensive marine wind electric field is because of with bank land grid contact more weak away from seashore, wind energy turbine set be difficult to by exchange and Traditional DC mode grid-connected, therefore, the synchronizing mode of voltage source converter type multi-terminal HVDC transmission becomes the grid-connected optimal selection of extensive offshore wind farm, and its correlative study and engineering practice receive to be paid close attention to widely ^[6-11].Meanwhile, along with increasing of VSC-HVDC power transmission engineering, interconnected with the flexibility strengthening DC transmission system and reliability by DC line between the current conversion station of different power transmission engineering, be equivalent to the VSC-MTDC transmission system that formation nodes is more.

In actual motion, due to current conversion station number and the running status of DC transmission system, current conversion station control model and command value, AC electrical network and DC network condition etc. different, VSC-MTDC transmission system has changeable operational mode.Along with the start and stop of current conversion station, the change etc. of AC ac grid voltage, current conversion station control model can occur to change to adapt to new service conditions accordingly, and DC transmission system changes its operational mode thereupon.In order to realize fast dispatch and the safe operation of DC transmission system, must calculate operation control model and the system state amount of VSC-MTDC transmission system at different operating conditions fast, accurately and real-time, this is significant to the regulation and control safely and fast of DC transmission system.

This patent is analyzed with typical five terminal DC transmission system, as shown in Figure 1; Easy for studying, suppose that each current conversion station adopts identical main circuit structure.This system comprises 5 current conversion stations: current conversion station 1 as leading current conversion station, the DC voltage control of primary responsibility DC network and power-balance; Current conversion station 2 is assist exchanging circuit station, assists and realizes DC voltage control; Current conversion station 3 is for determine active power controller (activepowercontrol, APC) current conversion station, and for the constant active power of its AC electrical grid transmission, meanwhile, current conversion station 3 is as the standby station of DC voltage control; Current conversion station 4 and 5 is wind energy turbine set current conversion station, is respectively used to collect the active power of wind energy turbine set 4 and wind energy turbine set 5 and feed-in DC network.Wind energy turbine set 4 and 5 possesses fast prompt drop and to exert oneself control, can reduce Power Output for Wind Power Field fast when DC network overtension.

Each current conversion station all adopts the dicyclo Vector Control Model based on Feedforward Decoupling, inner ring controls to adopt dq electric current rapid track and control, outer shroud controls to adopt meritorious and idle separate power control strategy, and introduces corresponding advanced control strategy in active power controller ring.Because system dc side voltage and active power are close coupling relation, the Reactive Power Control strategy not influential system DC voltage distribution substantially of current conversion station, therefore in steady-state optimization analytical method, only consider that the upper strata active power controller strategy of current conversion station can calculate the steady operation point of system fast.This patent supposes that each controlling unit is indifference and controls, and ignores the internal loss of current conversion station.

Summary of the invention

Object of the present invention is exactly to solve the problem, propose a kind of voltage source converter type multi-terminal direct current transmission system steady operation point optimization method, the method is by the characteristic equation under the different control model of each current conversion station of deriving, the steady operation point calculating VSC-MTDC transmission system for rapid Optimum provides a kind of new approach, can provide a kind of simple and reliable analytical method for the fast dispatch of multi-terminal direct current transmission system and security evaluation etc.

For achieving the above object, the present invention adopts following technical scheme:

A kind of voltage source converter type multi-terminal direct current transmission system steady operation point optimization method, comprises the following steps:

(1) getting converter, to flow to DC network be positive direction, and definition DC bus-bar voltage vector is: U=[U _dc1, U _dc2, U _dc3, U _dc4, U _dc5] ^t, DC bus current vector is: I=[I _dc1, I _dc2, I _dc3, I _dc4, I _dc5] ^t, building DC network equation is:

I＝[Y]U

Wherein, [Y] is admittance matrix;

(2) according to AC network condition and DC network parameter, the control model of each current conversion station of initialization and command value; Solve the direct voltage-current characteristics equation of each current conversion station; Described current conversion station comprises: dominate current conversion station, assist exchanging circuit station, determine active power controller current conversion station and wind energy turbine set current conversion station;

(3) suppose that each current conversion station all runs on normal condition, according to direct voltage-current characteristics equation and the DC network equation of each current conversion station, obtain characteristic equation group when system is normally run;

(4) Newton-Raphson solution by iterative method system performance equation group is utilized;

(5) all solution I of above-mentioned characteristic equation group are judged respectively _dciand U _dciwhether in normal range (NR), wherein, i=1,2,3,4,5; If so, then gained solution is the steady operation point of system; If there is the solution not in normal range (NR), then revise the control model of corresponding voltage source converter, again try to achieve system performance equation group, return step (4).

In described step (1), [Y] is 5 × 5 admittance matrixs, is specially:

$\left[Y\right]=\left[\begin{array}{ccccc}\frac{1}{R_{12}}+\frac{1}{R_{13}}& -\frac{1}{R_{12}}& -\frac{1}{R_{13}}& 0& 0\\ -\frac{1}{R_{13}}& \frac{1}{R_{12}}+\frac{1}{R_{24}}+\frac{1}{R_{25}}& 0& -\frac{1}{R_{24}}& -\frac{1}{R_{25}}\\ -\frac{1}{R_{13}}& 0& \frac{1}{R_{13}}+\frac{1}{R_{34}}& -\frac{1}{R_{34}}& 0\\ 0& -\frac{1}{R_{24}}& -\frac{1}{R_{24}}& \frac{1}{R_{24}}+\frac{1}{R_{34}}+\frac{1}{R_{45}}& -\frac{1}{R_{45}}\\ 0& -\frac{1}{R_{25}}& 0& -\frac{1}{R_{45}}& \frac{1}{R_{25}}+\frac{1}{R_{45}}\end{array}\right]$

Wherein, Ri _jrepresent the equivalent resistance of DC line between current conversion station i and current conversion station j.

In described step (2), the direct voltage-current characteristics equation of leading current conversion station is:

$\left\{\begin{array}{c}{I}_{\mathrm{dc}1}=\frac{(1-{\mathrm{\&lambda;}}_1)\mathrm{\&beta;}{P}_{1N}}{U_{\mathrm{dc}1}},I_{\mathrm{dc}1}\&GreaterEqual;I_{\mathrm{dc}1H}\\ U_{\mathrm{dc}1}=U_{\mathrm{dc}1\mathrm{ref}},I_{\mathrm{dc}1L}<I_{\mathrm{dc}1}<I_{\mathrm{dc}1H}\\ I_{\mathrm{dc}1}=-\frac{(1-{\mathrm{\&lambda;}}_1)\mathrm{\&beta;}{P}_{1N}}{U_{\mathrm{dc}1}},I_{\mathrm{dc}1}\&le;I_{\mathrm{dc}1L}\end{array}\right.$

Wherein, I _dc1and U _dc1current value and the magnitude of voltage of leading current conversion station DC side respectively, λ ₁fall degree for current conversion station AC line voltage leading under failure condition, β is the Overflow RateHT of alternating current, P _1Ntake the rated power of current conversion station as the leading factor, U _dc1reffor direct voltage command value, I _dc1H, I _dc1Lbe respectively direct current threshold value when leading current conversion station is cut into rectification current-limit mode, inversion current-limit mode by normal operation mode;

In above formula, work as I _dc1L< I _dc1< I _dc1Htime, leading current conversion station is in normal operating condition, is DC voltage control pattern; Work as I _dc1>=I _dc1Hand I _dc1≤ I _dc1Ltime, leading current conversion station is in abnormal operational conditions, runs on rectification current-limit mode and inversion current-limit mode respectively.

In described step (2), the direct voltage-current characteristics equation at assist exchanging circuit station is:

$\left\{\begin{array}{c}{I}_{\mathrm{dc}2}=\frac{(1-{\mathrm{\&lambda;}}_2)\mathrm{\&beta;}{P}_{2N}}{U_{\mathrm{dc}2}},I_{\mathrm{dc}2}\&GreaterEqual;I_{\mathrm{dc}2H}\\ I_{\mathrm{dc}2}=k_{\mathrm{droop}2}(U_{\mathrm{dc}2}-U_{\mathrm{dc}2\mathrm{ref}}),I_{\mathrm{dc}2L}<I_{\mathrm{dc}2}<I_{\mathrm{dc}2H}\\ I_{\mathrm{dc}2}=-\frac{(1-{\mathrm{\&lambda;}}_2)\mathrm{\&beta;}{P}_{2N}}{U_{\mathrm{dc}2}},I_{\mathrm{dc}2}\&le;I_{\mathrm{dc}2L}\end{array}\right.$

Wherein, U _dc2, U _dc2ref, I _dc2be respectively the direct voltage at assist exchanging circuit station, direct voltage reference value and direct current, k _droop2for the Slope Parameters that auxiliary station voltage drop controls, β is the Overflow RateHT of alternating current, λ ₂for assist exchanging circuit station ac grid voltage falls degree, P _2Nfor the rated power at assist exchanging circuit station, I _dc2H, I _dc2Lbe respectively direct current threshold value when assist exchanging circuit station is cut into rectification current-limit mode, inversion current-limit mode by normal operation mode;

Work as I _dc2L< I _dc2< I _dc2Htime, assist exchanging circuit station is in normal operating condition, is voltage drop control model; Work as I _dc2>=I _dc2Hand I _dc2≤ I _dc2Ltime, assist exchanging circuit station runs on abnormal operational conditions, is respectively rectification current-limit mode and inversion current-limit mode.

In described step (2), the direct voltage-current characteristics equation determining active power controller current conversion station is:

$\left\{\begin{array}{c}{I}_{\mathrm{dc}3}=\frac{(1-{\mathrm{\&lambda;}}_3)\mathrm{\&beta;}{P}_{3N}}{U_{\mathrm{dc}3}},I_{\mathrm{dc}3}\&GreaterEqual;I_{\mathrm{dc}3H}\\ I_{\mathrm{dc}3}=k_{\mathrm{droop}3}(U_{\mathrm{dc}3}-U_{\mathrm{dc}3L})+\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3L}},U_{\mathrm{dc}3}\&GreaterEqual;U_{\mathrm{dc}3H},\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3L}}\&le;I_{\mathrm{dc}3}<I_{\mathrm{dc}3H}\\ I_{\mathrm{dc}3}=\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3}},U_{\mathrm{dc}3L}\&le;U_{\mathrm{dc}3}<U_{\mathrm{dc}3H},\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3H}}\&le;I_{\mathrm{dc}3}<\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3L}}\\ I_{\mathrm{dc}3}=k_{\mathrm{droop}3}(U_{\mathrm{dc}3}-U_{\mathrm{dc}3H})+\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3H}},U_{\mathrm{dc}3}<U_{\mathrm{dc}3L},I_{\mathrm{dc}3L}<I_{\mathrm{dc}3}<\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3H}}\\ I_{\mathrm{dc}3}=-\frac{(1-{\mathrm{\&lambda;}}_3){\mathrm{\&beta;P}}_{3N}}{U_{\mathrm{dc}3}},I_{\mathrm{dc}3}\&le;I_{\mathrm{dc}3L}\end{array}\right.$

Wherein, P _3ref, I _dc3, U _dc3be respectively active power command value, direct current, the direct voltage of determining active power controller current conversion station, k _droop3for the Slope Parameters that voltage drop controls, β is the Overflow RateHT of alternating current, λ ₃degree is fallen, P for determining active power controller current conversion station ac grid voltage _3Nfor determining the rated power of active power controller current conversion station, U _dc3H, U _dc3Lbe respectively the active power controller of determining active power controller current conversion station and inversion decline control, rectification declines the direct voltage threshold value controlled when mutually switching, I _dc3H, I _dc3Lbe respectively the direct current threshold value of determining when active power controller current conversion station is cut into rectification current-limit mode, inversion current-limit mode by normal operation mode;

Work as U _dc3L≤ U _dc3< U _dc3Htime, determining active power controller current conversion station and run on normal operating condition, is active power controller pattern; Work as U _dc3>=U _dc3Hand U _dc3< U _dc3Ltime, determine active power controller current conversion station and be respectively inversion decline control model and rectification decline control model; Work as I _dc3>=I _dc3Hand I _dc3≤ I _dc3Ltime, determining active power controller current conversion station is rectification current-limit mode and inversion current-limit mode.

In described step (2), the direct voltage-current characteristics equation of wind energy turbine set current conversion station is:

$\left\{\begin{array}{c}{I}_{\mathrm{dc}4}=\frac{(1-{\mathrm{\&lambda;}}_4)\mathrm{\&alpha;\&beta;}{P}_{4N}}{U_{\mathrm{dc}4}},I_{\mathrm{dc}4}\&GreaterEqual;I_{\mathrm{dc}4H}\\ I_{\mathrm{dc}4}=\frac{f_4-f_{4N}+k_{f4}{P}_{\mathrm{wf}4N}}{k_{f4}{U}_{\mathrm{dc}4}},U_{\mathrm{dc}4}<U_{\mathrm{dc}4H},I_{\mathrm{dc}4h}\&le;I_{\mathrm{dc}4}<I_{\mathrm{dc}4H}\\ I_{\mathrm{dc}4}=k_{\mathrm{droop}4}(U_{\mathrm{dc}4}-U_{\mathrm{dc}4H})+I_{\mathrm{dc}4h},U_{\mathrm{dc}4}\&GreaterEqual;U_{\mathrm{dc}4H}\end{array}\right.$

Wherein, I _dc4, U _dc4, P _4Nbe respectively the direct current of wind energy turbine set current conversion station, direct voltage and power-handling capability, assuming that meritorious current limitation value is α times of flow restricter threshold value, β is the Overflow RateHT of alternating current, f ₄and f _4Nbe respectively real-time frequency and the rated frequency of wind energy turbine set current conversion station AC network, k _f4for the Slope Parameters of wind energy turbine set current conversion station active power and frequency control device, P _wf4Nfor the specified active power value of wind energy turbine set current conversion station, k _droop4for the Slope Parameters of wind energy turbine set current conversion station voltage drop controller, λ ₄for wind energy turbine set current conversion station ac grid voltage falls degree, I _dc4Hfor normal operation mode is cut into the direct current threshold value of rectification current-limit mode, I _dc4hfor direct voltage under normal control mode is U _dc4Htime corresponding DC current values;

Work as U _dc4< U _dc4H, I _dc4h≤ I _dc4< I _dc4Htime, wind energy turbine set current conversion station is in normal operating condition, is active power and frequency control pattern; Work as I _dc4>=I _dc4Htime, wind energy turbine set current conversion station is rectification current-limit mode; Work as U _dc4>=U _dc4Htime, wind energy turbine set current conversion station is voltage drop control model.

All solution I of characteristic equation group are judged in described step (5) _dciand U _dcidetailed process whether in normal range (NR) is:

1) all solution I of characteristic equation group are judged _dciwhether in normal range (NR), if so, go to step 3); Go to step 2 if not);

2) make i=1, judge I _dciwhether in normal range (NR), if not, revise the control model of corresponding current conversion station; If so, make i=i+1, judge I _dciwhether in normal range (NR), repeat said process, until all solution I of characteristic equation group _dciall judge complete, enter step 3);

3) all solution U of characteristic equation group are judged _dciwhether in normal range (NR), if so, go to step 5); If not, 4 are gone to step);

4) make i=3, judge U _dciwhether in normal range (NR), if not, revise the control model of corresponding current conversion station; If so, make i=i+1, judge U _dciwhether in normal range (NR), repeat said process, until all solution U of characteristic equation group _dciall judge complete;

5) judge to terminate.

The concrete grammar revising the control model of corresponding voltage source converter in described step (5) is:

According to current conversion station DC voltage value and the DC current values of system present control mode and last solving system equation, revise the control model of the out-of-limit current conversion station of quantity of state, and then the control model of current conversion station when determining that system equation calculates next time;

The control model at leading current conversion station and assist exchanging circuit station is revised based on the DC current values of current conversion station; The control model of determining active power controller current conversion station and wind energy turbine set current conversion station is revised based on the DC current values of current conversion station.

The control model correction at leading current conversion station and assist exchanging circuit station is mainly carried out between normal mode and current-limit mode, alternating current is the sole criterion that converter Current limited Control pattern starts and stops, therefore, unique reference values when DC current values is this two kinds of current conversion station Correction and Control patterns.The voltage drop control model of determining active power controller current conversion station and wind energy turbine set current conversion station is that the startup of this control model directly depends on DC voltage value in order to direct voltage under ensureing abnormal operational conditions can be in a kind of DC voltage control and power-balance means taked in zone of reasonableness.But the voltage drop control model at assist exchanging circuit station is its normal operation mode, the selection of its direct voltage initiation value needs to flow voltage-controlled cooperation based on leading standing erectly, and its DC voltage value does not affect the control model correction of this current conversion station.The modification method of control model is then revise according to priority list, and namely the reference state amount direct current of each current conversion station and the priority of direct voltage are revised.

When the DC current values of multiple current conversion station and DC voltage value exceed the range of operation of corresponding control model simultaneously, according to the correction based on DC current values, the correction based on DC voltage value and leading station, auxiliary station, determine the order priority of active power controller current conversion station, wind energy turbine set current conversion station, revise current conversion station control model successively according to the height of priority orders.

If when certain current conversion station is in shut down condition, then during initial calculation, the control model of this current conversion station is set to and determines active power controller, and active power command value is set to 0, and then solving system equation.

Beneficial effect of the present invention:

Direct voltage-electric current operation characteristic the equation group of the VSC-MTDC transmission system current conversion station that the present invention derives can react the DC side Steady of each current conversion station; By means of normal running, leading current conversion station AC Voltage Drop and the assist exchanging circuit station example of stopping transport under three kinds of different operating modes calculates, demonstrate operational mode and quantity of state that steady operation point calculating method of the present invention can obtain each current conversion station of multi-terminal direct current transmission system rapidly and accurately, meanwhile, the control model modification method based on priority can select current conversion station control model exactly under different operating mode.

The inventive method is that the steady operation point calculating VSC-MTDC transmission system fast provides a kind of new approach, can provide a kind of simple and reliable analytical method for the fast dispatch of multi-terminal direct current transmission system and security evaluation etc.

Accompanying drawing illustrates:

Fig. 1 is five terminal DC transmission system schematic diagram;

Fig. 2 is steady operation point calculating method flow chart of the present invention;

Fig. 3 is the control model schematic diagram of leading current conversion station;

Fig. 4 is the control model schematic diagram at assist exchanging circuit station;

Fig. 5 is the control model schematic diagram determining active power controller current conversion station;

Fig. 6 is wind energy turbine set current conversion station control model schematic diagram.

Embodiment:

Below in conjunction with accompanying drawing and embodiment, the present invention is further detailed.

1. system configuration

Typical five terminal DC transmission system is adopted to analyze herein, as shown in Figure 1; Easy for studying, suppose that each current conversion station adopts identical main circuit structure.This system comprises 5 current conversion stations: current conversion station 1 as leading current conversion station, the DC voltage control of primary responsibility DC network and power-balance; Current conversion station 2 is assist exchanging circuit station, assists and realizes DC voltage control; Current conversion station 3 is for determine active power controller (activepowercontrol, APC) current conversion station, and for the constant active power of its AC electrical grid transmission, meanwhile, current conversion station 3 is as the standby station of DC voltage control; Current conversion station 4 and 5 is wind energy turbine set current conversion station, is respectively used to collect the active power of wind energy turbine set 4 and wind energy turbine set 5 and feed-in DC network ^[11,17-21].Wind energy turbine set 4 and 5 possesses fast prompt drop and to exert oneself control, can reduce Power Output for Wind Power Field fast when DC network overtension.

Each current conversion station all adopts the dicyclo Vector Control Model based on Feedforward Decoupling, inner ring controls to adopt dq electric current rapid track and control, outer shroud controls to adopt meritorious and idle separate power control strategy, and introduces corresponding advanced control strategy in active power controller ring.Because system dc side voltage and active power are close coupling relation, the Reactive Power Control strategy not influential system DC voltage distribution substantially of current conversion station, therefore in steady-state analysis method, only consider that the upper strata active power controller strategy of current conversion station can calculate the steady operation point of system fast.Control This document assumes that each controlling unit is indifference, and ignore the internal loss of current conversion station.

2. the control model of current conversion station and DC side operation characteristic

2.1 leading current conversion stations

1) control model

Under normal circumstances, leading current conversion station is responsible for the DC voltage control of VSC-MTDC transmission system, adopt the vector control of band Feedforward Decoupling: Active Power Controller adopts constant DC voltage control, reactive power controller adopts to be determined Reactive Power Control or determines alternating voltage to control ^[17].When current conversion station ac-side current exceedes flow restricter threshold value, current conversion station incision current-limit mode runs.According to the converter running status before incision current-limit mode, herein current-limit mode is classified: if the current-limit mode triggered because rectified current exceedes current threshold is called rectification current-limit mode; Otherwise, due to inverter current out-of-limit and trigger be called inversion current-limit mode.Control model as shown in Figure 2.In figure: I _s1take current conversion station AC phase current as the leading factor, I _s1maxtake the flow restricter threshold value of current conversion station as the leading factor.

2) analysis on Operating

The flow restricter design of current conversion station can be divided into two kinds: based on the Dynamic stability limit with based on the thermally-stabilised limit.Dynamic stability limiting current is generally due to AC network fault, and grid voltage sags causes converter output current to rise, and now, needs Limited Current rapidly to rise; Thermally-stabilised limiting current is the long term overloading ability of converter.Both distinguish to some extent on action response time, and the former requires quick acting, the inertia time of the latter be generally tens minutes and more than, but both have certain interoperability in formulation process.The main steady operation point analysis considering VSC-MTDC transmission system, therefore, can ignore the setting time of flow restricter action herein.Conveniently analyze, assuming that the setting value of the dynamic and thermal effect limiting current of flow restricter is identical.Ignore current conversion station internal loss, express formula from the active power under dq synchronous rotating frame and line voltage vector oriented ^[17]:

$P_1=\frac{3}{2}{U}_{S1}{I}_{S1d}=U_{\mathrm{dc}1}{I}_{\mathrm{dc}1}---\left(1\right)$

Wherein, P ₁take the active power that station flows into DC network as the leading factor, U _s1take the amplitude of station AC electrical network phase voltage as the leading factor, I _s1dtake the real component of station AC phase current as the leading factor, U _dc1, I _dc1take direct voltage and the direct current at station as the leading factor.

When alternating current exceeds current limit levels, leading station enters current-limit mode.Because leading station major responsibility is the power-balance maintaining DC network, therefore, the design of its flow restricter is main considers active current restriction, I _s1dmaximum is its flow restricter threshold value I _s1max.Might as well define flow restricter threshold value is β specified phase current magnitude I doubly _s1N, namely β is the Overflow RateHT of alternating current, is one and depends on the constant (supposing that the current overload rate of all current conversion stations is identical herein) that flow restricter designs.When AC line voltage is steady state value, the DC side operation characteristic equation at leading station is:

$I_{\mathrm{dc}1}=\frac{{3U}_{S1}{I}_{S1\max }}{{2U}_{\mathrm{dc}1}}=\frac{3\mathrm{\&beta;}{U}_{S1}{I}_{S1N}}{{2U}_{\mathrm{dc}1}}---\left(2\right)$

Under there is no harm in assumed fault situation, the degree of falling of leading station AC line voltage is λ ₁, then U _s1=(1-λ ₁) U _s1N, U _s1Ntake the specified phase voltage amplitude of station AC electrical network as the leading factor, therefore formula (2) can be expressed as:

$I_{\mathrm{dc}1}=\frac{(1-{\mathrm{\&lambda;}}_1){\mathrm{\&beta;P}}_{1N}}{U_{\mathrm{dc}1}}---\left(3\right)$

Wherein, P1N takes the rated power at station as the leading factor.From formula (3), under current-limit mode, the DC voltage and current operation characteristic at leading station is the cluster curve depending on electrical network phase voltage amplitude.To sum up, the DC characteristic equation at leading station is:

$\left\{\begin{array}{c}{I}_{\mathrm{dc}1}=\frac{(1-{\mathrm{\&lambda;}}_1)\mathrm{\&beta;}{P}_{1N}}{U_{\mathrm{dc}1}},I_{\mathrm{dc}1}\&GreaterEqual;I_{\mathrm{dc}1H}\\ U_{\mathrm{dc}1}=U_{\mathrm{dc}1\mathrm{ref}},I_{\mathrm{dc}1L}<I_{\mathrm{dc}1}<I_{\mathrm{dc}1H}\\ I_{\mathrm{dc}1}=-\frac{(1-{\mathrm{\&lambda;}}_1)\mathrm{\&beta;}{P}_{1N}}{U_{\mathrm{dc}1}},I_{\mathrm{dc}1}\&le;I_{\mathrm{dc}1L}\end{array}\right.---\left(4\right)$

Wherein, U _dc1reffor direct voltage command value, I _dc1H, I _dc1Lbe respectively direct current threshold value when leading station is cut into rectification current-limit mode, inversion current-limit mode by normal operation mode.Direct current threshold value can be solved by formula (4):

$\left\{\begin{array}{c}{I}_{\mathrm{dc}1H}=\frac{(1-{\mathrm{\&lambda;}}_1)\mathrm{\&beta;}{P}_{1N}}{U_{\mathrm{dc}1}}\\ I_{\mathrm{dc}1L}=-\frac{(1-{\mathrm{\&lambda;}}_1){\mathrm{\&beta;P}}_{1N}}{U_{\mathrm{dc}1}}\end{array}\right.---\left(5\right)$

From above formula, direct current threshold value I _dc1Hand I _dc1Lcalculating and DC voltage value U _dc1relevant.

2.2 assist exchanging circuit stations

1) control model

When the current conversion station number of direct current system is more, system operation mode is changeable, capacity needed for DC network power-balance is comparatively large, only adopts leading station to be difficult to the demand meeting power-balance, needs to set up auxiliary station with the capacity of increase system for DC voltage control.Auxiliary station generally adopts the vector control of band Feedforward Decoupling: Active Power Controller adopts voltage drop to control, and reactive power controller adopts to be determined Reactive Power Control or determine alternating voltage to control ^[19-20].The current-limit mode of auxiliary station is stood similar with leading, and its control model as shown in Figure 3.In figure: I _s2for assist exchanging circuit station AC phase current, I _s2maxfor the flow restricter threshold value at assist exchanging circuit station.

2) operation characteristic

Decline control model is based on the adjustment of local d. c. voltage signal realization to active current command value, and active current and direct current have direct correlation, and therefore, the operation characteristic under decline control model can be expressed as ^[22]:

I _dc2＝k _droop2(U _dc2-U _dc2ref)(6)

Wherein, U _dc2, U _dc2ref, I _dc2be respectively the direct voltage of auxiliary station, direct voltage reference value and direct current, k _droop2for the Slope Parameters that auxiliary station voltage drop controls.The current-limit mode of auxiliary station is identical with leading ruuning situation of standing, and the design of its flow restricter is main considers active current current limliting, then the DC characteristic equation of auxiliary station is:

$\left\{\begin{array}{c}{I}_{\mathrm{dc}2}=\frac{(1-{\mathrm{\&lambda;}}_2)\mathrm{\&beta;}{P}_{2N}}{U_{\mathrm{dc}2}},I_{\mathrm{dc}2}\&GreaterEqual;I_{\mathrm{dc}2H}\\ I_{\mathrm{dc}2}=k_{\mathrm{droop}2}(U_{\mathrm{dc}2}-U_{\mathrm{dc}2\mathrm{ref}}),I_{\mathrm{dc}2L}<I_{\mathrm{dc}2}<I_{\mathrm{dc}2H}\\ I_{\mathrm{dc}2}=-\frac{(1-{\mathrm{\&lambda;}}_2)\mathrm{\&beta;}{P}_{2N}}{U_{\mathrm{dc}2}},I_{\mathrm{dc}2}\&le;I_{\mathrm{dc}2L}\end{array}\right.---\left(7\right)$

Wherein, λ ₂for auxiliary station ac grid voltage falls degree, P _2Nfor the rated power at assist exchanging circuit station, I _dc2H, I _dc2Lbe respectively direct current threshold value when auxiliary station is cut into rectification current-limit mode, inversion current-limit mode by normal operation mode.

2.3 determine active power controller current conversion station

1) control model

Determine active power controller (APC) current conversion station and be mainly used in DC network and AC network carries out constant power delivery, normal employing is with the vector control of Feedforward Decoupling: Active Power Controller adopts determines active power controller, and reactive power controller adopts to be determined alternating voltage control or determines Reactive Power Control ^[17].When its direct voltage exceeds normal operation range, APC current conversion station should provide certain active power capacity for realizing DC voltage control, maintains DC network power-balance, the reserve capacity of DC network power-balance when increasing normal operation.When direct voltage exceedes threshold value, APC current conversion station cuts decline control model by normal operation mode.The current-limit mode of APC current conversion station is stood similar with leading, and its control model is as Fig. 4.In figure: I _s3for APC current conversion station AC phase current, I _s3maxfor the flow restricter threshold value of APC current conversion station, U _dc3for the direct voltage of APC current conversion station, U _dc3H, U _dc3Lbe respectively the active power controller of APC current conversion station and inversion decline control, rectification declines the direct voltage threshold value controlled when mutually switching.

2) operation characteristic

Under normal operation mode, the active power of current conversion station is steady state value, that is:

P _3ref＝U _dc3I _dc3(8)

Wherein, P _3ref, I _dc3be respectively active power command value, the direct current of APC current conversion station.

When direct voltage is greater than threshold value U _dc3Htime, APC current conversion station incision inversion decline control model, the direct current of incision operating point is P _3ref/ U _dc3H.According to linear law, its operation characteristic equation is:

$I_{\mathrm{dc}3}=k_{\mathrm{droop}3}(U_{\mathrm{dc}3}-U_{\mathrm{dc}3H})+\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3H}}---\left(9\right)$

Wherein, k _droop3for the Slope Parameters that voltage drop controls.In like manner, when direct voltage is less than threshold value U _dc3Ltime, APC current conversion station incision rectification decline control model, its operation characteristic equation is:

$I_{\mathrm{dc}3}=k_{\mathrm{droop}3}(U_{\mathrm{dc}3}-U_{\mathrm{dc}3L})+\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3L}}---\left(10\right)$

The current-limit mode of APC current conversion station is identical with leading ruuning situation of standing, and the design of its flow restricter is main considers active current current limliting, then its DC characteristic equation is:

$\left\{\begin{array}{c}{I}_{\mathrm{dc}3}=\frac{(1-{\mathrm{\&lambda;}}_3)\mathrm{\&beta;}{P}_{3N}}{U_{\mathrm{dc}3}},I_{\mathrm{dc}3}\&GreaterEqual;I_{\mathrm{dc}3H}\\ I_{\mathrm{dc}3}=k_{\mathrm{droop}3}(U_{\mathrm{dc}3}-U_{\mathrm{dc}3L})+\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3L}},U_{\mathrm{dc}3}\&GreaterEqual;U_{\mathrm{dc}3H},\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3L}}\&le;I_{\mathrm{dc}3}<I_{\mathrm{dc}3H}\\ I_{\mathrm{dc}3}=\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3}},U_{\mathrm{dc}3L}\&le;U_{\mathrm{dc}3}<U_{\mathrm{dc}3H},\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3H}}\&le;I_{\mathrm{dc}3}<\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3L}}\\ I_{\mathrm{dc}3}=k_{\mathrm{droop}3}(U_{\mathrm{dc}3}-U_{\mathrm{dc}3H})+\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3H}},U_{\mathrm{dc}3}<U_{\mathrm{dc}3L},I_{\mathrm{dc}3L}<I_{\mathrm{dc}3}<\frac{P_{3\mathrm{ref}}}{U_{\mathrm{dc}3H}}\\ I_{\mathrm{dc}3}=-\frac{(1-{\mathrm{\&lambda;}}_3){\mathrm{\&beta;P}}_{3N}}{U_{\mathrm{dc}3}},I_{\mathrm{dc}3}\&le;I_{\mathrm{dc}3L}\end{array}\right.---\left(11\right)$

Wherein, λ ₃for APC current conversion station ac grid voltage falls degree, P _3Nfor the rated power of APC current conversion station, I _dc3H, I _dc3Lbe respectively direct current threshold value when auxiliary station is cut into rectification current-limit mode, inversion current-limit mode by normal operation mode.

2.4 wind energy turbine set current conversion stations

1) control model

Wind energy turbine set current conversion station is often connected with the AC network of wind energy turbine set, for collecting the active power of wind energy turbine set, and is responsible for the FREQUENCY CONTROL of wind farm network.Such current conversion station often adopts the vector control of band Feedforward Decoupling: its Active Power Controller wind energy turbine set current conversion station active power and frequency control, and reactive power controller adopts determines alternating voltage control ^[1,10-11].Because wind energy turbine set adopts fast prompt drop to exert oneself control, therefore, when DC network overtension, current conversion station 4 and 5 cut-in voltage decline control model, possesses certain DC voltage control ability.Because wind energy turbine set current conversion station only runs on rectification state, its current-limit mode also only has rectification current-limit mode a kind of, and its control model is as Fig. 5.In figure: I _s4dfor the real component of wind energy turbine set current conversion station AC phase current, I _s4dmaxfor the active current cut-off current of wind energy turbine set current conversion station flow restricter, U _dc4for the direct voltage of wind energy turbine set current conversion station, U _dc4Hvoltage drop for wind energy turbine set current conversion station controls direct voltage threshold value when mutually switching with active power and frequency control.

2) operation characteristic

In practical application, the active power controller of wind energy turbine set current conversion station adopts the active power and frequency control based on slop control strategy, to ensure under the prerequisite meeting wind farm grid-connected medium standard frequency rate control overflow, make current conversion station control wind energy turbine set AC network frequency in real time, and carry out active power controller according to Power Output for Wind Power Field size.Pass between wind energy turbine set frequency and current conversion station active power is ^[1]:

f ₄＝f _4N-k _f4(P _wf4N-P _4ref)(12)

Wherein, f ₄and f _4Nbe respectively real-time frequency and the rated frequency of wind energy turbine set 4 AC network, P _4reffor the active power command value of wind energy turbine set current conversion station 4, P _wf4Nfor the specified active power of wind energy turbine set 4, k _f4for the Slope Parameters of current conversion station 4 active power and frequency control device.When windfarm system frequency is rated value, i.e. f ₄=f _4N, wind energy turbine set is in full hair-like state, and the active power command value of current conversion station 4 is P _4ref=P _wf4N.Ignore current conversion station internal loss, active power of wind power field can be expressed as the product P of current conversion station 4 direct voltage and direct current ₄=U _dc4i _dc4, then above formula can be expressed as again:

$I_{\mathrm{dc}4}=\frac{f_4-f_{4N}+k_{f4}{P}_{\mathrm{wf}4N}}{k_{f4}{U}_{\mathrm{dc}4}}---\left(13\right)$

When direct voltage is higher than U _dc4Htime, wind energy turbine set current conversion station enters direct voltage decline control model, ensures that its direct voltage is not out-of-limit at zone of reasonableness, and its operation characteristic equation is:

I _dc4＝k _droop4(U _dc4-U _dc4max)(14)

Wherein, U _dc4maxfor the maximum DC voltage value of wind energy turbine set current conversion station 4, k _droop4for the Slope Parameters of current conversion station 4 voltage drop controller.After DC network fault causes wind energy turbine set current conversion station to enter voltage drop control model, wind energy turbine set must take fast prompt drop to exert oneself measure, reduces rapidly active power of wind power field and exports, to ensure the frequency stability of wind farm network.

First wind energy turbine set current conversion station needs the alternating voltage maintaining AC electrical network, simultaneously for collecting the active power of wind energy turbine set.Therefore, active power controller and Reactive Power Control of equal importance, therefore need when flow restricter designs to take into account active current and reactive current.The meritorious current limitation value of supposition is herein α times of flow restricter threshold value, and active current cut-off current is I _s4dmax=α I _s4max, then reactive current cut-off current is I _s4qmax=sqrt (1-α ²) I _s4max.Easy and unified for studying, assuming that wind energy turbine set current conversion station enters current-limit mode when active current reaches cut-off current.Similar leading station, can obtain the characteristic equation of current conversion station under rectification current-limit mode:

$I_{\mathrm{dc}4}=\frac{(1-{\mathrm{\&lambda;}}_4)\mathrm{\&alpha;\&beta;}{P}_{4N}}{U_{\mathrm{dc}4}}---\left(5\right)$

Wherein, P _4Nfor the rated power of wind energy turbine set current conversion station.To sum up, the DC characteristic equation of such current conversion station is:

$\left\{\begin{array}{c}{I}_{\mathrm{dc}4}=\frac{(1-{\mathrm{\&lambda;}}_4)\mathrm{\&alpha;\&beta;}{P}_{4N}}{U_{\mathrm{dc}4}},I_{\mathrm{dc}4}\&GreaterEqual;I_{\mathrm{dc}4H}\\ I_{\mathrm{dc}4}=\frac{f_4-f_{4N}+k_{f4}{P}_{\mathrm{wf}4N}}{k_{f4}{U}_{\mathrm{dc}4}},U_{\mathrm{dc}4}<U_{\mathrm{dc}4H},I_{\mathrm{dc}4h}\&le;I_{\mathrm{dc}4}<I_{\mathrm{dc}4H}\\ I_{\mathrm{dc}4}=k_{\mathrm{droop}4}(U_{\mathrm{dc}4}-U_{\mathrm{dc}4H})+I_{\mathrm{dc}4h},U_{\mathrm{dc}4}\&GreaterEqual;U_{\mathrm{dc}4H}\end{array}\right.---\left(16\right)$

Wherein, λ ₄for wind energy turbine set current conversion station 4 ac grid voltage falls degree, I _dc4Hfor normal operation mode is cut into the direct current threshold value of rectification current-limit mode, I _dc4hfor direct voltage under normal control mode is U _dc4Htime corresponding DC current values.Wind energy turbine set current conversion station 5 is identical with the operation characteristic of current conversion station 4, repeats no more.

3. steady operation point calculates

3.1 DC power flows calculate

Getting converter, to flow to DC network be positive direction, and definition DC bus-bar voltage vector is: U=[U _dc1, U _dc2, U _dc3, U _dc4, U _dc5] ^t, DC bus current vector is: I=[I _dc1, I _dc2, I _dc3, I _dc4, I _dc5] ^t, then DC network equation is:

I＝[Y]U(17)

Wherein, [Y] is 5 × 5 admittance matrixs.DC line adopts equivalent resistance model, then can obtain admittance matrix [Y] according to Fig. 1 is:

$\left[Y\right]=\left[\begin{array}{ccccc}\frac{1}{R_{12}}+\frac{1}{R_{13}}& -\frac{1}{R_{12}}& -\frac{1}{R_{13}}& 0& 0\\ -\frac{1}{R_{13}}& \frac{1}{R_{12}}+\frac{1}{R_{24}}+\frac{1}{R_{25}}& 0& -\frac{1}{R_{24}}& -\frac{1}{R_{25}}\\ -\frac{1}{R_{13}}& 0& \frac{1}{R_{13}}+\frac{1}{R_{34}}& -\frac{1}{R_{34}}& 0\\ 0& -\frac{1}{R_{24}}& -\frac{1}{R_{24}}& \frac{1}{R_{24}}+\frac{1}{R_{34}}+\frac{1}{R_{45}}& -\frac{1}{R_{45}}\\ 0& -\frac{1}{R_{25}}& 0& -\frac{1}{R_{45}}& \frac{1}{R_{25}}+\frac{1}{R_{45}}\end{array}\right]---\left(18\right)$

Wherein, Ri _jfor the equivalent resistance of DC line between current conversion station i and current conversion station j.

3.2 steady state point calculation process

The calculation process of steady operation point as shown in Figure 6.When calculating beginning, according to AC network condition and DC network parameter, the control model of each current conversion station of initialization and command value, then solving system equation; If the direct voltage of some or several current conversion station or current value exceed normal range (NR) in steady state point result of calculation, then need the control model revising corresponding current conversion station; Then, according to the characteristic equation solving system equation under new model, and judge, in the range of operation of result of calculation whether under corresponding control model, to repeat according to this, until obtain steady operation point.The characteristic equation that all types of current conversion station is under different control model can with reference to formula (4) (7) (11) (16).

Suppose that each current conversion station all runs on normal condition, then during first time solving system equation, the direct voltage-current characteristics equation of each current conversion station is:

$\left\{\begin{array}{c}{U}_{\mathrm{dc}1}=U_{\mathrm{dc}1\mathrm{ref}}\\ I_{\mathrm{dc}2}=k_{\mathrm{droop}2}(U_{\mathrm{dc}2}-U_{\mathrm{dc}2\mathrm{ref}})\\ I_{\mathrm{dc}3}=P_{3\mathrm{ref}}/U_{\mathrm{dc}3}\\ I_{\mathrm{dc}4}=(f_4-f_{4N}+k_{f4}{P}_{\mathrm{wf}4N})/\left(k_{f4}{U}_{\mathrm{dc}4}\right)\\ I_{\mathrm{dc}5}=(f_5-f_{5N}+k_{f5}{P}_{\mathrm{wf}5N})/\left(k_{f5}{U}_{\mathrm{dc}5}\right)\end{array}\right.---\left(19\right)$

Above formula is substituted into formula (17), cancellation nuisance variable, the characteristic equation group when system that can obtain normally is run:

$\left[\begin{array}{c}{I}_{\mathrm{dcl}}\\ k_{\mathrm{droop}2}(U_{\mathrm{dc}2}-U_{\mathrm{dc}2\mathrm{ref}})\\ P_{3\mathrm{ref}}/U_{\mathrm{dc}3}\\ (f_4-f_{4N}+k_{f4}{P}_{\mathrm{wf}4N})/\left(k_{f4}{U}_{\mathrm{dc}4}\right)\\ (f_5-f_{5N}+k_{f5}{P}_{\mathrm{wf}4N})/\left(k_{f5}{U}_{\mathrm{dc}5}\right)\end{array}\right]=\left[Y\right]\left[\begin{array}{c}{U}_{\mathrm{dc}1\mathrm{ref}}\\ U_{\mathrm{dc}2}\\ U_{\mathrm{dc}3}\\ U_{\mathrm{dc}4}\\ U_{\mathrm{dc}5}\end{array}\right]---\left(20\right)$

As from the foregoing, I under normal circumstances _dc1, U _dc2, U _dc3, U _dc4, U _dc5for unknown quantity, all the other are known quantity.This equation group is quadratic nonlinearity equation group, can by Newton-Raphson solution by iterative method.If when certain current conversion station is in shut down condition, then during initial calculation, the control model of this current conversion station is set to and determines active power controller, and active power command value is set to 0, and then solving system equation.Under different operational mode, the method for solving of system performance equation group is with similar under normal circumstances, repeats no more.

3.3 current conversion station control model modification methods

The modification method of current conversion station control model is current conversion station DC voltage value according to system present control mode and last solving system equation and DC current values, revise the control model of quantity of state out-of-limit current conversion station, and then the control model of current conversion station when determining that system equation calculates next time.According to the difference of reference state amount, control model modification method can be divided into the modification method based on DC current values and the modification method two parts based on DC voltage value; And according to the impact on system operation mode, the former has higher priority than the latter.

For the current-limit mode of all current conversion stations, alternating current is the sole criterion that this control model starts and stops.According to formula (2), if known ac grid voltage value and inverter design parameter, then alternating current threshold value can be converted to direct current threshold value, so reference value when DC current values can be adopted to carry out current-limit mode correction as all current conversion stations.The control model correction of leading station and auxiliary station is mainly carried out between normal mode and current-limit mode, therefore, and unique reference values when DC current values is this two kinds of current conversion station Correction and Control patterns.

The voltage drop control model of APC current conversion station and wind energy turbine set current conversion station is that the startup of this control model directly depends on DC voltage value in order to direct voltage under ensureing abnormal operational conditions can be in a kind of DC voltage control and power-balance means taked in zone of reasonableness.The voltage drop control model of auxiliary station is its normal operation mode, and the selection of its direct voltage initiation value needs to flow voltage-controlled cooperation based on leading standing erectly, and its DC voltage value does not affect the control model correction of this current conversion station.

In order to prevent the impact on system operation mode after control mode switch, when the DC current values of multiple current conversion station and DC voltage value exceed the range of operation of corresponding control model simultaneously, according to the priority orders of " leading station, auxiliary station, APC current conversion station, wind energy turbine set current conversion station " and " correction based on DC current values, the correction based on DC voltage value ", only revise the high current conversion station control model of priority.Upper analysis, can obtain the priority orders table (sequence number is less, and priority is higher) of control model modification method according to this, as shown in table 1.

The priority list of table 1 control model modification method

Note: leading current conversion station and assist exchanging circuit station be not based on the modification method of DC voltage value.

In five terminal DC transmission system example herein, APC current conversion station is as the voltage-controlled standby usage station of system dc, and wind energy turbine set current conversion station 4 and 5 is common as the second standby station.When the power of feed-in DC network too high and cause direct voltage to continue to rise time, first current conversion station 3 cuts decline control model, next is wind energy turbine set current conversion station 4 and 5, and wind energy turbine set current conversion station controls to coordinate with the power-balance maintaining wind farm network and frequency stabilization by exerting oneself with fast prompt drop simultaneously.But when DC network voltage keeps declines, wind energy turbine set current conversion station 4 and 5 is limited to output of wind electric field restriction, enough active power cannot be provided to support, and current conversion station 3 is unique standby stations of DC voltage control.

4. sample calculation analysis

The DC line length parameter of the five terminal DC transmission system adopted herein is L ₁₂=200km, L ₁₃=180km, L ₂₄=120km, L ₂₅=L ₃₄=L ₄₅=100km, direct current cables adopts 800mm ²copper core cable, its 20 DEG C of maximum resistance are 0.0224 Ω/km; The rated power of each current conversion station is 400MVA, and wind energy turbine set rated power is 380MW; The Overflow RateHT of converter is β=1.1, wind energy turbine set converter parameter alpha=0.9.Direct current power fiducial value is 400MW, and DC voltage reference value is 400kV, and direct current fiducial value is 1kA.

The selection principle of current conversion station controller parameter has: 1) auxiliary station realizes the DC voltage control under accidental conditions with leading cooperation of standing; 2) the falling controller cooperation of APC current conversion station and wind energy turbine set current conversion station, realizes the DC voltage control under abnormal condition; 3) impact considering controller static receiver error and stability is needed when determining the Slope Parameters of voltage drop controller; 4) the active power and frequency control device demand fulfillment " wind energy turbine set access power system technology regulation " of wind energy turbine set current conversion station ^[23]in requirement to refrequency control range.According to above principle, the command value of each current conversion station and controller parameter (perunit value) are: leading station U _dc1ref=1.0pu; Auxiliary station U _dc2ref=1.0011pu, k _droop2=-276; APC current conversion station U _dc3H=1.04pu, U _dc3L=0.96pu, k _droop3=-200; Wind energy turbine set current conversion station U _dc4H=U _dc5H=1.08pu, k _droop4=k _droop5=-100, k _f4=k _f5=0.0117.

For five terminal DC transmission system, MATLAB programming realization steady operation point calculating method in this paper, control model modification method adopts look-up table to be achieved, systematic steady state operating point under three kinds of operating modes that calculating normal condition, leading station ac grid voltage fall and auxiliary station stops transport.

4.1 accidental conditions

Under nominal situation, it is P that each current conversion station AC Voltage Drop degree is 0, APC current conversion station active power command value _3ref=-0.5pu, calculate the running status that wind power is VSC-MTDC transmission system in 10%, 30% and 100% 3 kind of situation of its rated value respectively, result of calculation is as table 2.

Result of calculation under table 2 nominal situation

Note: in table, the unit of each variable is pu, in table, the positive direction of power and electric current is that AC network flows to DC network, ' ' represent that this variable does not exist.

Under these three kinds of operating modes, each current conversion station all runs on normal control mode.As shown in Table 2, when the active power of wind energy turbine set current conversion station 4 and 5 is 0.095pu, because APC current conversion station is to the active power of its AC electrical grid transmission 0.5pu, leading current conversion station 1 and assist exchanging circuit station 2 are respectively to DC network feed-in power, and its active power value is respectively 0.1465pu and 0.1645pu; When wind power is 0.285pu, two wind energy turbine set generated outputs are just greater than the active power transfer demand of APC current conversion station, therefore, active power capacity for dc-voltage balance after removing DC network loss is smaller, and current conversion station 1 and current conversion station 2 are respectively to the active power of its AC network feed-in 0.0210pu and 0.0476pu; When wind power completely send out be 0.95pu time, current conversion station 1 and current conversion station 2 are respectively 0.6032pu and 0.7873pu to the active power value of its AC electrical network feed-in.Under these three kinds of operating modes, all do not produce that direct voltage is out-of-limit or direct current is out-of-limit, the control model without the need to revising current conversion station can obtain the steady operation point of system.

As from the foregoing, under the acting in conjunction at leading current conversion station and assist exchanging circuit station, power-balance when direct current system can maintain different output of wind electric field and direct voltage constant; Computational methods in this paper accurately can calculate the steady operation point of direct current system under nominal situation.

4.2 leading station AC grid voltage sags

Wind power is completely sent out, and APC current conversion station active power command value is P _3ref=-0.2pu, leading current conversion station 1 AC grid voltage sags 30%, i.e. λ ₁=0.3, calculate VSC-MTDC transmission system running status, result of calculation is as table 3 and table 4.Table 3 is first time solving system equation result, and namely each current conversion station is the result of calculation under normal control mode; The result of calculation that station is modified to second time solving system equation after inversion current-limit mode taken as the leading factor by table 4.

During the grid voltage sags of table 3 leading station first time system equation result of calculation

Second time system equation result of calculation during the grid voltage sags of table 4 leading station

As shown in Table 3, when leading current conversion station 1 AC grid voltage sags is to 0.7pu, leading station DC current values is-0.8013pu, to AC network feed-in power 0.8013pu.According to current line voltage condition and converter parameter, the direct current threshold value that can calculate leading station inversion current-limit mode is-0.77pu.Amplitude due to leading station actual current is greater than the amplitude of direct current threshold value, and leading station cannot maintain normal control mode and enter inversion current-limit mode, and after solving system equation, current conversion station control model is modified to inversion current-limit mode for the first time.As shown in Table 4, after leading station enters inversion current-limit mode, its direct current maintains its direct current threshold value-0.7697pu, its direct voltage can not maintain command value 1.0pu, but 1.0003pu, leading station loses DC voltage control ability, and now DC voltage control is by the voltage drop control realization of auxiliary station.

Contrast table 3 is known with table 4, and after leading current conversion station 1 is cut into inversion current-limit mode from normal control mode, lose DC voltage control ability, its active power value is reduced to-0.7700pu by-0.8013pu; DC network power-balance task transfers is to current conversion station 2, and assist exchanging circuit station 2 active power value rises to-0.9196 by-0.8881pu, and its direct current rises to-0.9156, does not reach its current-limit mode threshold value-1.0952.Through verification, direct current system quantity of state all meets the demands, therefore second time system equation result of calculation is steady operation point.

As from the foregoing, in the grid voltage sags situation of leading station, leading station enters current-limit mode, and other current conversion station control models of system are constant, and auxiliary station assume responsibility for DC voltage control task; The steady operation point that computational methods in this paper can realize under this operating mode calculates.

Stop transport in 4.3 assist exchanging circuit stations

Wind power is completely sent out, and APC current conversion station active power command value is P _3ref=-0.5pu, assist exchanging circuit station because of the reasons such as internal fault out of service, calculate VSC-MTDC transmission system running status, result of calculation is as shown in table 5, table 6 and table 7.Table 5 is first time solving system equation result, the operational mode of auxiliary station is set to determine active power controller pattern and active power command value is 0, and other current conversion stations are normal control mode; The result of calculation that station is modified to second time solving system equation after inversion current-limit mode taken as the leading factor by table 6; Table 7 is modified to the result of calculation of the solving system equation of third time after inversion decline control model for APC current conversion station.

Time stoppage in transit in table 5 assist exchanging circuit station first time system equation result of calculation

Second time system equation result of calculation time stoppage in transit in table 6 assist exchanging circuit station

Time stoppage in transit in table 7 assist exchanging circuit station third time system equation result of calculation

When auxiliary station stops transport, leading station individual responsibility DC voltage control.Known by table 5, for the first time in system equation result, leading station actual DC current value is-1.3801pu, and the direct current threshold value-1.1000pu of its inversion current-limit mode, leading station direct current is out-of-limit, cannot maintain system dc voltage, therefore, leading station operational mode is corrected for inversion current-limit mode.

As shown in Table 6, after only dominating station incision current-limit mode, the direct voltage of DC network will be out of hand, and each current conversion station direct voltage final calculation result is 564.6818pu.The most basic reason producing this situation is that after leading station incision current-limit mode, direct current system loses the current conversion station carrying out DC voltage control; Meanwhile, current conversion station for subsequent use is not also modified to voltage drop control model.According to control model modification method, APC current conversion station is the first standby station, wind energy turbine set current conversion station 4 and 5 is the second current conversion station for subsequent use, therefore APC current conversion station need be modified to inverter voltage decline control model by normal control mode, and the DC voltage control of direct current system is responsible for by APC current conversion station.

Third time, when calculating, leading station was current-limit mode, and APC current conversion station is inverter voltage decline control model.Known by table 7, after leading station enters current-limit mode, its actual DC current values equals direct current threshold value, is-1.0597pu; Due to U in APC current conversion station inversion decline control model _dc4H=1.04pu, each current conversion station direct voltage of system all maintains about 1.04pu, and keeps stable; Through verification, this state is the steady operation point under this operating mode.

As from the foregoing, after auxiliary station stops transport, leading station enters current-limit mode because realizing DC voltage control separately, and direct voltage is out of hand, rises to high level; When APC current conversion station direct voltage reaches its inversion decline control model threshold value U _dc4Htime, APC current conversion station cut-in voltage decline control model, carries out DC voltage control with auxiliary direct current system; Computational methods in this paper can calculate the steady operation point under this operating mode rapidly and accurately.

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (9)

1. a voltage source converter type multi-terminal direct current transmission system steady operation point optimization method, is characterized in that, comprise the following steps:

(1) getting converter, to flow to DC network be positive direction, and definition direct voltage vector is: U=[U _dc1, U _dc2, U _dc3, U _dc4, U _dc5] ^t, direct current vector is: I=[I _dc1, I _dc2, I _dc3, I _dc4, I _dc5] ^t, building DC network equation is:

I＝[Y]U

Wherein, [Y] is admittance matrix; U _dc1take the magnitude of voltage of current conversion station DC side as the leading factor, U _dc1for the direct voltage at assist exchanging circuit station, U _dc3for determining the DC voltage value of active power controller current conversion station, U _dc4be the DC voltage value of the first wind energy turbine set current conversion station, U _dc5it is the DC voltage value of the second wind energy turbine set current conversion station;

I _dc1take the current value of current conversion station DC side as the leading factor, I _dc2for the direct current at assist exchanging circuit station, I _dc3for determining the direct current baric flow of active power controller current conversion station, I _dc4be the DC current values of the first wind energy turbine set current conversion station, I _dc5it is the DC voltage value of the second wind energy turbine set current conversion station;

(2) according to AC network condition and DC network parameter, the control model of each current conversion station of initialization and command value; Solve the direct voltage-current characteristics equation of each current conversion station; Described current conversion station comprises: dominate current conversion station, assist exchanging circuit station, determine active power controller current conversion station and wind energy turbine set current conversion station;

(3) suppose that each current conversion station all runs on normal condition, according to direct voltage-current characteristics equation and the DC network equation of each current conversion station, obtain characteristic equation group when system is normally run;

(4) Newton-Raphson solution by iterative method system performance equation group is utilized;

(5) all solution I of above-mentioned characteristic equation group are judged respectively _dciand U _dciwhether in normal range (NR), wherein, i=1,2,3,4,5; If so, then gained solution is the steady operation point of system; If there is the solution not in normal range (NR), then revise the control model of corresponding voltage source converter, again try to achieve system performance equation group, return step (4);

The concrete grammar revising the control model of corresponding voltage source converter in described step (5) is:

According to current conversion station DC voltage value and the DC current values of system present control mode and last solving system equation, revise the control model of the out-of-limit current conversion station of quantity of state, and then the control model of current conversion station when determining that system equation calculates next time;

The control model at leading current conversion station and assist exchanging circuit station is revised based on the DC current values of current conversion station; The control model of determining active power controller current conversion station and wind energy turbine set current conversion station is revised based on the DC current values of current conversion station.

2. a kind of voltage source converter type multi-terminal direct current transmission system steady operation point optimization method as claimed in claim 1, it is characterized in that, in described step (1), [Y] is 5 × 5 admittance matrixs, is specially:

$\&lsqb;Y\&rsqb;=\left[\begin{array}{ccccc}\frac{1}{R_{12}}+\frac{1}{R_{13}}& -\frac{1}{R_{12}}& -\frac{1}{R_{13}}& 0& 0\\ -\frac{1}{R_{12}}& \frac{1}{R_{12}}+\frac{1}{R_{24}}+\frac{1}{R_{25}}& 0& -\frac{1}{R_{24}}& -\frac{1}{R_{25}}\\ -\frac{1}{R_{13}}& 0& \frac{1}{R_{13}}+\frac{1}{R_{34}}& -\frac{1}{R_{34}}& 0\\ 0& -\frac{1}{R_{24}}& -\frac{1}{R_{34}}& \frac{1}{R_{24}}+\frac{1}{R_{34}}+\frac{1}{R_{45}}& -\frac{1}{R_{45}}\\ 0& -\frac{1}{R_{25}}& 0& -\frac{1}{R_{45}}& \frac{1}{R_{25}}+\frac{1}{R_{45}}\end{array}\right]$

Wherein, R _ijrepresent the equivalent resistance of DC line between current conversion station i and current conversion station j, j=1,2,3,4,5.

3. a kind of voltage source converter type multi-terminal direct current transmission system steady operation point optimization method as claimed in claim 1, is characterized in that, in described step (2), the direct voltage-current characteristics equation of leading current conversion station is:

$\left\{\begin{array}{c}{I}_{dc1}=\frac{\left(1-{\mathrm{\&lambda;}}_1\right){\mathrm{\&beta;P}}_{1N}}{U_{dc1}},I_{dc1}\&GreaterEqual;I_{dc1H}\\ U_{dc1}=U_{dc1ref},I_{dc1L}<I_{dc1}<I_{dc1H}\\ I_{dc1}=-\frac{\left(1-{\mathrm{\&lambda;}}_1\right){\mathrm{\&beta;P}}_{1N}}{U_{dc1}},I_{dc1}\&le;I_{dc1L}\end{array}\right.$

Wherein, I _dc1and U _dc1current value and the magnitude of voltage of leading current conversion station DC side respectively, λ ₁fall degree for current conversion station AC line voltage leading under failure condition, β is the Overflow RateHT of alternating current, P _1Ntake the rated power of current conversion station as the leading factor, U _dc1reffor direct voltage command value, I _dc1Htake direct current threshold value when current conversion station is cut into rectification current-limit mode by normal operation mode as the leading factor; I _dc1Ltake direct current threshold value when current conversion station is cut into inversion current-limit mode by normal operation mode as the leading factor;

In above formula, work as I _dc1L< I _dc1< I _dc1Htime, leading current conversion station is in normal operating condition, is DC voltage control pattern; Work as I _dc1>=I _dc1Htime, leading current conversion station is in abnormal operational conditions, runs on rectification current-limit mode; Work as I _dc1≤ I _dc1Ltime, leading current conversion station is in abnormal operational conditions, runs on inversion current-limit mode.

4. a kind of voltage source converter type multi-terminal direct current transmission system steady operation point optimization method as claimed in claim 1, it is characterized in that, in described step (2), the direct voltage-current characteristics equation at assist exchanging circuit station is:

$\left\{\begin{array}{c}{I}_{dc2}=\frac{\left(1-{\mathrm{\&lambda;}}_2\right){\mathrm{\&beta;P}}_{2N}}{U_{dc2}},I_{dc2}\&GreaterEqual;I_{dc2H}\\ I_{dc2}=k_{droop2}\left(U_{dc2}-U_{dc2ref}\right),I_{dc2L}<I_{dc2}<I_{dc2H}\\ I_{dc2}=-\frac{\left(1-{\mathrm{\&lambda;}}_2\right){\mathrm{\&beta;P}}_{2N}}{U_{dc2}},I_{dc2}\&le;I_{dc2L}\end{array}\right.$

Wherein, U _dc2for the direct voltage at assist exchanging circuit station, U _dc2reffor the direct voltage reference value at assist exchanging circuit station, I _dc2for the direct current at assist exchanging circuit station, k _droop2for the Slope Parameters that auxiliary station voltage drop controls, β is the Overflow RateHT of alternating current, λ ₂for assist exchanging circuit station ac grid voltage falls degree, P _2Nfor the rated power at assist exchanging circuit station, I _dc2Hfor direct current threshold value when assist exchanging circuit station is cut into rectification current-limit mode by normal operation mode; I _dc2Lfor direct current threshold value when assist exchanging circuit station is cut into inversion current-limit mode by normal operation mode;

Work as I _dc2L< I _dc2< I _dc2Htime, assist exchanging circuit station is in normal operating condition, is voltage drop control model;

Work as I _dc2>=I _dc2Htime, assist exchanging circuit station runs on abnormal operational conditions, is rectification current-limit mode;

Work as I _dc2≤ I _dc2Ltime, assist exchanging circuit station runs on abnormal operational conditions, is inversion current-limit mode.

5. a kind of voltage source converter type multi-terminal direct current transmission system steady operation point optimization method as claimed in claim 1, it is characterized in that, in described step (2), the direct voltage-current characteristics equation determining active power controller current conversion station is:

$\left\{\begin{array}{c}{I}_{dc3}=\frac{\left(1-{\mathrm{\&lambda;}}_3\right){\mathrm{\&beta;P}}_{3N}}{U_{dc3}},I_{dc3}\&GreaterEqual;I_{dc3H}\\ I_{dc3}=k_{droop3}\left(U_{dc3}-U_{dc3L}\right)+\frac{P_{3ref}}{U_{dc3L}},U_{dc3}\&GreaterEqual;U_{dc3H},\frac{P_{3ref}}{U_{dc3L}}\&le;I_{dc3}<I_{dc3H}\\ I_{dc3}=\frac{P_{3ref}}{U_{dc3}},U_{dc3L}\&le;U_{dc3}<U_{dc3H},\frac{P_{3ref}}{U_{dc3H}}\&le;I_{dc3}<\frac{P_{3ref}}{U_{dc3L}}\\ I_{dc3}=k_{droop3}\left(U_{dc3}-U_{dc3H}\right)+\frac{P_{3ref}}{U_{dc3H}},U_{dc3}<U_{dc3L},I_{dc3L}<I_{dc3}<\frac{P_{3ref}}{U_{dc3H}}\\ I_{dc3}=-\frac{\left(1-{\mathrm{\&lambda;}}_3\right){\mathrm{\&beta;P}}_{3N}}{U_{dc3}},I_{dc3}\&le;I_{dc3L}\end{array}\right.$

Wherein, P _3reffor determining the active power command value of active power controller current conversion station, I _dc3for determining the direct current of active power controller current conversion station, U _dc3for determining the direct voltage of active power controller current conversion station, k _droop3for the Slope Parameters that voltage drop controls, β is the Overflow RateHT of alternating current, λ ₃degree is fallen, P for determining active power controller current conversion station ac grid voltage _3Nfor determining the rated power of active power controller current conversion station, U _dc3Hfor the active power controller and inversion of determining active power controller current conversion station decline the direct voltage threshold value controlled when mutually switching, U _dc3Lfor the active power controller and rectification of determining active power controller current conversion station decline the direct voltage threshold value controlled when mutually switching, I _dc3Hfor determining direct current threshold value when active power controller current conversion station is cut into rectification current-limit mode by normal operation mode, I _dc3Lfor determining direct current threshold value when active power controller current conversion station is cut into inversion current-limit mode by normal operation mode;

Work as U _dc3L≤ U _dc3< U _dc3Htime, determining active power controller current conversion station and run on normal operating condition, is active power controller pattern;

Work as U _dc3>=U _dc3Htime, determining active power controller current conversion station is inversion decline control model;

Work as U _dc3< U _dc3Ltime, determining active power controller current conversion station is rectification decline control model;

Work as I _dc3>=I _dc3Htime, determining active power controller current conversion station is rectification current-limit mode;

Work as I _dc3≤ I _dc3Ltime, determining active power controller current conversion station is inversion current-limit mode.

6. a kind of voltage source converter type multi-terminal direct current transmission system steady operation point optimization method as claimed in claim 1, it is characterized in that, in described step (2), the direct voltage-current characteristics equation of wind energy turbine set current conversion station is:

$\left\{\begin{array}{c}{I}_{dc4}=\frac{\left(1-{\mathrm{\&lambda;}}_4\right){\mathrm{\&alpha;\&beta;P}}_{4N}}{U_{dc4}},I_{dc4}\&GreaterEqual;I_{dc4H}\\ I_{dc4}=\frac{f_4-f_{4N}+k_{f4}{P}_{wf4N}}{k_{f4}{U}_{dc4}},U_{dc4}<U_{dc4H},I_{dc4h}\&le;I_{dc4}<I_{dc4H}\\ I_{dc4}=k_{droop4}\left(U_{dc4}-U_{dc4H}\right)+I_{dc4H},U_{dc4}\&GreaterEqual;U_{dc4H}\end{array}\right.$

Wherein, I _dc4be the direct current of the first wind energy turbine set current conversion station, U _dc4be the direct voltage of the first wind energy turbine set current conversion station, P _4Nfor the power-handling capability of wind energy turbine set current conversion station, assuming that meritorious current limitation value is α times of flow restricter threshold value, β is the Overflow RateHT of alternating current, f ₄for the real-time frequency of wind energy turbine set current conversion station AC network, f _4Nfor the rated frequency of wind energy turbine set current conversion station AC network, k _f4for the Slope Parameters of wind energy turbine set current conversion station active power and frequency control device, P _wf4Nfor the specified active power value of wind energy turbine set current conversion station, k _droop4for the Slope Parameters of wind energy turbine set current conversion station voltage drop controller, λ ₄for wind energy turbine set current conversion station ac grid voltage falls degree, I _dc4Hfor normal operation mode is cut into the direct current threshold value of rectification current-limit mode, I _dc4hfor direct voltage under normal control mode is U _dc4Htime corresponding DC current values;

Work as U _dc4< U _dc4H, I _dc4h≤ I _dc4< I _dc4Htime, wind energy turbine set current conversion station is in normal operating condition, is active power and frequency control pattern; Work as I _dc4>=I _dc4Htime, wind energy turbine set current conversion station is rectification current-limit mode; Work as U _dc4>=U _dc4Htime, wind energy turbine set current conversion station is voltage drop control model.

7. a kind of voltage source converter type multi-terminal direct current transmission system steady operation point optimization method as claimed in claim 1, is characterized in that, judges all solution I of characteristic equation group in described step (5) _dciand U _dcidetailed process whether in normal range (NR) is:

1) all solution I of characteristic equation group are judged _dciwhether in normal range (NR), if so, go to step 3); Go to if not and go to step 2);

2) make i=1, judge I _dciwhether in normal range (NR), if not, revise the control model of corresponding current conversion station; If so, make i=i+1, judge I _dciwhether in normal range (NR), repeat said process, until all solution I of characteristic equation group _dciall judge complete, enter step 3);

3) all solution U of characteristic equation group are judged _dciwhether in normal range (NR), if so, go to step 5); If not, 4 are gone to step);

4) make i=3, judge U _dciwhether in normal range (NR), if not, revise the control model of corresponding current conversion station; If so, make i=i+1, judge U _dciwhether in normal range (NR), repeat said process, until all solution U of characteristic equation group _dciall judge complete;

5) judge to terminate.

8. a kind of voltage source converter type multi-terminal direct current transmission system steady operation point optimization method as claimed in claim 1, it is characterized in that, when the DC current values of multiple current conversion station and DC voltage value exceed the range of operation of corresponding control model simultaneously, according to the correction based on DC current values, the correction based on DC voltage value and leading station, auxiliary station, determine the order priority of active power controller current conversion station, wind energy turbine set current conversion station, revise current conversion station control model successively according to the height of priority orders.

9. a kind of voltage source converter type multi-terminal direct current transmission system steady operation point optimization method as claimed in claim 1, it is characterized in that, if when certain current conversion station is in shut down condition, then during initial calculation, the control model of this current conversion station is set to and determines active power controller, and active power command value is set to 0, and then solving system equation.