CN104362642B - 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 standby optimization method of dynamic reactive 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 nothing improving the medium-term and long-term voltage stabilization of alternating current-direct current electrical network The standby optimization method of merit.

Background technology

Since Voltage-stabilizing Problems is paid attention to by Chinese scholars, have developed into multiple research branch, voltage stabilization there has also been bright The most reasonably definition, studies effort through for many years, and electric power scholars have achieved rich in some field of Voltage-stabilizing Problems Large achievement, as to the Small disturbance voltage stability in static voltage stability analysis, Dynamic voltage stability and Transient stability analysis In, the most define the most perfect a set of research theory and analysis method, in sides such as electric power system dispatching operation and Monitoring and Controlling Face all plays irreplaceable effect.But the research of current domestic centering long-term voltage stability problem is the most deep enough, does not has Forming the most unified understanding, people's centering long term voltage stability mechanism and process can not carry out the most rigorous analysis, therefore, Study medium-term and long-term Voltage-stabilizing Problems and there is very important theory significance.

After power system suffers large disturbances, owing to the pressure sensitive of load may temporarily keep voltage stabilization, but power system In much affect the elements of voltage stability and all there is slow motion state course of action, along with the changing-over of on-load transformer tap changer, And have load restoration characteristic element power recover, after a longer time course, system yet suffer from occur electricity The possibility of pressure collapse, here it is medium-term and long-term Voltage-stabilizing Problems, the studied time domain scale of medium-term and long-term Voltage Stability Analysis is a few minutes Even dozens of minutes.Load restoration characteristic centering long term voltage stability has extreme influence, has the main thoughts of element of recovery characteristics Induction motor and constant temperature load, on-load transformer tap changer changing-over simultaneously is the major reason causing load restoration.Due to upper The responsive time constant stating 3 kinds of dynamic elements is different in size, thus forms the medium-term and long-term Voltage Instability process that fast and slow dynamics combines.

Currently, lacking Voltage Stability Control method effective, quick, adaptable is also the major reason causing large-scale blackout One of.Although China had not occurred the large-scale blackout caused by Voltage-stabilizing Problems, but along with " transferring electricity from the west to the east, north and south supplies mutually " The formation of power system interconnection general layout, load center level constantly increases, and Large Copacity long distance power transmission is continuously increased, China's electric power The voltage stabilization sex chromosome mosaicism of system becomes increasingly conspicuous, and the probability that Voltage Instability accident occurs is the most increasing.Due to Voltage-stabilizing Problems Have disguised and sudden, be difficult to during accident discover, collapse of voltage once occurs, under China's current electric grid practical situation, The hugest loss certainly will be caused.Therefore, research improves the standby optimization problem of dynamic reactive of medium-term and long-term voltage stabilization, effectively Prevent Voltage Instability and collapse of voltage accident from occurring, there is important theory value and practical significance.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the present invention provides a kind of and improves the dynamic of the medium-term and long-term voltage stabilization of alternating current-direct current electrical network Reactive Power Reserve optimization method, provides aid decision support, to carrying for improving the medium-term and long-term Voltage Stability Level of multi-feed HVDC electrical network The high extensive medium-term and long-term voltage stability margin of alterating and direct current net, set up give, power transm ission corridor unimpeded between receiving end, promote and hand over Direct current transportation passage conveying capacity, improves economy and the quality of power supply of operation of power networks, is respectively provided with important meaning.

In order to realize foregoing invention purpose, the present invention adopts the following technical scheme that:

The present invention provides a kind of standby optimization method of dynamic reactive improving the medium-term and long-term voltage stabilization of alternating current-direct current electrical network, described method bag Include following steps:

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: adjust the idle of dynamic passive compensation equipment and exert oneself, and calculate the sensitivity of dynamic passive compensation equipment；

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

Step 4: calculate dynamic passive compensation equipment sparing capacity, set up the standby Optimized model of dynamic reactive, and it is dynamic to solve this Reactive Power Reserve Optimized model.

In described step 1, alternating current-direct current electrical network is carried out fault scanning, 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, Z_TiFor system Thevenin's equivalence impedance；

Choose K_MVSiMinima is the voltage stability margin of alternating current-direct current electrical network, is designated as K_MVSI, according to the voltage stabilization of alternating current-direct current electrical network Margin value determines the serious conditions of fault, obtains critical failure, thus obtains critical failure set.

In described step 2, dynamic passive compensation equipment includes electromotor, SVC and STATCOM.

Described step 2 specifically includes following steps:

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

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

Step 2-3: under long-term time scale, for multiple faults, calculates sensitivity S I of dynamic passive compensation equipment j_j。

In described step 2-2, for certain fault l, sensitivity S I of dynamic passive compensation equipment j_l,jIt is 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_j0The most idle exerting oneself for dynamic passive compensation equipment j；ΔQ_jFor adjusting the nothing of dynamic passive compensation equipment j Merit power variation；ΔQ_RjFor adjusting the Reactive Power Reserve variable quantity of dynamic passive compensation equipment j；k_MVSI,l(Q_j0+ΔQ_j) for adjusting After dynamic passive compensation equipment j idle is exerted oneself, in fault F_lUnder, the load margin value of alternating current-direct current electrical network；k_MVSI,l(Q_j0) for adjusting Before whole dynamic passive compensation equipment j idle is exerted oneself, in fault F_lUnder, the load margin value of alternating current-direct current electrical network.

In described step 2-3, for multiple faults, sensitivity S I of dynamic passive compensation equipment j_jIt is 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 includes following steps:

Step 3-1: according to SI_jM dynamic passive compensation equipment is ranked up, SI_jMaximum characterizes this dynamic passive compensation The percentage contribution of equipment centering long-term voltage stability is maximum, and the dynamic passive compensation equipment that percentage contribution is big reserves more Reactive Power Reserve Amount；

Step 3-2: with SI_jMaximum SI_maxOn the basis of, normalized SI_j, calculate the weight system of dynamic passive compensation equipment Number p_j, have p_j=SI_j/|SI_max|。

Described step 4 specifically includes following steps:

Step 4-1: calculate spare capacity Q of dynamic passive compensation equipment_RM；

Step 4-2: to improve Q_RMAs the standby optimization aim of dynamic reactive, set up the standby Optimized model of dynamic reactive；

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

In described step 4-1, spare capacity Q of dynamic passive compensation equipment_RMIt is 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, Q in medium-term and long-term voltage stabilization_gjFor dynamic reactive The most idle the exerting oneself of compensation equipment j.

In described step 4-2, the object function of the standby Optimized model of dynamic reactive is:

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

The constraints of the standby Optimized model of dynamic reactive includes power flow equation constraint and variable bound；Described variable bound is for controlling Variable bound and state variable constraint；

(1) power flow equation constraint:

In the standby Optimized model of dynamic reactive, 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_GiMeritorious the exerting oneself being respectively generators in power systems node is exerted oneself with idle；P_LiAnd Q_LiIt is respectively negative Meritorious the exerting oneself of lotus node is exerted oneself with idle；Q_CiReactive compensation capacity for node；G_irAnd B_irIt is respectively between node i, r Conductance and susceptance；V_iAnd V_rIt is respectively node i, the voltage of r；δ_irFor the phase difference of voltage between node i, r；N is node Sum；P_ti(dc)And Q_ti(dc)It is respectively the meritorious input of DC node and idle input, is divided into following two situation:

1) node i is on rectification side change of current bus, P_ti(dc)And Q_ti(dc)It is 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_pNumber of poles for inverter；U_dRFor rectification side DC voltage；I_dFor DC line electric current；K_dRFor rectification side Converter power transformer no-load voltage ratio；B is 6 pulse wave cascaded bridges numbers of every pole；V_RAc bus voltage magnitude for rectification side；

2) node i is on inverter side change of current bus, P_ti(dc)And Q_ti(dc)It is 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 DC voltage；K_dIFor inverter side converter power transformer no-load voltage ratio；V_IAc bus electricity for inverter side Pressure amplitude value；

(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 electromotor nodes, SVC nodes, STATCOM nodes, shnt capacitor nodes, transformator application of adjustable tap number and DC network nodes；V_GiFor The terminal voltage of electromotor node, V_GiminAnd V_GimaxIt is respectively V_GiLower limit and higher limit；V_SVCgSave for SVC The terminal voltage of point, V_SVCgminAnd V_SVCgmaxIt is respectively V_SVCgLower limit and higher limit；V_SVGhFor STATCOM node Terminal voltage, V_SVGhminAnd V_SVGhmaxIt is respectively V_SVGhLower limit and higher limit；Q_CuFor the compensation capacity of Shunt Capacitor Unit, Q_CuminAnd Q_CumaxIt is respectively Q_CuLower limit and higher limit；T_kFor transformator application of adjustable tap, T_kminAnd T_kmaxIt is respectively T_kUnder Limit value and higher limit；U_dl、I_dm、P_dnAnd θ_drIt is respectively converter Control voltage, controls electric current, control power and control Angle, U_dlminAnd U_dlmax、I_dmminAnd I_dmmax、P_dnminAnd P_dnmax、θ_drminAnd θ_drmaxRepresent corresponding lower limit and upper respectively Limit value；

(3) state variable constraint:

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

Wherein, N_LFor load bus number；Q_GiExert oneself for electromotor node is idle, Q_GiminAnd Q_GimaxIt is respectively Q_GiLower limit Value and higher limit；B_SVCgFor SVC susceptance, B_SVCgminAnd B_SVCgmaxIt is respectively B_SVCgLower limit and higher limit； I_SVGhFor STATCOM current amplitude, I_SVGhminAnd I_SVGhmaxIt is respectively I_SVGhLower limit and higher limit；V_LpIt is negative Lotus node voltage amplitude, V_LpminAnd V_LpmaxIt is respectively V_LpLower limit and higher limit.

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

There is no the dynamic reactive standby optimization skill improving medium-term and long-term voltage stabilization being applicable to multi-infeed HVDC electrical network feature the most at present Art, the present invention proposes a kind of multi-infeed HVDC electrical network feature that is applicable to innovatively and improves the dynamic reactive of medium-term and long-term voltage stabilization Standby optimization method；

2., with compared with static traditional Reactive Power Reserve optimization method, this method considers the dynamic characteristic of system in detail, it is possible to More accurately determining dynamic passive compensation equipment sparing capacity, the optimization for electrical network runs offer basis；

3. analyzed by time-domain-simulation, can quick and easy, accurately determine the participation factors of each reactive source, can be applicable to advise greatly The standby optimization of dynamic reactive of mould power system, the algorithm overcoming conventional electric power system dynamic reactive-load optimization can be only applied to little system The shortcoming of system.

Accompanying drawing explanation

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

Fig. 2 is employing genetic algorithm for solving dynamic reactive standby Optimized model flow chart in the embodiment of the present invention；

Fig. 3 is 3 machine 10 node regulation test ac and dc systems schematic diagram during the present invention implements；

Fig. 4 be in the embodiment of the present invention electromotor relative to merit angle change curve；

Fig. 5 is the magnetizing current curve figure of electromotor 2 and electromotor 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 be in the embodiment of the present invention optimize before and after node 3 (electromotor G3 machine end) voltage curve；

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

Detailed description of the invention

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

The present invention provides a kind of standby optimization method of dynamic reactive improving the medium-term and long-term voltage stabilization of alternating current-direct current electrical network, described method bag Include following steps:

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: adjust the idle of dynamic passive compensation equipment and exert oneself, and calculate the sensitivity of dynamic passive compensation equipment；

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

Step 4: calculate dynamic passive compensation equipment sparing capacity, set up the standby Optimized model of dynamic reactive, and it is dynamic to solve this Reactive Power Reserve Optimized model.

In described step 1, alternating current-direct current electrical network is carried out fault scanning, 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, Z_TiFor system Thevenin's equivalence impedance；

Choose K_MVSiMinima is the voltage stability margin of alternating current-direct current electrical network, is designated as K_MVSI, according to the voltage stabilization of alternating current-direct current electrical network Margin value determines the serious conditions of fault, obtains critical failure, thus obtains critical failure set.

In described step 2, dynamic passive compensation equipment includes electromotor, SVC and STATCOM.

Described step 2 specifically includes following steps:

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

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

Step 2-3: under long-term time scale, for multiple faults, calculates sensitivity S I of dynamic passive compensation equipment j_j。

In described step 2-2, for certain fault l, sensitivity S I of dynamic passive compensation equipment j_l,jIt is 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_j0The most idle exerting oneself for dynamic passive compensation equipment j；ΔQ_jFor adjusting the nothing of dynamic passive compensation equipment j Merit power variation；ΔQ_RjFor adjusting the Reactive Power Reserve variable quantity of dynamic passive compensation equipment j；k_MVSI,l(Q_j0+ΔQ_j) for adjusting After dynamic passive compensation equipment j idle is exerted oneself, in fault F_lUnder, the load margin value of alternating current-direct current electrical network；k_MVSI,l(Q_j0) for adjusting Before whole dynamic passive compensation equipment j idle is exerted oneself, in fault F_lUnder, the load margin value of alternating current-direct current electrical network.

In described step 2-3, for multiple faults, sensitivity S I of dynamic passive compensation equipment j_jIt is 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 includes following steps:

Step 3-1: according to SI_jM dynamic passive compensation equipment is ranked up, SI_jMaximum characterizes this dynamic passive compensation The percentage contribution of equipment centering long-term voltage stability is maximum, and the dynamic passive compensation equipment that percentage contribution is big reserves more Reactive Power Reserve Amount；

Step 3-2: with SI_jMaximum SI_maxOn the basis of, normalized SI_j, calculate the weight system of dynamic passive compensation equipment Number p_j, have p_j=SI_j/|SI_max|。

Described step 4 specifically includes following steps:

Step 4-1: calculate spare capacity Q of dynamic passive compensation equipment_RM；

Step 4-2: to improve Q_RMAs the standby optimization aim of dynamic reactive, set up the standby Optimized model of dynamic reactive；

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

In described step 4-1, spare capacity Q of dynamic passive compensation equipment_RMIt is 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, Q in medium-term and long-term voltage stabilization_gjFor dynamic reactive The most idle the exerting oneself of compensation equipment j.

In described step 4-2, the object function of the standby Optimized model of dynamic reactive 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 the standby Optimized model of dynamic reactive includes power flow equation constraint and variable bound；Described variable bound is for controlling Variable bound and state variable constraint；

(1) power flow equation constraint:

In the standby Optimized model of dynamic reactive, 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_GiMeritorious the exerting oneself being respectively generators in power systems node is exerted oneself with idle；P_LiAnd Q_LiIt is respectively negative Meritorious the exerting oneself of lotus node is exerted oneself with idle；Q_CiReactive compensation capacity for node；G_irAnd B_irIt is respectively between node i, r Conductance and susceptance；V_iAnd V_rIt is respectively node i, the voltage of r；δ_irFor the phase difference of voltage between node i, r；N is node Sum；P_ti(dc)And Q_ti(dc)It is respectively the meritorious input of DC node and idle input, is divided into following two situation:

1) node i is on rectification side change of current bus, P_ti(dc)And Q_ti(dc)It is 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_pNumber of poles for inverter；U_dRFor rectification side DC voltage；I_dFor DC line electric current；K_dRFor rectification side Converter power transformer no-load voltage ratio；B is 6 pulse wave cascaded bridges numbers of every pole；V_RAc bus voltage magnitude for rectification side；

2) node i is on inverter side change of current bus, P_ti(dc)And Q_ti(dc)It is 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 DC voltage；K_dIFor inverter side converter power transformer no-load voltage ratio；V_IAc bus electricity for inverter side Pressure amplitude value；

(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 electromotor nodes, SVC nodes, STATCOM nodes, shnt capacitor nodes, transformator application of adjustable tap number and DC network nodes；V_GiFor The terminal voltage of electromotor node, V_GiminAnd V_GimaxIt is respectively V_GiLower limit and higher limit；V_SVCgSave for SVC The terminal voltage of point, V_SVCgminAnd V_SVCgmaxIt is respectively V_SVCgLower limit and higher limit；V_SVGhFor STATCOM node Terminal voltage, V_SVGhminAnd V_SVGhmaxIt is respectively V_SVGhLower limit and higher limit；Q_CuFor the compensation capacity of Shunt Capacitor Unit, Q_CuminAnd Q_CumaxIt is respectively Q_CuLower limit and higher limit；T_kFor the no-load voltage ratio of transformator, T_kminAnd T_kmaxIt is respectively T_kLower limit And higher limit；U_dl、I_dm、P_dnAnd θ_drIt is respectively converter Control voltage, controls electric current, control power and pilot angle, U_dlmin And U_dlmax、I_dmminAnd I_dmmax、P_dnminAnd P_dnmax、θ_drminAnd θ_drmaxRepresent corresponding lower limit and higher limit respectively；

(3) state variable constraint:

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

Wherein, N_LFor load bus number；Q_GiExert oneself for electromotor node is idle, Q_GiminAnd Q_GimaxIt is respectively Q_GiLower limit Value and higher limit；B_SVCgFor SVC susceptance, B_SVCgminAnd B_SVCgmaxIt is respectively B_SVCgLower limit and higher limit； I_SVGhFor STATCOM current amplitude, I_SVGhminAnd I_SVGhmaxIt is respectively I_SVGhLower limit and higher limit；V_LpIt is negative Lotus node voltage amplitude, V_LpminAnd V_LpmaxIt is respectively V_LpLower limit and higher limit.

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

The basic thought of genetic algorithm is, a group under certain specific environment is individual, owing to environment limits, the most adaptable Can survive, and weak person is eliminated, they adapt to the merit of environment can entail offspring.GA is applied to Reactive Power Reserve optimization It is to be understood that one group of initial trend solution under power system during problem, retrained by various constraintss, commented by object function Its quality of valency, low being abandoned of evaluation of estimate, what only evaluation of estimate was high has an opportunity its feature iteration to next round solution, finally tends to Optimum.

Detailed process is as follows:

(1) first, randomly generate first generation parent 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 electromotor node respectively；

X_iIf V_SVCg, then X_imax、X_imaxRepresent the terminal voltage bound of SVC 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.As 1+5 × 0.025% transformator its The span of YT is 1～11.Coding uses binary number, every five orders to 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) each individuality in A is decoded according to formula (13), revises value corresponding in original flow data, then start Load flow calculation, the flow calculation program of the present invention uses 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、ΔV_SVCg、ΔV_SVGh、ΔQ_Cu、ΔT_kThere is level to regulate cell value to dependent variable；

Y_Vgi、Y_Vsvcg、Y_Vsvgh、Y_Qcu、Y_TkRepresent the integer variable of the control variable position of the switch；

Y_Vgi=1, represent that i-th electromotor node side voltage is transferred to maximum；

Y_Vsvcg=1, represent that the g SVC node side voltage is transferred to maximum；

Y_Vsvgh=1, represent that the h STATCOM node side voltage is transferred to maximum；

Y_Qcu=1, represent that jth capacitor puts into one group of capacitance；

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

(3) through Load flow calculation, it is thus achieved that the data such as the voltage of each node, idle and dynamic reactive spare capacity, and by its by Big to little sequence；

(4) according to adaptive value size, each individuality is ranked up, retains individual composition groups of individuals B that affinity is big, simultaneously to B Interior individuality carries out cross and variation operation, the individuality that after reservation operations, overall adaptive value is big, forms groups of individuals C；According to adaptive value Size rearranges groups of individuals D to B, C；

(5) check iteration termination condition, if reached, terminating, otherwise turning next step；

(6) randomly generate one group of new groups of individuals E, collectively constitute a new generation's iterative computation groups of individuals F with D, go to step (2), Restart to calculate.

Embodiment

As it is shown on figure 3, for 3 machine 10 node systems, 500kV bus (Bus6) is powered to the two of load area loads, Industrial load therein (node Bus7) is connected with 500kV load bus by OLTC transformator, and resident load and business Load (node Bus10) then represents the impedance of secondary transmission system by two OLTC transformators and one section and is connected on 500kV and bears Lotus bus.There is the equivalent electromotor (node Bus3) of a 1600MVA in load area, and have employed substantial amounts of shunt compensation dress Put, node 8 has been respectively configured SVC (SVC) that capacity is ± 240Mvar and capacity is the electricity of 600Mvar Container group, the every pool-size of this Capacitor banks is 100Mvar, totally 6 groups.The electromotor in two distant places passes through 4 500kV circuits Power is carried to load area with 1 time bipolar direct current transmission line.The main models that emulation is used: transformator (Bus9～Bus10) For OLTC transformator, other tap keeps constant；Load on node Bus7 is invariable power model, and other load is constant-resistance Anti-model；Electromotor on electromotor 2 and 3 (node Bus2 and Bus3) has overexcitation to limit device, electromotor 1 (node Bus1) it is infinitely great electromotor.

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

Fig. 4 represents electromotor 2, electromotor 3 merit angle relative with between electromotor 1 rocking curve respectively.From fig. 4, it can be seen that this The initial fast transient process that disturbance causes can quickly disappear, and shows that system can keep transient rotor angle stability, follow-up in Though merit angle is waved in long process, but angle is smaller, shows that system can also keep medium-term and long-term angle stability.

In Fig. 5, the exciting current of overexcitation limiter indicates electromotor 2 and electromotor 3 electromotive force E_qResponse, this is electronic Gesture is proportional to exciting current.As it can be seen, after disturbance, the exciting current of electromotor 2 and electromotor 3 can fly up, as Fruit has exceeded rotor current restriction, will start mechanism between the inverse time of overexcitation limiter.After disturbance, the fortune of OLTC transformator Row imposes a very heavy reactive requirement to electromotor.This demand is degrading rotor overload further, until final mistake Excitation Limiter is energized, and causes exciting current to return to its rated value.Noting, this overexciation limiter is integral form, so that In E_qIt is forced to E_q ^lim.Subsequently tap conversion cause transient exciting current to raise, this rising exciting current quickly by Overexcitation limiter is detected (such as the maximum of points of electromotor 2,3 exciting current in Fig. 5), and corrects.

Fig. 6 gives node 9 and the voltage of node 10, high-voltage side bus 9 voltage of the OLTC i.e. powered and load to load Side gusset 10 voltage.As seen from the figure, in transient process, node 9 can stable operation at 0.87p.u..OLTC transformator 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 changes Device brings into operation, and about 55 seconds, after 5 tap_changings, busbar voltage rose to 0.915pu, closely accident Front level, the exciting current output of electromotor 2 and 3 is consequently increased the demand (Fig. 5) meeting system to reactive power.But When being by 347 seconds, start action owing to the overexcitation of electromotor 3 limits device, limit its output electric current so that this machine Reactive power output decline the most therewith, cause the voltage of load bus 10 again to decline.For ensureing voltage, load tap changer Continuation action 18 times.When 442 seconds, the overexcitation of electromotor 2 limited device and also begins to action, and the reactive power of system lacks Mouth is greatly increased, and result in the generation of collapse of voltage.

After obtain each control variable of reactive power reserve optimization problem by the present invention, time-domain-simulation checking is utilized to analyze institute's extracting method Effectiveness.

The permanent short trouble of three-phase, 0.09s after fault is there is in an alternating current interconnection between node 5～node 6 in node 6 side Tripping faulty line node 6 side switchs, and 0.1s tripping faulty line node 5 side switchs.Fig. 7 and Fig. 8 is respectively electromotor G3 Set end voltage and node 10 voltage curve, it can be seen that the medium-term and long-term voltage stability of system is wanted than before optimizing after You Huaing Good, the optimized algorithm that this explanation uses the present invention to propose can be effectively improved the medium-term and long-term voltage stability of electrical network.

Finally should be noted that: above example only in order to illustrate that technical scheme is not intended to limit, art Those of ordinary skill still the detailed description of the invention of the present invention can be modified or equivalent with reference to above-described embodiment, These are without departing from any amendment of spirit and scope of the invention or equivalent, the claim of the present invention all awaited the reply in application Within protection domain.

Claims (9)

1. improve the standby optimization method of dynamic reactive of the medium-term and long-term voltage stabilization of alternating current-direct current electrical network, it is characterised in that: described method bag Include following steps:

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: adjust the idle of dynamic passive compensation equipment and exert oneself, and calculate the sensitivity of dynamic passive compensation equipment；

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

Step 4: calculate dynamic passive compensation equipment sparing capacity, set up the standby Optimized model of dynamic reactive, and it is dynamic to solve this Reactive Power Reserve Optimized model；

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

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

Wherein, Z_LiFor the load equivalent impedance at load bus i, Z_TiFor system Thevenin's equivalence impedance；

Choose K_MVSiMinima is the voltage stability margin of alternating current-direct current electrical network, is designated as K_MVSI, according to the voltage stabilization of alternating current-direct current electrical network Margin value determines the serious conditions of fault, obtains critical failure, thus obtains critical failure set.

The standby optimization method of dynamic reactive of the raising medium-term and long-term voltage stabilization of alternating current-direct current electrical network the most according to claim 1, its Being characterised by: in described step 2, dynamic passive compensation equipment includes that electromotor, SVC and Static Synchronous compensate Device.

The standby optimization method of dynamic reactive of the raising medium-term and long-term voltage stabilization of alternating current-direct current electrical network the most according to claim 1, its It is characterised by: described step 2 specifically includes following steps:

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

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

Step 2-3: under long-term time scale, for multiple faults, calculates sensitivity S I of dynamic passive compensation equipment j_j。

The standby optimization method of dynamic reactive of the raising medium-term and long-term voltage stabilization of alternating current-direct current electrical network the most according to claim 3, its It is characterised by: in described step 2-2, for certain fault l, sensitivity S I of dynamic passive compensation equipment j_l,jIt is expressed as:

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

Wherein, Q_j0The most idle exerting oneself for dynamic passive compensation equipment j；ΔQ_jFor adjusting the nothing of dynamic passive compensation equipment j Merit power variation；ΔQ_RjFor adjusting the Reactive Power Reserve variable quantity of dynamic passive compensation equipment j；k_MVSI,l(Q_j0+ΔQ_j) for adjusting After dynamic passive compensation equipment j idle is exerted oneself, under fault l, the load margin value of alternating current-direct current electrical network；k_MVSI,l(Q_j0) for adjusting Before whole dynamic passive compensation equipment j idle is exerted oneself, under fault l, the load margin value of alternating current-direct current electrical network.

The standby optimization method of dynamic reactive of the raising medium-term and long-term voltage stabilization of alternating current-direct current electrical network the most according to claim 3, its It is characterised by: in described step 2-3, for multiple faults, sensitivity S I of dynamic passive compensation equipment j_jIt is expressed as:

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

Wherein, N_lFor critical failure sum.

The standby optimization method of dynamic reactive of the raising medium-term and long-term voltage stabilization of alternating current-direct current electrical network the most according to claim 3, its It is characterised by: described step 3 specifically includes following steps:

Step 3-1: according to SI_jM dynamic passive compensation equipment is ranked up, SI_jMaximum characterizes this dynamic passive compensation The percentage contribution of equipment centering long-term voltage stability is maximum, and the dynamic passive compensation equipment that percentage contribution is big reserves more Reactive Power Reserve Amount；

Step 3-2: with SI_jMaximum SI_maxOn the basis of, normalized SI_j, calculate the weight system of dynamic passive compensation equipment Number p_j, have p_j=SI_j/|SI_max|。

The standby optimization method of dynamic reactive of the raising medium-term and long-term voltage stabilization of alternating current-direct current electrical network the most according to claim 1, its It is characterised by: described step 4 specifically includes following steps:

Step 4-1: calculate spare capacity Q of dynamic passive compensation equipment_RM；

Step 4-2: to improve Q_RMAs the standby optimization aim of dynamic reactive, set up the standby Optimized model of dynamic reactive；

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

The standby optimization method of dynamic reactive of the raising medium-term and long-term voltage stabilization of alternating current-direct current electrical network the most according to claim 7, its It is characterised by: in described step 4-1, spare capacity Q of dynamic passive compensation equipment_RMIt is expressed as:

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

Wherein, Q_gjmaxFor the idle upper limit of exerting oneself of dynamic passive compensation equipment j, Q in medium-term and long-term voltage stabilization_gjFor dynamic reactive The most idle the exerting oneself of compensation equipment j.

The standby optimization method of dynamic reactive of the raising medium-term and long-term voltage stabilization of alternating current-direct current electrical network the most according to claim 7, its Being characterised by: in described step 4-2, the object function of the standby Optimized model of dynamic reactive is:

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

The constraints of the standby Optimized model of dynamic reactive includes power flow equation constraint and variable bound；Described variable bound is for controlling Variable bound and state variable constraint；

(1) power flow equation constraint:

In the standby Optimized model of dynamic reactive, each node meritorious is exerted oneself and idle exerting oneself all meets following power flow equation, has:

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

Wherein, P_GiAnd Q_GiMeritorious the exerting oneself being respectively generators in power systems node is exerted oneself with idle；P_LiAnd Q_LiIt is respectively negative Meritorious the exerting oneself of lotus node is exerted oneself with idle；Q_CiReactive compensation capacity for node；G_irAnd B_irIt is respectively between node i, r Conductance and susceptance；V_iAnd V_rIt is respectively node i, the voltage of r；δ_irFor the phase difference of voltage between node i, r；N is node Sum；P_ti(dc)And Q_ti(dc)It is respectively the meritorious input of DC node and idle input, is divided into following two situation:

1) node i is on rectification side change of current bus, P_ti(dc)And Q_ti(dc)It is expressed as:

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

Wherein, k_pNumber of poles for inverter；U_dRFor rectification side DC voltage；I_dFor DC line electric current；K_dRFor rectification side Converter power transformer no-load voltage ratio；B is 6 pulse wave cascaded bridges numbers of every pole；V_RAc bus voltage magnitude for rectification side；

2) node i is on inverter side change of current bus, P_ti(dc)And Q_ti(dc)It is expressed as:

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

Wherein, U_dIFor inverter side DC voltage；K_dIFor inverter side converter power transformer no-load voltage ratio；V_IAc bus electricity for inverter side Pressure amplitude value；

(2) control variables constraint:

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

Wherein, N_G、N_SVC、N_SVG、N_C、N_TAnd N_dcBe respectively electromotor nodes, SVC nodes, STATCOM nodes, shnt capacitor nodes, transformator application of adjustable tap number and DC network nodes；V_GiFor The terminal voltage of electromotor node, V_GiminAnd V_GimaxIt is respectively V_GiLower limit and higher limit；V_SVCgSave for SVC The terminal voltage of point, V_SVCgminAnd V_SVCgmaxIt is respectively V_SVCgLower limit and higher limit；V_SVGhFor STATCOM node Terminal voltage, V_SVGhminAnd V_SVGhmaxIt is respectively V_SVGhLower limit and higher limit；Q_CuFor the compensation capacity of Shunt Capacitor Unit, Q_CuminAnd Q_CumaxIt is respectively Q_CuLower limit and higher limit；T_kFor transformator application of adjustable tap, T_kminAnd T_kmaxIt is respectively T_kUnder Limit value and higher limit；U_dl、I_dm、P_dnAnd θ_drIt is respectively converter Control voltage, controls electric current, control power and control Angle, U_dlminAnd U_dlmax、I_dmminAnd I_dmmax、P_dnminAnd P_dnmax、θ_drminAnd θ_drmaxRepresent corresponding lower limit and upper respectively Limit value；

(3) state variable constraint:

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

Wherein, N_LFor load bus number；Q_GiExert oneself for electromotor node is idle, Q_GiminAnd Q_GimaxIt is respectively Q_GiLower limit And higher limit；B_SVCgFor SVC susceptance, B_SVCgminAnd B_SVCgmaxIt is respectively B_SVCgLower limit and higher limit； I_SVGhFor STATCOM current amplitude, I_SVGhminAnd I_SVGhmaxIt is respectively I_SVGhLower limit and higher limit；V_LpIt is negative Lotus node voltage amplitude, V_LpminAnd V_LpmaxIt is respectively V_LpLower limit and higher limit.