CN104701864A - Reactive power planning method using SVC as reactive power compensation equipment - Google Patents

Abstract

The invention discloses a reactive power planning method for an electrical power system. The reactive power planning method uses SVC and considers the transient process stability constraint of the system after large power system disturbance. The reactive power planning method using the SVC as reactive power compensation equipment includes that generating a reactive power compensation equipment selected-point index matrix through different voltage stabilization principles, and using fuzzy clustering to perform reactive power compensation device selected-point arrangement to obtain a reactive power compensation point distribution scheme suitable for the SVC running performance; through building a reactive power compensation optimization model based on different running modes and a dynamic model based on complex high-order system equipment, using a time domain simulation and optimization algorithm to obtain the optimal result of the SVC capacity configuration of the corresponding reactive power compensation point so as to realize SVC reactive power planning. According to a fuzzy clustering theory, a dynamic electrical power system theory, a time domain simulation technology and an interior point method optimization synthesis algorithm, the reactive power planning method realizes the reactive power planning which considers the transient process stability constraint after the system goes wrong, fully develops the dynamic response characteristic of the SVC and enables the reactive power compensation running efficiency of the electric power system to be effectively improved.

Description

A kind of SVC that adopts is as the idle planing method of reactive-load compensation equipment

Technical field

The present invention relates to a kind of SVC that adopts as the idle planing method of reactive-load compensation equipment, in order to improve power system planning and to run the stability of a system controlled.Belong to power system planning and operation field.

Background technology

Idle planning is by analyzing the idle characteristic under Power System Steady-state and dynamic operating condition, control the distribution of reactive power in the whole network and flowing, distribute installation site and the compensation capacity of reactive-load compensation equipment rationally, optimize voltage-regulation means, to improve system run all right, improve interregional tie-line power transmission, meet the safe operation of electrical network in Steady state and transient state situation and the demand of control voltage fluctuation.

Traditional idle planning acquiescence adopts switching type Shunt Capacitor Unit as reactive power compensator, and compensation equipment is a fundamental frequency equivalence capacitive reactance model.Idle planning application research contents comprises: the reconnaissance planning of (1) newly-increased reactive-load compensation equipment; (2) capacity planning of newly-increased reactive-load compensation equipment.

Along with being on the increase of power system reactive power compensation equipment, except original Shunt Capacitor Unit, the FACTS type reactive-load compensation equipment that SVC, STATCOM etc. have fast dynamic response characteristic is widely used gradually.

In the research of power system reactive power planning problem, for the actual utility of power system reactive power planning, the input of reactive-load compensation equipment is the voltage stability in order to improve system.For this reason, consider the idle planning problem of the transient process response of the dynamic devices such as generator, excitation system, SVC, in Transient Stability Constraints condition except equation of rotor motion and angle stability, also should consider the Voltage Stability Constraints in transient process.Except the constraints under stable situation, the constraints in transient process also comprises: (1) generator amature angle is relative to the range constraint at inertia center; (2) system each node transient process Voltage Stability Constraints; (3) the operation equation constraint of dynamic device.

Summary of the invention

Technical problem: for solving the problems of the technologies described above, the invention provides a kind of employing SVC simultaneously considering that steady operation and the transient process stability of a system retrain and carries out the idle planing method of power transmission network.

Technical scheme: a kind of SVC that adopts of the present invention as the idle planing method of reactive-load compensation equipment,

Concrete steps are as follows:

Step 1: based on system failure ranking method, calculates the transient process voltage stability index after most catastrophe failure respectively according to formula (1), (2), (3) under peak load, average load level:

System transient modelling Voltage Drop:

$V_{\mathrm{dip}}=\frac{V_0-V_s}{V_0}=\frac{\mathrm{\ΔV}}{V_0}\×100\%---\left(1\right)$

Wherein, V _sfor short-term stability process interior joint voltage lowest amplitude, V ₀for node voltage initial magnitude;

Variation index in transient process:

Low-voltage duration index in transient process: $\mathrm{LVDI}=\{\underset{t\&ni;(t_{\mathrm{cl}},t_f)}{\mathrm{\&Sigma;}}t/T|V\left(t\right)<0.8V_0,\&ForAll;t\&Element;(t_{\mathrm{cl}},t_f)\}$ $\left(3\right)$

Wherein, wherein, t _clfor the fault clearance time, t _ffor the emulation termination time;

Step 2: each voltage stability index in the transient process under the peak load obtained according to step 1, average load level, adopt fuzzy clustering method, obtain respectively SVC under system peak load, average load level the node i location sets N of candidate's reactive power compensation _c;

Step 3: set up SVC capacity planning optimal model:

Select three rank or more generator model, single order excitation system model and mixing load model:

Three rank generator models:

$\left\{\begin{array}{c}\frac{\mathrm{d\&delta;}\left(t\right)}{\mathrm{dt}}=(\mathrm{\&omega;}\left(t\right)-1){\mathrm{\&omega;}}_B\\ T_j\frac{\mathrm{d\&omega;}\left(t\right)}{\mathrm{dt}}=T_m-T_e\left(t\right)-D(\mathrm{\&omega;}\left(t\right)-1)\\ T_{d0}^{\&prime;}\frac{{\mathrm{dE}}_q^{\&prime;}\left(t\right)}{\mathrm{dt}}=E_f\left(t\right)-E_q^{\&prime;}\left(t\right)-(X_d-X_d^{\&prime;})I_d\left(t\right)\end{array}\right.$

Wherein, δ (t) is for q axle is relative to the angular displacement of synchronous rotating frame; ω _brotor rated speed and rotor t angular speed is respectively with ω (t); T _jwith T ' _d0for time constant, T _mwith T _et () is respectively mechanical force moment and dynamo-electric moment; E _f, E ' _qbe respectively stator excitation electromotive force and motor q axle transient internal voltage; X _dwith X ' _dbe respectively d axle synchronous reactance and d axle transient reactance; I _dfor d shaft current;

Its set end voltage equation is:

$\left\{\begin{array}{c}{V}_d\left(t\right)=x_q{I}_q\left(t\right)-r_a{I}_d\left(t\right)\\ V_q\left(t\right)=E_q^{\&prime;}\left(t\right)-x_d^{\&prime;}{I}_d\left(t\right)-r_a{I}_q\left(t\right)\end{array}\right.$

Wherein, V _d, V _q(I _d, I _q) be respectively d shaft voltage and q shaft voltage (electric current); x _q, r _abe respectively q axle synchronous reactance and winding resistance;

Single order excitation system model:

$T_A\frac{{\mathrm{dE}}_f\left(t\right)}{\mathrm{dt}}=K_A(V_{\mathrm{ref}}-V_m\left(t\right))-E_f\left(t\right)+E_{f0}$

Wherein, T _afor time constant; K _afor control coefrficient; V _refand V _mbe respectively node voltage reference value and amplitude; E _f0for excitation electric gesture initial value;

Target function is made for condition so that the idle input cost of SVC is minimum:

$\min \underset{i=1}{\overset{N_b}{\mathrm{\&Sigma;}}}[C_{\mathrm{fix}\_i}+C_{i\_\mathrm{vl}}\max \left(Q_{\mathrm{SVCi}}^{+}\right)+C_{i\_v2}\max \left(\right|Q_{\mathrm{SVCi}}^{-}\left|\right)]$

Wherein, C _{fix_i}for idle investment fixed cost; C _{i_v1}for capacitive reactive power variable cost; C _{i_v2}for the idle variable cost of perception; for node i capacitive SVC compensation capacity; for the SVC compensation capacity of perception;

Static Security Constraints condition is

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-P_{\mathrm{Li}}-V_i\underset{\mathrm{j\&omega;i}}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})=0\\ Q_{\mathrm{Gi}}+Q_{\mathrm{ci}}{y}_i-Q_{\mathrm{Li}}-V_i\underset{\mathrm{j\&omega;i}}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})=0\\ \begin{array}{cc}{V}_{i\min }\&le;V_i\&le;V_{i\max }& i\&Element;N_b\end{array}\\ \begin{array}{cc}{P}_{\mathrm{Gi}\min }\&le;P_{\mathrm{Gi}}\&le;P_{\mathrm{Gi}\max }& i\&Element;N_G\end{array}\\ \begin{array}{cc}{Q}_{\mathrm{Gi}\min }\&le;Q_{\mathrm{Gi}}\&le;Q_{\mathrm{Gi}\max }& i\&Element;N_G\end{array}\\ -S_{\mathrm{ij}\max }\&le;S_{\mathrm{ij}}\&le;S_{\mathrm{ij}\max }\\ Q_{\mathrm{SVCi}\min }\&le;Q_{\mathrm{SVCi}}\&le;Q_{\mathrm{SVCi}\max }\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i=N_c\end{array}\right.$

In constraints, P _gi, P _lithe generated power at node i place is exerted oneself and load is gained merit demand respectively; Q _gi, Q _lithe generator reactive at node i place is exerted oneself and reactive load demand respectively; Q _cifor the reactive compensation capacity of node i; N _bfor node set, N _gfor system generator set, N _cfor SVC compensates node set; G _ijwith B _ijbe respectively conductance and the susceptance of node admittance matrix; θ _ijfor the phase angle difference of node i and node j; V _i, V _imax, V _iminbe respectively node i voltage magnitude, voltage magnitude maximum and minimum value; P _imax, P _iminbe respectively generator node i meritorious output maximum and minimum value; Q _imax, Q _iminbe respectively the idle output maximum of generator node i and minimum value; Q _sVCi, Q _sVCimaxand Q _sVCiminbe respectively reactive power compensation both candidate nodes i reactive compensation capacity, reactive power compensation maximum and minimum value; S _ij, S _ijmaxbe respectively apparent power and the maximum thereof of circuit ij; y _ifor Boolean variable, y _i=1 represents that node i is candidate's reactive power compensation point;

In transient process, Voltage Stability Constraints comprises:

Short-term Voltage falls constraint:

Low-voltage duration constraints in Short-term Voltage Stability process: load bus voltage is at 0.75V ₀≤ V _s(t)≤0.8V ₀the duration of scope can not more than 20 cycles, i.e. 0.4s;

Reach voltage magnitude constraint: V after new steady-state process _i>=0.95V _0ii=1 ..., N _b;

Step 4: adopt hiding-trapezium integral method, by differential equation differencing method, changes algebraic step differentiation equation into by the differential equation in Optimized model; According to time-domain-simulation method and interior some optimization, according to target function and constraints, calculate the reactive compensation capacity of the idle planned position of each candidate of SVC under system peak load, average load operational mode respectively;

Step 5: the SVC reconnaissance factor obtained under different load level according to step 2,4, in conjunction with time-domain-simulation analysis, checks position and capacity that SVC finally needs compensation.

Fuzzy clustering algorithm in described step 2:

Based on each load bus index of transient process after catastrophe failure under two kinds of load levels that step 1 calculates, carry out data normalization;

Calculate the similarity r between each node i and j _ij, form fuzzy similarity matrix;

By the calculating of transitive closure, obtain fuzzy equivalent matrix;

By the element in fuzzy equivalent matrix, adopt fuzzy nonhierarchial clustering to be classified by all PQ nodes, accept horizontal threshold values λ by dynamic conditioning, λ is increased to gradually close to 1 from a less threshold values, obtains dynamic clustering result; Obtain some group nodes weak in all nodes;

Carry out F inspection, the newly-increased SVC candidate infield under selected catastrophe failure.

If the newly-increased reactive power compensation point position under two kinds of operating conditions is identical, then this newly-increased compensated position selected, and the reactive capability optimum results under complex optimum two kinds of operation levels.

If the newly-increased reactive power compensation point position under two kinds of operating conditions is different, then respectively on the basis of existing optimum results, optimize the planned capacity of newly-increased SVC after catastrophe failure under another operating condition.

When adopting TSC-TCR type SVC as planning apparatus, the principle that should be the 1/N of SVC total capacity according to the Capacity Selection of TCR carries out the configuration of TCR capacity.

Beneficial effect: compared with prior art, the inventive method has the following advantages:

The present invention is based on fuzzy clustering algorithm, time-domain-simulation analysis and interior point method optimum theory, adopt SVC alternatively reactive-load compensation equipment, consider its dynamic response characteristic, simultaneously, based on the dynamic action of three rank generator models and single order excitation system, consider above-mentioned constraints, invented under meeting the different operational mode of system, consider the idle planing method of steady operation and the constraint of the transient process stability of a system simultaneously.Carry out enforcement checking based on IEEE test macro, after considering fault under utilizing the quick features of response of SVC to achieve different running method, the power system reactive power of transient process scleronomic constraint is planned.Embodiment analysis shows, effective configuration SVC reactive power compensation, while guarantee economy, can realize the idle planning meeting different scleronomic constraint requirement, have theoretical and engineer applied value.

Accompanying drawing explanation

Fig. 1 is the idle planning flow chart of newly-increased SVC;

Fig. 2 is Dynamic Fuzzy Clustering Algorithm process schematic;

Fig. 3 is the membership function schematic diagram of variation index VDI;

Fig. 4 is transient process generator's power and angle situation of change schematic diagram under most catastrophe failure under peak load;

Fig. 5 is transient process load bus voltage magnitude situation of change schematic diagram under most catastrophe failure under peak load;

Fig. 6 is transient process system voltage recovery curve figure after compensating containing SVC under peak load;

Fig. 7 is the change curve at relative inertness center, generator amature angle in transient process after peak load level compensates containing SVC;

Fig. 8 is without SVC bucking-out system transient process load bus voltage change curve figure under average load level.

Embodiment

Below in conjunction with embodiment and Figure of description; the execution mode of technical solution of the present invention and concrete operating process are elaborated; but embodiment is only the preferred embodiment of the present invention; be noted that for those skilled in the art; under the premise without departing from the principles of the invention; can also make some improvement and equivalent replacement, these improve the claims in the present invention and are equal to the technical scheme after replacing, and all fall into protection scope of the present invention.

Fig. 1 is the idle planning flow chart of newly-increased SVC.As shown in Figure 1, the present invention relates to the idle planing method adopting SVC as reactive-load compensation equipment, concrete steps are as follows:

Step 1: based on system failure ranking method, calculates the transient process voltage stability index after most catastrophe failure respectively according to formula (1), (2), (3) under peak load, average load level:

System transient modelling Voltage Drop:

$V_{\mathrm{dip}}=\frac{V_0-V_s}{V_0}=\frac{\mathrm{\&Delta;V}}{V_0}\&times;100\%---\left(1\right)$

Wherein, V _sfor short-term stability process interior joint voltage lowest amplitude, V ₀for node voltage initial magnitude;

Variation index in transient process:

Low-voltage duration index in transient process: $\mathrm{LVDI}=\{\underset{t\&ni;(t_{\mathrm{cl}},t_f)}{\mathrm{\&Sigma;}}t/T|V\left(t\right)<0.8V_0,\&ForAll;t\&Element;(t_{\mathrm{cl}},t_f)\}$ $\left(3\right)$

Wherein, wherein, t _clfor the fault clearance time, t _ffor the emulation termination time, the starting point divided by T is that this index does not have dimension, is a normalized index.

Step 2: each voltage stability index in the transient process under the peak load obtained according to step 1, average load level, adopt fuzzy clustering method, obtain respectively SVC under system peak load, average load level the node i location sets N of candidate's reactive power compensation _c;

Step 3: set up SVC capacity planning optimal model:

Select three rank or more generator model, single order excitation system model and mixing load model:

The generator amature equation of motion adopts third-order model:

$\left\{\begin{array}{c}\frac{\mathrm{d\&delta;}\left(t\right)}{\mathrm{dt}}=(\mathrm{\&omega;}\left(t\right)-1){\mathrm{\&omega;}}_B\\ M\frac{\mathrm{d\&omega;}\left(t\right)}{\mathrm{dt}}=T_m-T_e\left(t\right)-D(\mathrm{\&omega;}\left(t\right)-1)\\ T_{d0}^{\&prime;}\frac{{\mathrm{dE}}_q^{\&prime;}\left(t\right)}{\mathrm{dt}}=E_f\left(t\right)-E_q^{\&prime;}\left(t\right)-(X_d-X_d^{\&prime;})I_d\left(t\right)\end{array}\right.$

Its voltage equation is $\left\{\begin{array}{c}{V}_d\left(t\right)=x_q{I}_q\left(t\right)-r_a{I}_d\left(t\right)\\ V_q\left(t\right)=E_q^{\&prime;}\left(t\right)-x_d^{\&prime;}{I}_d\left(t\right)-r_a{I}_q\left(t\right)\end{array}\right..$

In formula, δ is the angular displacement of rotor q axle relative to synchronous rotating frame real axis x; Time constant M, T ' _d0, D, T _afor famous value (unit s); Its dependent variable is per unit value.V _d, V _q, I _d, I _qfor the voltage and current phasor under d-q coordinate,

Single order excitation model:

$T_A\frac{{\mathrm{dE}}_f\left(t\right)}{\mathrm{dt}}=K_A(V_{\mathrm{ref}}-V_m\left(t\right))-E_f\left(t\right)+E_{f0}$

V _mfor voltage magnitude.V _reffor reference voltage amplitude.T _e＝E′ _qI _q-(X′ _d-X _q)I _dI _q。

According to the principle that state variable is not suddenlyd change, generator rotor angle and E ' can be obtained _q, E _f0and T _minitial value:

$\left\{\begin{array}{c}{E}_{q0}^{\&prime;}=U_{q0}+X_d^{\&prime;}{I}_{d0}+r_a{I}_{q0}\\ E_{f0}=U_{q0}+X_d{I}_{d0}+r_a{I}_{q0}\\ T_{m0}=E_{q0}^{\&prime;}{I}_{q0}-(X_d^{\&prime;}-X_q)I_{d0}{I}_{q0}\end{array}\right.$

Transient process stable constraint after consideration system generation catastrophe failure, the target function of concrete optimization problem and constraints are:

(1), target function

Adopt SVC as reactive-load compensation equipment, consider that the newly-increased reactive power compensation object of planning function of transient process scleronomic constraint is chosen for idle investment cost minimum:

$\min \underset{i=1}{\overset{N_b}{\mathrm{\&Sigma;}}}[C_{\mathrm{fix}\_i}+C_{i\_\mathrm{vl}}\max \left(Q_{\mathrm{SVCi}}^{+}\right)+C_{i\_v2}\max \left(\right|Q_{\mathrm{SVCi}}^{-}\left|\right)]$

(2), Static Security Constraints condition

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-P_{\mathrm{Li}}-V_i\underset{\mathrm{j\&omega;i}}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})=0\\ Q_{\mathrm{Gi}}+Q_{\mathrm{ci}}{y}_i-Q_{\mathrm{Li}}-V_i\underset{\mathrm{j\&omega;i}}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})=0\\ \begin{array}{cc}{V}_{i\min }\&le;V_i\&le;V_{i\max }& i\&Element;N_b\end{array}\\ \begin{array}{cc}{P}_{\mathrm{Gi}\min }\&le;P_{\mathrm{Gi}}\&le;P_{\mathrm{Gi}\max }& i\&Element;N_G\end{array}\\ \begin{array}{cc}{Q}_{\mathrm{Gi}\min }\&le;Q_{\mathrm{Gi}}\&le;Q_{\mathrm{Gi}\max }& i\&Element;N_G\end{array}\\ -S_{\mathrm{ij}\max }\&le;S_{\mathrm{ij}}\&le;S_{\mathrm{ij}\max }\\ Q_{\mathrm{SVCi}\min }\&le;Q_{\mathrm{SVCi}}\&le;Q_{\mathrm{SVCi}\max }\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i=N_c\end{array}\right.$

Static Security Constraints comprises system load flow equality constraint, voltage magnitude constraint, generated power, the constraint of idle bound, line transmission capacity-constrained, reactive-load compensation equipment capacity bound and reactive power compensation point restricted number.

Wherein, C _{fix_i}for idle investment fixed cost; C _{i_v1}for capacitive reactive power variable cost; C _{i_v2}for the idle variable cost of perception; for node i capacitive SVC compensation capacity; for the SVC compensation capacity of perception; In constraints, P _gi, P _lithe generated power at node i place is exerted oneself and load is gained merit demand respectively; Q _gi, Q _lithe generator reactive at node i place is exerted oneself and reactive load demand respectively; Q _cifor the reactive compensation capacity of node i; N _bfor node set, N _gfor system generator set, N _cfor SVC compensates node set; G _ijwith B _ijbe respectively conductance and the susceptance of node admittance matrix; θ _ijfor the phase angle difference of node i and node j; V _i, V _imax, V _iminbe respectively node i voltage magnitude, voltage magnitude maximum and minimum value; P _imax, P _iminbe respectively generator node i meritorious output maximum and minimum value; Q _imax, Q _iminbe respectively the idle output maximum of generator node i and minimum value; Q _sVCi, Q _sVCimaxand Q _sVCiminbe respectively reactive power compensation both candidate nodes i reactive compensation capacity, reactive power compensation maximum and minimum value; S _ij, S _ijmaxbe respectively apparent power and the maximum thereof of circuit ij; y _ifor Boolean variable, y _i=1 represents that node i is candidate's reactive power compensation point;

(3), transient process scleronomic constraint

A. the center of inertia COI of selecting system is reference, and transient process angle stability constraint representation is:

$\begin{array}{cc}|{\mathrm{\&delta;}}_i\left(t\right)-{\mathrm{\&delta;}}_{\mathrm{COI}}\left(t\right)|\&le;{\mathrm{\&delta;}}_{\max }& \&ForAll;i\&Element;N_G\end{array}$

Wherein, set δ herein _maxbe 2, unit is rad.

On the other hand, for transient process Voltage-stabilizing Problems, need to consider to occur in the transient process of N-1 fault in system, the operational factor of system voltage within the limits prescribed.According to voltage time domain running orbit, NERC/WECC evaluation criterion, adopts following index:

B. transient process Voltage Drop constraint

First, according to the definition of system transient modelling Voltage Drop: wherein, V _sfor transient process interior joint voltage lowest amplitude, V ₀for node voltage initial magnitude.

Require load bus V _dip≤ 25%, non-load bus V _dip≤ 30%; Or load bus meets V within continuous 20 cycles _dip≤ 20%.

For load bus, i.e. V _s(t)≤0.75V ₀.Meanwhile, for preventing generator overexcitation, need to set voltage magnitude upper limit constraint V simultaneously _max.Therefore, transient process Voltage Drop constraint representation is:

C. transient process low-voltage duration constraints

Load bus voltage is at 0.75V ₀≤ V _s(t)≤0.8V ₀the duration of scope can not more than 20 cycles, i.e. 0.4s.

D. voltage magnitude constraint after new steady-state process is reached

V _i≥0.95V _0ii＝1,...,N _b

From the Optimized model set up above, consider that the power system reactive power planning problem of multiple reactive-load compensation equipment is a Nonlinear Mixed Integer Programming Problem containing differential-algebraic equation.Dimension is solved, by PROBLEM DECOMPOSITION for newly-increased SVC reconnaissance and capacity optimize two processes for reducing.Meanwhile, consider different operational modes and catastrophe failure, the optimal result of reactive power compensation is determined in comprehensive analysis.Contingency screening and optimizing process adopt based on hiding-trapezium integral method time-domain-simulation, and integration step is 0.01s.

Step 4: adopt hiding-trapezium integral method, by differential equation differencing method, changes algebraic step differentiation equation into by the differential equation in Optimized model; According to time-domain-simulation method and interior some optimization, according to target function and constraints, calculate the reactive compensation capacity of each idle planned position of SVC under different load operational mode respectively;

Step 5: the SVC reconnaissance factor obtained under different load level according to step 2,4, in conjunction with time-domain-simulation analysis, checks position and capacity that SVC finally needs compensation.

1.2 times that system based on IEEE3 machine 9 node system, and is gained merit by the specific embodiment of the invention, load or burden without work rises to initial data.Correspondingly, the meritorious of generator is exerted oneself also according to the proportional increase of its original situation of exerting oneself 1.2 times.The average load level of system as system to be planned will be obtained.For this basic load operation operating mode, setting peak load be when load gain merit, reactive requirement level brings up to 1.2 times time situation.

In the specific embodiment of the invention, due under different load levels, the situation that most catastrophe failure occurs generally can be different, and the newly-increased compensation point position of SVC thus will be caused different, and added compensation capacity is different.Therefore, for distributing SVC compensation point position rationally, the present embodiment is based on two kinds of different operating conditions: under peak load level and average load level (average load level), carry out reconnaissance analysis respectively, consider the idle planning of SVC of transient process Voltage Stability Constraints to SVC.

In step 1, each transient process voltage stability index after most catastrophe failure is all based on phasor form, and each index describes the voltage stabilization situation comprising each load bus of power system network.

Before idle work optimization, that selects suitable reactive power compensation position effectively can reduce whole planning problem solves difficulty, and Reduction Computation time greatly.Consider SVC to be installed on load bus, therefore the present invention is only concerned about and sets up the relevant dynamic indicator of load bus.Based on domain simulation eur, the bus voltage stability index of step 1 is set up as follows:

The first: variation index in transient process;

Define according to system transient modelling Voltage Drop:

$V_{\mathrm{dip}}=\frac{V_0-V_s}{V_0}=\frac{\mathrm{\&Delta;V}}{V_0}\&times;100\%$

Wherein, V _sfor transient process node voltage lowest amplitude, V ₀for node voltage initial magnitude.

According to V _dipdefinition, be eliminate step effect, adopt the S type function of expansion, definition variation index VDI (Voltage Deviation Index):

The second: transient process low-voltage duration index;

After calculating fault clearance, [t _cl, t _f] period T=t _f-t _clinterior each load bus voltage is lower than 0.8V ₀accumulative total time, definition low-voltage duration index LVDI (Low Voltage Duration Index):

$\mathrm{LVDI}=\{\underset{t\&ni;(t_{\mathrm{cl}},t_f)}{\mathrm{\&Sigma;}}t/T|V\left(t\right)<0.8V_0,\&ForAll;t\&Element;(t_{\mathrm{cl}},t_f)\}$

Wherein, t _clfor the fault clearance time, t _ffor the emulation termination time.

Adopt the set that obtains of fuzzy clustering algorithm respectively based on the disturbance under system different load level run pattern in step 2, belong to the result that many cover operational systems calculate respectively.Its computational process is:

Step 21: data normalization: because the Principles and ways of each Index Establishment is different, initial data aims of standardization eliminate the difference between different indexs in dimension and dimension, under making each index all be distributed in unified scale.Usually, data normalization is interval to [0,1].

Step 22: form fuzzy similarity matrix: based on the matrix after the normalization obtained above, can similarity r between computing node i and j _ij, form fuzzy similarity matrix.

Step 23: calculate fuzzy equivalent matrix: for making matrix meet reflectivity, symmetry and transitivity simultaneously, further by the calculating of transitive closure, fuzzy equivalent matrix can be obtained.

Step 24: Dynamic Fuzzy Clustering Algorithm: according to fuzzy equivalent matrix, can carry out the Dynamic Fuzzy Clustering Algorithm analysis of system.For different threshold values, the λ Level Matrix of system can be obtained, draw final cluster result.Dynamic clustering process as shown in Figure 2.

Step 25:F checks: according to different threshold values, and calculate F value, larger F value shows to there is more obvious difference between each grouping.

For selecting the reasonability of suitable value assessment classification, adopt F inspection

$F=\frac{\underset{j=1}{\overset{r}{\mathrm{\&Sigma;}}}{n}_j{\left|\right|v_j-\stackrel{\&OverBar;}{x}\left|\right|}^2/(r-1)}{\underset{j=1}{\overset{r}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{n_j}{\mathrm{\&Sigma;}}}{n}_j{\left|\right|x_k^j-v_j\left|\right|}^2/(n-r)}$

In formula: n _jit is the node number of jth group in fuzzy clustering result; R is the group number of fuzzy cluster analysis

$x_k^j=(x_{k1},x_{k2},...,x_{\mathrm{km}}),k=1,...,n_j;$

$v_j=(v_1^j,v_2^j,...,v_m^j),v_1^j=\frac{1}{n_j}\underset{k=1}{\overset{n_j}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}}^j;$

$\stackrel{\&OverBar;}{x}=({\stackrel{\&OverBar;}{x}}_1,{\stackrel{\&OverBar;}{x}}_2,...,{\stackrel{\&OverBar;}{x}}_m),{\stackrel{\&OverBar;}{x}}_i=\frac{1}{n}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ki}},i=1,...,m;$

F is that to obey the degree of freedom be the statistic that the F of (r-1, n-r) distributes.According to different threshold values, calculate F value, larger F value shows may there is more obvious difference between each grouping.

By early stage shunt capacitor program results and SVC program results carry out integrated decision-making analysis.If the SVC reconnaissance obtained under peak load level and under average load level is consistent, then using optimum results higher for SVC value in the two optimum results as final SVC program results.If the SVC dot position obtained under two kinds of load levels is different, then the SVC program results under peak load is first adopted to check the transient process stability under average load level.If the transient process stability under average load level can be maintained, then the very final program results of the SVC program results obtained under peak load level; Otherwise, when the horizontal SVC program results of peak load drops into, by the SVC candidate compensation point determined under average load level progressively little step-length increase progressively the mode of SVC capacity, check through time-domain-simulation, obtain final SVC program results.

The aspect considered in complex optimum interpretation of result in steps of 5 mainly comprises:

A. due under different load levels, the situation that most catastrophe failure occurs generally can be different, and the newly-increased compensation point position of SVC thus will be caused different, and added compensation capacity is different.Therefore, consider that the idle planning of SVC of transient process Voltage Stability Constraints need consider the problem broken down under peak load level and average load level two kinds of different running method.

If the newly-increased reactive power compensation point position b. under two kinds of operating conditions is identical, then this newly-increased compensated position selected, and the reactive capability optimum results under complex optimum two kinds of operation levels, generally, select capability value that optimum results under two kinds of operation levels is larger as optimum capacity configuration result;

If the newly-increased reactive power compensation point position c. under two kinds of operating conditions is different, then respectively on the basis of existing optimum results, optimize the planned capacity of newly-increased SVC after catastrophe failure under another operating condition.

D. finally in conjunction with time-domain-simulation analysis, position and capacity that SVC finally needs compensation is checked.

E., when adopting TSC-TCR type SVC as planning apparatus, the principle that should be the 1/N of SVC total capacity according to the Capacity Selection of TCR carries out the configuration of TCR capacity.

In the specific embodiment of the invention, under two kinds of different operation levels, setting failure mode is that in system, a certain bar circuit, when 0.1s, three-phase ground short trouble occurs, and fault continues 0.1s (5 power frequency periods), line disconnection afterwards, excision fault.

(1) the idle planning under peak load

In peak load level run situation, most catastrophe failure is that circuit 8 (node 8-node 9), when node 8 is in 0.1s, three-phase ground short circuit occurs, and cut-offs circuit excision fault after 0.1s.When dropping into without SVC, time-domain-simulation obtains in transient process that generator's power and angle curve is as Fig. 4, and load bus voltage change curve is as Fig. 5.

After 0.2s moment fault clearance, system voltage sharply declines, and voltage stability index destroys, and when 0.6s, system exciting voltage reaches the highest, causes voltage keeps to vibrate, and finally there occurs voltage collapse event.Voltage lose stable after, there is merit angle unstability.For this reason, need to consider that planning drops into the reactive-load compensation equipment with fast dynamic response ability, stablize as SVC etc. maintains system transient modelling process voltage.

(i) SVC reconnaissance

Based on the present embodiment situation, calculate the index that each load bus is corresponding, as shown in table 1.

The each load bus index of transient process after table 1 two kinds of catastrophe failures

Fig. 2 is specific embodiment of the invention Dynamic Fuzzy Clustering Algorithm process schematic.As shown in Figure 2, under peak load level, the Data Source of fuzzy clustering is VDI and LVDI of table 1.

Fuzzy clustering algorithm is through data normalization: because the Principles and ways of each Index Establishment is different, initial data aims of standardization eliminate the difference between different indexs in dimension and dimension, under making each index all be distributed in unified scale; Usually, data normalization is interval to [0,1];

Obtain the matrix after based on the normalization obtained above, can similarity r between computing node i and j _ij, form fuzzy similarity matrix; By the calculating of transitive closure, obtain fuzzy equivalent matrix; Fuzzy equivalent matrix is:

$\underset{~}{R}=\left[\begin{array}{cccccc}1.0& 0& 0.61& 0.66& 0.57& 0.74\\ 0& 1.0& 0& 0& 0& 0\\ 0.61& 0& 1.0& 0.61& 0.57& 0.61\\ 0.66& 0& 0.61& 1.0& 0.57& 0.66\\ 0.57& 0& 0.57& 0.57& 1.0& 0.57\\ 0.74& 0& 0.61& 0.66& 0.57& 1.0\end{array}\right]$

By element in matrix, adopts fuzzy nonhierarchial clustering to be classified by all 6 PQ nodes, accepts horizontal threshold values λ by dynamic conditioning, λ is increased to gradually close to 1 from a less threshold values, obtains dynamic clustering result.Node 5, node 6 are classified as two the weakest group nodes earlier respectively.

Finally in conjunction with F inspection, selected catastrophe failure lower node 5, node 6 are newly-increased SVC candidate infield.

(ii) the capacity optimization of SVC

Target function adopts newly-increased idle input to minimize, and using the SVC optimum results do not considered in transient process Voltage Stability Constraints situation as running initial value, under peak load level, node 5, node 6 increase SVC susceptance capacity newly and be 0.Calculation optimization model obtains considering that the SVC idle work optimization result of transient process Voltage Stability Constraints is:

Need to set up SVC capacity susceptance 0.7687p.u. in node 5 transient process, inductive susceptance 0p.u..

Newly-increased SVC capacity susceptance 0.4883p.u. is needed, inductive susceptance 0p.u. in node 6 transient process.

Based on time-domain-simulation, consider catastrophe failure form mentioned above, obtain compensating rear system voltage recovery curve as shown in Figure 6 containing SVC, containing relative inertness center, generator amature angle change curve in system transient modelling process after SVC compensation as shown in Figure 7.Emulation continues 10s.Easily see that system meets angle stability constraint, and reach a new poised state.The frequency stability of transient process also obtains checking checking.

(2) the idle planning under average load

Under average load level, most catastrophe failure is that circuit 8 (node 8-node 9), when node 8 is in 0.1s, three-phase ground short circuit occurs, and cut-off circuit excision fault after 0.1s, time-domain-simulation continues 3s.Fig. 8 is each load bus change in voltage situation in transient process.In this transient process, occurred the situation that NERC/WECC voltage indexes destroys, but last voltage resume is to a more stable value, system is stabilized to a new state again.System does not lose angle stability in transient process.In addition, when arranging after other each circuits of system occur three phase short circuit fault separately, all do not occur the situation that NERC/WECC voltage indexes destroys, system merit angle also remains stable.

(i) SVC reconnaissance

Under average load level, Data Source is VDI and the LVDI index of table 1.Adopt similar thinking, the node 5 that is easy to get is regarded as the most weak node of voltage always and is separated with other node clusters.In conjunction with F inspection, the newly-increased SVC candidate infield obtained under average load level is node 5.

(ii) the capacity optimization of SVC

Under average load level, consider that the SVC idle work optimization result of transient process Voltage Stability Constraints is: need to set up SVC capacity susceptance 0.5615p.u. in node 5 transient process, inductive susceptance 0p.u..

After increasing SVC compensation, after system generation catastrophe failure, transient process voltage stability index and transient stability index all meet rule.Omit herein and compensate the curve of rear system parameters in transient process, analytical method is identical with the check method under peak load mentioned above.After optimizing, under fault, transient process index all meets indication range, and the verification of transient process frequency stabilization is passed through.

(3) unified plan result

The optimum results obtained when comprehensive different operation level and catastrophe failure, the result of study of SVC configuration is comprehensively analyzed, can determine that idle program results is:

Node 5 need increase configuration capacity susceptance 0.7687p.u., inductive susceptance 0p.u. newly;

Node 6 need increase configuration capacity susceptance 0.4883p.u., inductive susceptance 0p.u. newly.

When adopting TSC-TCR type SVC as planning apparatus, the principle that should be the 1/N of SVC total capacity according to the Capacity Selection of TCR carries out the configuration of TCR capacity.

The above is only the preferred embodiment of the present invention; be noted that for those skilled in the art; under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (5)

1. adopt SVC as an idle planing method for reactive-load compensation equipment, it is characterized in that: concrete steps are as follows:

Step 1: based on system failure ranking method, calculates the transient process voltage stability index after most catastrophe failure respectively according to formula (1), (2), (3) under peak load, average load level:

System transient modelling Voltage Drop:

$V_{\mathrm{dip}}=\frac{V_0-V_s}{V_0}=\frac{\mathrm{\&Delta;V}}{V_0}\&times;100\%---\left(1\right)$

Wherein, V _sfor short-term stability process interior joint voltage lowest amplitude, V ₀for node voltage initial magnitude;

Variation index in transient process:

Low-voltage duration index in transient process:

Wherein, wherein, t _clfor the fault clearance time, t _ffor the emulation termination time;

Step 2: each voltage stability index in the transient process under the peak load obtained according to step 1, average load level, adopt fuzzy clustering method, obtain respectively SVC under system peak load, average load level the node i location sets N of candidate's reactive power compensation _c;

Step 3: set up SVC capacity planning optimal model:

Select three rank or more generator model, single order excitation system model and mixing load model:

Three rank generator models:

$\left\{\begin{array}{c}\frac{\mathrm{d\&delta;}\left(t\right)}{\mathrm{dt}}=(\mathrm{\&omega;}\left(t\right)-1){\mathrm{\&omega;}}_B\\ T_j\frac{\mathrm{d\&omega;}\left(t\right)}{\mathrm{dt}}=T_m-T_e\left(t\right)-D(\mathrm{\&omega;}\left(t\right)-1)\\ T_{d0}^{\&prime;}\frac{{\mathrm{dE}}_q^{\&prime;}\left(t\right)}{\mathrm{dt}}=E_f\left(t\right)-E_q^{\&prime;}\left(t\right)-(X_d-X_d^{\&prime;})I_d\left(t\right)\end{array}\right.$

Wherein, δ (t) is for q axle is relative to the angular displacement of synchronous rotating frame; ω _brotor rated speed and rotor t angular speed is respectively with ω (t); T _jwith T ' _d0for time constant, T _mwith T _et () is respectively mechanical force moment and dynamo-electric moment; E _f, E ' _qbe respectively stator excitation electromotive force and motor q axle transient internal voltage; X _dwith X ' _dbe respectively d axle synchronous reactance and d axle transient reactance; I _dfor d shaft current;

Its set end voltage equation is:

$\left\{\begin{array}{c}{V}_d\left(t\right)=x_q{I}_q\left(t\right)-r_a{I}_d\left(t\right)\\ V_q\left(t\right)=E_q^{\&prime;}\left(t\right)-x_d^{\&prime;}{I}_d\left(t\right)-r_a{I}_q\left(t\right)\end{array}\right.$

Wherein, V _d, V _q(I _d, I _q) be respectively d shaft voltage and q shaft voltage (electric current); x _q, r _abe respectively q axle synchronous reactance and winding resistance;

Single order excitation system model:

$T_A\frac{{\mathrm{dE}}_f\left(t\right)}{\mathrm{dt}}=K_A(V_{\mathrm{ref}}-V_m\left(t\right))-E_f\left(t\right)+E_{f0}$

Wherein, T _afor time constant; K _afor control coefrficient; V _refand V _mbe respectively node voltage reference value and amplitude; E _f0for excitation electric gesture initial value;

Target function is made for condition so that the idle input cost of SVC is minimum:

$\min \underset{i=1}{\overset{N_b}{\mathrm{\&Sigma;}}}[C_{\mathrm{fix}\_i}+C_{i\_v1}\max \left(Q_{\mathrm{SVCi}}^{+}\right)+C_{i\_v2}\max \left(\right|Q_{\mathrm{SVCi}}^{-}\left|\right)]$

Wherein, C _{fix_i}for idle investment fixed cost; C _{i_v1}for capacitive reactive power variable cost; C _{i_v2}for the idle variable cost of perception; for node i capacitive SVC compensation capacity; for the SVC compensation capacity of perception;

Static Security Constraints condition is

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-P_{\mathrm{Li}}-V_i\underset{\mathrm{j\&omega;i}}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}})=0\\ Q_{\mathrm{Gi}}+Q_{\mathrm{ci}}{y}_i-Q_{\mathrm{Li}}-V_i\underset{\mathrm{j\&omega;i}}{\mathrm{\&Sigma;}}{V}_j(G_{\mathrm{ij}}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\&theta;}}_{\mathrm{ij}})=0\\ \begin{array}{cc}{V}_{i\min }\&le;V_i\&le;V_{i\max }& i\&Element;N_b\end{array}\\ \begin{array}{cc}{P}_{\mathrm{Gi}\min }\&le;P_{\mathrm{Gi}}\&le;P_{\mathrm{Gi}\max }& i\&Element;N_G\end{array}\\ \begin{array}{cc}{Q}_{\mathrm{Gi}\min }\&le;Q_{\mathrm{Gi}}\&le;Q_{\mathrm{Gi}\max }& i\&Element;N_G\end{array}\\ -S_{\mathrm{ij}\max }\&le;S_{\mathrm{ij}}\&le;S_{\mathrm{ij}\max }\\ Q_{\mathrm{SVCi}\min }\&le;Q_{\mathrm{SVCi}}\&le;Q_{\mathrm{SVCi}\max }\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i=N_c\end{array}\right.$

In constraints, P _gi, P _lithe generated power at node i place is exerted oneself and load is gained merit demand respectively; Q _gi, Q _lithe generator reactive at node i place is exerted oneself and reactive load demand respectively; Q _cifor the reactive compensation capacity of node i; N _bfor node set, N _gfor system generator set, N _cfor SVC compensates node set; G _ijwith B _ijbe respectively conductance and the susceptance of node admittance matrix; θ _ijfor the phase angle difference of node i and node j; V _i, V _imax, V _iminbe respectively node i voltage magnitude, voltage magnitude maximum and minimum value; P _imax, P _iminbe respectively generator node i meritorious output maximum and minimum value; Q _imax, Q _iminbe respectively the idle output maximum of generator node i and minimum value; Q _sVCi, Q _sVCimaxand Q _sVCiminbe respectively reactive power compensation both candidate nodes i reactive compensation capacity, reactive power compensation maximum and minimum value; S _ij, S _ijmaxbe respectively apparent power and the maximum thereof of circuit ij; y _ifor Boolean variable, y _i=1 represents that node i is candidate's reactive power compensation point;

In transient process, Voltage Stability Constraints comprises:

Short-term Voltage falls constraint:

Low-voltage duration constraints in Short-term Voltage Stability process: load bus voltage is at 0.75V ₀≤ V _s(t)≤0.8V ₀the duration of scope can not more than 20 cycles, i.e. 0.4s;

Reach voltage magnitude constraint: V after new steady-state process _i>=0.95V _0ii=1 ..., N _b;

Step 4: adopt hiding-trapezium integral method, by differential equation differencing method, changes algebraic step differentiation equation into by the differential equation in Optimized model; According to time-domain-simulation method and interior some optimization, according to target function and constraints, calculate the reactive compensation capacity of the idle planned position of each candidate of SVC under system peak load, average load operational mode respectively;

Step 5: the SVC reconnaissance factor obtained under different load level according to step 2,4, in conjunction with time-domain-simulation analysis, checks position and capacity that SVC finally needs compensation.

2. employing SVC according to claim 1 is as the idle planing method of reactive-load compensation equipment, it is characterized in that: the fuzzy clustering algorithm in described step 2:

Based on each load bus index of transient process after catastrophe failure under two kinds of load levels that step 1 calculates, carry out data normalization;

Calculate the similarity r between each node i and j _ij, form fuzzy similarity matrix;

By the calculating of transitive closure, obtain fuzzy equivalent matrix;

By the element in fuzzy equivalent matrix, adopt fuzzy nonhierarchial clustering to be classified by all PQ nodes, accept horizontal threshold values λ by dynamic conditioning, λ is increased to gradually close to 1 from a less threshold values, obtains dynamic clustering result; Obtain some group nodes weak in all nodes;

Carry out F inspection, the newly-increased SVC candidate infield under selected catastrophe failure.

3. employing SVC according to claim 1 is as the idle planing method of reactive-load compensation equipment, it is characterized in that: if the newly-increased reactive power compensation point position under two kinds of operating conditions is identical, then this newly-increased compensated position selected, and the reactive capability optimum results under complex optimum two kinds of operation levels.

4. employing SVC according to claim 1 is as the idle planing method of reactive-load compensation equipment, it is characterized in that: if the newly-increased reactive power compensation point position under two kinds of operating conditions is different, then respectively on the basis of existing optimum results, optimize the planned capacity of newly-increased SVC after catastrophe failure under another operating condition.

5. employing SVC according to claim 1 is as the idle planing method of reactive-load compensation equipment, it is characterized in that: when adopting TSC-TCR type SVC as planning apparatus, the principle that should be the 1/N of SVC total capacity according to the Capacity Selection of TCR carries out the configuration of TCR capacity.