CN104616081A - Disperse relaxation factor tidal current model based minimum electricity generating cost incremental quantity obtaining method - Google Patents

Abstract

The invention discloses a disperse relaxation factor tidal current model based minimum electricity generating cost incremental quantity obtaining method. When a minimum electricity generating cost incremental quantity model only containing one balance node tidal current model is solved, the total demand unit change of a system is fixed on a balance node, and an obtained lambda, namely electricity generating cost minimum incremental quantity cannot reflect actual operation of the system in most cases during total demand unit change of a system. The disperse relaxation factor tidal current model based minimum electricity generating cost incremental quantity obtaining method adopts solves the provided model by means of an original antithesis interior point method, and the lambda of the system is controllable according to selected disperse relaxing factors.

Description

Based on the minimum incremental generating cost acquisition methods of dispersion relaxation factor tide model

Technical field

Invention belongs to Operation of Electric Systems and control technology field, particularly a kind of minimum incremental generating cost acquisition methods based on dispersion relaxation factor tide model.

Background technology

For each electric system, when load generation unit change (namely unit change can be assigned to each node of system according to dispersion relaxation factor) that system is total, generator active power has an optimum unit increment, and λ is exactly minimum incremental generating cost corresponding to this optimum unit increment.

The size of General System λ depends on tide model used, and therefore when solving the economic load dispatching of traditional tide model, the system λ obtained is the smallest incremental of system total demand unit change generator expense when being fixed on balance node.Specifically, if two interacted systems obtain the λ of system according to respective balance node, be now skimble-skamble.Therefore one is not also had can to obtain system λ fast and effectively in the prior art, and the method for control system λ.

Summary of the invention

Goal of the invention: the object of the invention is to for the deficiencies in the prior art, provides and required λ can be made more to tally with the actual situation and controlled a kind of minimum incremental generating cost acquisition methods based on dispersion relaxation factor tide model.

Technical scheme: the invention provides a kind of minimum incremental generating cost acquisition methods based on dispersion relaxation factor tide model, comprise the following steps:

Step 1: set up dispersion relaxation factor power flow algorithm:

In formula, x=[P _τ, U, δ], f ^px () is meritorious residual error, f ^qx () is idle residual error, Δ δ, Δ U, Δ P _τbe the correction of voltage phase angle, voltage magnitude, meritorious amount of unbalance respectively, in above formula, left side is Jacobian matrix;

Step 2: the minimum incremental generating cost computation model setting up dispersion relaxation factor tide model:

obj. min.C(P _g)

s.t. P _τ＝0

$\underset{\‾}{P_g}\≤P_g\≤\stackrel{-}{P_g}$

In formula, C (P _g) be objective function, P _τ=0 is equality constraint, P _τrepresent meritorious amount of unbalance; for inequality constrain condition, P _grepresent generator meritorious go out force value, p _g with represent respectively generator meritorious go out the upper and lower bound of force value;

Step 3: the network parameter obtaining electric system;

Step 4: according to the Optimal Power Flow Problems model containing Hybrid HVDC set up in step 2, structure Lagrangian function is as follows:

$L=C\left(P_g\right)-{\mathrm{yP}}_{\mathrm{\τ}}{z}^T[P_g-l\underset{\‾}{P_g}]-w^T[P_g+u-\stackrel{\‾}{P_g}]-\mathrm{\μ}\underset{j=1}{\overset{r}{\mathrm{\Σ}}}\ln \left(l_j\right)-\mathrm{\μ}\underset{j=1}{\overset{r}{\mathrm{\Σ}}}\ln \left(u_j\right)$

Wherein y=[y ₁..., y _m] ^tfor the Lagrange multiplier of equality constraint, z=[z ₁..., z _r] ^t, w=[w ₁..., w _r] ^tfor the Lagrange multiplier of inequality constrain, l=[l ₁..., l _r] ^t, u=[u ₁..., u _r] ^tfor the slack variable of inequality constrain, μ is Discontinuous Factors;

Step 5: program initialization, arranges quantity of state and arranges initial value, Lagrange multiplier initial value and penalty factor initial value, node order optimization, forms bus admittance matrix, recovers iteration count k'=1, arranges accuracy requirement and maximum iteration time K _max;

Step 6: definition duality gap C _gap=l ^tz-u ^tw, calculates C _gapvalue and judge C _gapvalue whether to be less than in step 4 the accuracy requirement ε of setting, if be less than, then export result of calculation and stop performing subsequent step, if be not less than, then continuing to perform step 7;

Step 7: according to formula μ=σ C _gap/ 2r calculation perturbation factor mu;

Step 8: by P _gthe model solution be updated in step 1 obtains voltage U, phase angle δ, and upgrades P _g

Step 9: according to following equation solution Δ P _g, Δ y, Δ z, Δ l, Δ u, Δ w:

$\left[\begin{array}{cc}{H}^{\′}& {\▿}_{P_g}{P}_{\mathrm{\τ}}\\ {\▿}_{P_g}^T& 0\end{array}\right]\left[\begin{array}{c}{\mathrm{\ΔP}}_g\\ \mathrm{\Δy}\end{array}\right]=\left[\begin{array}{c}{L}_{P_g}^{\′}\\ 0\end{array}\right]$

$\left[\begin{array}{cc}I& L^{-1}Z\\ 0& I\end{array}\right]\left[\begin{array}{c}\mathrm{\Δz}\\ \mathrm{\Δl}\end{array}\right]=\left[\begin{array}{c}{-L}^{-1}{L}_l^{\mathrm{\μ}}\\ L_z+{\▿}_{P_g}^T{P}_g{\mathrm{\ΔP}}_g\end{array}\right]$

$\left[\begin{array}{cc}I& U^{-1}W\\ 0& I\end{array}\right]\left[\begin{array}{c}\mathrm{\Δw}\\ \mathrm{\Δu}\end{array}\right]=\left[\begin{array}{c}{-U}^{-1}{L}_u^{\mathrm{\μ}}\\ -L_w-{\mathrm{\Δ}}_{P_g}^T{P}_g{\mathrm{\ΔP}}_g\end{array}\right]$

Wherein: Δ P _g, Δ y, Δ z, Δ l, Δ u, Δ w be P _g, y, z, l, u, w correction;

Step 10: the iteration step length determining original variable and dual variable:

${\mathrm{\&alpha;}}_p=0.9995\min \{\min (\frac{{-l}_{r^{\&prime;}}}{{\mathrm{\&Delta;l}}_{r^{\&prime;}}},{\mathrm{\&Delta;l}}_{r^{\&prime;}}<0;\frac{u_{r^{\&prime;}}}{{\mathrm{\&Delta;u}}_{r^{\&prime;}}},{\mathrm{\&Delta;u}}_{r^{\&prime;}}<0),1\}$

${\mathrm{\&alpha;}}_d=0.9995\min \{\min (\frac{{-z}_{r^{\&prime;}}}{{\mathrm{\&Delta;z}}_{r^{\&prime;}}},{\mathrm{\&Delta;z}}_{r^{\&prime;}}<0;\frac{{-w}_{r^{\&prime;}}}{{\mathrm{\&Delta;w}}_{r^{\&prime;}}},{\mathrm{\&Delta;w}}_{r^{\&prime;}}<0),1\}$

Step 11: upgrade original variable and Lagrange multiplier;

Step 12: judge whether iterations is greater than K _maxif be greater than, then quit a program and export the result calculating and do not restrain, if be not more than, then put iterations k' value and add 1, return step 6.

Further, the objective function in step 2 in formula, P _githe active power that i-th generator sends, a _2i, a _1i, a _0ifor consumption family curve parameter.

Beneficial effect: compared with existing model, the present invention proposes the minimum incremental generating cost computation model based on dispersion relaxation factor tide model, adopts computation model provided by the invention, required λ is more tallied with the actual situation; And solve with prim al-dual interior point m ethod, solve this model with prim al-dual interior point m ethod, when prim al-dual interior point m ethod solves, maintain its original efficient convergence and robustness, and according to disperseing the selection of relaxation factor, the λ of system is controlled.The number of times of iteration of the present invention is few, and acquisition speed is faster.

Accompanying drawing explanation

Fig. 1 is the inventive method process flow diagram.

Embodiment

Below technical solution of the present invention is described in detail, but protection scope of the present invention is not limited to described embodiment.

Embodiment:

Step 1: set up dispersion relaxation factor power flow algorithm:

In formula, x=[P _τ, U, δ], Δ δ, Δ U, Δ P _τthe correction f of voltage phase angle, voltage magnitude, meritorious amount of unbalance respectively ^px () is meritorious residual error, f ^qx () is idle residual error:

${f_i}^p(\mathrm{\&delta;},U,P_{\mathrm{\&tau;}})=P_{\mathrm{gi}}^0-P_{\mathrm{li}}-P_{\mathrm{ei}}(\mathrm{\&delta;},U)+{\mathrm{\&alpha;}}_i{P}_{\mathrm{\&tau;}}$

${f_i}^q(\mathrm{\&delta;},U)=Q_{\mathrm{gi}}-Q_{\mathrm{li}}-Q_{\mathrm{ei}}(\mathrm{\&delta;},U)$

$P_{\mathrm{ei}}(\mathrm{\&delta;},U){=U}_i\underset{j=1}{\overset{j=n}{\mathrm{\&Sigma;}}}{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\&delta;}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\&delta;}}_{\mathrm{ij}})$

$Q_{\mathrm{ei}}(\mathrm{\&delta;},U)=U_i\underset{j=1}{\overset{j=n}{\mathrm{\&Sigma;}}}{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\&delta;}}_{\mathrm{ij}}-B_{\mathrm{ij}}{\cos \mathrm{\&delta;}}_{\mathrm{ij}})$

In formula: represent the initial value that i-th node generated power is exerted oneself; P _lirepresent the burden with power of i-th node, P _ei(δ, U) is expressed as the meritorious injection calculated value of i-th node; I is the numbering of node.Q _girepresent that i-th node generator reactive goes out force value; Q _lirepresent the load or burden without work of i-th node; Q _ei(δ, U) is expressed as the idle injection calculated value of the i-th node.U _irepresent the voltage of i-th node, U _jrepresent the voltage of a jth node, i and j all belongs to n, and n represents total number of bus nodes.G _ijrepresent conductance, the B between node i and j _ijrepresent susceptance, the δ between node i and j _ijnode i and j phase angle difference.α _irepresent the dispersion relaxation factor of i-th node.

Wherein, relaxation factor α is disperseed _ithree kinds are had to set up mode:

(I) the dispersion relaxation factor of system balancing node is set to 1, and other node is 0.The tide model obtained under this mode is ordinary tides flow model, and the amount of unbalance of the whole network power is only born by a generator.

(II) according to initially given generator active power, calculate each generator output ratio, determine to disperse relaxation factor, calculate by following formula:

$\begin{array}{cc}{\mathrm{\&alpha;}}_i=\frac{P_{\mathrm{gi}}^0}{\underset{t\&Element;G}{\mathrm{\&Sigma;}}{P}_{\mathrm{gt}}^0}& \&ForAll;i\&Element;G\end{array}$

In formula: G is the node total number with generator.T represents the numbering of the node with generator. represent t the meritorious initial value of exerting oneself with the node of generator.

After carrying out a Load flow calculation, then upgrade P according to the following formula _gi

P _gi＝P _gi+α _iP _τ

In formula, P _girepresent that i-th node generated power goes out force value; P _τrepresent meritorious amount of unbalance.

(III) according to initially given each node load active power, calculate each node load ratio, determine the loose factor, calculate by following formula:

$\begin{array}{cc}{\mathrm{\&alpha;}}_i=\frac{P_{\mathrm{li}}^0}{\underset{i\&Element;N}{\mathrm{\&Sigma;}}{P}_{\mathrm{li}}^0}& \&ForAll;i\&Element;N^{\&prime;}\end{array}$

Because each node of system likely has load, the meaning of above formula is proportionally assigned on each node by total meritorious amount of unbalance.N' represents the set of all bus nodes; represent the initial value of the burden with power of i-th node.

In formula, Jacobian matrix is:

$\begin{array}{cc}H=-\frac{{\&PartialD;f}^p\left(x\right)}{\&PartialD;\mathrm{\&delta;}}& J=-\frac{{\&PartialD;f}^p\left(x\right)}{\&PartialD;U}\end{array}$

$\begin{array}{cc}K=-\frac{{\&PartialD;f}^q\left(x\right)}{\&PartialD;\mathrm{\&delta;}}& L=-\frac{{\&PartialD;f}^q\left(x\right)}{\&PartialD;U}\end{array}$

$\begin{array}{cc}\mathrm{MM}=-\frac{{\&PartialD;f}^p}{{\&PartialD;P}_{\mathrm{\&tau;}}}& \mathrm{NN}=-\frac{{\&PartialD;f}^q\left(x\right)}{{\&PartialD;P}_{\mathrm{\&tau;}}}\end{array}$

Step 2: the minimum incremental generating cost computation model setting up dispersion relaxation factor tide model:

obj. min.C(P _g)

s.t. P _τ＝0

$\underset{\&OverBar;}{P_g}\&le;P_g\&le;\stackrel{\&OverBar;}{P_g}$

In formula, P _grepresent generator send out active power, C (P _g) be objective function, be generally generator expense, a _2i, a _1i, a _0ifor consumption family curve parameter; P _τ=0 is equality constraint, and equality constraint number is 1; for inequality constrain condition, suppose that inequality constrain number is r.

Step 3: the network parameter obtaining electric system; Comprise: bus numbering, title, bear merit, reactive load, building-out capacitor, the branch road of transmission line of electricity number, headend node and endpoint node numbering, resistance in series, series reactance, shunt conductance, shunt susceptance, transformer voltage ratio and impedance, generated power is exerted oneself, idle bound, economic parameters;

Step 4: according to the Optimal Power Flow Problems model containing Hybrid HVDC set up in step 2, structure Lagrangian function is as follows:

$L=C\left(P_g\right)-{\mathrm{yP}}_{\mathrm{\&tau;}}-z^T[P_g-l-\underset{\&OverBar;}{P_g}]-w^T[P_g+u-\stackrel{\&OverBar;}{P_g}]-\mathrm{\&mu;}\underset{j=1}{\overset{r}{\mathrm{\&Sigma;}}}\ln \left(l_j\right)-\mathrm{\&mu;}\underset{j=1}{\overset{r}{\mathrm{\&Sigma;}}}\ln \left(u_j\right)$

Wherein, y is the Lagrange multiplier of equality constraint, z=[z ₁..., z _r] ^t, w=[w ₁..., w _r] ^tbe respectively the upper and lower limit Lagrange multiplier of inequality constrain, l=[l ₁..., l _r] ^t, u=[u ₁..., u _r] ^tbe respectively the upper and lower limit slack variable of inequality constrain, μ is Discontinuous Factors, and wherein, r' ∈ r, r' represents r' inequality constrain.

Step 5: program initialization, arranges quantity of state and arranges initial value, Lagrange multiplier initial value and penalty factor initial value, node order optimization, forms bus admittance matrix, recovers iteration count k'=1, arranges accuracy requirement ε and maximum iteration time K _max; Wherein, accuracy requirement ε is 10^-6.

Step 6: definition duality gap C _gap=l ^tz-u ^tw, calculates C _gapvalue and judge C _gapvalue whether to be less than in step 4 the accuracy requirement ε of setting, if be less than, then export result of calculation and stop performing subsequent step, if be not less than, then continuing to perform step 7;

Step 7: by P _gthe model solution be updated in step 1 obtains voltage U, phase angle δ, and upgrades P _g;

Step 8: calculation perturbation factor mu;

KKT (Karush-Kuhn-Tucker) condition of this problem is:

$\left\{\begin{array}{c}{L}_{P_g}={\&dtri;}_{P_g}C\left(P_g\right)-{\&dtri;}_{P_g}{P}_{\mathrm{\&tau;}}y-{\&dtri;}_{P_g}{P}_g(z+w)=0\\ L_y=P_{\mathrm{\&tau;}}=0\\ L_z=P_g-l-\underset{\&OverBar;}{P_g}=0\\ L_w=P_g+u-\stackrel{\&OverBar;}{P_g}=0\\ L_l=z{-\mathrm{\&mu;L}}^{-1}e=0\\ L_u=-w-{\mathrm{\&mu;U}}^{-1}e=0\end{array}\right.$

In formula: for C (P _g) to P _g1 order derivative, be respectively P _τ, P _gjacobian matrix.

Wherein, L=diag (l ₁..., l _r), U=diag (u ₁..., u _r), Z=diag (z ₁..., z _r), W=diag (w ₁..., w _r), L ^-1=diag (1/l ₁..., 1/l _r), U ^-1=diag (1/u ₁..., 1/u _r), e=[1 ..., 1] ^t.

Can be in the hope of by latter two equation in formula KKT condition

μ=(l ^tz-u ^tw)/2r, definition C _gap=l ^tz-u ^tw.

But facts have proved, when the parameter in objective function is poor according to convergence during above formula value, generally adopt

μ＝σC _Gap/2r，

Wherein σ is called Center Parameter, generally gets 0.1, can obtain reasonable convergence in most occasion.

Nonlinear System of Equations in step 9:KKT condition can solve by the inferior method of newton-pressgang, by its linearization, can obtain:

$\left[\begin{array}{cc}{H_1}^{\&prime;}& {\&dtri;}_{P_g}{P}_{\mathrm{\&tau;}}\\ {\&dtri;}_{P_g}^T{P}_{\mathrm{\&tau;}}& 0\end{array}\right]\left[\begin{array}{c}{\mathrm{\&Delta;P}}_g\\ \mathrm{\&Delta;y}\end{array}\right]=\left[\begin{array}{c}{L}_{P_g}^{\&prime;}\\ 0\end{array}\right]$

$\left[\begin{array}{cc}I& L^{-1}Z\\ 0& I\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;z}\\ \mathrm{\&Delta;l}\end{array}\right]=\left[\begin{array}{c}{-L}^{-1}{L}_l^{\mathrm{\&mu;}}\\ L_z+{\&dtri;}_{P_g}^T{P}_g{\mathrm{\&Delta;P}}_g\end{array}\right]$

$\left[\begin{array}{cc}I& U^{-1}W\\ 0& I\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;w}\\ \mathrm{\&Delta;u}\end{array}\right]=\left[\begin{array}{c}{-U}^{-1}{L}_u^{\mathrm{\&mu;}}\\ -L_w-{\mathrm{\&Delta;}}_{P_g}^T{P}_g{\mathrm{\&Delta;P}}_g\end{array}\right]$

Wherein: Δ P _g, Δ y, Δ z, Δ l, Δ u, Δ w be P _g, y, z, l, u, w correction; be a mathematic sign, represent the transposition of local derviation, I representation unit matrix; In above-mentioned matrix,

$L_{P_g}^{\&prime;}=L_{P_g}+{\&dtri;}_{P_g}{P}_g[L^{-1}(L_l^{\mathrm{\&mu;}}+{\mathrm{ZL}}_z)+U^{-1}(L_u^{\mathrm{\&mu;}}+{\mathrm{WL}}_w)]$

${H_1}^{\&prime;}=H_1-{\&dtri;}_{P_g}{P}_g[L^{-1}Z-U^{-1}W]{\&dtri;}_{P_g}^T{P}_g$

$H_1=-[{\&dtri;}_{P_g}^{2}C\left(P_g\right)-{\&dtri;}_{P_g}^2{P}_{\mathrm{\&tau;}}y-{\&dtri;}_{P_g}^2{P}_g(z+w)]$

Wherein, μ is Discontinuous Factors, the above-mentioned three prescription journeys of solving equation can obtain kth ' the correction of secondary iteration.

Step 10: the iteration step length determining original variable and dual variable:

${\mathrm{\&alpha;}}_p=0.9995\min \{\min (\frac{{-l}_{r^{\&prime;}}}{{\mathrm{\&Delta;l}}_{r^{\&prime;}}},{\mathrm{\&Delta;l}}_{r^{\&prime;}}<0;\frac{u_{r^{\&prime;}}}{{\mathrm{\&Delta;u}}_{r^{\&prime;}}},{\mathrm{\&Delta;u}}_{r^{\&prime;}}<0),1\}$

${\mathrm{\&alpha;}}_d=0.9995\min \{\min (\frac{{-z}_{r^{\&prime;}}}{{\mathrm{\&Delta;z}}_{r^{\&prime;}}},{\mathrm{\&Delta;z}}_{r^{\&prime;}}<0;\frac{{-w}_{r^{\&prime;}}}{{\mathrm{\&Delta;w}}_{r^{\&prime;}}},{\mathrm{\&Delta;w}}_{r^{\&prime;}}<0),1\}$

Step 11: upgrade original variable and Lagrange multiplier;

$\left\{\begin{array}{c}{P_g}^{(k^{\&prime;}+1)}={P_g}^{\left(k^{\&prime;}\right)}+{\mathrm{\&alpha;}}_p{\mathrm{\&Delta;P}}_g\\ l^{(k^{\&prime;}+1)}=l^{\left(k^{\&prime;}\right)}+{\mathrm{\&alpha;}}_p\mathrm{\&Delta;l}\\ u^{(k^{\&prime;}+1)}=u^{\left(k^{\&prime;}\right)}+{\mathrm{\&alpha;}}_p\mathrm{\&Delta;u}\end{array}\right.,\left\{\begin{array}{c}{y}^{(k^{\&prime;}+1)}=y^{\left(k^{\&prime;}\right)}+{\mathrm{\&alpha;}}_d\mathrm{\&Delta;y}\\ z^{(k^{\&prime;}+1)}=z^{\left(k^{\&prime;}\right)}+{\mathrm{\&alpha;}}_d\mathrm{\&Delta;z}\\ w^{(k^{\&prime;}+1)}=w^{\left(k^{\&prime;}\right)}+{\mathrm{\&alpha;}}_d\mathrm{\&Delta;w}\end{array}\right.$

Step 12: judge whether iterations is greater than K _maxif be greater than, then quit a program and export the result calculating and do not restrain, if be not more than, then put iterations k' value and add 1, return step 6.Wherein, K _maxbe 50.

Table 1 after listing IEEE-14 node optimization the meritorious of each generator exert oneself, the generating expense (unit is $/h) of system, the λ (unit is $/MW-h) of system.

Table 1 generator output

Can find out in table 1, under three kinds of different dispersion relaxation factors choose mode, PDIPM algorithm (in former antithesis, send out by point, hereinafter be called for short PDIPM algorithm) optimize after generated power exert oneself and be more or less the same, illustrate that the difference of disperseing relaxation factor to choose mode affects not quite on meritorious the exerting oneself after generator optimization, this is because when close to optimum point, total meritorious amount of unbalance P _τclose to 0, by α _ip _τcan find out dispersion relaxation factor on generated power exert oneself impact very little.

In table 1, when the balance node of mode I becomes node 2 from node 1, PDIPM algorithm corresponding system λ becomes 3839.8 $/MW-h from 3653.2 $/MW-h respectively, 3634.2 $/MW-h become 3823.0 $/MW-h, the intension of these λ is, when load generation unit change (unit change can be assigned to each node of system according to dispersion relaxation factor) that system is total, generator active power has an optimum unit increment, and λ is exactly minimum incremental generating cost corresponding to this optimum unit increment.

The meaning of λ is, if system call person knows that the load of which node is about to change, corresponding dispersion relaxation factor is determined, the λ of system is also determined.The system λ determined in this way more meets the actual motion of system.In table 1, the system λ under three kinds of modes is not identical, and the system λ of mode III is obviously greater than other two kinds of modes, this is because the change of load is almost assigned to each node of system under mode III.

The system λ of the different example of table 2

Table 2 lists the different example of PDIPM Algorithm for Solving, and the system λ obtained, MP-2383 are 2383 node systems in Matpower commercial packages.Under table 3 gives different example, the contrast table of the iterations of the method for Lagrange multipliers (hereinafter referred TJM) that PDIPM algorithm and prior art adopt.

The iterations of the different example of table 3

Can find out in table 2, under different example, the system λ of mode III is all greater than mode I, II, and this is because under mode III, the change of load is almost assigned to each node of system.

In table 2,3, different example, under same way, efficient convergence is still remain compared with the algorithm that PDIPM and prior art improve, the number of times of iteration is less than the method that prior art provides substantially, wherein, MP-2383 node only needs 12 iteration to restrain, and therefore show that PDIPM Algorithm robustness is stronger.

Claims (2)

1., based on a minimum incremental generating cost acquisition methods for dispersion relaxation factor tide model, it is characterized in that: comprise the following steps:

Step 1: set up dispersion relaxation factor power flow algorithm:

In formula, x=[P _τ, U, δ], f ^px () is meritorious residual error, f ^qx () is idle residual error, Δ δ, Δ U, Δ P _τbe the correction of voltage phase angle, voltage magnitude, meritorious amount of unbalance respectively, in above formula, left side is Jacobian matrix;

Step 2: the minimum incremental generating cost computation model setting up dispersion relaxation factor tide model:

obj. min.C(P _g)

s.t. P _τ＝0

$\underset{\&OverBar;}{P_g}\&le;P_g\&le;\stackrel{\&OverBar;}{P_g}$

In formula, C (P _g) be objective function, P _τ=0 is equality constraint, P _τrepresent meritorious amount of unbalance; for inequality constrain condition, P _grepresent generator meritorious go out force value, with represent respectively generator meritorious go out the upper and lower bound of force value;

Step 3: the network parameter obtaining electric system;

Step 4: according to the Optimal Power Flow Problems model containing Hybrid HVDC set up in step 2, structure Lagrangian function is as follows:

$L=C\left(P_g\right)-y{P}_{\mathrm{\&tau;}}-z^T[P_g-l-\underset{\&OverBar;}{P_g}]-w^T[P_g+u-\stackrel{\&OverBar;}{P_g}]-\mathrm{\&mu;}\underset{j=1}{\overset{r}{\mathrm{\&Sigma;}}}\ln \left(l_j\right)-\mathrm{\&mu;}\underset{j=1}{\overset{r}{\mathrm{\&Sigma;}}}\ln \left(u_j\right)$

Wherein y=[y ₁..., y _m] ^tfor the Lagrange multiplier of equality constraint, z=[z ₁..., z _r] ^t, w=[w ₁..., w _r] ^tfor the Lagrange multiplier of inequality constrain, l=[l ₁..., l _r] ^t, u=[u ₁..., u _r] ^tfor the slack variable of inequality constrain, μ is Discontinuous Factors;

Step 5: program initialization, arranges quantity of state and arranges initial value, Lagrange multiplier initial value and penalty factor initial value, node order optimization, forms bus admittance matrix, recovers iteration count k'=1, arranges accuracy requirement and maximum iteration time K _max;

Step 6: definition duality gap C _gap=l ^tz-u ^tw, calculates C _gapvalue and judge C _gapvalue whether to be less than in step 4 the accuracy requirement ε of setting, if be less than, then export result of calculation and stop performing subsequent step, if be not less than, then continuing to perform step 7;

Step 7: according to formula μ=σ C _gap/ 2r calculation perturbation factor mu;

Step 8: by P _gthe model solution be updated in step 1 obtains voltage U, phase angle δ, and upgrades P _g

Step 9: according to following equation solution Δ P _g, Δ y, Δ z, Δ l, Δ u, Δ w:

$\left[\begin{array}{cc}{H}^{\&prime;}& {\&dtri;}_{P_g}{P}_{\mathrm{\&tau;}}\\ {\&dtri;}_{P_g}^T{P}_{\mathrm{\&tau;}}& 0\end{array}\right]\left[\begin{array}{c}{\mathrm{\&Delta;P}}_g\\ \mathrm{\&Delta;y}\end{array}\right]=\left[\begin{array}{c}{L}_{P_g}^{\&prime;}\\ 0\end{array}\right]$

$\left[\begin{array}{cc}I& L^{-1}Z\\ 0& I\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;z}\\ \mathrm{\&Delta;l}\end{array}\right]=\left[\begin{array}{c}{-L}^{-1}{L}_l^{\mathrm{\&mu;}}\\ L_z+{\&dtri;}_{P_g}^T{P}_g{\mathrm{\&Delta;P}}_g\end{array}\right]$

$\left[\begin{array}{cc}I& U^{-1}W\\ 0& I\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;w}\\ \mathrm{\&Delta;u}\end{array}\right]=\left[\begin{array}{c}{-U}^{-1}{L}_u^{\mathrm{\&mu;}}\\ {-L}_w-{\&dtri;}_{P_g}^T{P}_g{\mathrm{\&Delta;P}}_g\end{array}\right]$

Wherein: Δ P _g, Δ y, Δ z, Δ l, Δ u, Δ w be P _g, y, z, l, u, w correction;

Step 10: the iteration step length determining original variable and dual variable:

${\mathrm{\&alpha;}}_p=0.9995\min \{\min (\frac{{-l}_{r^{\&prime;}}}{{\mathrm{\&Delta;l}}_{r^{\&prime;}}},{\mathrm{\&Delta;l}}_{r^{\&prime;}}<0;\frac{{-u}_{r^{\&prime;}}}{{\mathrm{\&Delta;u}}_{r^{\&prime;}}},{\mathrm{\&Delta;u}}_{r^{\&prime;}}<0),1\}$

${\mathrm{\&alpha;}}_d=0.9995\min \{\min (\frac{{-z}_{r^{\&prime;}}}{{\mathrm{\&Delta;z}}_{r^{\&prime;}}},{\mathrm{\&Delta;z}}_{r^{\&prime;}}<0;\frac{{-w}_{r^{\&prime;}}}{{\mathrm{\&Delta;w}}_{r^{\&prime;}}},{\mathrm{\&Delta;w}}_{r^{\&prime;}}<0),1\}$

Step 11: upgrade original variable and Lagrange multiplier;

Step 12: judge whether iterations is greater than K _maxif be greater than, then quit a program and export the result calculating and do not restrain, if be not more than, then put iterations k' value and add 1, return step 6.

2. the minimum incremental generating cost acquisition methods based on dispersion relaxation factor tide model according to claim 1, is characterized in that: the objective function in step 2 in formula, P _githe active power that i-th generator sends, a _2i, a _1i, a _0ifor consumption family curve parameter.