CN105404786A - Power network equivalent parameter fast calculation method based on nonlinear variable substitution - Google Patents

Abstract

The present invention provides a power network equivalent parameter fast calculation method based on nonlinear variable substitution. The method comprises the following steps of: step 1, acquiring generator voltage values of four different active and reactive power outputs of a target power generator. step 2, substituting data of the four different active and reactive power outputs into a single-machine infinite-bus system circuit formula to obtain simultaneous nonlinear equations; step 3, performing variable substitution on the formula obtained in the step 2, and converting the nonlinear equations into linear equations; step 4, solving the linear equations obtained in the step 3 to obtain the value of an intermediate variable; and step 5, obtaining system equivalent impedance and equivalent voltage by the obtained value of the intermediate variable. According to the power network equivalent parameter fast calculation method based on the nonlinear variable substitution disclosed by the present invention, the equivalent voltage and impedance can be obtained by quartic power flow calculation, and the solving of the nonlinear equations is avoided by the nonlinear variable substitution, so that the computational complexity is greatly lowered and the computational amount is reduced; and the method has the characteristics of high calculation speed, high accuracy, easiness for application and the like.

Description

Based on the network equivalence parameter quick calculation method of non-linear substitution of variable

Technical field

The present invention relates to the calculating field of electric system network equivalence parameter, specifically a kind of network equivalence parameter quick calculation method based on non-linear substitution of variable.

Background technology

Calculate at the Excitation System Modeling of electric system, generator enters phase depth calculation and the analysis of generator steady state stability limit and multilayer output feedback network etc. relate in the calculating of genset and electric system mutual relationship, widespread use be electric system Infinite bus power system model.In actual tests with in calculating, the threshold voltage V such as the parameter system of Infinite bus system _s, system equivalent impedance R, X for calculate key parameter, its degree of accuracy directly will affect result of calculation.

In engineering reality, system equivalent voltage V _s, system equivalent impedance R, X be often difficult to direct acquisition, in the calculation carries out simplification and assumption more, makes approximate processing to system.Wherein using more simplification and assumption to be the backbone point be directly connected with research object genset in selecting system is system node, supposes that its voltage constant is constant, will be attached thereto the line impedance that connects as approximate system equivalent impedance.Although can obtain the systematic parameter be similar to like this, in fact backbone point voltage often changes with the working conditions change of research object genset, causes the error of calculation larger.

Summary of the invention

The invention provides a kind of network equivalence parameter quick calculation method based on non-linear substitution of variable, can the problem that not easily obtains of the threshold voltage such as resolution system and impedance, Solving Nonlinear Systems of Equations is avoided by non-linear substitution of variable, greatly reduce the complexity of calculating, save calculated amount, had that computing velocity is fast, precision is high and be easy to the features such as application.

Based on a network equivalence parameter quick calculation method for non-linear substitution of variable, comprise the steps:

Step one, obtain object generator gain merit four differences, idle exert oneself under set end voltage value;

Step 2, four differences are gained merit, idle exert oneself under data substitute into the Nonlinear System of Equations that one machine infinity bus system circuit formula obtains simultaneous:

Step 3, substitution of variable is carried out to the formula that step 2 obtains, Nonlinear System of Equations is transformed to system of linear equations;

The system of linear equations that step 4, solution step 3 obtain, obtains the value of intermediate variable;

Step 5, by solve by the value of intermediate variable try to achieve system equivalent impedance and etc. threshold voltage.

Further, described step one is specially:

Research object generator is carried out under four different operating modes test or simulation calculation, record or calculating generator set end voltage value, obtain four differences gain merit, idle exert oneself under set end voltage, if under four different operating modes, generated power is exerted oneself, idlely to exert oneself and set end voltage is respectively:

	Meritorious	Idle	Set end voltage
				Operating mode 1	P 1	Q 1	V G1
Operating mode 2	P 2	Q 2	V G2
				Operating mode 3	P 3	Q 3	V G3
Operating mode 4	P4	Q4	V G4

Further, described step 2 is specially:

The data of four operating modes are substituted into the Nonlinear System of Equations that following formula obtains simultaneous:

$\left\{\begin{array}{c}{P_1}^2+{Q_1}^2-\frac{2V_{G1}^{2}R}{Z^2}{P}_1-\frac{2V_{G1}^{2}X}{Z^2}{Q}_1+\frac{V_{G1}^2(V_{G1}^2-V_S^2)}{Z^2}=0\\ {P_2}^2+{Q_2}^2-\frac{2V_{G2}^{2}R}{Z^2}{P}_2-\frac{2V_{G2}^{2}X}{Z^2}{Q}_2+\frac{V_{G2}^2(V_{G2}^2-V_S^2)}{Z^2}=0\\ {P_3}^2+{Q_3}^2-\frac{2V_{G3}^{2}R}{Z^2}{P}_3-\frac{2V_{G3}^{2}X}{Z^2}{Q}_3+\frac{V_{G4}^2(V_{G4}^2-V_S^2)}{Z^2}=0\\ {P_4}^2+{Q_4}^2-\frac{2V_{G4}^{2}R}{Z^2}{P}_4-\frac{2V_{G4}^{2}X}{Z^2}{Q}_3+\frac{V_{G4}^2(V_{G4}^2-V_S^2)}{Z^2}=0\end{array}\right.---\left(1\right)$

Wherein R is system equivalent resistance, and X is system equivalent reactance, V _sfor system equivalent voltage, P, Q are respectively generated power and exert oneself and idlely to exert oneself, V _gfor generator terminal voltage, Z ²=R ²+ X ².

Further, described step 3 is specially:

Introduce intermediate variable k _p, k _q, k _zand k _v, non-linear substitution of variable is carried out to formula (1), order:

$\left\{\begin{array}{c}{k}_p=\frac{R}{Z^2}\\ k_q=\frac{X}{Z^2}\\ k_v=\frac{V_S^2}{Z^2}\\ k_z=\frac{1}{Z^2}\end{array}\right.---\left(2\right)$

Then formula (1) is variable turns to system of linear equations:

$\left\{\begin{array}{c}2V_{G1}^2{P}_1{k}_p+2V_{G1}^2{Q}_1{k}_q-V_{G1}^4{k}_z+V_{G1}^2{k}_z={P_1}^2+{Q_1}^2\\ 2V_{G2}^2{P}_2{k}_p+2V_{G2}^2{Q}_2{k}_q-V_{G2}^4{k}_z+V_{G2}^2{k}_z={P_2}^2+{Q_2}^2\\ 2V_{G3}^2{P}_3{k}_p+2V_{G3}^2{Q}_3{k}_q-V_{G3}^4{k}_z+V_{G3}^2{k}_z={P_3}^2+{Q_3}^2\\ 2V_{G4}^2{P}_4{k}_p+2V_{G4}^2{Q}_4{k}_q-V_{G4}^4{k}_z+V_{G4}^2{k}_z={P_4}^2+{Q_4}^2\end{array}\right.---\left(3\right)$

Described step 4 is specially: solve linear equations (3), obtains k _p, k _q, k _zand k _v.

Further, described step 5 is specially: by the k solved _p, k _q, k _zand k _vtry to achieve system equivalent impedance by following formula and wait threshold voltage:

$\left\{\begin{array}{c}R=\frac{k_p}{k_z}\\ X=\frac{k_q}{k_z}\\ V_s=\sqrt{\frac{k_v}{k_z}}\end{array}\right.---\left(4\right)$

Beneficial effect of the present invention:

1, only need to carry out four working condition measurings or calculating, can obtain system equivalent model, step is simple, the time of greatly having saved test or having calculated;

2, computation model remains whole resistance and the reactance of system equivalent, ensure that the degree of accuracy of calculating;

3, by nonlinear transformation, Nonlinear System of Equations is transformed to system of linear equations time, greatly reduces and solve difficulty, avoid many solutions problem, and save calculated amount.

Accompanying drawing explanation

Fig. 1 is equivalent one machine infinity bus system electrical network schematic diagram of the present invention;

Fig. 2 is equivalent one machine infinity bus system voltage of the present invention, current vector figure.

Embodiment

Below in conjunction with the accompanying drawing in the present invention, the technical scheme in the present invention is clearly and completely described.

The present invention is the quick calculation method of the network equivalence parameter based on non-linear substitution of variable, and described method comprises the steps:

Step one, obtain object generator gain merit four differences, idle exert oneself under set end voltage value; Concrete, research object generator is carried out under four different operating modes test or simulation calculation, record or calculating generator set end voltage value, obtain four differences gain merit, idle exert oneself under set end voltage, if under four different operating modes, generated power is exerted oneself, idlely to exert oneself and set end voltage is respectively:

	Meritorious	Idle	Set end voltage
				Operating mode 1	P 1	Q 1	V G1
Operating mode 2	P 2	Q 2	V G2
				Operating mode 3	P 3	Q 3	V G3
Operating mode 4	P4	Q4	V G4

Electric system equivalence wherein outside research object generator is an one machine infinity bus system as shown in Figure 1, and wherein system equivalent resistance is R, and system equivalent reactance is X, and system equivalent voltage is V _s.

Step 2, four differences are gained merit, idle exert oneself under data substitute into the Nonlinear System of Equations that one machine infinity bus system circuit formula obtains simultaneous, concrete, the data of four operating modes are substituted into the Nonlinear System of Equations that following formula obtains simultaneous:

$\left\{\begin{array}{c}{P_1}^2+{Q_1}^2-\frac{2V_{G1}^{2}R}{Z^2}{P}_1-\frac{2V_{G1}^{2}X}{Z^2}{Q}_1+\frac{V_{G1}^2(V_{G1}^2-V_S^2)}{Z^2}=0\\ {P_2}^2+{Q_2}^2-\frac{2V_{G2}^{2}R}{Z^2}{P}_2-\frac{2V_{G2}^{2}X}{Z^2}{Q}_2+\frac{V_{G2}^2(V_{G2}^2-V_S^2)}{Z^2}=0\\ {P_3}^2+{Q_3}^2-\frac{2V_{G3}^{2}R}{Z^2}{P}_3-\frac{2V_{G3}^{2}X}{Z^2}{Q}_3+\frac{V_{G4}^2(V_{G4}^2-V_S^2)}{Z^2}=0\\ {P_4}^2+{Q_4}^2-\frac{2V_{G4}^{2}R}{Z^2}{P}_4-\frac{2V_{G4}^{2}X}{Z^2}{Q}_3+\frac{V_{G4}^2(V_{G4}^2-V_S^2)}{Z^2}=0\end{array}\right.---\left(1\right)$

Wherein R is system equivalent resistance, and X is system equivalent reactance, V _sfor system equivalent voltage, P, Q are respectively generated power and exert oneself and idlely to exert oneself, V _gfor generator terminal voltage, Z ²=R ²+ X ²;

Step 3, substitution of variable is carried out to the formula that step 2 obtains, Nonlinear System of Equations is transformed to system of linear equations, concrete, introduce intermediate variable k _p, k _q, k _zand k _v, non-linear substitution of variable is carried out to formula (1), order:

$\left\{\begin{array}{c}{k}_p=\frac{R}{Z^2}\\ k_q=\frac{X}{Z^2}\\ k_v=\frac{V_S^2}{Z^2}\\ k_z=\frac{1}{Z^2}\end{array}\right.---\left(2\right)$

Then formula (1) is variable turns to system of linear equations:

$\left\{\begin{array}{c}2V_{G1}^2{P}_1{k}_p+2V_{G1}^2{Q}_1{k}_q-V_{G1}^4{k}_z+V_{G1}^2{k}_z={P_1}^2+{Q_1}^2\\ 2V_{G2}^2{P}_2{k}_p+2V_{G2}^2{Q}_2{k}_q-V_{G2}^4{k}_z+V_{G2}^2{k}_z={P_2}^2+{Q_2}^2\\ 2V_{G3}^2{P}_3{k}_p+2V_{G3}^2{Q}_3{k}_q-V_{G3}^4{k}_z+V_{G3}^2{k}_z={P_3}^2+{Q_3}^2\\ 2V_{G4}^2{P}_4{k}_p+2V_{G4}^2{Q}_4{k}_q-V_{G4}^4{k}_z+V_{G4}^2{k}_z={P_4}^2+{Q_4}^2\end{array}\right.---\left(3\right)$

The system of linear equations that step 4, solution step 3 obtain, obtains the value of intermediate variable; Concrete, solve linear equations (3), obtains k _p, k _q, k _zand k _v;

Step 5, by solve by the value of intermediate variable try to achieve system equivalent impedance and etc. threshold voltage, concrete, by the k solved _p, k _q, k _zand k _vtry to achieve system equivalent impedance by following formula and wait threshold voltage:

$\left\{\begin{array}{c}R=\frac{k_p}{k_z}\\ X=\frac{k_q}{k_z}\\ V_s=\sqrt{\frac{k_v}{k_z}}\end{array}\right.---\left(4\right)$

Below in conjunction with an instantiation, this method is described further:

The A genset rated capacity accessing a large-scale power system is 388MVA, and its machine end rated voltage is 20kV, and existing needs calculates when Generation in Leading Phase Operation, and set end voltage is the different idle limit output under exerting oneself of gaining merit under being not less than 19.15kV constraint condition.

Utilize method of the present invention calculate connecting system equivalent impedance R, X and etc. threshold voltage V _safter, then calculate with the voltage under one machine infinity bus system that formulae discovery is idle exerts oneself, and and the precise results retaining complete electrical network compare.

By this generator difference is meritorious and idle exert oneself under carry out Load flow calculation, the set end voltage value that can obtain under this unit four different operating modes is as follows:

Meritorious (MW)	Idle (MVar)	Set end voltage (kV)
			300	-47	19.1075
330	-50	19.0472
			240	0	19.5737
165	-53	19.1548

By formula (3), following system of equations can be obtained:

$\left\{\begin{array}{c}219058.1630k_p-34319.1122k_q-133295.7744k_z+365.0969k_v=92209\\ 239446.0006k_p-36279.6970k_q-131621.6419k_z+362.7969k_v=111400\\ 183902.4591k_p-146788.6912k_z+383.1301k_v=57600\\ 121078.8469k_p-38891.9932k_p-134619.7169k_z+366.9055k_v=30034\end{array}\right.---\left(5\right)$

Xie Zhi, can obtain:

$\left\{\begin{array}{c}{k}_p=1.2344752\×{10}^{-1}\\ k_q=6.0017931\\ k_z=3.6131976\×{10}^1\\ k_v=1.3934334\×{10}^4\end{array}\right.---\left(6\right)$

Formula (6) is updated to formula (4), system equivalent voltage and impedance can be tried to achieve:

$\left\{\begin{array}{c}{V}_S=19.6379kV\\ R=0.00345\mathrm{\Ω}\\ X=0.1661\mathrm{\Ω}\end{array}\right.---\left(8\right)$

The system equivalent voltage utilizing method of the present invention to obtain and impedance, can calculate each idle limit output under exerting oneself of gaining merit with the circuit formula under one machine infinity bus system, and be compared as follows with the exact computation results retaining complete electrical network:

From above result, utilize method of the present invention, enter error between phase result of calculation and the exact computation results retaining complete electrical network within 0.002%, engineering can be ignored.Can prove that the system equivalent impedance that computing method of the present invention obtain and system equivalent voltage have high degree of accuracy thus.

The above; be only the specific embodiment of the present invention, but protection scope of the present invention is not limited thereto, anyly belongs to those skilled in the art in the technical scope that the present invention discloses; the change that can expect easily or replacement, all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.

Claims (5)

1., based on a network equivalence parameter quick calculation method for non-linear substitution of variable, it is characterized in that comprising the steps:

Step one, obtain object generator gain merit four differences, idle exert oneself under set end voltage value;

Step 2, four differences are gained merit, idle exert oneself under data substitute into the Nonlinear System of Equations that one machine infinity bus system circuit formula obtains simultaneous:

Step 3, substitution of variable is carried out to the formula that step 2 obtains, Nonlinear System of Equations is transformed to system of linear equations;

The system of linear equations that step 4, solution step 3 obtain, obtains the value of intermediate variable;

Step 5, by solve by the value of intermediate variable try to achieve system equivalent impedance and etc. threshold voltage.

2., as claimed in claim 1 based on the network equivalence parameter quick calculation method of non-linear substitution of variable, it is characterized in that described step one is specially:

Research object generator is carried out under four different operating modes test or simulation calculation, record or calculating generator set end voltage value, obtain four differences gain merit, idle exert oneself under set end voltage, if under four different operating modes, generated power is exerted oneself, idlely to exert oneself and set end voltage is respectively:

Meritorious Idle Set end voltage Operating mode 1 P ₁ Q ₁ V _G1 Operating mode 2 P ₂ Q ₂ V _G2 Operating mode 3 P ₃ Q ₃ V _G3 Operating mode 4 P4 Q4 V _G4

3., as claimed in claim 2 based on the network equivalence parameter quick calculation method of non-linear substitution of variable, it is characterized in that described step 2 is specially:

The data of four operating modes are substituted into the Nonlinear System of Equations that following formula obtains simultaneous:

$\left\{\begin{array}{c}{P_1}^2+{Q_1}^2-\frac{2V_{G1}^{2}R}{Z^2}{P}_1-\frac{2V_{G1}^{2}X}{Z^2}{Q}_1+\frac{V_{G1}^2(V_{G1}^2-V_S^2)}{Z^2}=0\\ {P_2}^2+{Q_2}^2-\frac{2V_{G2}^{2}R}{Z^2}{P}_2-\frac{2V_{G2}^{2}X}{Z^2}{Q}_2+\frac{V_{G2}^2(V_{G2}^2-V_S^2)}{Z^2}=0\\ {P_3}^2+{Q_3}^2-\frac{2V_{G3}^{2}R}{Z^2}{P}_3-\frac{2V_{G3}^{2}X}{Z^2}{Q}_3+\frac{V_{G3}^2(V_{G3}^2-V_S^2)}{Z^2}=0\\ {P_4}^2+{Q_4}^2-\frac{2V_{G4}^{2}R}{Z^2}{P}_4-\frac{2V_{G4}^{2}X}{Z^2}{Q}_3+\frac{V_{G4}^2(V_{G4}^2-V_S^2)}{Z^2}=0\end{array}\right.---\left(1\right)$

Wherein R is system equivalent resistance, and X is system equivalent reactance, V _sfor system equivalent voltage, P, Q are respectively generated power and exert oneself and idlely to exert oneself, V _gfor generator terminal voltage, Z ²=R ²+ X ².

4., as claimed in claim 3 based on the network equivalence parameter quick calculation method of non-linear substitution of variable, it is characterized in that described step 3 is specially:

Introduce intermediate variable k _p, k _q, k _zand k _v, non-linear substitution of variable is carried out to formula (1), order:

$\left\{\begin{array}{c}{k}_p=\frac{R}{Z^2}\\ k_q=\frac{X}{Z^2}\\ k_v=\frac{V_S^2}{Z^2}\\ k_z=\frac{1}{Z^2}\end{array}\right.---\left(2\right)$

Then formula (1) is variable turns to system of linear equations:

$\left\{\begin{array}{c}2V_{G1}^2{P}_1{k}_p+2V_{G1}^2{Q}_1{k}_q-V_{G1}^4{k}_z+V_{G1}^2{k}_v={P_1}^2+{Q_1}^2\\ 2V_{G2}^2{P}_2{k}_p+2V_{G2}^2{Q}_2{k}_q-V_{G2}^4{k}_z+V_{G2}^2{k}_v={P_2}^2+{Q_2}^2\\ 2V_{G3}^2{P}_3{k}_p+2V_{G3}^2{Q}_3{k}_q-V_{G3}^4{k}_z+V_{G3}^2{k}_v={P_3}^2+{Q_3}^2\\ 2V_{G4}^2{P}_4{k}_p+2V_{G4}^2{Q}_4{k}_q-V_{G4}^4{k}_z+V_{G4}^2{k}_v={P_4}^2+{Q_4}^2\end{array}\right.---\left(3\right)$

Described step 4 is specially: solve linear equations (3), obtains k _p, k _q, k _zand k _v.

5., as claimed in claim 4 based on the network equivalence parameter quick calculation method of non-linear substitution of variable, it is characterized in that described step 5 is specially: by the k solved _p, k _q, k _zand k _vtry to achieve system equivalent impedance by following formula and wait threshold voltage:

$\left\{\begin{array}{c}R=\frac{k_p}{k_z}\\ X=\frac{k_q}{k_z}\\ V_s=\sqrt{\frac{k_v}{k_z}}\end{array}\right.---\left(4\right).$