CN104362642A - Dynamic reactive reserved optimizing method for improving long-term voltage stabilization in AC/DC (Alternating Current/Direct Current) power grid - Google Patents

Abstract

The invention provides a dynamic reactive reserved optimizing method for improving the long-term voltage stabilization in an AC/DC (Alternating Current/Direct Current) power grid. The method comprises the steps below: determining a key failure integration for affecting the long-term voltage stabilization in the AC/DC power grid; adjusting reactive power output of dynamic reactive compensation equipment, and calculating the flexibility of the dynamic reactive compensation equipment; ordering m dynamic reactive compensation equipments, and calculating the weighting coefficients of the dynamic reactive compensation equipments; calculating the reserved capacity of the dynamic reactive compensation equipments, and building and resolving a dynamic reactive reserved optimization model. According to the method provided by the invention, the auxiliary decision support can be provided to improve the long-term voltage stabilization level in a multi DC droppoint power grid; furthermore, the dynamic reactive reserved optimizing method has significance on the improvement on the long-term voltage stabilization allowance in the AC/DC power grid, the construction of the smooth power transmission channels between a transmission end and a receiving end, the improvement on the delivery capacity of a DC power transmission channel, and the improvement on the economy and power quality of the operation of the power grid.

Description

Improve the dynamic reactive optimization method for subsequent use of the medium-term and long-term voltage stabilization of alternating current-direct current electrical network

Technical field

The invention belongs to technical field of power systems, be specifically related to a kind of dynamic reactive optimization method for subsequent use improving the medium-term and long-term voltage stabilization of alternating current-direct current electrical network.

Background technology

Since Voltage-stabilizing Problems is paid attention to by Chinese scholars, develop into multiple research branch, clear and definite reasonably definition be there has also been to voltage stabilization, through studying effort for many years, electric power scholars achieve great successes in some field of Voltage-stabilizing Problems, as in the Small disturbance voltage stability in static voltage stability analysis, Dynamic voltage stability and Transient stability analysis, all define a set of comparatively perfect research theory and analytical method, in power system dispatching operation and Monitoring and Controlling etc., all play irreplaceable effect.But the research of current domestic centering long-term voltage stability problem is still not deep enough, do not have to form comparatively unified understanding, people's centering long term voltage stability mechanism and process can not carry out analysis rigorous in detail, therefore, study medium-term and long-term Voltage-stabilizing Problems and have very important theory significance.

After electric power system suffers large disturbances, because the pressure sensitive of load temporarily may keep voltage stabilization, but all there is slow motion state course of action in the element much affecting voltage stability in electric power system, along with the changing-over of on-load transformer tap changer, and the element power with load restoration characteristic is recovered, after a longer time course, still there is the possibility that voltage collapse occurs in system, Here it is medium-term and long-term Voltage-stabilizing Problems, time domain scale that medium-term and long-term Voltage Stability Analysis is studied is a few minutes even dozens of minutes.Load restoration characteristic centering long term voltage stability has extreme influence, and the element with recovery characteristics mainly contains induction motor and constant temperature load, and on-load transformer tap changer changing-over is the major reason causing load restoration simultaneously.Because the responsive time constant of above-mentioned 3 kinds of dynamic elements is different in size, thus form the medium-term and long-term Voltage Instability process of fast and slow dynamics combination.

Current, lacking effective, quick, adaptable Voltage Stability Control method is also one of major reason causing large-scale blackout.Although there is not the large-scale blackout caused by Voltage-stabilizing Problems in China, but along with the formation of " transferring electricity from the west to the east; north and south supplies mutually " power system interconnection general layout, load center level constantly increases, Large Copacity long distance power transmission constantly increases, the voltage stabilization sex chromosome mosaicism of China's electric power system becomes increasingly conspicuous, and the probability that Voltage Instability accident occurs is also increasing.Because Voltage-stabilizing Problems has disguised and sudden, be difficult to during accident discover, once there is voltage collapse, under China's current electric grid actual conditions, extremely huge loss certainly will be caused.Therefore, research improves the dynamic reactive optimization problem for subsequent use of medium-term and long-term voltage stabilization, effectively prevents Voltage Instability and voltage collapse accident from occurring, has important theory value and practical significance.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the invention provides a kind of dynamic reactive optimization method for subsequent use improving the medium-term and long-term voltage stabilization of alternating current-direct current electrical network, aid decision support is provided for improving the medium-term and long-term Voltage Stability Level of multi-feed HVDC electrical network, to the medium-term and long-term voltage stability margin of the extensive alternating current-direct current electrical network of raising, set up give, power transm ission corridor unimpeded between receiving end, promote AC-HVDC passage conveying capacity, improve economy and the quality of power supply of operation of power networks, be all significant.

In order to realize foregoing invention object, the present invention takes following technical scheme:

The invention provides a kind of dynamic reactive optimization method for subsequent use improving the medium-term and long-term voltage stabilization of alternating current-direct current electrical network, said method comprising the steps of:

Step 1: determine the critical failure set affecting the medium-term and long-term voltage stabilization of alternating current-direct current electrical network;

Step 2: idle the exerting oneself of adjustment dynamic passive compensation equipment, and calculate the sensitivity of dynamic passive compensation equipment;

Step 3: m dynamic passive compensation equipment is sorted, and calculates the weight coefficient of dynamic passive compensation equipment;

Step 4: calculate dynamic passive compensation equipment sparing capacity, set up dynamic reactive Optimized model for subsequent use, and solve this dynamic reactive Optimized model for subsequent use.

In described step 1, fault scanning is carried out to alternating current-direct current electrical network, the voltage stability margin K of calculated load bus i _mVSi, have:

$K_{\mathrm{MVSi}}=\frac{\left|Z_{\mathrm{Li}}\right|-\left|Z_{\mathrm{Ti}}\right|}{\left|Z_{\mathrm{Li}}\right|}$

Wherein, Z _lifor the load equivalent impedance at load bus i place, Z _tifor the impedance of system Thevenin's equivalence;

Choose K _mVSiminimum value is the voltage stability margin of alternating current-direct current electrical network, is designated as K _mVSI, according to the serious conditions of the voltage stability margin value determination fault of alternating current-direct current electrical network, obtain critical failure, thus obtain critical failure set.

In described step 2, dynamic passive compensation equipment comprises generator, Static Var Compensator and STATCOM.

Described step 2 specifically comprises the following steps:

Step 2-1: adjust each the idle of dynamic passive compensation equipment respectively and exert oneself, and again time-domain-simulation is carried out to critical failure;

Step 2-2: under long-term time scale, for certain fault l, calculate the sensitivity S I of dynamic passive compensation equipment j _l,j;

Step 2-3: under long-term time scale, for multiple fault, calculate the sensitivity S I of dynamic passive compensation equipment j _j.

In described step 2-2, for certain fault l, the sensitivity S I of dynamic passive compensation equipment j _l,jbe expressed as:

${\mathrm{SI}}_{l,j}=\frac{k_{\mathrm{MVSI},l}(Q_{j0}+{\mathrm{\ΔQ}}_j)-k_{\mathrm{MVSI},l}\left(Q_{j0}\right)}{{\mathrm{\ΔQ}}_{\mathrm{Rj}}}$

Wherein, Q _j0for the initially idle of dynamic passive compensation equipment j is exerted oneself; Δ Q _jfor the reactive power variable quantity of adjustment dynamic passive compensation equipment j; Δ Q _rjfor the Reactive Power Reserve variable quantity of adjustment dynamic passive compensation equipment j; k _{mVSI, l}(Q _j0+ Δ Q _j) for after adjustment dynamic passive compensation equipment j idle exert oneself, at fault F _lunder, the load margin value of alternating current-direct current electrical network; k _{mVSI, l}(Q _j0) for before adjustment dynamic passive compensation equipment j idle exert oneself, at fault F _lunder, the load margin value of alternating current-direct current electrical network.

In described step 2-3, for multiple fault, the sensitivity S I of dynamic passive compensation equipment j _jbe expressed as:

${\mathrm{SI}}_j=\underset{l=1}{\overset{N_l}{\mathrm{\Σ}}}{\mathrm{SI}}_{l,j}$

Wherein, N _lfor critical failure sum.

Described step 3 specifically comprises the following steps:

Step 3-1: according to SI _jm dynamic passive compensation equipment is sorted, SI _jthe percentage contribution that maximum characterizes this dynamic passive compensation equipment centering long-term voltage stability is maximum, and the dynamic passive compensation equipment that percentage contribution is large reserves more Reactive Power Reserve amounts;

Step 3-2: with SI _jmaximum SI _maxfor benchmark, normalized SI _j, calculate the weight coefficient p of dynamic passive compensation equipment _j, have p _j=SI _j/ | SI _max|.

Described step 4 specifically comprises the following steps:

Step 4-1: the reserve capacity Q calculating dynamic passive compensation equipment _rM;

Step 4-2: to improve Q _rMas dynamic reactive optimization aim for subsequent use, set up dynamic reactive Optimized model for subsequent use;

Step 4-3: adopt this dynamic reactive of genetic algorithm for solving Optimized model for subsequent use.

In described step 4-1, the reserve capacity Q of dynamic passive compensation equipment _rMbe expressed as:

$Q_{\mathrm{RM}}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{p}_j(Q_{\mathrm{gj}\max }-Q_{\mathrm{gj}})$

Wherein, Q _gjmaxfor the idle upper limit of exerting oneself of dynamic passive compensation equipment j in medium-term and long-term voltage stabilization, Q _gjfor the current idle of dynamic passive compensation equipment j is exerted oneself.

In described step 4-2, the target function of dynamic reactive Optimized model for subsequent use is:

$\max Q_{\mathrm{RM}}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{p}_j(Q_{\mathrm{gj}\max }-Q_{\mathrm{gj}})$

The constraints of dynamic reactive Optimized model for subsequent use comprises power flow equation constraint and variable bound; Described variable bound is control variables constraint and state variable constrain;

(1) power flow equation constraint:

In dynamic reactive Optimized model for subsequent use, each node meritorious is exerted oneself and idle exerting oneself all meets following power flow equation, has:

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-P_{\mathrm{Li}}-P_{\mathrm{ti}\left(\mathrm{dc}\right)}-V_i\underset{r=1}{\overset{n}{\mathrm{\Σ}}}{V}_r(G_{\mathrm{ir}}\cos {\mathrm{\δ}}_{\mathrm{ir}}+B_{\mathrm{ir}}\sin {\mathrm{\δ}}_{\mathrm{ir}})=0\\ Q_{\mathrm{Gi}}+Q_{\mathrm{Ci}}-Q_{\mathrm{Li}}-Q_{\mathrm{ti}\left(\mathrm{dc}\right)}-V_i\underset{r=1}{\overset{n}{\mathrm{\Σ}}}{V}_r(G_{\mathrm{ir}}\sin {\mathrm{\δ}}_{\mathrm{ir}}-B_{\mathrm{ir}}\cos {\mathrm{\δ}}_{\mathrm{ir}})=0\end{array}\right.$

Wherein, P _giand Q _giwhat be respectively generators in power systems node meritoriously exerts oneself and idlely to exert oneself; P _liand Q _liwhat be respectively load bus meritoriously exerts oneself and idlely to exert oneself; Q _cifor the reactive compensation capacity of node; G _irand B _irbe respectively the conductance between node i, r and susceptance; V _iand V _rbe respectively the voltage of node i, r; δ _irfor the phase difference of voltage between node i, r; N is node total number; P _{ti (dc)}and Q _{ti (dc)}be respectively the meritorious input of DC node and idle input, be divided into following two kinds of situations:

1) node i is on rectification side change of current bus, P _{ti (dc)}and Q _{ti (dc)}be expressed as:

$\left\{\begin{array}{c}{P}_{\mathrm{ti}\left(\mathrm{dc}\right)}=k_p{U}_{\mathrm{dR}}{I}_d\\ Q_{\mathrm{ti}\left(\mathrm{dc}\right)}=k_p{I}_d\sqrt{{\left(\frac{3\sqrt{2}}{{\mathrm{\πK}}_{\mathrm{dR}}}{\mathrm{bV}}_R\right)}^2-U_{\mathrm{dR}}^2}\end{array}\right.$

Wherein, k _pfor the number of poles of converter; U _dRfor rectification side direct voltage; I _dfor DC line electric current; K _dRfor rectification side converter transformer no-load voltage ratio; B is 6 pulse wave cascaded bridges numbers of every pole; V _rfor the ac bus voltage magnitude of rectification side;

2) node i is on inverter side change of current bus, P _{ti (dc)}and Q _{ti (dc)}be expressed as:

$\left\{\begin{array}{c}{P}_{\mathrm{ti}\left(\mathrm{dc}\right)}=-k_p{U}_{\mathrm{dI}}{I}_d\\ Q_{\mathrm{ti}\left(\mathrm{dc}\right)}=k_p{I}_d\sqrt{{\left(\frac{3\sqrt{2}}{{\mathrm{\πK}}_{\mathrm{dI}}}{\mathrm{bV}}_I\right)}^2-U_{\mathrm{dI}}^2}\end{array}\right.$

Wherein, U _dIfor inverter side direct voltage; K _dIfor inverter side converter transformer no-load voltage ratio; V _ifor the ac bus voltage magnitude of inverter side;

(2) control variables constraint:

$\left\{\begin{array}{c}{V}_{\mathrm{Gi}\min }\≤V_{\mathrm{Gi}}\≤V_{\mathrm{Gi}\max },i=\mathrm{1,2},...,N_G\\ V_{\mathrm{SVCg}\min }\≤V_{\mathrm{SVCg}}\≤V_{\mathrm{SVCg}\max },g=\mathrm{1,2},...,N_{\mathrm{SVC}}\\ V_{\mathrm{SVGh}\min }\≤V_{\mathrm{SVGh}}\≤V_{\mathrm{SVGh}\max },h=\mathrm{1,2},...,N_{\mathrm{SVG}}\\ Q_{\mathrm{Cu}\min }\≤Q_{\mathrm{Cu}}\≤Q_{\mathrm{Cu}\max },u=\mathrm{1,2},...,N_C\\ T_{k\min }\≤T_k\≤T_{k\max },k=\mathrm{1,2},...,N_T\\ U_{\mathrm{dl}\min }\≤U_{\mathrm{dl}}\≤U_{\mathrm{dl}\max },l=\mathrm{1,2},...,N_{\mathrm{dc}}\\ I_{\mathrm{dm}\min }\≤I_{\mathrm{dm}}\≤I_{\mathrm{dm}\max },m=\mathrm{1,2},...,N_{\mathrm{dc}}\\ P_{\mathrm{dn}\min }\≤P_{\mathrm{dn}}\≤P_{\mathrm{dn}\max },n=\mathrm{1,2},...,N_{\mathrm{dc}}\\ {\mathrm{\θ}}_{\mathrm{dr}\min }\≤{\mathrm{\θ}}_{\mathrm{dr}}\≤{\mathrm{\θ}}_{\mathrm{dr}\max },r=\mathrm{1,2},...,N_{\mathrm{dc}}\end{array}\right.$

Wherein, N _g, N _sVC, N _sVG, N _c, N _tand N _dcbe respectively generator nodes, Static Var Compensator nodes, STATCOM nodes, shunt capacitor nodes, transformer application of adjustable tap number and DC network nodes; V _gifor the terminal voltage of generator node, V _giminand V _gimaxbe respectively V _gilower limit and higher limit; V _sVCgfor the terminal voltage of Static Var Compensator node, V _sVCgminand V _sVCgmaxbe respectively V _sVCglower limit and higher limit; V _sVGhfor the terminal voltage of STATCOM node, V _sVGhminand V _sVGhmaxbe respectively V _sVGhlower limit and higher limit; Q _cufor the compensation capacity of Shunt Capacitor Unit, Q _cuminand Q _cumaxbe respectively Q _culower limit and higher limit; T _kfor transformer application of adjustable tap, T _kminand T _kmaxbe respectively T _klower limit and higher limit; U _dl, I _dm, P _dnand θ _drbe respectively converter control voltage, control electric current, control power and pilot angle, U _dlminand U _dlmax, I _dmminand I _dmmax, P _dnminand P _dnmax, θ _drminand θ _drmaxrepresent corresponding lower limit and higher limit respectively;

(3) state variable constrain:

$\left\{\begin{array}{c}{Q}_{\mathrm{Gi}\min }\≤Q_{\mathrm{Gi}}\≤Q_{\mathrm{Gi}\max },i=\mathrm{1,2},...,N_G\\ B_{\mathrm{SVCg}\min }\≤B_{\mathrm{SVCg}}\≤B_{\mathrm{SVCg}\max },g=\mathrm{1,2},...,N_{\mathrm{SVC}}\\ I_{\mathrm{SVGh}\min }\≤I_{\mathrm{SVGh}}\≤I_{\mathrm{SVGh}\max },h=\mathrm{1,2},...,N_{\mathrm{SVG}}\\ V_{\mathrm{Lp}\min }\≤V_{\mathrm{Lp}}\≤V_{\mathrm{Lp}\max },p=\mathrm{1,2},...,N_L\end{array}\right.$

Wherein, N _lfor load bus number; Q _giexert oneself for generator node is idle, Q _giminand Q _gimaxbe respectively Q _gilower limit and higher limit; B _sVCgfor Static Var Compensator susceptance, B _sVCgminand B _sVCgmaxbe respectively B _sVCglower limit and higher limit; I _sVGhfor STATCOM current amplitude, I _sVGhminand I _sVGhmaxbe respectively I _sVGhlower limit and higher limit; V _lpfor load bus voltage magnitude, V _lpminand V _lpmaxbe respectively V _lplower limit and higher limit.

Compared with prior art, beneficial effect of the present invention is:

1. there is no the dynamic reactive optimisation technique for subsequent use of the medium-term and long-term voltage stabilization of raising being applicable to multi-infeed HVDC electrical network feature at present, the present invention proposes innovatively and is a kind ofly applicable to the dynamic reactive optimization method for subsequent use that multi-infeed HVDC electrical network feature improves medium-term and long-term voltage stabilization;

2. compared with the traditional Reactive Power Reserve optimization method based on static state, this method considers the dynamic characteristic of system in detail, can determine dynamic passive compensation equipment sparing capacity more exactly, and the optimizing operation for electrical network provides basis;

3. analyzed by time-domain-simulation, the participation factors of each reactive source can be determined quick and easy, exactly, can be applicable to the dynamic reactive optimization for subsequent use of large-scale electrical power system, the algorithm overcoming the optimization of conventional electric power system dynamic reactive-load can only be applied to the shortcoming of mini system.

Accompanying drawing explanation

Fig. 1 is the dynamic reactive optimization method flow chart for subsequent use improving the medium-term and long-term voltage stabilization of alternating current-direct current electrical network in the embodiment of the present invention;

Fig. 2 adopts genetic algorithm for solving dynamic reactive Optimized model flow chart for subsequent use in the embodiment of the present invention;

Fig. 3 is 3 machine 10 node regulation test ac and dc systems schematic diagrames in the invention process;

Fig. 4 is generator relative merit angle change curve in the embodiment of the present invention;

Fig. 5 is the magnetizing current curve figure of generator 2 and generator 3 in the embodiment of the present invention;

Fig. 6 is embodiment of the present invention interior joint 9 and node 10 voltage change curve figure;

Fig. 7 is node 3 (generator G3 machine end) voltage curve before and after optimizing in the embodiment of the present invention;

Fig. 8 is node 10 voltage curve before and after optimizing in the embodiment of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

The invention provides a kind of dynamic reactive optimization method for subsequent use improving the medium-term and long-term voltage stabilization of alternating current-direct current electrical network, said method comprising the steps of:

Step 1: determine the critical failure set affecting the medium-term and long-term voltage stabilization of alternating current-direct current electrical network;

Step 2: idle the exerting oneself of adjustment dynamic passive compensation equipment, and calculate the sensitivity of dynamic passive compensation equipment;

Step 3: m dynamic passive compensation equipment is sorted, and calculates the weight coefficient of dynamic passive compensation equipment;

Step 4: calculate dynamic passive compensation equipment sparing capacity, set up dynamic reactive Optimized model for subsequent use, and solve this dynamic reactive Optimized model for subsequent use.

In described step 1, fault scanning is carried out to alternating current-direct current electrical network, the voltage stability margin K of calculated load bus i _mVSi, have:

$K_{\mathrm{MVSi}}=\frac{\left|Z_{\mathrm{Li}}\right|-\left|Z_{\mathrm{Ti}}\right|}{\left|Z_{\mathrm{Li}}\right|}---\left(1\right)$

Wherein, Z _lifor the load equivalent impedance at load bus i place, Z _tifor the impedance of system Thevenin's equivalence;

Choose K _mVSiminimum value is the voltage stability margin of alternating current-direct current electrical network, is designated as K _mVSI, according to the serious conditions of the voltage stability margin value determination fault of alternating current-direct current electrical network, obtain critical failure, thus obtain critical failure set.

In described step 2, dynamic passive compensation equipment comprises generator, Static Var Compensator and STATCOM.

Described step 2 specifically comprises the following steps:

Step 2-1: adjust each the idle of dynamic passive compensation equipment respectively and exert oneself, and again time-domain-simulation is carried out to critical failure;

Step 2-2: under long-term time scale, for certain fault l, calculate the sensitivity S I of dynamic passive compensation equipment j _l,j;

Step 2-3: under long-term time scale, for multiple fault, calculate the sensitivity S I of dynamic passive compensation equipment j _j.

In described step 2-2, for certain fault l, the sensitivity S I of dynamic passive compensation equipment j _l,jbe expressed as:

${\mathrm{SI}}_{l,j}=\frac{k_{\mathrm{MVSI},l}(Q_{j0}+{\mathrm{\ΔQ}}_j)-k_{\mathrm{MVSI},l}\left(Q_{j0}\right)}{{\mathrm{\ΔQ}}_{\mathrm{Rj}}}---\left(2\right)$

Wherein, Q _j0for the initially idle of dynamic passive compensation equipment j is exerted oneself; Δ Q _jfor the reactive power variable quantity of adjustment dynamic passive compensation equipment j; Δ Q _rjfor the Reactive Power Reserve variable quantity of adjustment dynamic passive compensation equipment j; k _{mVSI, l}(Q _j0+ Δ Q _j) for after adjustment dynamic passive compensation equipment j idle exert oneself, at fault F _lunder, the load margin value of alternating current-direct current electrical network; k _{mVSI, l}(Q _j0) for before adjustment dynamic passive compensation equipment j idle exert oneself, at fault F _lunder, the load margin value of alternating current-direct current electrical network.

In described step 2-3, for multiple fault, the sensitivity S I of dynamic passive compensation equipment j _jbe expressed as:

${\mathrm{SI}}_j=\underset{l=1}{\overset{N_l}{\mathrm{\Σ}}}{\mathrm{SI}}_{l,j}---\left(3\right)$

Wherein, N _lfor critical failure sum.

Described step 3 specifically comprises the following steps:

Step 3-1: according to SI _jm dynamic passive compensation equipment is sorted, SI _jthe percentage contribution that maximum characterizes this dynamic passive compensation equipment centering long-term voltage stability is maximum, and the dynamic passive compensation equipment that percentage contribution is large reserves more Reactive Power Reserve amounts;

Step 3-2: with SI _jmaximum SI _maxfor benchmark, normalized SI _j, calculate the weight coefficient p of dynamic passive compensation equipment _j, have p _j=SI _j/ | SI _max|.

Described step 4 specifically comprises the following steps:

Step 4-1: the reserve capacity Q calculating dynamic passive compensation equipment _rM;

Step 4-2: to improve Q _rMas dynamic reactive optimization aim for subsequent use, set up dynamic reactive Optimized model for subsequent use;

Step 4-3: adopt this dynamic reactive of genetic algorithm for solving Optimized model for subsequent use.

In described step 4-1, the reserve capacity Q of dynamic passive compensation equipment _rMbe expressed as:

$Q_{\mathrm{RM}}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{p}_j(Q_{\mathrm{gj}\max }-Q_{\mathrm{gj}})---\left(4\right)$

Wherein, Q _gjmaxfor the idle upper limit of exerting oneself of dynamic passive compensation equipment j in medium-term and long-term voltage stabilization, Q _gjfor the current idle of dynamic passive compensation equipment j is exerted oneself.

In described step 4-2, the target function of dynamic reactive Optimized model for subsequent use is:

$\max Q_{\mathrm{RM}}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{p}_j(Q_{\mathrm{gj}\max }-Q_{\mathrm{gj}})---\left(5\right)$

The constraints of dynamic reactive Optimized model for subsequent use comprises power flow equation constraint and variable bound; Described variable bound is control variables constraint and state variable constrain;

(1) power flow equation constraint:

In dynamic reactive Optimized model for subsequent use, each node meritorious is exerted oneself and idle exerting oneself all meets following power flow equation, has:

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-P_{\mathrm{Li}}-P_{\mathrm{ti}\left(\mathrm{dc}\right)}-V_i\underset{r=1}{\overset{n}{\mathrm{\Σ}}}{V}_r(G_{\mathrm{ir}}\cos {\mathrm{\δ}}_{\mathrm{ir}}+B_{\mathrm{ir}}\sin {\mathrm{\δ}}_{\mathrm{ir}})=0\\ Q_{\mathrm{Gi}}+Q_{\mathrm{Ci}}-Q_{\mathrm{Li}}-Q_{\mathrm{ti}\left(\mathrm{dc}\right)}-V_i\underset{r=1}{\overset{n}{\mathrm{\Σ}}}{V}_r(G_{\mathrm{ir}}\sin {\mathrm{\δ}}_{\mathrm{ir}}-B_{\mathrm{ir}}\cos {\mathrm{\δ}}_{\mathrm{ir}})=0\end{array}\right.---\left(6\right)$

Wherein, P _giand Q _giwhat be respectively generators in power systems node meritoriously exerts oneself and idlely to exert oneself; P _liand Q _liwhat be respectively load bus meritoriously exerts oneself and idlely to exert oneself; Q _cifor the reactive compensation capacity of node; G _irand B _irbe respectively the conductance between node i, r and susceptance; V _iand V _rbe respectively the voltage of node i, r; δ _irfor the phase difference of voltage between node i, r; N is node total number; P _{ti (dc)}and Q _{ti (dc)}be respectively the meritorious input of DC node and idle input, be divided into following two kinds of situations:

1) node i is on rectification side change of current bus, P _{ti (dc)}and Q _{ti (dc)}be expressed as:

$\left\{\begin{array}{c}{P}_{\mathrm{ti}\left(\mathrm{dc}\right)}=k_p{U}_{\mathrm{dR}}{I}_d\\ Q_{\mathrm{ti}\left(\mathrm{dc}\right)}=k_p{I}_d\sqrt{{\left(\frac{3\sqrt{2}}{{\mathrm{\πK}}_{\mathrm{dR}}}{\mathrm{bV}}_R\right)}^2-U_{\mathrm{dR}}^2}\end{array}\right.---\left(7\right)$

Wherein, k _pfor the number of poles of converter; U _dRfor rectification side direct voltage; I _dfor DC line electric current; K _dRfor rectification side converter transformer no-load voltage ratio; B is 6 pulse wave cascaded bridges numbers of every pole; V _rfor the ac bus voltage magnitude of rectification side;

2) node i is on inverter side change of current bus, P _{ti (dc)}and Q _{ti (dc)}be expressed as:

$\left\{\begin{array}{c}{P}_{\mathrm{ti}\left(\mathrm{dc}\right)}=-k_p{U}_{\mathrm{dI}}{I}_d\\ Q_{\mathrm{ti}\left(\mathrm{dc}\right)}=k_p{I}_d\sqrt{{\left(\frac{3\sqrt{2}}{{\mathrm{\πK}}_{\mathrm{dI}}}{\mathrm{bV}}_I\right)}^2-U_{\mathrm{dI}}^2}\end{array}\right.---\left(8\right)$

Wherein, U _dIfor inverter side direct voltage; K _dIfor inverter side converter transformer no-load voltage ratio; V _ifor the ac bus voltage magnitude of inverter side;

(2) control variables constraint:

$\left\{\begin{array}{c}{V}_{\mathrm{Gi}\min }\≤V_{\mathrm{Gi}}\≤V_{\mathrm{Gi}\max },i=\mathrm{1,2},...,N_G\\ V_{\mathrm{SVCg}\min }\≤V_{\mathrm{SVCg}}\≤V_{\mathrm{SVCg}\max },g=\mathrm{1,2},...,N_{\mathrm{SVC}}\\ V_{\mathrm{SVGh}\min }\≤V_{\mathrm{SVGh}}\≤V_{\mathrm{SVGh}\max },h=\mathrm{1,2},...,N_{\mathrm{SVG}}\\ Q_{\mathrm{Cu}\min }\≤Q_{\mathrm{Cu}}\≤Q_{\mathrm{Cu}\max },u=\mathrm{1,2},...,N_C\\ T_{k\min }\≤T_k\≤T_{k\max },k=\mathrm{1,2},...,N_T\\ U_{\mathrm{dl}\min }\≤U_{\mathrm{dl}}\≤U_{\mathrm{dl}\max },l=\mathrm{1,2},...,N_{\mathrm{dc}}\\ I_{\mathrm{dm}\min }\≤I_{\mathrm{dm}}\≤I_{\mathrm{dm}\max },m=\mathrm{1,2},...,N_{\mathrm{dc}}\\ P_{\mathrm{dn}\min }\≤P_{\mathrm{dn}}\≤P_{\mathrm{dn}\max },n=\mathrm{1,2},...,N_{\mathrm{dc}}\\ {\mathrm{\θ}}_{\mathrm{dr}\min }\≤{\mathrm{\θ}}_{\mathrm{dr}}\≤{\mathrm{\θ}}_{\mathrm{dr}\max },r=\mathrm{1,2},...,N_{\mathrm{dc}}\end{array}\right.---\left(9\right)$

Wherein, N _g, N _sVC, N _sVG, N _c, N _tand N _dcbe respectively generator nodes, Static Var Compensator nodes, STATCOM nodes, shunt capacitor nodes, transformer application of adjustable tap number and DC network nodes; V _gifor the terminal voltage of generator node, V _giminand V _gimaxbe respectively V _gilower limit and higher limit; V _sVCgfor the terminal voltage of Static Var Compensator node, V _sVCgminand V _sVCgmaxbe respectively V _sVCglower limit and higher limit; V _sVGhfor the terminal voltage of STATCOM node, V _sVGhminand V _sVGhmaxbe respectively V _sVGhlower limit and higher limit; Q _cufor the compensation capacity of Shunt Capacitor Unit, Q _cuminand Q _cumaxbe respectively Q _culower limit and higher limit; T _kfor the no-load voltage ratio of transformer, T _kminand T _kmaxbe respectively T _klower limit and higher limit; U _dl, I _dm, P _dnand θ _drbe respectively converter control voltage, control electric current, control power and pilot angle, U _dlminand U _dlmax, I _dmminand I _dmmax, P _dnminand P _dnmax, θ _drminand θ _drmaxrepresent corresponding lower limit and higher limit respectively;

(3) state variable constrain:

$\left\{\begin{array}{c}{Q}_{\mathrm{Gi}\min }\≤Q_{\mathrm{Gi}}\≤Q_{\mathrm{Gi}\max },i=\mathrm{1,2},...,N_G\\ B_{\mathrm{SVCg}\min }\≤B_{\mathrm{SVCg}}\≤B_{\mathrm{SVCg}\max },g=\mathrm{1,2},...,N_{\mathrm{SVC}}\\ I_{\mathrm{SVGh}\min }\≤I_{\mathrm{SVGh}}\≤I_{\mathrm{SVGh}\max },h=\mathrm{1,2},...,N_{\mathrm{SVG}}\\ V_{\mathrm{Lp}\min }\≤V_{\mathrm{Lp}}\≤V_{\mathrm{Lp}\max },p=\mathrm{1,2},...,N_L\end{array}\right.---\left(10\right)$

Wherein, N _lfor load bus number; Q _giexert oneself for generator node is idle, Q _giminand Q _gimaxbe respectively Q _gilower limit and higher limit; B _sVCgfor Static Var Compensator susceptance, B _sVCgminand B _sVCgmaxbe respectively B _sVCglower limit and higher limit; I _sVGhfor STATCOM current amplitude, I _sVGhminand I _sVGhmaxbe respectively I _sVGhlower limit and higher limit; V _lpfor load bus voltage magnitude, V _lpminand V _lpmaxbe respectively V _lplower limit and higher limit.

In step 4-3, adopt this dynamic reactive of genetic algorithm for solving Optimized model for subsequent use;

The basic thought of genetic algorithm is, a group under certain specific environment is individual, and due to environmental limitations, only have and adaptablely to survive, and weak person is eliminated, the merit that they conform can entail offspring.GA can be understood as when being applied to Reactive Power Reserve optimization problem: one group under electric power system initial trend solution, retrain by various constraints, its quality is evaluated by target function, low being abandoned of evaluation of estimate, only have evaluation of estimate high to have an opportunity its feature iteration to next round solution, finally tend to optimum.

Detailed process is as follows:

(1) first, produce first generation parent at random according to following formula, have:

X _i＝INT(RND(X _imax-X _iimn))+X _imin(11)

Wherein, RND is random number, and 0<RND<1; INT (*) is for rounding;

X _iif V _gi, then X _imax, X _imaxrepresent the terminal voltage bound of generator node respectively;

X _iif V _sVCg, then X _imax, X _imaxrepresent the terminal voltage bound of Static Var Compensator node respectively;

X _iif V _sVGh, then X _imax, X _imaxrepresent the terminal voltage bound of STATCOM node respectively;

X _iif Q _cu, then X _imax, X _imaxrepresent the compensation capacity bound of Shunt Capacitor Unit respectively;

X _iif T _k, then X _imax, X _imaxthe no-load voltage ratio bound of indication transformer respectively.

Formula (11) makes the constraint equation of variable can be converted into the constraint equation of integer variable.Span as its YT of transformer of 1+5 × 0.025% is 1 ~ 11.Coding adopts binary number, and every five orders represent Y _vgi, Y _vsvcg, Y _vsvgh, Y _qcu, Y _tkvalue:

H＝[…,b _5i-4,…,b _5i,…,b _5g-4,…b _5g,…,b _5h-4,…b _5h,…,b _5u-4,…,b _5u,…,b _5k-4,…,b _5k,…] (12)

(2) decode according to formula (13) to each individuality in A, revise value corresponding in original flow data, then start Load flow calculation, what flow calculation program of the present invention adopted is N-R method;

$\left\{\begin{array}{c}{V}_{\mathrm{Gi}}=V_{\mathrm{Gi}\max }+(1+Y_{\mathrm{Vgi}}){\mathrm{\&Delta;V}}_{\mathrm{Gi}}\\ V_{\mathrm{SVCg}}=V_{\mathrm{SVCg}\max }+(1-Y_{\mathrm{Vsvcg}}){\mathrm{\&Delta;V}}_{\mathrm{SVCg}}\\ V_{\mathrm{SVGh}}=V_{\mathrm{SVGh}\max }+(1-Y_{\mathrm{Vsvgh}}){\mathrm{\&Delta;V}}_{\mathrm{SVGh}}\\ Q_{\mathrm{Cu}}=Y_{\mathrm{Qcu}}\&times;{\mathrm{\&Delta;Q}}_{\mathrm{Cu}}\\ T_k=T_{k\max }+(1-Y_{\mathrm{Tk}}){\mathrm{\&Delta;T}}_k\end{array}\right.---\left(13\right)$

In formula: Δ V _gi, Δ V _sVCg, Δ V _sVGh, Δ Q _cu, Δ T _ka grade regulon value is had to dependent variable;

Y _vgi, Y _vsvcg, Y _vsvgh, Y _qcu, Y _tkrepresent the integer variable of the control variables position of the switch;

Y _vgi=1, represent that i-th generator node side voltage is transferred to maximum;

Y _vsvcg=1, represent that g Static Var Compensator node side voltage is transferred to maximum;

Y _vsvgh=1, represent that h STATCOM node side voltage is transferred to maximum;

Y _qcu=1, represent that a jth capacitor drops into one group of capacitance;

Y _tk=1, represent that a kth load tap changer is placed in no-load voltage ratio maximum position;

(3) through Load flow calculation, the data such as the voltage of each node, idle and dynamic reactive reserve capacity are obtained, and by its descending sequence;

(4) according to adaptive value size, each individuality is sorted, retain the individuality composition groups of individuals B that affinity is large, cross and variation operation is carried out to the individuality in B, the individuality that after reservation operations, overall adaptive value is large, composition groups of individuals C simultaneously; According to adaptive value size, groups of individuals D is rearranged to B, C;

(5) check iteration termination condition, if reached, terminate, otherwise turn next step;

(6) the groups of individuals E that random generation one group is new, jointly forms iterative computation groups of individuals F of new generation with D, goes to step (2), restarts to calculate.

Embodiment

As shown in Figure 3, for 3 machine 10 node systems, 500kV bus (Bus6) is powered to two loads of load area, industrial load (Node B us7) is wherein connected with 500kV load bus by OLTC transformer, and the impedance that resident load and Commercial Load (Node B us10) then represent secondary transmission system by two OLTC transformers and a section is connected on 500kV load bus.There is the equivalent generator (Node B us3) of a 1600MVA in load area, and have employed a large amount of paralleling compensating devices, the Static Var Compensator (SVC) that capacity that node 8 is configured with respectively is ± 240Mvar and capacity are the Capacitor banks of 600Mvar, the every pool-size of this Capacitor banks is 100Mvar, totally 6 groups.The generator in two distant places by 4 500kV circuits and 1 time bipolar direct current transmission line to load area transmission power.Emulate the main models adopted: transformer (Bus9 ~ Bus10) is OLTC transformer, and other tap remains unchanged; Load on Node B us7 is invariable power model, and other load is constant-impedance model; Generator on generator 2 and 3 (Node B us2 and Bus3) has overexcitation restraint device, and generator 1 (Node B us1) is infinitely great generator.

Fault scanning is carried out to this system, determines the critical failure set of the medium-term and long-term voltage stabilization of threat system.In order to the validity of TSI index is described easily, this example only investigates the most serious N-1 fault, the permanent short trouble of three-phase is there is in alternating current interconnection when failure mode is t=0.1s between node 5 ~ node 6 in node 6 side, 0.09s tripping faulty line node 6 side switch after fault, 0.1s tripping faulty line node 5 side switch.

Fig. 4 represents generator 2, generator 3 merit angle relative between generator 1 swing curve respectively.As seen from Figure 4, the initial fast transient process that this disturbance causes can disappear very soon, shows that system can keep transient rotor angle stability, though merit angle is waved in follow-up medium-term and long-term process, but angle is all smaller, show that system also can keep medium-term and long-term angle stability.

In Fig. 5, the exciting current of overexcitation limiter indicates generator 2 and generator 3 electromotive force E _qresponse, this electromotive force is proportional to exciting current.As shown in the figure, after disturbance, the exciting current of generator 2 and generator 3 can rise suddenly, if exceeded rotor current restriction, and mechanism between the inverse time that will start overexcitation limiter.After disturbance, the operation of OLTC transformer imposes a reactive requirement weighed very much to generator.This demand is degrading rotor overload further, until final overexcitation limiter is energized, causes exciting current to get back to its rated value.Note, this overexciation limiter is integral form, to such an extent as to E _qbe forced to E _q ^lim.Tap conversion subsequently causes transient exciting current to raise, exciting current of this rising very soon detect by overexcitation limiter (maximum of points as generator in Fig. 52,3 exciting current), and to correct.

Fig. 6 gives the voltage of node 9 and node 10, high-voltage side bus 9 voltage of the OLTC namely powered to load and load side node 10 voltage.As seen from the figure, in transient process, node 9 can in the stable operation of 0.87p.u. place.OLTC transformer is by reducing no-load voltage ratio T _k, manage to recover load side node 10 voltage.After the initial time delay of 30 seconds, OLTC transducer brings into operation, about 55 seconds, after 5 tap_changings, busbar voltage rises to 0.915pu, closely level before accident, the exciting current of generator 2 and 3 exports and also increases to meet the demand (Fig. 5) of system to reactive power thereupon.But during by 347 seconds, because the overexcitation restraint device of generator 3 starts action, limit its output current, the reactive power of this machine is exported and also declines thereupon, cause the voltage of load bus 10 again to decline.For ensureing voltage, load tap changer continues action 18 times.442 seconds time, the overexcitation restraint device of generator 2 also starts action, and the reactive power breach of system increases greatly, result in the generation of voltage collapse.

After obtain each control variables of reactive power reserve optimization problem with the present invention, utilize the validity of time-domain-simulation check analysis institute extracting method.

There is the permanent short trouble of three-phase in node 6 side in an alternating current interconnection between node 5 ~ node 6,0.09s tripping faulty line node 6 side switch after fault, 0.1s tripping faulty line node 5 side switch.Fig. 7 and Fig. 8 is respectively generator G3 set end voltage and node 10 voltage curve, as can be seen from the figure, after optimizing, the medium-term and long-term voltage stability of system is than good before optimization, and this illustrates that the optimized algorithm adopting the present invention to propose effectively can improve the medium-term and long-term voltage stability of electrical network.

Finally should be noted that: above embodiment is only in order to illustrate that technical scheme of the present invention is not intended to limit; those of ordinary skill in the field still can modify to the specific embodiment of the present invention with reference to above-described embodiment or equivalent replacement; these do not depart from any amendment of spirit and scope of the invention or equivalent replacement, are all applying within the claims of the present invention awaited the reply.

Claims (10)

1. improve the dynamic reactive optimization method for subsequent use of the medium-term and long-term voltage stabilization of alternating current-direct current electrical network, it is characterized in that: said method comprising the steps of:

Step 1: determine the critical failure set affecting the medium-term and long-term voltage stabilization of alternating current-direct current electrical network;

Step 2: idle the exerting oneself of adjustment dynamic passive compensation equipment, and calculate the sensitivity of dynamic passive compensation equipment;

Step 3: m dynamic passive compensation equipment is sorted, and calculates the weight coefficient of dynamic passive compensation equipment;

Step 4: calculate dynamic passive compensation equipment sparing capacity, set up dynamic reactive Optimized model for subsequent use, and solve this dynamic reactive Optimized model for subsequent use.

2. the dynamic reactive optimization method for subsequent use of the medium-term and long-term voltage stabilization of raising alternating current-direct current electrical network according to claim 1, is characterized in that: in described step 1, carries out fault scanning to alternating current-direct current electrical network, the voltage stability margin K of calculated load bus i _mVSi, have:

$K_{\mathrm{MVSi}}=\frac{\left|Z_{\mathrm{Li}}\right|-\left|Z_{\mathrm{Ti}}\right|}{\left|Z_{\mathrm{Li}}\right|}$

Wherein, Z _lifor the load equivalent impedance at load bus i place, Z _tifor the impedance of system Thevenin's equivalence;

Choose K _mVSiminimum value is the voltage stability margin of alternating current-direct current electrical network, is designated as K _mVSI, according to the serious conditions of the voltage stability margin value determination fault of alternating current-direct current electrical network, obtain critical failure, thus obtain critical failure set.

3. the dynamic reactive optimization method for subsequent use of the medium-term and long-term voltage stabilization of raising alternating current-direct current electrical network according to claim 1, it is characterized in that: in described step 2, dynamic passive compensation equipment comprises generator, Static Var Compensator and STATCOM.

4. the dynamic reactive optimization method for subsequent use of the medium-term and long-term voltage stabilization of raising alternating current-direct current electrical network according to claim 1, is characterized in that: described step 2 specifically comprises the following steps:

Step 2-1: adjust each the idle of dynamic passive compensation equipment respectively and exert oneself, and again time-domain-simulation is carried out to critical failure;

Step 2-2: under long-term time scale, for certain fault l, calculate the sensitivity S I of dynamic passive compensation equipment j _l,j;

Step 2-3: under long-term time scale, for multiple fault, calculate the sensitivity S I of dynamic passive compensation equipment j _j.

5. the dynamic reactive optimization method for subsequent use of the medium-term and long-term voltage stabilization of raising alternating current-direct current electrical network according to claim 4, is characterized in that: in described step 2-2, for certain fault l, and the sensitivity S I of dynamic passive compensation equipment j _l,jbe expressed as:

${\mathrm{SI}}_{l,j}=\frac{k_{\mathrm{MVSI},l}(Q_{j0}+\mathrm{\&Delta;}{Q}_j)-k_{\mathrm{MVSI},l}\left(Q_{j0}\right)}{\mathrm{\&Delta;}{Q}_{\mathrm{Rj}}}$

Wherein, Q _j0for the initially idle of dynamic passive compensation equipment j is exerted oneself; Δ Q _jfor the reactive power variable quantity of adjustment dynamic passive compensation equipment j; Δ Q _rjfor the Reactive Power Reserve variable quantity of adjustment dynamic passive compensation equipment j; k _{mVSI, l}(Q _j0+ Δ Q _j) for after adjustment dynamic passive compensation equipment j idle exert oneself, at fault F _lunder, the load margin value of alternating current-direct current electrical network; k _{mVSI, l}(Q _j0) for before adjustment dynamic passive compensation equipment j idle exert oneself, at fault F _lunder, the load margin value of alternating current-direct current electrical network.

6. the dynamic reactive optimization method for subsequent use of the medium-term and long-term voltage stabilization of raising alternating current-direct current electrical network according to claim 4, is characterized in that: in described step 2-3, for multiple fault, and the sensitivity S I of dynamic passive compensation equipment j _jbe expressed as:

${\mathrm{SI}}_j=\underset{l=1}{\overset{N_l}{\mathrm{\&Sigma;}}}{\mathrm{SI}}_{l,j}$

Wherein, N _lfor critical failure sum.

7. the dynamic reactive optimization method for subsequent use of the medium-term and long-term voltage stabilization of raising alternating current-direct current electrical network according to claim 4, is characterized in that: described step 3 specifically comprises the following steps:

Step 3-1: according to SI _jm dynamic passive compensation equipment is sorted, SI _jthe percentage contribution that maximum characterizes this dynamic passive compensation equipment centering long-term voltage stability is maximum, and the dynamic passive compensation equipment that percentage contribution is large reserves more Reactive Power Reserve amounts;

Step 3-2: with SI _jmaximum SI _maxfor benchmark, normalized SI _j, calculate the weight coefficient p of dynamic passive compensation equipment _j, have p _j=SI _j/ | SI _max|.

8. the dynamic reactive optimization method for subsequent use of the medium-term and long-term voltage stabilization of raising alternating current-direct current electrical network according to claim 1, is characterized in that: described step 4 specifically comprises the following steps:

Step 4-1: the reserve capacity Q calculating dynamic passive compensation equipment _rM;

Step 4-2: to improve Q _rMas dynamic reactive optimization aim for subsequent use, set up dynamic reactive Optimized model for subsequent use;

Step 4-3: adopt this dynamic reactive of genetic algorithm for solving Optimized model for subsequent use.

9. the dynamic reactive optimization method for subsequent use of the medium-term and long-term voltage stabilization of raising alternating current-direct current electrical network according to claim 8, is characterized in that: in described step 4-1, the reserve capacity Q of dynamic passive compensation equipment _rMbe expressed as:

$Q_{\mathrm{RM}}=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{p}_j(Q_{\mathrm{gj}\max }-Q_{\mathrm{gj}})$

Wherein, Q _gjmaxfor the idle upper limit of exerting oneself of dynamic passive compensation equipment j in medium-term and long-term voltage stabilization, Q _gjfor the current idle of dynamic passive compensation equipment j is exerted oneself.

10. the dynamic reactive optimization method for subsequent use of the medium-term and long-term voltage stabilization of raising alternating current-direct current electrical network according to claim 8, is characterized in that: in described step 4-2, and the target function of dynamic reactive Optimized model for subsequent use is:

$\max Q_{\mathrm{RM}}=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{p}_j(Q_{\mathrm{gj}\max }-Q_{\mathrm{gj}})$

The constraints of dynamic reactive Optimized model for subsequent use comprises power flow equation constraint and variable bound; Described variable bound is control variables constraint and state variable constrain;

(1) power flow equation constraint:

In dynamic reactive Optimized model for subsequent use, each node meritorious is exerted oneself and idle exerting oneself all meets following power flow equation, has:

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-P_{\mathrm{Li}}-P_{\mathrm{ti}\left(\mathrm{dc}\right)}-V_i\underset{r=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_r(G_{\mathrm{ir}}\cos {\mathrm{\&delta;}}_{\mathrm{ir}}+B_{\mathrm{ir}}\sin {\mathrm{\&delta;}}_{\mathrm{ir}})=0\\ Q_{\mathrm{Gi}}+Q_{\mathrm{Ci}}-Q_{\mathrm{Li}}-Q_{\mathrm{ti}\left(\mathrm{dc}\right)}-V_i\underset{r=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_r(G_{\mathrm{ir}}\sin {\mathrm{\&delta;}}_{\mathrm{ir}}-B_{\mathrm{ir}}\cos {\mathrm{\&delta;}}_{\mathrm{ir}})=0\end{array}\right.$

Wherein, P _giand Q _giwhat be respectively generators in power systems node meritoriously exerts oneself and idlely to exert oneself; P _liand Q _liwhat be respectively load bus meritoriously exerts oneself and idlely to exert oneself; Q _cifor the reactive compensation capacity of node; G _irand B _irbe respectively the conductance between node i, r and susceptance; V _iand V _rbe respectively the voltage of node i, r; δ _irfor the phase difference of voltage between node i, r; N is node total number; P _{ti (dc)}and Q _{ti (dc)}be respectively the meritorious input of DC node and idle input, be divided into following two kinds of situations:

1) node i is on rectification side change of current bus, P _{ti (dc)}and Q _{ti (dc)}be expressed as:

$\left\{\begin{array}{c}{P}_{\mathrm{ti}\left(\mathrm{dc}\right)}=k_p{U}_{\mathrm{dR}}{I}_d\\ Q_{\mathrm{ti}\left(\mathrm{dc}\right)}=k_p{I}_d\sqrt{{\left(\frac{3\sqrt{2}}{\mathrm{\&pi;}{K}_{\mathrm{dR}}}b{V}_R\right)}^2-U_{\mathrm{dR}}^2}\end{array}\right.$

Wherein, k _pfor the number of poles of converter; U _dRfor rectification side direct voltage; I _dfor DC line electric current; K _dRfor rectification side converter transformer no-load voltage ratio; B is 6 pulse wave cascaded bridges numbers of every pole; V _rfor the ac bus voltage magnitude of rectification side;

2) node i is on inverter side change of current bus, P _{ti (dc)}and Q _{ti (dc)}be expressed as:

$\left\{\begin{array}{c}{P}_{\mathrm{ti}\left(\mathrm{dc}\right)}={-k}_p{U}_{\mathrm{dI}}{I}_d\\ Q_{\mathrm{ti}\left(\mathrm{dc}\right)}=k_p{I}_d\sqrt{{\left(\frac{3\sqrt{2}}{\mathrm{\&pi;}{K}_{\mathrm{dI}}}b{V}_I\right)}^2-U_{\mathrm{dI}}^2}\end{array}\right.$

Wherein, U _dIfor inverter side direct voltage; K _dIfor inverter side converter transformer no-load voltage ratio; V _ifor the ac bus voltage magnitude of inverter side;

(2) control variables constraint:

$\left\{\begin{array}{c}{V}_{\mathrm{Gi}\min }\&le;V_{\mathrm{Gi}}\&le;V_{\mathrm{Gi}\max },i=\mathrm{1,2},...,N_G\\ V_{\mathrm{SVCg}\min }\&le;V_{\mathrm{SVCg}}\&le;V_{\mathrm{SVCg}\max },g=\mathrm{1,2},...,N_{\mathrm{SVC}}\\ V_{\mathrm{SVGh}\min }\&le;V_{\mathrm{SVGh}}\&le;V_{\mathrm{SVGh}\max },h=\mathrm{1,2},...,N_{\mathrm{SVG}}\\ Q_{\mathrm{Cu}\min }\&le;Q_{\mathrm{Cu}}\&le;Q_{\mathrm{Cu}\max },u=\mathrm{1,2},...,N_C\\ T_{k\min }\&le;T_k\&le;T_{k\max },k=\mathrm{1,2},...,N_T\\ U_{\mathrm{dl}\min }\&le;U_{\mathrm{dl}}\&le;U_{\mathrm{dl}\max },l=\mathrm{1,2},...,N_{\mathrm{dc}}\\ I_{\mathrm{dm}\min }\&le;I_{\mathrm{dm}}\&le;I_{\mathrm{dm}\max },m=\mathrm{1,2},...,N_{\mathrm{dc}}\\ P_{\mathrm{dn}\min }\&le;P_{\mathrm{dn}}\&le;P_{\mathrm{dn}\max },n=\mathrm{1,2},...,N_{\mathrm{dc}}\\ {\mathrm{\&theta;}}_{\mathrm{dr}\min }\&le;{\mathrm{\&theta;}}_{\mathrm{dr}}\&le;{\mathrm{\&theta;}}_{\mathrm{dr}\max },r=\mathrm{1,2},...,N_{\mathrm{dc}}\end{array}\right.$

Wherein, N _g, N _sVC, N _sVG, N _c, N _tand N _dcbe respectively generator nodes, Static Var Compensator nodes, STATCOM nodes, shunt capacitor nodes, transformer application of adjustable tap number and DC network nodes; V _gifor the terminal voltage of generator node, V _giminand V _gimaxbe respectively V _gilower limit and higher limit; V _sVCgfor the terminal voltage of Static Var Compensator node, V _sVCgminand V _sVCgmaxbe respectively V _sVCglower limit and higher limit; V _sVGhfor the terminal voltage of STATCOM node, V _sVGhminand V _sVGhmaxbe respectively V _sVGhlower limit and higher limit; Q _cufor the compensation capacity of Shunt Capacitor Unit, Q _cuminand Q _cumaxbe respectively Q _culower limit and higher limit; T _kfor transformer application of adjustable tap, T _kminand T _kmaxbe respectively T _klower limit and higher limit; U _dl, I _dm, P _dnand θ _drbe respectively converter control voltage, control electric current, control power and pilot angle, U _dlminand U _dlmax, I _dmminand I _dmmax, P _dnminand P _dnmax, θ _drminand θ _drmaxrepresent corresponding lower limit and higher limit respectively;

(3) state variable constrain:

$\left\{\begin{array}{c}{Q}_{\mathrm{Gi}\min }\&le;Q_{\mathrm{Gi}}\&le;Q_{\mathrm{Gi}\max },i=\mathrm{1,2},...,N_G\\ B_{\mathrm{SVCg}\min }\&le;B_{\mathrm{SVCg}}\&le;B_{\mathrm{SVCg}\max },g=\mathrm{1,2},...,N_{\mathrm{SVC}}\\ I_{\mathrm{SVGh}\min }\&le;I_{\mathrm{SVGh}}\&le;I_{\mathrm{SVGh}\max },h=\mathrm{1,2},...,N_{\mathrm{SVG}}\\ V_{\mathrm{Lp}\min }\&le;V_{\mathrm{Lp}}\&le;V_{\mathrm{Lp}\max },p=\mathrm{1,2},...,N_L\end{array}\right.$

Wherein, N _lfor load bus number; Q _giexert oneself for generator node is idle, Q _giminand Q _gimaxbe respectively Q _gilower limit and higher limit; B _sVCgfor Static Var Compensator susceptance, B _sVCgminand B _sVCgmaxbe respectively B _sVCglower limit and higher limit; I _sVGhfor STATCOM current amplitude, I _sVGhminand I _sVGhmaxbe respectively I _sVGhlower limit and higher limit; V _lpfor load bus voltage magnitude, V _lpminand V _lpmaxbe respectively V _lplower limit and higher limit.