CN100585977C - Imbalance compensation and ant colony optimization method of static reactive compensator - Google Patents

Abstract

The invention discloses an imbalance compensation and the ant colony optimization method for an SVC. The method is based on a variable structure to control the SVC, wherein, the variable structure control method comprises two aspects of the unbalanced load equalization compensation and the parameter control of a PI controller, wherein, the unbalanced load equalization compensation adopts the SVC compensation susceptance computational method which is based on the synchronous rotation reference coordinate transformation of a virtual symmetrical three-phase system; meanwhile, in the stabilization control of the system voltage, the ant colony algorithm optimization method is adopted to real time adjust and to optimize the parameter kp and ki of the PI controller. The invention ensures that the SVC can not only complete the unbalanced load equalization compensation but also control the stabilization, thereby raising the precision of the susceptance computation of the SVC, guaranteeing the balance compensation of the charge, improving the performance in the stabilization control of the SVC voltage and maintaining the voltage stabilization of a common connection joint. Therefore, the invention has high robustness and high response speed.

Description

A kind of imbalance compensation of Static Var Compensator and ant colony optimization method

Technical field

The present invention relates to a kind of control method, particularly a kind of imbalance compensation of Static Var Compensator and ant colony optimization method.

Background technology

Increasing along with non-linear, impact in the power distribution network and uncompensated load, power quality problems such as the voltage fluctuation in the power distribution network, voltage flicker and Voltage unbalance are also serious day by day, brought adverse effect for electric power system and important power consumer, distribution network electric energy quality control is very urgent.Static Var Compensator SVC is a kind of important custom power device, is applied to the dynamic passive compensation aspect of arc furnace etc. because of its ratio of performance to price is optimum, the above-mentioned power quality problem of solution that can be comprehensive.SVC has the function of uncompensated load equilibrating compensation and the stable control of system voltage, therefore carries out uneven research with Voltage Stability Control is had great importance.

When uncompensated load is balanced compensated, TSC+TCR type static passive compensation device (SVC) is used to the dynamic passive compensation aspect of arc furnace etc. because of its cost performance is optimum, by the phase-splitting adjusting three-phase asymmetric load is carried out the equilibrating compensation to eliminate negative sequence component, also provide capacitive reactive power simultaneously by passive filter filtering harmonic wave in parallel.Li Peng, stone the new year, the auspicious people of grade of fine strain of millet will is derived by arc furnace equilibrating compensation Practical Formula and checking has been done detailed inference to the equilibrating compensation scheme of SVC theoretically, but these methods are based upon under the situation of not taking into account system voltage, current distortion mostly, and in the industrial power distribution systems, having a large amount of harmonic waves in its voltage, the electric current, the energy imbalance of voltage is also very serious, if not harmonic carcellation and unbalanced influence, then result of calculation has bigger error.

When SVC was used for Electrical Power System Dynamic Voltage Stability Control and reactive power compensation, Static Var Compensator can compensate idle, burning voltage, inhibition voltage flicker of supply network etc., so the design of SVC controller also just becomes the focus of research.Peng Jianchun is at article " the intelligent adaptive PID design of Controller [J] of Static Var Compensator " (Hunan University's journal (natural science edition), 1999,26 (5): adopt fuzzy logic and neural net to combine 50-55), proposed the intelligent adaptive pid control mode.Ceng Guang is in article " the fuzzy-PID control method [J] that is used for the reactive static complement system " (electrotechnics journal, 2006,21 (6): studied the non-linear SVC control mode based on fuzzy algorithmic approach 40-43).And ant group algorithm obtained good effect when finding the solution problems such as Combinatorial Optimization, Power System Economic Load Dispatch, distribution network planning, but the pertinent literature that is applied in the concrete reactive power compensator is less as a kind of novel intelligent optimization algorithm.

Summary of the invention

For overcoming the shortcoming of prior art, goal of the invention of the present invention aims to provide a kind of imbalance compensation and ant colony optimization method of Static Var Compensator, can be on the basis of the performance that promotes the SVC device, reach that governing speed is fast, the compensation susceptance calculate simple, control is simple and the wide effect of range of operation.

For achieving the above object, the technical scheme that technical solution problem of the present invention is adopted is: a kind of imbalance compensation of Static Var Compensator and ant colony optimization method, based on becoming structure Static Var Compensator SVC is controlled, variable structure control method comprises two aspects of parameter control of uncompensated load equilibrating compensation and PI controller, wherein the SVC compensation susceptance computational methods based on the synchronous rotary reference coordinate transform of virtual symmetrical three-phase system are adopted in uncompensated load equilibrating compensation, can effectively eliminate imbalance and influence of harmonic; Simultaneously be easy to realize and the static reactive system is difficult for setting up the problem of precise math model, when the stable control of system voltage, adopt the ant group algorithm optimization method, the parameter k of PI controller at traditional PI controller simple in structure _p, k _iAdjust in real time, optimizing, make the dynamic response process of SVC system reach optimization.

Above-mentioned uncompensated load equilibrating compensation method is, utilizes the synthesized voltage vector of virtual symmetrical three-phase system to form rotating coordinate system, the steps include: at first to utilize the symmetrical three-phase system u of the phase voltage constructing virtual in the line voltage _Abc, then to the three-phase voltage u of virtual symmetrical three-phase system _AbcWith load current i _LabcImplement to obtain after the α β coordinate transform voltage vector u and current phasor i on the α βPing Mian respectively; The d axle of definition dq rotating coordinate system overlaps with the synthesized voltage vector u of the positive sequence symmetry three-phase system of extraction;

The synchronizing current that obtains current phasor projection under voltage vector is:

$\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]=\left[\begin{array}{cc}\frac{u_{\mathrm{\&alpha;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}& \frac{u_{\mathrm{\&beta;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}\\ -\frac{u_{\mathrm{\&beta;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}& \frac{u_{\mathrm{\&alpha;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}\end{array}\right]\&CenterDot;\left[\begin{array}{c}\frac{i_{\mathrm{\&alpha;}}{u}_{\mathrm{\&alpha;}}+i_{\mathrm{\&beta;}}{u}_{\mathrm{\&beta;}}}{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}\&CenterDot;u_{\mathrm{\&alpha;}}\\ \frac{i_{\mathrm{\&alpha;}}{u}_{\mathrm{\&alpha;}}+i_{\mathrm{\&beta;}}{u}_{\mathrm{\&beta;}}}{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}\&CenterDot;u_{\mathrm{\&beta;}}\end{array}\right]=R\left(\mathrm{\&theta;}\right)\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}}\\ i_{\mathrm{\&beta;}}\end{array}\right]=\left[\begin{array}{c}\frac{i_{\mathrm{\&alpha;}}{u}_{\mathrm{\&alpha;}}+i_{\mathrm{\&beta;}}{u}_{\mathrm{\&beta;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}\\ 0\end{array}\right]=\left[\begin{array}{c}{\stackrel{\&OverBar;}{i}}_d+{\tilde{i}}_{\mathrm{<figure-callout\; id="0"\; label="d"\; filenames="C2008100305590019H2.png"\; state="\{\{state\}\}">d</figure-callout>}}\\ 0\end{array}\right]$

By following formula as seen, current phasor reactive current i in the projection under the voltage vector _qBe zero, active current i _dContain DC component and alternating current component, with i _dBy low pass filter, can obtain the DC component i of synchronizing current _d, be the component that has synchronous speed with the line voltage vector, that is the fundamental positive sequence real component in the load current;

With the real axis of d axle as the complex coordinates system, the q axle has just corresponding to the imaginary axis so $u_{a+}=\sqrt{6}{u}_{\mathrm{\&alpha;}+}/3,$ $\left[\begin{array}{c}{\stackrel{\&OverBar;}{i}}_d\\ {\stackrel{\&OverBar;}{i}}_q\end{array}\right]=\frac{3}{2}\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="I"\; filenames="C2008100305590018H1.png,C2008100305590019H2.png"\; state="\{\{state\}\}">I</figure-callout>}}_1\cos {\mathrm{\&theta;}}_1\\ {\mathrm{<figure-callout\; id="1"\; label="I"\; filenames="C2008100305590018H1.png,C2008100305590019H2.png"\; state="\{\{state\}\}">I</figure-callout>}}_1\sin {\mathrm{\&theta;}}_1\end{array}\right],$ Thereby can get: $\mathrm{Im}{\stackrel{\&CenterDot;}{I}}_{\mathrm{la}+}=I_1\sin {\mathrm{\&theta;}}_1=\frac{2}{3}{\stackrel{\&OverBar;}{i}}_q,$ With the electric current in the α β coordinate by negative phase-sequence transformation matrix R (θ) be transformed into the dq coordinate system after, in like manner can be in the hope of the real part and the imaginary part of negative sequence component, substitution again $\left\{\begin{array}{c}{B}_{\mathrm{rab}}=-(\mathrm{Im}{\stackrel{.}{I}}_{\mathrm{la}+}-\sqrt{3}\mathrm{Re}{\stackrel{.}{I}}_{\mathrm{la}-}+\mathrm{Im}{\stackrel{.}{I}}_{\mathrm{la}-})/3U\\ B_{\mathrm{rbc}}=-(\mathrm{Im}{\stackrel{.}{I}}_{\mathrm{la}+}-2\mathrm{Im}{\stackrel{.}{I}}_{\mathrm{la}-})/3U\\ B_{\mathrm{rca}}=-(\mathrm{Im}{\stackrel{.}{I}}_{\mathrm{la}+}+\sqrt{3}\mathrm{Re}{\stackrel{.}{I}}_{\mathrm{la}-}+\mathrm{Im}{\stackrel{.}{I}}_{\mathrm{la}-})/3U\end{array}\right.$ Calculate, draw the susceptance value of three-phase compensation.

Above-mentioned ant group algorithm optimization method, adopt the ITAE criterion as target function:

$J={\&Integral;}_0^{t}t\left|e\left(t\right)\right|\mathrm{dt}$

Convergence criterion is shown below:

$\left|\frac{J^{\left(\max \right)}-J^{\left(\min \right)}}{J^{\left(\min \right)}}\right|<\mathrm{\&epsiv;}$

E is V in the formula _RefWith V _SLAnd V _RmsDifference, promptly as the error signal of ant group optimization PI controller; V _RmsRoot mean square value for system voltage; V _RefBe system reference voltage; V _SLIt is the bucking voltage of SVC; J ^(max)Be the maximum of points of optimizing, J ^(mm)Be the minimum point of optimizing, ε is given positive error amount, and voltage stable optimized parameter k thus can be guaranteed _p, k _iValue, thus the dynamic property of SVC improved;

According to target function and convergence criterion, use the parameter k of ant colony optimization algorithm to the PI controller _p, k _iCarry out optimizing.

The imbalance compensation of described Static Var Compensator provided by the invention and ant colony optimization method, its beneficial effect is that SVC can carry out uncompensated load equilibrating compensation, again can be to stable control, improved the precision that the Static Var Compensator susceptance calculates, that guarantees to load is balanced compensated, performance when having improved the SVC Voltage Stability Control, the voltage of keeping points of common connection is stable, has higher robustness and response speed.

The present invention is further illustrated below in conjunction with drawings and Examples.

Description of drawings

Fig. 1 is a control flow block diagram of the present invention;

Fig. 2 is the admittance backoff algorithm block diagram based on synchronous rotary reference coordinate method of the present invention;

Fig. 3 is voltage vector of the present invention and current phasor schematic diagram;

Fig. 4 is node and the path schematic diagram that ant group algorithm of the present invention is optimized the PI control method.

Embodiment

As shown in Figure 1, be based on the SVC control block diagram that becomes structure.V among the figure _RmsRoot mean square value for system voltage; V _RefBe system reference voltage; V _SLBe the bucking voltage of SVC, as V _RefCorrection be the feedback amount of SVC controller, calculate by formula (1), permanent speed regulation K can be taken as 3% in the formula (1); B _RefInput variable for TCR/TSC susceptance distribution module, be to calculate through optimum PI algorithm computation or based on the SVC compensation susceptance method of the synchronous rotary reference coordinate transform of virtual symmetrical three-phase system by error signal Δ V, obtain after the processing through the amplitude limit link, its size has determined the quantity of TSC input and the susceptance B that TCR should export again _Tcr, as can be seen from the figure the output susceptance of TCR is transformed into angle (angle of flow of thyristor) through susceptance one angle function and has controlled what of perceptual idle input electrical network; The number that TSC logic controller output high level or low level control capacitor drop into electrical network.When switch S is connected on position 1 among the figure, be the Voltage Stability Control mode of belt current feedback, SVC can carry out Voltage Stability Control, when S is connected on position 2, is open loop control mode, and SVC is as uncompensated load equilibrating compensate function;

V _SL＝K*I _SVC (1)

Uncompensated load equilibrating compensation admittance method, implementation method is as follows:

Practical admittance computing formula is:

$\left\{\begin{array}{c}{B}_{\mathrm{rab}}=-(\mathrm{Im}{\stackrel{.}{I}}_{\mathrm{la}+}-\sqrt{3}\mathrm{Re}{\stackrel{.}{I}}_{\mathrm{la}-}+\mathrm{Im}{\stackrel{.}{I}}_{\mathrm{la}-})/3U\\ B_{\mathrm{rbc}}=-(\mathrm{Im}{\stackrel{.}{I}}_{\mathrm{la}+}-2\mathrm{Im}{\stackrel{.}{I}}_{\mathrm{la}-})/3U\\ B_{\mathrm{rca}}=-(\mathrm{Im}{\stackrel{.}{I}}_{\mathrm{la}+}+\sqrt{3}\mathrm{Re}{\stackrel{.}{I}}_{\mathrm{la}-}+\mathrm{Im}{\stackrel{.}{I}}_{\mathrm{la}-})/3U\end{array}\right.---\left(2\right)$

From formula (2) as can be seen, if can directly obtain the imaginary part of the positive sequence component of line current, the real part of negative sequence component and the positive sequence effective value of imaginary part and phase voltage, so just can obtain the three-phase susceptance value of required compensation easily.

In order to reduce the detection error of reference synchronization coordinate method under the unbalanced source voltage condition, can utilize the basic thought of the synthesized voltage vector formation rotating coordinate system of virtual symmetrical three-phase system based on the line voltage vector.At first utilize the symmetrical three-phase system (only consider the amplitude imbalance of line voltage, satisfy the actual electric network situation) of the phase voltage constructing virtual in the line voltage and in fact do like this.With a phase voltage is example, with 60 ° of a phase voltage time-delays and anti-phase formation c phase voltage, just can obtain the b phase voltage by a, c phase voltage.

If a phase voltage is:

In the formula, U _AmBe the amplitude of a phase voltage, Be initial phase angle.After 60 ° of a phase voltage time-delays and the anti-phase c phase voltage that obtains be:

So can get the b phase voltage be:

By the three-phase system that (3), (4) and (5) constitute, present embodiment is referred to as virtual symmetrical three-phase system.With the synthesized voltage vector of virtual symmetrical three-phase system d axle as rotating coordinate system, just can realize the resultant vector of the line voltage fundamental positive sequence that equivalence that the d axle of rotating coordinate system can be similar to is actual, rotational coordinates can at the uniform velocity rotate.If consider the distortion situation of line voltage, the first-harmonic that can insert a phase voltage before the structure of virtual symmetrical three-phase system extracts circuit, but does the time-delay that can increase control system like this.When specific implementation,, can adopt the method for signal estimation in order to solve above-mentioned latency issue.

The theory diagram of whole detection method as shown in Figure 2.What " constructing symmetrical three-phase system " part among the figure adopted is aforesaid virtual symmetrical three-phase system building method based on the time-delay of a phase voltage.

Three-phase voltage u to virtual symmetrical three-phase system _AbcWith load current i _LabcImplement to obtain after the α β coordinate transform voltage vector u and current phasor i on the α βPing Mian respectively, see Fig. 3.The d axle of definition dq rotating coordinate system overlaps with the synthesized voltage vector u of the positive sequence symmetry three-phase system of extraction among the figure.

Can get by the geometrical relationship among Fig. 3:

$\cos \mathrm{\&theta;}=\frac{u_{\mathrm{\&alpha;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}---\left(6\right)$

$\sin \mathrm{\&theta;}=\frac{u_{\mathrm{\&beta;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}$

In α β coordinate, the component in order to obtain rotating synchronously with line voltage vector u among the load current vector i projects to current phasor i on the voltage vector u, can get:

$i_u=\left[\begin{array}{c}\frac{i_{\mathrm{\&alpha;}}{u}_{\mathrm{\&alpha;}}+i_{\mathrm{\&beta;}}{u}_{\mathrm{\&beta;}}}{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}\&CenterDot;u_{\mathrm{\&alpha;}}\\ \frac{i_{\mathrm{\&alpha;}}{u}_{\mathrm{\&alpha;}}+i_{\mathrm{\&beta;}}{u}_{\mathrm{\&beta;}}}{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}\&CenterDot;u_{\mathrm{\&beta;}}\end{array}\right]---\left(7\right)$

And α β coordinate transform to dq transformation of coordinates pass is:

$\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}\\ -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right]\&CenterDot;\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}}\\ i_{\mathrm{\&beta;}}\end{array}\right]---\left(8\right)$

The synchronizing current that can be obtained current phasor projection under voltage vector by Fig. 3 and Shi (6), (7) and (8) is:

$\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]=\left[\begin{array}{cc}\frac{u_{\mathrm{\&alpha;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}& \frac{u_{\mathrm{\&beta;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}\\ -\frac{u_{\mathrm{\&beta;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}& \frac{u_{\mathrm{\&alpha;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}\end{array}\right]\&CenterDot;\left[\begin{array}{c}\frac{i_{\mathrm{\&alpha;}}{u}_{\mathrm{\&alpha;}}+i_{\mathrm{\&beta;}}{u}_{\mathrm{\&beta;}}}{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}\&CenterDot;u_{\mathrm{\&alpha;}}\\ \frac{i_{\mathrm{\&alpha;}}{u}_{\mathrm{\&alpha;}}+i_{\mathrm{\&beta;}}{u}_{\mathrm{\&beta;}}}{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}\&CenterDot;u_{\mathrm{\&beta;}}\end{array}\right]=R\left(\mathrm{\&theta;}\right)\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}}\\ i_{\mathrm{\&beta;}}\end{array}\right]=\left[\begin{array}{c}\frac{i_{\mathrm{\&alpha;}}{u}_{\mathrm{\&alpha;}}+i_{\mathrm{\&beta;}}{u}_{\mathrm{\&beta;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}\\ 0\end{array}\right]=\left[\begin{array}{c}{\stackrel{\&OverBar;}{i}}_d+{\tilde{i}}_d\\ 0\end{array}\right]---\left(9\right)$

As seen, current phasor reactive current i in the projection under the voltage vector _qBe zero, active current i _dContain DC component and alternating current component, with i _dBy low pass filter, can obtain the DC component i of synchronizing current _d, be the component that has synchronous speed with the line voltage vector, that is the fundamental positive sequence real component in the load current.

By Fig. 3, if with the real axis of d axle as the complex coordinates system, the q axle has just corresponding to the imaginary axis so

$u_{a+}=\sqrt{6}{u}_{\mathrm{\&alpha;}+}/3---\left(10\right)$

$\left[\begin{array}{c}{\stackrel{\&OverBar;}{i}}_d\\ {\stackrel{\&OverBar;}{i}}_q\end{array}\right]=\frac{3}{2}\left[\begin{array}{c}{I}_1\cos {\mathrm{\&theta;}}_1\\ I_1\sin {\mathrm{\&theta;}}_1\end{array}\right]---\left(11\right)$

Thereby can get:

$\mathrm{Im}{\stackrel{\&CenterDot;}{I}}_{\mathrm{la}+}=I_1\sin {\mathrm{\&theta;}}_1=\frac{2}{3}{\stackrel{\&OverBar;}{i}}_q---\left(12\right)$

With the electric current in the α β coordinate by negative phase-sequence transformation matrix R (θ) be transformed into the dq coordinate system after, in like manner can be in the hope of the real part and the imaginary part of negative sequence component, substitution formula again (2) is calculated the susceptance value that just can draw three-phase compensation.

Ant group algorithm is optimized the PI control method, and specific implementation process is as follows:

E is V _RefWith V _SLAnd V _RmsDifference, promptly as the error signal of ant group optimization PI controller.Less for the overshoot of the input e transient response that guarantees the SVC voltage regulator, and vibration there are enough damping actions, the employing time takes advantage of integral of absolute value of error ITAE criterion as target function:

$J={\&Integral;}_0^{t}t\left|e\left(t\right)\right|\mathrm{dt}---\left(13\right)$

Convergence criterion is shown below:

$\left|\frac{J^{\left(\max \right)}-J^{\left(\min \right)}}{J^{\left(\min \right)}}\right|<\mathrm{\&epsiv;}---\left(14\right)$

J in the formula ^(max)Be the maximum of points of optimizing, J ^(min)Be the minimum point of optimizing, ε is given positive error amount, and voltage stable optimized parameter k thus can be guaranteed _p, k _iValue, thus the dynamic property of SVC improved.

The transfer function of conventional PI controller can be expressed as:

$U\left(s\right)=(k_p+\frac{k_p}{T_{i}s})E\left(s\right)---\left(15\right)$

K in the formula _pBe proportional gain, T _iBe integration time constant, E (s) is the input variable of system and the error between the output variable, and U (s) is a controlled quentity controlled variable.In discrete domain, the PI control law can be expressed as:

$u\left(k\right)=u_p\left(k\right)+u_i\left(k\right)=k_{p}e\left(k\right)+k_i\underset{j=0}{\overset{k}{\mathrm{\&Sigma;}}}e\left(j\right)---\left(16\right)$

In the formula, k _i=k _pT/T _i, T is the sampling period.

According to PI controller parameter value condition, its parameter all is 5 position effective digitals, wherein k _pTwo of integers, T _iOne of integer for ease of adopting ant group algorithm, is illustrated in these two parameter values on the XOY plane, abstractively as shown in Figure 4.On XOY plane, always have 10 * 10 nodes, with symbol Knot (x _i, y _{I, j}) node of expression, x _iBe line segment L _iAbscissa (i ≈ 1～10), y _{I, j}Be L _iThe ordinate of last node j (j=0～9), each node is represented a numerical value, it equals the ordinate value y of this node _{I, j}

If certain ant is from the origin of coordinates, when it crawls into L ₁₀When upward some arbitrarily, finish once circulation, its path of creeping can be expressed as: Path={o, Knot (x ₁, y _{1, j}) ..., Knot (x ₁₀, y _{10, j}), node Knot (x here _i, y _{I, j}) expression is positioned at L _iOn.The k of obvious this paths representative _pAnd T _iValue can be calculated as follows:

$\left\{\begin{array}{c}{k}_p=\underset{i=1}{\overset{5}{\mathrm{\&Sigma;}}}{y}_{i,j}\&times;{10}^{2-i}\\ T_i=\underset{n=6}{\overset{10}{\mathrm{\&Sigma;}}}{y}_{n,j}\&times;{10}^{6-n}\end{array}\right.---\left(17\right)$

Suppose that every ant is from line segment L _iGo up arbitrary node and crawl into next line segment L _I+1The time of going up arbitrary node equates, with range-independence, all from initial point, then they will arrive each bar line segment simultaneously and circulate to finishing once as if all ants.

Establish the ant group at moment t and crawl into line segment L _iOn, make b _j(j=0～9) are engraved in L during for t _iThe ant number at last node j place, then the ant sum can be expressed as:

$m=\underset{j=0}{\overset{9}{\mathrm{\&Sigma;}}}{b}_j\left(t\right)---\left(18\right)$

Be engraved in node Knot (x during t _i, y _{I, j}) pheromones left over is τ (x _i, y _{I, j}, t), the pheromones that each node of initial time is left over is equal, i.e. τ (x _i, y _{I, j}, 0)=c, c is a constant, i=1～10, j=0～9, then Δ τ (x _i, y _{I, j}, 0)=0.If P _k(x _i, y _{I, j}, t) expression t constantly k ant by L _I-1Last any point is to Knot (x _i, y _{I, j}) probability of creeping, then have:

$P_k(x_i,y_{i,j},t)=\frac{{\mathrm{\&tau;}}^{\mathrm{\&alpha;}}(x_i,y_{i,j},t){\mathrm{\&eta;}}^{\mathrm{\&beta;}}(x_i,y_{i,j},t)}{\underset{j=0}{\overset{9}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}^{\mathrm{\&alpha;}}(x_i,y_{i,j},t){\mathrm{\&eta;}}^{\mathrm{\&beta;}}(x_i,y_{i,j},t)}---\left(19\right)$

α is the heuristic factor of information in the formula, and β inspires the factor, η (x for expectation information _i, y _{I, j}, t) be node Knot (x _i, y _{I, j}) on heuristic function, be defined as:

$\mathrm{\&eta;}(x_i,y_{i,j},t)=\frac{10-|y_{i,j}-y_{i,j}^{*}|}{10}---\left(20\right)$

Y in the formula _{I, j} ^*(i=1～10, j=0～9) are value as follows: in the circulation first time of ant group algorithm, and y _{I, j} ^*Be the PI parameter k that obtains by the Ziegler-Nichols method _P0, T _I0Value be mapped in 10 pairing ordinate values of node on Fig. 4, afterwards in each time circulation, y _{I, j} ^*Then be the pairing PI parameter of the optimal path k that is produced in the last circulation _p ^*, T _i ^*Value be mapped in 10 pairing ordinate values of node on Fig. 4.

Cause too much that for fear of the residual risk element residual risk floods heuristic information, every ant is finished after once circulation is creeped, and upgrade processing to node residual risk element on the path.Thus, be engraved in node Knot (x during t+n _i, y _{I, j}) on amount of information can adjust according to the following rules

τ(x _i，y _i，j，t+n)＝(1-ρ)Δτ(t)+Δτ(t) (21)

$\mathrm{\&Delta;\&tau;}\left(t\right)=\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{\mathrm{\&tau;}}_k(x_i,y_{i,j})---\left(22\right)$

ρ represents the pheromones volatility coefficient in the formula, and then 1-ρ represents the residual factor of information number, and in order to prevent the unlimited accumulation of information, the span of ρ is: $\mathrm{\&rho;}\&Subset;\left[\mathrm{0,1}\right);$ Δ τ (t) represents node Knot (x in this circulation _i, y _{I, j}) on the pheromones increment, Δ τ _k(x _i, y _{I, j}) expression k ant stay node Knot (x in this circulation _i, y _{I, j}) on pheromones.

Q represents pheromones intensity in the formula, influences convergence of algorithm speed to a certain extent, J _kRepresent the target function value of k ant in this circulation.

It is as follows that ant group algorithm is optimized PI CALCULATION OF PARAMETERS step:

(I) utilize Ziegler-Nichols to calculate PI parameter k _P0, T _I0

(II) set ant and count m, and define an one-dimension array Path for every ant k with 10 elements _k, in this array, deposit the ordinate value of 10 nodes that this ant will pass through successively;

(III) make time counter t=0, cycle-index N _c=0, set maximum cycle N _CmaxAnd the value τ (x of pheromones on each node of initial time _i, y _{I, j}, 0)=c (i=1～10, j=0～9), make Δ τ (x _i, y _{I, j})=0 places initial point with whole ants;

(IV) put variable i=1;

(V) utilize formula (19) to calculate these ants to line segment L _iGo up the probability that each node shifts, according to these probability, adopting the roulette wheel method is every ant k (k=1～m) at line segment L _iNode of last selection, and ant k moved on to this node, the ordinate value with this node deposits Path in simultaneously _kI element;

(VI) put i=i+1,, otherwise jump to (VII) step if i≤10 then jump to (V) step;

(VII) according to ant k (path of k=1～m) passed by, i.e. array Path _k, utilize the PI parameter k of formula (17) calculating path correspondence _p ^k, T _i ^k, utilize formula (15) and (16) to calculate the pairing target function J of ant k respectively _kWith pairing convergence numerical value ε _k, write down the optimal path in this circulation, and deposit PI parameter corresponding in k with it _p ^*, T _i ^*

(VIII) make t ← t+10, N _c← N _c+ 1, upgrade the pheromones on each node according to formula (21), (22), (23), and with Path _k(all elements zero clearing among the k=1～m);

(IX) as N _c＜N _CmaxAnd whole ant group does not converge to walk the same road footpath or convergence numerical value ε＞assigned error as yet, then once more whole ants is placed initial point and jump to (IV) to go on foot, as N _c＜N _CmaxBut whole ant group has converged to walk the same road footpath or ε＜assigned error, and then algorithm finishes, output optimal path and pairing optimum PI parameter k thereof _p ^*, T _i ^*

Claims (2)

1, a kind of imbalance compensation of Static Var Compensator and ant colony optimization method, based on becoming structure Static Var Compensator SVC is controlled, it is characterized in that, variable structure control method comprises two aspects of parameter control of uncompensated load equilibrating compensation and PI controller, and wherein the SVC compensation susceptance computational methods based on the dq rotating coordinate transformation of virtual symmetrical three-phase system are adopted in uncompensated load equilibrating compensation; When virtual symmetrical three-phase system Voltage Stability Control, adopt simultaneously, be applied among the Static Var Compensator SVC, the proportional gain k of its PI controller based on the ant group algorithm optimization method of ITAE criterion as target function _pWith storage gain k _iAdjust in real time, optimizing;

It is described that ant group algorithm optimization as target function comprises the steps: based on the ITAE criterion

Adopt the ITAE criterion as target function:

$J={\&Integral;}_0^{t}t\left|e\left(t\right)\right|\mathrm{dt}---\left(1\right)$

Convergence criterion is shown below:

$\left|\frac{J^{\left(\max \right)}-J^{\left(\min \right)}}{J^{\left(\min \right)}}\right|<{\mathrm{\&epsiv;}}_{\mathrm{ref}}---\left(2\right)$

E is V in the formula _RefWith V _SLAnd V _RmsDifference, promptly as the error signal of ant group optimization PI controller; V _RmsRoot mean square value for line voltage; V _RefBe virtual symmetrical three-phase system reference voltage; V _SLIt is the bucking voltage of SVC; J ^(max)Be the maximum of points of optimizing, J ^(min)Be the minimum point of optimizing, ε _RefBe given positive error amount, the best proportion gain k that the voltage that can be guaranteed thus is stable _pWith storage gain k _iThereby, improve the dynamic property of SVC; According to target function and convergence criterion, use the proportional gain k of ant colony optimization algorithm at last to the PI controller _pWith storage gain k _iCarry out optimizing;

It is as follows to optimize PI CALCULATION OF PARAMETERS step based on the ITAE criterion as the ant group algorithm of target function:

(I) utilize Ziegler-Nichols to calculate PI parameter k _P0, k _I0

(II) set ant and count m, and define an one-dimension array Path for every ant k with 10 elements _k, in this array, deposit the ordinate value of 10 nodes that this ant will pass through successively;

(III) make time counter t=0, cycle-index N _c=0, set maximum cycle N _CmaxAnd the value τ (x of pheromones on each node of initial time _i, y _{I, j}, 0)=c, i=1～10 wherein, j=0～9 make Δ τ (x _i, y _{I, j})=0 places initial point with whole ants;

(IV) put variable i=1;

(V) utilize formula (3) to calculate these ants to line segment L _iGo up the probability that each node shifts, according to these probability, adopting the roulette wheel method is that every ant k is at line segment L _iNode of last selection, and ant k moved on to this node, the ordinate value with this node deposits Path in simultaneously _kI element;

(VI) put i=i+1,, otherwise jump to (VII) step if i≤10 then jump to (V) step;

(VII) path of being passed by, i.e. array Path according to ant k _k, utilize the PI parameter k of formula (4) calculating path correspondence _p ^k, k _i ^k, utilize formula (1) and (2) to calculate the pairing target function J of ant k respectively _kWith pairing convergence numerical value ε _k, write down the optimal path in this circulation, and deposit PI parameter corresponding in optimum PI parameter k with it _p ^*, k _i ^*

(VIII) make t ← t+10, N _c← N _c+ 1, according to formula (5), (6), (7) upgrade the pheromones on each node, and with Path _kIn all elements zero clearing;

(IX) as N _c＜N _CmaxAnd whole ant group does not converge to walk the same road footpath or convergence numerical value ε as yet _k＞assigned error then places initial point with whole ants and jumps to (IV) to go on foot, as N once more _c＜N _CmaxBut whole ant group has converged to walk the same road footpath or convergence numerical value ε _k＜assigned error, then algorithm finishes, output optimal path and pairing optimum PI parameter k thereof _p ^*, k _j ^*

Formula and the parameter-definition used are as follows:

$P_k(x_i,y_{i,j},t)=\frac{{\mathrm{\&tau;}}^{\mathrm{\&alpha;}}(x_i,y_{i,j},t){\mathrm{\&eta;}}^{\mathrm{\&beta;}}(x_i,y_{i,j},t)}{\underset{j=0}{\overset{9}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}^{\mathrm{\&alpha;}}(x_i,y_{i,j},t){\mathrm{\&eta;}}^{\mathrm{\&beta;}}(x_i,y_{i,j},t)}---\left(3\right)$

τ (x in the formula _i, y _{I, j}, be engraved in node Knot (x when t) representing t _i, y _{I, j}) pheromones left over; P _k(x _i, y _{I, j}, t) expression t constantly k ant by L _I-1Last any point is to Knot (x _j, y _{I, j}) probability of creeping; α is the heuristic factor of information, and β inspires the factor, η (x for expectation information _i, y _{I, j}, t) be node Knot (x _i, y _{I, j}) on heuristic function;

$\left\{\begin{array}{c}{k}_p=\underset{i=1}{\overset{5}{\mathrm{\&Sigma;}}}{y}_{i,j}\&times;{10}^{2-i}\\ k_i=\underset{n=6}{\overset{10}{\mathrm{\&Sigma;}}}{y}_{n,j}\&times;{10}^{6-n}\end{array}\right.---\left(4\right)$

τ(x _i，y _i，j，t+n)＝(1-ρ)Δτ(t)+Δτ(t) (5)

$\mathrm{\&Delta;\&tau;}\left(t\right)=\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{\mathrm{\&tau;}}_k(x_i,y_{i,j})---\left(6\right)$

ρ represents the pheromones volatility coefficient in the formula, and then 1-ρ represents the residual factor of information number, and in order to prevent the unlimited accumulation of information, the span of ρ is: $\mathrm{\&rho;}\&Subset;\left[\mathrm{0,1}\right);$ Δ τ (t) represents node Knot (x in this circulation _i, y _{I, j}) on the pheromones increment, Δ τ _k(x _i, y _{I, j}) expression k ant stay node Knot (x in this circulation _i, y _{I, j}) on pheromones;

Q represents pheromones intensity in the formula, influences convergence of algorithm speed to a certain extent, J _kRepresent the target function value of k ant in this circulation, wherein k=1～m.

2, according to the imbalance compensation and the ant colony optimization method of the described Static Var Compensator of claim 1, it is characterized in that, described uncompensated load equilibrating compensation method is: at first utilize the synthesized voltage vector of virtual symmetrical three-phase system to form the dq rotating coordinate system, utilize the phase voltage u in the line voltage _aThe symmetrical three-phase system of constructing virtual is then to the three-phase voltage u of virtual symmetrical three-phase system _AbcWith the load line current i _LabcImplement to obtain after the α β coordinate transform voltage vector u and the current phasor i of α β coordinate system respectively; The d axle of definition dq rotating coordinate system overlaps with the synthesized voltage vector u of the virtual symmetrical three-phase system of positive sequence of extraction; The synthesized voltage vector u of the virtual symmetrical three-phase system of positive sequence that extracts and three-phase voltage u to virtual symmetrical three-phase system _AbcThe voltage vector u that can obtain α β coordinate system after the enforcement α β coordinate transform is same vector;

The synchronizing current that obtains current phasor i projection under voltage vector u of α β coordinate system is:

$\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]=\left[\begin{array}{cc}\frac{u_{\mathrm{\&alpha;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}& \frac{u_{\mathrm{\&beta;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}\\ -\frac{u_{\mathrm{\&beta;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}& \frac{u_{\mathrm{\&alpha;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}\end{array}\right]\&CenterDot;\left[\begin{array}{c}\frac{i_{\mathrm{\&alpha;}}{u}_{\mathrm{\&alpha;}}+i_{\mathrm{\&beta;}}{u}_{\mathrm{\&beta;}}}{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}\&CenterDot;u_{\mathrm{\&alpha;}}\\ \frac{i_{\mathrm{\&alpha;}}{u}_{\mathrm{\&alpha;}}+i_{\mathrm{\&beta;}}{u}_{\mathrm{\&beta;}}}{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}\&CenterDot;u_{\mathrm{\&beta;}}\end{array}\right]=R\left(\mathrm{\&theta;}\right)\&CenterDot;\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}}\\ i_{\mathrm{\&beta;}}\end{array}\right]=\left[\begin{array}{c}\frac{i_{\mathrm{\&alpha;}}{u}_{\mathrm{\&alpha;}}+i_{\mathrm{\&beta;}}{u}_{\mathrm{\&beta;}}}{\sqrt{{u_{\mathrm{\&alpha;}}}^2+{u_{\mathrm{\&beta;}}}^2}}\\ 0\end{array}\right]=\left[\begin{array}{c}{\stackrel{\&OverBar;}{i}}_d+{\tilde{i}}_d\\ 0\end{array}\right]$

In the formula, u _α, u _βBe respectively that voltage vector u is at α β coordinate system α, the component of β axle; i _α, i _βBe respectively that current phasor i is at α β coordinate system α, the component of β axle; θ is the angle of voltage vector u and α axle in the α β coordinate system; R (θ) is the positive sequence transformation matrix of α β coordinate transform to the dq rotating coordinate system, $R\left(\mathrm{\&theta;}\right)=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}\\ -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right]=\begin{array}{c}\end{array}\left[\begin{array}{cc}\frac{u_{\mathrm{\&alpha;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+{\mathrm{\&mu;}}_{\mathrm{\&beta;}}^2}}& \frac{u_{\mathrm{\&beta;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}\\ -\frac{u_{\mathrm{\&beta;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}& \frac{u_{\mathrm{\&alpha;}}}{\sqrt{u_{\mathrm{\&alpha;}}^2+u_{\mathrm{\&beta;}}^2}}\end{array}\right];$

Reactive current i in the projection of current phasor i under voltage vector u of α β coordinate system _qBe zero, active current i _dContain DC component i _dAnd alternating current component

With active current i _dBy low pass filter, can obtain active current i _dDC component i _d, the synthesized voltage vector u of the virtual symmetrical three-phase system of positive sequence that is and extracts has the component of synchronous speed that is load line current i _LabcIn the fundamental positive sequence real component;

With the d axle of the dq rotating coordinate system real axis as complex coordinates system, the q axle imaginary axis that just corresponding to complex coordinates is has so $u_{a+}=\sqrt{6}{u}_{\mathrm{\&alpha;}+}/3,\left[\begin{array}{c}{\stackrel{\&OverBar;}{i}}_d\\ {\stackrel{\&OverBar;}{i}}_q\end{array}\right]=\frac{3}{2}\left[\begin{array}{c}{I}_1\cos {\mathrm{\&theta;}}_1\\ I_1\sin {\mathrm{\&theta;}}_1\end{array}\right],$ Thereby can get: $\mathrm{Im}{\stackrel{\&CenterDot;}{I}}_{\mathrm{la}+}=I_1\sin {\mathrm{\&theta;}}_1=\frac{2}{3}{\stackrel{\&OverBar;}{i}}_q,$ With the current phasor i of α β coordinate system by negative phase-sequence transformation matrix R (θ) be transformed into the dq rotating coordinate system after, in like manner can be in the hope of the load line current i _LabcThe real part of negative sequence component and imaginary part, substitution again $\left\{\begin{array}{c}{B}_{\mathrm{rab}}=-(\mathrm{Im}{\stackrel{\&CenterDot;}{I}}_{\mathrm{la}+}-\sqrt{3}\mathrm{Re}{\stackrel{\&CenterDot;}{I}}_{\mathrm{la}-}+\mathrm{Im}{\stackrel{\&CenterDot;}{I}}_{\mathrm{la}-})/3U\\ B_{\mathrm{rbc}}=-(\mathrm{Im}{\stackrel{\&CenterDot;}{I}}_{\mathrm{la}+}-2\mathrm{Im}{\stackrel{\&CenterDot;}{I}}_{\mathrm{la}-})/3U\\ B_{\mathrm{rca}}=-(\mathrm{Im}{\stackrel{\&CenterDot;}{I}}_{\mathrm{la}+}+\sqrt{3}\mathrm{Re}{\stackrel{\&CenterDot;}{I}}_{\mathrm{la}-}+\mathrm{Im}{\stackrel{\&CenterDot;}{I}}_{\mathrm{la}-})/3U\end{array}\right.$ Calculate, draw the susceptance value of three-phase compensation;

Parameter-definition in the above-mentioned formula is as follows:

u _A+: a phase fundamental voltage positive sequence component;

u _α+: the α axle component of a phase fundamental voltage positive sequence component;

θ ₁: the initial phase of a phase fundamental voltage positive sequence component;

I ₁: the amplitude of load first-harmonic line current positive sequence component;

i _La+: the vector representation of a phase load first-harmonic line current positive sequence component;

i _La-: the vector representation of a phase load first-harmonic line current negative sequence component;

i _q: reactive current i _qThe DC component that contains;

(θ): α β coordinate transform is to the negative phase-sequence transformation matrix of dq rotating coordinate system for R;

B _Rab, B _Rbc, B _Rca: the three-phase admittance value that compensate;

The effective value of U:a phase fundamental voltage positive sequence component.

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