CN106385035A - DC power flow calculation method considering charging capacitance - Google Patents

Abstract

The invention relates to a DC power flow calculation method considering charging capacitance. The DC power flow calculation method comprises steps of (1) calculating a trigonometric function simplification method and an approximation coefficient, (2) constructing a DC power flow model considering a charging capacitance, (3) incorporating a circuit model containing a charging capacitor and a grounding admittance, (4) using a complete admittance matrix parameter to calculate a coefficient matrix, (5) solving voltage amplitudes of all PQ nodes through back substitution of a correction phase angle to obtain voltage amplitudes and phase angles of all nodes in a network and using complex power flow equation to calculate line circuit complex power. Compared with a DC power flow algorithm without considering a charging capacitance, the DC power flow calculation method improves calculation accuracy of the voltage amplitude and the reactive power flow on the premise that the active power flow calculation accuracy of the current DC power flow algorithm is maintained, and enables the power flow algorithm to be adapted to calculation of reactive power flow of a power transmission system.

Description

A kind of meter and the DC power flow computational methods of charging capacitor

Technical field

The present invention relates to the DC power flow computational methods of a kind of meter and charging capacitor, belong to Power System Analysis technology neck Domain.

Background technology

DC power flow is the simplification algorithm that AC power flow calculates, wide because its mathematical model has linear expression and rapidity General be applied to power system generation schedule check a few days ago, economic load dispatching, electricity market congestion management and power system chain therefore Many occasions such as barrier analysis.In existing DC power flow computational methods, standard direct current power flow algorithm is to x/r ratio close to 4, electricity The system that pressure amplitude value standard deviation is less than 0.02 has preferable calculating effect, but in actual applications, systematic parameter may not necessarily expire The computational accuracy of sufficient above-mentioned requirements, therefore this algorithm is difficult to ensure that.In order to improve the computational accuracy of DC power flow algorithm, can be utilized Known AC power flow section forms correction term or obtains the duty values such as network loss by iteration and be used for revising node power, but front Person has how choosing suitable history AC power flow section, and the latter's presence can not calculate voltage magnitude and need iteration Problem；In order to solve due to ignoring balance nodes injecting power substantially irrational problem that network loss is brought, in circuit model Middle consideration resistance, considers the idle injecting power of node in network equation, can consider voltage magnitude wave characteristic and network loss While the computational accuracy of DC power flow is substantially improved, but be only used for calculating active power, the not calculating to reactive power is done Analyze further.On the basis of standard direct current power flow algorithm, combine active power using supposition power factor, can directly estimate Calculate circuit reactive power, but using the method process obtain reactive power flow direction with active flow to completely the same and idle Size with select power factor relevant, there is very big randomness it is difficult to calculate accurate reactive power flow.Therefore current Still lack a kind of DC power flow computational methods that can simultaneously take into account active power and reactive power calculating precision.

Content of the invention

Present invention aims to the deficiencies in the prior art, a kind of meter and the DC power flow of charging capacitor is provided to calculate Method.

The technical scheme is that, the present invention, on the basis of the DC flow model considering resistance, will be grounded branch road meter Enter in circuit model, to reflect the impact that the parallel element such as idle injection and ground connection branch road is distributed to System Reactive Power；By structure Make parallel element admittance item and further linearization process made to power flow equation, be deduced without iteration, can calculate node electricity The DC power flow equation of the linear forms of the higher precision of pressure amplitude value.

The DC power flow computational methods of a kind of meter of the present invention and charging capacitor mainly include the following steps that：

The method for simplifying of step (1) trigonometric function and the calculating of approximation coefficient.

The structure of the DC flow model of step (2) meter and charging capacitor.

Step (3) contains the circuit model of charging capacitor and being incorporated to of ground connection admittance.

Step (4) utilizes complete admittance matrix parameters design factor matrix.

Step (5) obtains the voltage magnitude of all PQ nodes by revising the back substitution of phase angle, and then obtains the whole network node electricity Pressure amplitude value and phase angle, calculate circuit complex power using complex power power flow equation.

Being calculated as follows of the method for simplifying of step (1) trigonometric function of the present invention and approximation coefficient：

The power balance equation of AC power flow is as follows

$P_i=v_i\underset{j=1}{\overset{n}{\Σ}}\left|Y_{ij}\right|v_{j}cos({\mathrm{\θ}}_{ij}-{\mathrm{\δ}}_{ij})---\left(1\right)$

$Q_i=-v_i\underset{j=1}{\overset{n}{\Σ}}\left|Y_{ij}\right|v_{j}sin({\mathrm{\θ}}_{ij}-{\mathrm{\δ}}_{ij})---\left(2\right)$

In formula：θ_ijFor node i, the branch impedance angle between j；δ_ijFor node i, the phase difference of voltage of j；Y_ijLead for node Receive the i-th row jth column element of matrix Y；P_iAnd Q_iIt is respectively node and inject active and reactive power；v_iFor voltage magnitude.

Circuit both end voltage phase angle difference is typically little, then have δ_ij≈ 0, sin δ_ij≈δ_ij, cos δ_ij≈1.

After above-mentioned simplification, formula (1) can be written as following form with the trigonometric function in formula (2).

cos(θ_ij-δ_ij)≈λ₁(cosθ_ij+(sinθ_ij)δ_ij) (3)

sin(θ_ij-δ_ij)≈λ₂(sinθ_ij-(cosθ_ij)δ_ij) (4)

λ in formula₁、λ₂For Ratio for error modification, its calculating formula is obtained by formula (5) and formula (6) respectively, and assumes its denominator not It is zero：

λ₁=cos (θ_ij-δ_ij)/(cosθ_ij+(sinθ_ij)δ_ij) (5)

λ₂=sin (θ_ij-δ_ij)/(sinθ_ij-(cosθ_ij)δ_ij) (6)

Little bigger than 30 ° of the phase difference of voltage of circuit two ends node in transmission system, therefore desirable δ_ijScope arrives for -30 ° 30 °, and suppose that the whole network impedance angle is a steady state value, then to a fixing impedance angle, λ₁、λ₂Can calculate in above-mentioned phase angle range And take average to try to achieve.Table 1 gives the recommendation value of λ under part r/x ratio.Typically can use λ₁For 0.97, λ₂For 0.95；R represents Resistance；X represents reactance；

λ 1, λ 2 value under the different r/x ratio of table 1

r/x	0.1	0.25	0.5	0.75	1
						λ1	0.98	0.97	0.97	0.97	0.96
λ2	0.95	0.95	0.95	0.95	0.95

More specifically, the structure of the DC flow model of step (2) base meter of the present invention and charging capacitor, as follows：

Formula (3), formula (4) are substituted into formula (1) respectively, formula (2) obtains：

$P_i={\mathrm{\λ}}_1{v}_i\underset{j=1}{\overset{n}{\Σ}}\left(\right|Y_{ij}|{\mathrm{cos\θ}}_{ij}{v}_j-|Y_{ij}\left|{\mathrm{sin\θ}}_{ij}{v}_j{\mathrm{\δ}}_{ij}\right)={\mathrm{\λ}}_1\[\underset{j=1}{\overset{n}{\Σ}}{G}_{ij}{v}_i{v}_j+\underset{j=1}{\overset{n}{\Σ}}{B}_{ij}(v_i{v}_j{\mathrm{\δ}}_i-v_i{v}_j{\mathrm{\δ}}_j)\]---\left(7\right)$

$Q_i=-{\mathrm{\λ}}_2{v}_i\underset{j=1}{\overset{n}{\Σ}}\left(\right|Y_{ij}|{\mathrm{sin\θ}}_{ij}{v}_j-|Y_{ij}\left|{\mathrm{cos\θ}}_{ij}{v}_j{\mathrm{\δ}}_{ij}\right)=-{\mathrm{\λ}}_2\[\underset{j=1}{\overset{n}{\Σ}}{B}_{ij}{v}_i{v}_j-\underset{j=1}{\overset{n}{\Σ}}{G}_{ij}(v_i{v}_j{\mathrm{\δ}}_i-v_i{v}_j{\mathrm{\δ}}_j)\]---\left(8\right)$

Node i differs typically little, i.e. v with the voltage magnitude of the node j being associated_i≈v_j(j is the section being associated with i Point), and the G when j is not associated with i_ij=B_ij=0, therefore v in formula (7), (8)_iV can directly be replaced with_j, after simplification, equation is as follows.

$P_i=\underset{j=1}{\overset{n}{\Σ}}{G}_{ij}^{\′}{v}_j^2+\underset{j=1}{\overset{n}{\Σ}}{B}_{ij}^{\′}({\mathrm{\δ}}_i^{\′}-{\mathrm{\δ}}_j^{\′})---\left(9\right)$

$Q_i=-\underset{j=1}{\overset{n}{\Σ}}{B}_{ij}^{\′\′}{v}_j^2+\underset{j=1}{\overset{n}{\Σ}}{G}_{ij}^{\′\′}({\mathrm{\δ}}_i^{\′}-{\mathrm{\δ}}_j^{\′})---\left(10\right)$

In formula：

G′_ij=λ₁G_ij；B′_ij=λ₁B_ij；G″_ij=λ₂G_ij；B″_ij=λ₂B_ij；

Step (3) of the present invention contains the circuit model filling an electric capacity and is grounded being incorporated to of admittance, as follows：

The circuit model that node admittance contains ground connection branch road as shown in Figure 1 determines, the real part of node self-admittance and imaginary part calculate Formula is as follows.

$G_{ii}=-\underset{j\∈i}{\Σ}{G}_{ij}+G_{sh.i}---\left(11\right)$

$B_{ii}=\underset{l,t\∈i}{\underset{j\∈i}{\Σ}}(-B_{ij}+0.5B_1+B_t)+B_{sh.i}---\left(12\right)$

In formula：Bl is the susceptance of the equivalent line charging electric capacity at node i；Bt is the non-standard no-load voltage ratio associating with node i The shunt susceptance of transformator π type equivalent circuit；Bsh.i is the shunt susceptance of node i；Gsh.i is the shunt conductance of node i.

Formula (11) and formula (12) are arranged and can obtain：

$\underset{j=1}{\overset{n}{\Σ}}{G}_{ij}=G_{sh.i}---\left(13\right)$

$\underset{j=1}{\overset{n}{\Σ}}{B}_{ij}=\underset{t\∈i}{\underset{l\∈i}{\Σ}}(0.5B_1+B_t)+B_{sh.i}---\left(14\right)$

Definition,Then C_i、D_iOnly it is made up of shunt admittance item, note C, D are respectively by C_i、D_i The n dimensional vector constituting, represents, with subscript d, n × n diagonal matrix that n-dimensional vector is constituted, constructs diagonal matrix Cd=respectively with C and D Diag (C), Dd=diag (D).

After above-mentioned definition, formula (9) and formula (10) can be written as matrix form：

$\[\tilde{P}\]=\[G^{\′}\]\[v^2\]-\[B^{\′}\]\[{\mathrm{\δ}}^{\′}\]+\[C_d\]\[{\widetilde{\mathrm{\δ}}}^{\′}\]=\[G^{\′}\]\[v^2\]+\[C_B\]\[{\widetilde{\mathrm{\δ}}}^{\′}\]---\left(15\right)$

$\[\tilde{Q}\]=\[-B^{\′\′}\]\[v^2\]-\[G^{\′\′}\]\[{\mathrm{\δ}}^{\′}\]+\[D_d\]\[{\widetilde{\mathrm{\δ}}}^{\′}\]=-\[B^{\′\′}\]\[v^2\]+\[D_G\]\[{\widetilde{\mathrm{\δ}}}^{\′}\]---\left(16\right)$

[CB]=[Cd]-[B'] in formula, [DG]=[Dd]-[G "].

Step (4) of the present invention utilizes complete admittance matrix parameters design factor matrix, as follows：

It is assumed that node 1 is balance nodes, node 2～m is PV node, and node m+1～n is PQ node.Represented with subscript (m) Sequence number 1～m, subscript (n) represents sequence number m+1～n, then formula (15), formula (16) piecemeal are：

$\left[\begin{array}{c}{\tilde{P}}^{\left(m\right)}\\ {\tilde{P}}^{\left(n\right)}\end{array}\right]=\left[\begin{array}{cc}{G}^{\′\left(mm\right)}& G^{\′\left(mn\right)}\\ G^{\′\left(nm\right)}& G^{\′\left(nn\right)}\end{array}\right]\left[\begin{array}{c}{v}^{2\left(m\right)}\\ v^{2\left(n\right)}\end{array}\right]+\left[\begin{array}{cc}{C}_B^{\left(mm\right)}& C_B^{\left(mn\right)}\\ C_B^{\left(nm\right)}& C_B^{\left(nn\right)}\end{array}\right]\left[\begin{array}{c}{\widetilde{\mathrm{\δ}}}^{\′\left(m\right)}\\ {\widetilde{\mathrm{\δ}}}^{\′\left(n\right)}\end{array}\right]---\left(17\right)$

$\left[\begin{array}{c}{\tilde{Q}}^{\left(m\right)}\\ {\tilde{Q}}^{\left(n\right)}\end{array}\right]=\left[\begin{array}{cc}{B}^{\′\′\left(mm\right)}& B^{\′\′\left(mn\right)}\\ B^{\′\′\left(nm\right)}& B^{\′\′\left(nn\right)}\end{array}\right]\left[\begin{array}{c}{v}^{2\left(m\right)}\\ v^{2\left(n\right)}\end{array}\right]+\left[\begin{array}{cc}{D}_G^{\left(mm\right)}& D_G^{\left(mn\right)}\\ D_G^{\left(nm\right)}& D_G^{\left(nn\right)}\end{array}\right]\left[\begin{array}{c}{\widetilde{\mathrm{\δ}}}^{\′\left(m\right)}\\ {\widetilde{\mathrm{\δ}}}^{\′\left(n\right)}\end{array}\right]---\left(18\right)$

Formula (18) is launched the second row and is obtained：

$\[v^{2\left(n\right)}\]=-{\[B^{\′\′\left(nn\right)}\]}^{-1}(\[{\tilde{Q}}^{\left(n\right)}\]+\[B^{\′\′\left(nm\right)}\]\[v^{2\left(m\right)}\]+\[D_G^{\left(nm\right)}\]\[{\widetilde{\mathrm{\δ}}}^{\′\left(m\right)}\]+\[D_G^{\left(nn\right)}\]\[{\widetilde{\mathrm{\δ}}}^{\′\left(n\right)}\])---\left(19\right)$

Formula (19) is substituted into formula (17), the matrix equation obtaining after arranging is as follows：

$\[{\tilde{H}}_{11}\]\[{\widetilde{\mathrm{\δ}}}^{\′\left(m\right)}\]+\[{\tilde{H}}_{12}\]\[{\widetilde{\mathrm{\δ}}}^{\′\left(n\right)}\]=\[{\tilde{P}}^{\left(m\right)}\]-\[{\tilde{P}}_{vQ}^{\left(m\right)}\]---\left(20\right)$

$\[{\tilde{H}}_{21}\]\[{\widetilde{\mathrm{\δ}}}^{\′\left(m\right)}\]+\[{\tilde{H}}_{22}\]\[{\widetilde{\mathrm{\δ}}}^{\′\left(n\right)}\]=\[{\tilde{P}}^{\left(n\right)}\]-\[{\tilde{P}}_{vQ}^{\left(n\right)}\]---\left(21\right)$

Shown in computing formula such as formula (the 22)-formula (25) of four coefficient matrixes occurring in formula (20)-formula (21).

$\[H_{11}\]=\[C_B^{\left(mm\right)}\]+\[G^{\′\left(mn\right)}\]{\[B^{\′\′\left(nn\right)}\]}^{-1}\[D_G^{\left(nm\right)}\]---\left(22\right)$

$\[H_{12}\]=\[C_B^{\left(mn\right)}\]+\[G^{\′\left(mn\right)}\]{\[B^{\′\′\left(nn\right)}\]}^{-1}\[D_G^{\left(nn\right)}\]---\left(23\right)$

$\[H_{21}\]=\[C_B^{\left(nm\right)}\]+\[G^{\′\left(nn\right)}\]{\[B^{\′\′\left(nn\right)}\]}^{-1}\[D_G^{\left(nm\right)}\]---\left(24\right)$

$\[H_{22}\]=\[C_B^{\left(nn\right)}\]+\[G^{\′\left(nn\right)}\]{\[B^{\′\′\left(nn\right)}\]}^{-1}\[D_G^{\left(nn\right)}\]---\left(25\right)$

Formula (20), formula (21) can be written as after merging

$\[\tilde{H}\]\[{\widetilde{\mathrm{\δ}}}^{\′}\]=\[\tilde{P}\]-\[{\tilde{P}}_{vQ}\]---\left(26\right)$

In formula：

$\[\tilde{H}\]=\[{\tilde{h}}_{ij}\]=\left[\begin{array}{cc}{\tilde{H}}_{11}& {\tilde{H}}_{12}\\ {\tilde{H}}_{21}& {\tilde{H}}_{22}\end{array}\right]---\left(27\right)$

$\[{\tilde{P}}_{vQ}\]=\left[\begin{array}{cc}{L}_{vm}& L_{Qm}\\ L_{vn}& L_{Qn}\end{array}\right]\left[\begin{array}{c}{v}^{2\left(m\right)}\\ {\tilde{Q}}^{\left(n\right)}\end{array}\right]---\left(28\right)$

In formula, four sub- block matrix calculating formulas of L battle array are as follows.

[L_vm]=[G'^(mm)]-[G'^(mn)][B″⁽ⁿⁿ⁾]^-1[B″^(nm)] (29)

[L_Qm]=- [G'^(mn)][B″⁽ⁿⁿ⁾]^-1(30)

[L_vn]=[G'^(nm)]-[G'⁽ⁿⁿ⁾][B″⁽ⁿⁿ⁾]^-1[B″^(nm)] (31)

[L_Qn]=- [G'⁽ⁿⁿ⁾][B″⁽ⁿⁿ⁾]^-1(32)

Step (5) of the present invention obtains the voltage magnitude of all PQ nodes by revising the back substitution of phase angle, and then obtains the whole network Node voltage amplitude and phase angle, calculate circuit complex power using complex power power flow equation, as follows：

1) calculating of node voltage phase angle

Assume balance nodes voltage phase angle δ₁=0, then δ₁'=0, substitutes into formula (26) and obtains：

[H] [δ ']=[P]-[P_vQ] (34)

[δ ']=[H]^-1([P]-[P_vQ]) (35)

Node voltage phase angle is：

${\mathrm{\δ}}_i={{\mathrm{\δ}}_i}^{\′}/v_i^2---\left(36\right)$

2) calculating of node voltage amplitude

The voltage magnitude that can calculate all PQ nodes after radical sign is opened in δ ' the back substitution that formula (27) is tried to achieve to formula (19).

3) calculating of branch road complex power

Node voltage phasor V is substituted into the Load flow calculation formula of matrixing, can directly try to achieve the complex power of circuit, as formula (37) and shown in formula (38)：

$S_f={\left(C_{f}V\right)}_d{I}_f^{*}={\left(C_{f}V\right)}_d{Y}_f^{*}{V}^{*}---\left(37\right)$

$S_t={\left(C_{t}V\right)}_d{I}_t^{*}={\left(C_{t}V\right)}_d{Y}_t^{*}{V}^{*}---\left(38\right)$

In formula：S_fFor circuit head end complex power；S_tFor line end complex power；V is the node voltage phasor of nb × 1；C_fWith C_tIncidence matrix (nl is circuitry number, and nb is nodes) for nl × nb；Y_fAnd Y_tBranch admittance matrix for nl × nb；Subscript * Represent conjugate of symbol；Subscript d represents the diagonal matrix of vector composition.

The invention has the beneficial effects as follows, the present invention, on the basis of considering idle injection and line resistance, has counted and has connect The impact of ground leg, by the linearisation to power balance equation, has obtained the DC power flow equation still with linear forms, profit With the DC power flow Equation for Calculating voltage magnitude that is derived by and phase angle.Present invention research points out charging capacitor to transmission line of electricity Reactive power distribution has the impact of highly significant, can not be ignored during the reactive power flow of computing electric power line.Proposed by the present invention Algorithm, compared with the DC power flow algorithm not considering to be grounded branch road, can keep active power on the premise of higher computational accuracy Obtain more accurately rational voltage magnitude and reactive power, make DC power flow algorithm have wider array of application prospect.

Brief description

Fig. 1 is the circuit model containing ground connection branch road；

Fig. 2 is IEEE-118 node system node phase angle error ε_δ；

Fig. 3 is IEEE-118 node system node amplitude error ε_v；

Fig. 4 is IEEE-118 node system circuit head end active power error ε_P；

Fig. 5 is IEEE-118 node system circuit head end reactive power error ε_Q；

Fig. 6 is IEEE-118 node system circuit head end reactive power；

Fig. 7 is to calculate time distribution map；

Fig. 8 is the DC power flow computational methods flow chart of a kind of meter of the present invention and charging capacitor.

Specific embodiment

In order to better illustrate effectiveness of the invention, with specific embodiment, the present invention is made further below in conjunction with the accompanying drawings Describe in detail

Fig. 8 is the process step of the DC power flow computational methods of a kind of meter of the present embodiment and charging capacitor.

Specific embodiment takes IEEE118 node system (containing 14 node shunt capacitances), in Intel i7-47903.6GHz On platform, Simulation Example is carried out using MATLAB platform.Using Newton-Laphson method calculation of tidal current as benchmark (convergence precision For 10-5), the calculation error of relatively more several difference DC power flow computational methods.For ease of narration, defining Newton-Laphson method is Method 0, standard direct current power flow algorithm are method 1 it is considered to the DC power flow algorithm of loss compensation is method 2, considers idle injection DC flow model be method 3, algorithm proposed by the present invention be method 4, wherein λ₁And λ₂Take 0.97 and 0.95 respectively.Use ε_δ、 ε_v、ε_P、ε_QRespectively as node phase angle error and amplitude error, the active error of circuit head end and reactive power error, subscript i (i=0, 1 ... 4) computational methods are represented.

${\mathrm{\ϵ}}_{\mathrm{\δ}}^i=\left|{\mathrm{\δ}}^i-{\mathrm{\δ}}^0\right|---\left(39\right)$

${\mathrm{\ϵ}}_v^i=\left|v^i-v^0\right|---\left(40\right)$

${\mathrm{\ϵ}}_P^i=\left|P^i-P^0\right|---\left(41\right)$

${\mathrm{\ϵ}}_Q^i=\left|Q^i-Q^0\right|---\left(42\right)$

In method 1 and method 2, all node voltage amplitude are taken as 1, and circuit is idle is approximately 0, therefore are not involved in idle tide The analysis of stream calculation error.Method 3 does not provide the reactive power flow computing formula of simplification, but can with calculate node voltage magnitude and Phase angle, therefore the complex power that the node voltage phasor that the method is calculated substitutes into formula (37) calculating circuit head end participates in comparing.

1) node voltage phase angle compares

Fig. 2 is the node voltage phase angle error curve under four kinds of DC power flow computational methods, and method 1 is standard DC power flow Algorithm, each node voltage phase angle error calculated is all larger, is not suitable for the Load flow calculation of IEEE-118 node system, The calculation error of method 2,3,4 improves significantly with respect to method 1, and the calculation error scope of method 4 and method 2,3 is near Seemingly, show ground connection branch road counts the calculation error that can't increase active power.

2) node voltage amplitude compares

As shown in figure 3, method 1 and 2 all assume that the perunit value of node voltage amplitude is 1, so their curve of error Overlap；Method 3 and method 4 consider the idle injecting power of node, and calculated voltage magnitude error will the side of being significantly less than Method 1 and method 2；Further look at and can obtain：On the larger node of some amplitude errors of method 3, the error of method 4 will Ratio method 3 is much smaller, can be effectively improved the computational accuracy to voltage magnitude for the DC power flow algorithm after illustrating to count charging capacitor.

3) circuit active power compares

Fig. 4 is the error of the calculated circuit head end active power of four kinds of DC power flow algorithms.When circuit r/x ratio relatively Hour, the transmission of active power is mainly affected by voltage phase angle, and therefore the higher method of phase calculation precision 2,3,4 is active Power calculation effect is also relatively more preferable.

4) circuit reactive power compares

Under the simplification of method 1 and method 2, the reactive power of system is zero, and only method 3 and method 4 can computing systems Voltage magnitude, therefore only the reactive power of comparative approach 3 and method 4 calculates error, as shown in Figure 5.Method 3 have ignored line charging The parallel element such as electric capacity and node shunt admittance is it is impossible to reflection is grounded the impact that branch road is distributed to system reactive power.From Fig. 5 It can be seen that reactive power on many branch roads for the method 3 calculates error is greater than method 4.For dividing of display reactive power flow directly perceived Cloth, Fig. 6 gives the method for being respectively adopted 3, method 4 and the calculated reactive power of Newton-Laphson method in the lump.Result shows, To idle level off to 0 circuit, two methods calculation error is approximate, but the circuit heavier to some reactive powers, the meter of method 4 Calculate error and be significantly less than method 3.

The reactive power flow analysis of transmission system is primarily upon the larger circuit of idle through-put power in circuit.For ease of comparing The idle calculation error of DC power flow algorithm counterweight reactive line, it is idle that table 2 lists separated time road head end in the middle part of IEEE118 system Power absolute value is more than the branch road of 50Mvar and four kinds of tidal current computing methods including inventive algorithm are corresponding idle Power computation, wherein method DC adopt standard direct current power flow algorithm to calculate active power, and are supposing line power factor For being calculated reactive power with reference to active result of calculation under conditions of 0.95.Load flow calculation knot with Newton-Laphson method (NR) Fruit is compared, and is not difficult to find out that the wattless power meter calculator of a lot of branch roads in the DC flow model considering idle injection has relatively Big calculation error, and after inventive algorithm considers ground connection branch road, the computational accuracy of reactive power considers that network loss is equivalent negative relatively The DC flow model of lotus has and is significantly lifted.And directly using the result of calculation of power factor method then have very big with Meaning property is although more accurate to indivedual branch road result of calculations, but also result in the idle unreasonable of other branch roads simultaneously, wherein props up The reactive power on road 107,127 occurs reversely, easily causing larger interference to reactive power flow analysis.

The comparison of table 2 reactive power

Weight reactive line	NR	The present invention	The DC power flow of idle injection	DC
					7	-89.73	-81.09	-46.35	-147.91
8	124.73	130.85	134.16	110.94
					36	92.97	134.05	153.28	75.30
51	113.60	181.45	223.58	79.73
					93	67.48	103.66	132.66	49.95
94	-67.48	-40.48	-17.44	-49.95
					96	-57.63	-43.98	-31.20	-53.25
97	-66.49	-43.89	-25.42	-60.30
					107	112.82	120.80	132.87	-21.78
127	75.54	114.16	154.19	-18.81

5) the calculating time compares

Method 1 is little with the amount of calculation difference of method 4 with method 2, method 3, therefore choosing method 1 (DC) and method 4 (this Bright algorithm) carry out the comparison of calculating speed as typical DC power flow algorithm and Newton method, as shown in table 3.Wherein, three kinds of algorithms Calculating speed near being respectively slowly standard direct current power flow algorithm, inventive algorithm and Newton method.

Table 3 calculates the comparison of time

Distinct methods	NR	DC	The present invention
				Iterationses	2	1	1
The calculating time	0.004184	0.001084	0.002672

Fig. 7 gives the block diagram of each several part matrix operationss time that inventive algorithm is related to, it can be seen that meter Calculate H battle array and consume the substantial amounts of calculating time, and solve voltage phase angle δ, amplitude V and time used by line power S and only account for total time Sub-fraction.Matrix H includes matrix L and is all calculated merely with bus admittance matrix item, and its value is completely by the structure of circuit Parameter determines, as shown in formula (22)～(25) and formula (29)～(32)), only matrix PvQ, voltage magnitude computing formula and phase angle meter Calculating formula needs to use node injecting power, as shown in formula (28), (19), (35).When network structure does not change, only save During point injection rate change, directly carrying out calculating using known constant matricess H and L can be substantially improved computational efficiency, be particularly suitable for Occasion in the frequent change of network topology structure change frequency is less node power injection rate.

Claims (7)

1. the DC power flow computational methods of a kind of meter and charging capacitor are it is characterised in that methods described is in the direct current considering resistance On the basis of tide model, ground connection branch road is contributed in circuit model, to reflect the parallel element of idle injection and ground connection branch road Impact to System Reactive Power distribution；By constructing parallel element admittance item, power flow equation is made with further linearization process, derive Go out the DC power flow equation of the linear forms without iteration, the higher precision being capable of calculate node voltage magnitude；Methods described According to the following steps：

(1) calculating of the method for simplifying of trigonometric function and approximation coefficient, sets up the power balance equation of AC power flow；

(2) structure of the DC flow model of meter and charging capacitor；

(3) circuit model of charging capacitor and being incorporated to of ground connection admittance are contained；

(4) utilize complete admittance matrix parameters design factor matrix；

(5) obtain the voltage magnitude of all PQ nodes by revising the back substitution of phase angle, so obtain the whole network node voltage amplitude and Phase angle, calculates circuit complex power using complex power power flow equation.

2. the DC power flow computational methods of a kind of meter according to claim 1 and charging capacitor are it is characterised in that described three The method for simplifying of angle function and the calculating of approximation coefficient, level off to 0 according to circuit both end voltage difference in magnitude and phase angle difference, derive three The method for simplifying of angle function, and calculate corresponding approximation coefficient：

The power balance equation of AC power flow is as follows：

$P_i=v_i\underset{j=1}{\overset{n}{\Σ}}\left|Y_{ij}\right|v_{j}cos({\mathrm{\θ}}_{ij}-{\mathrm{\δ}}_{ij})---\left(1\right)$

$Q_i=-v_i\underset{j=1}{\overset{n}{\Σ}}\left|Y_{ij}\right|v_{j}sin({\mathrm{\θ}}_{ij}-{\mathrm{\δ}}_{ij})---\left(2\right)$

In formula：θ_ijFor node i, the branch impedance angle between j；δ_ijFor node i, the phase difference of voltage of j；Y_ijFor node admittance square The i-th row jth column element of battle array Y；P_iAnd Q_iIt is respectively node and inject active and reactive power；v_iVoltage magnitude for i point；v_jFor j The voltage magnitude of point；

Circuit both end voltage phase angle difference is typically little, then have δ_ij≈ 0, sin δ_ij≈δ_ij, cos δ_ij≈1；

After above-mentioned simplification, formula (1) can be written as following form with the trigonometric function in formula (2)：

cos(θ_ij-δ_ij)≈λ₁(cosθ_ij+(sinθ_ij)δ_ij) (3)

sin(θ_ij-δ_ij)≈λ₂(sinθ_ij-(cosθ_ij)δ_ij) (4)

λ in formula₁、λ₂For Ratio for error modification, its calculating formula is obtained by formula (5) and formula (6) respectively, and assumes that its denominator is not zero：

λ₁=cos (θ_ij-δ_ij)/(cosθ_ij+(sinθ_ij)δ_ij) (5)

λ₂=sin (θ_ij-δ_ij)/(sinθ_ij-(cosθ_ij)δ_ij) (6)

Little bigger than 30 ° of the phase difference of voltage of circuit two ends node in transmission system, therefore desirable δ_ijScope is -30 ° to 30 °, And suppose that the whole network impedance angle is a steady state value, then to a fixing impedance angle, λ₁、λ₂Can calculate in above-mentioned phase angle range and take Average is tried to achieve.

3. the DC power flow computational methods of a kind of meter according to claim 1 and charging capacitor are it is characterised in that described meter And the structure of the DC flow model of charging capacitor is as follows：

Circuit both end voltage amplitude and phase angle difference away from little, voltage approximately equal,

Formula (3), formula (4) are substituted into formula (1) respectively, formula (2) obtains：

$P_i={\mathrm{\λ}}_1{v}_i\underset{j=1}{\overset{n}{\Σ}}\left(\right|Y_{ij}|{\mathrm{cos\θ}}_{ij}{v}_j-|Y_{ij}\left|{\mathrm{sin\θ}}_{ij}{v}_j{\mathrm{\δ}}_{ij}\right)={\mathrm{\λ}}_1\[\underset{j=1}{\overset{n}{\Σ}}{G}_{ij}{v}_i{v}_j+\underset{j=1}{\overset{n}{\Σ}}{B}_{ij}(v_i{v}_j{\mathrm{\δ}}_i-v_i{v}_j{\mathrm{\δ}}_j)\]---\left(7\right)$

$Q_i=-{\mathrm{\λ}}_2{v}_i\underset{j=1}{\overset{n}{\Σ}}\left(\right|Y_{ij}|{\mathrm{sin\θ}}_{ij}{v}_j-|Y_{ij}\left|{\mathrm{cos\θ}}_{ij}{v}_j{\mathrm{\δ}}_{ij}\right)=-{\mathrm{\λ}}_2\[\underset{j=1}{\overset{n}{\Σ}}{B}_{ij}{v}_i{v}_j-\underset{j=1}{\overset{n}{\Σ}}{G}_{ij}(v_i{v}_j{\mathrm{\δ}}_i-v_i{v}_j{\mathrm{\δ}}_j)\]---\left(8\right)$

Node i differs typically little, i.e. v with the voltage magnitude of the node j being associated_i≈v_j(j is the node being associated with i), and The G when j is not associated with i_ij=B_ij=0, therefore v in formula (7), (8)_iV can directly be replaced with_j, after simplification, equation is as follows：

$P_i=\underset{j=1}{\overset{n}{\Σ}}{G}_{ij}^{\′}{v}_j^2+\underset{j=1}{\overset{n}{\Σ}}{B}_{ij}^{\′}({\mathrm{\δ}}_i^{\′}-{\mathrm{\δ}}_j^{\′})---\left(9\right)$

$Q_i=-\underset{j=1}{\overset{n}{\Σ}}{B}_{ij}^{\′\′}{v}_j^2+\underset{j=1}{\overset{n}{\Σ}}{G}_{ij}^{\′\′}({\mathrm{\δ}}_i^{\′}-{\mathrm{\δ}}_j^{\′})---\left(10\right)$

In formula：

G′_ij=λ₁G_ij；B′_ij=λ₁B_ij；G″_ij=λ₂G_ij；B″_ij=λ₂B_ij；

4. the DC power flow computational methods of a kind of meter according to claim 1 and charging capacitor are it is characterised in that described contain The circuit model of charging capacitor and ground connection being incorporated to of admittance, in the DC power flow branch model of standard, meter and charging capacitor, will Charging capacitor is included in DC power flow admittance matrix：

In complete circuit model, the real part of node self-admittance and imaginary part computing formula are as follows：

$G_{ii}=-\underset{j\∈i}{\Σ}{G}_{ij}+G_{sh.i}---\left(11\right)$

$B_{ii}=\underset{l,t\∈i}{\underset{j\∈i}{\Σ}}(-B_{ij}+0.5B_1+B_t)+B_{sh.i}---\left(12\right)$

In formula：B₁Susceptance for the equivalent line charging electric capacity at node i；B_tIt is the non-standard no-load voltage ratio transformator associating with node i The shunt susceptance of π type equivalent circuit；B_sh.iShunt susceptance for node i；G_sh.iShunt conductance for node i；

Formula (11) and formula (12) are arranged and can obtain：

$\underset{j=1}{\overset{n}{\Σ}}{G}_{ij}=G_{sh.i}---\left(13\right)$

$\underset{j=1}{\overset{n}{\Σ}}{B}_{ij}=\underset{t\∈i}{\underset{l\∈i}{\Σ}}(0.5B_1+B_t)+B_{sh.i}---\left(14\right)$

Definition,Then C_i、D_iOnly it is made up of shunt admittance item, note C, D are respectively by C_i、D_iConstitute N dimensional vector, n × n diagonal matrix that n-dimensional vector is constituted is represented with subscript d, diagonal matrix C is constructed respectively with C and D_d=diag (C), D_d=diag (D)；

After above-mentioned definition, formula (9) and formula (10) can be written as matrix form：

$\[\tilde{P}\]=\[G^{\′}\]\[v^2\]-\[B^{\′}\]\[{\mathrm{\δ}}^{\′}\]+\[C_d\]\[{\widetilde{\mathrm{\δ}}}^{\′}\]=\[G^{\′}\]\[v^2\]+\[C_B\]\[{\widetilde{\mathrm{\δ}}}^{\′}\]---\left(15\right)$

$\[\tilde{Q}\]=\[-B^{\′\′}\]\[v^2\]-\[G^{\′\′}\]\[{\mathrm{\δ}}^{\′}\]+\[D_d\]\[{\widetilde{\mathrm{\δ}}}^{\′}\]=-\[B^{\′\′}\]\[v^2\]+\[D_G\]\[{\widetilde{\mathrm{\δ}}}^{\′}\]---\left(16\right)$

[C in formula_B]=[C_d]-[B'], [D_G]=[D_d]-[G”].

5. according to claim 1 a kind of meter and charging capacitor DC power flow computational methods, derivation linear forms straight Corresponding coefficient matrix computing formula in stream Load flow calculation equation：

It is assumed that node 1 is balance nodes, node 2～m is PV node, and node m+1～n is PQ node；Use subscript^(m)Represent sequence number 1 ～m, subscript⁽ⁿ⁾Represent sequence number m+1～n, then formula (15), formula (16) piecemeal are：

$\left[\begin{array}{c}{\tilde{P}}^{\left(m\right)}\\ {\tilde{P}}^{\left(n\right)}\end{array}\right]=\left[\begin{array}{cc}{G}^{\′\left(mm\right)}& G^{\′\left(mn\right)}\\ G^{\′\left(nm\right)}& G^{\′\left(nn\right)}\end{array}\right]\left[\begin{array}{c}{v}^{2\left(m\right)}\\ v^{2\left(n\right)}\end{array}\right]+\left[\begin{array}{cc}{C}_B^{\left(mm\right)}& C_B^{\left(mn\right)}\\ C_B^{\left(nm\right)}& C_B^{\left(nn\right)}\end{array}\right]\left[\begin{array}{c}{\widetilde{\mathrm{\δ}}}^{\′\left(m\right)}\\ {\widetilde{\mathrm{\δ}}}^{\′\left(n\right)}\end{array}\right]---\left(17\right)$

$\left[\begin{array}{c}{\tilde{Q}}^{\left(m\right)}\\ {\tilde{Q}}^{\left(n\right)}\end{array}\right]=\left[\begin{array}{cc}{B}^{\′\′\left(mm\right)}& B^{\′\′\left(mn\right)}\\ B^{\′\′\left(nm\right)}& B^{\′\′\left(nn\right)}\end{array}\right]\left[\begin{array}{c}{v}^{2\left(m\right)}\\ v^{2\left(n\right)}\end{array}\right]+\left[\begin{array}{cc}{D}_G^{\left(mm\right)}& D_G^{\left(mn\right)}\\ D_G^{\left(nm\right)}& D_G^{\left(nn\right)}\end{array}\right]\left[\begin{array}{c}{\widetilde{\mathrm{\δ}}}^{\′\left(m\right)}\\ {\widetilde{\mathrm{\δ}}}^{\′\left(n\right)}\end{array}\right]---\left(18\right)$

Formula (18) is launched the second row and is obtained：

$\[v^{2\left(n\right)}\]=-{\[B^{\′\′\left(nn\right)}\]}^{-1}(\[{\tilde{Q}}^{\left(n\right)}\]+\[B^{\′\′\left(nm\right)}\]\[v^{2\left(m\right)}\]+\[D_G^{\left(nm\right)}\]\[{\widetilde{\mathrm{\δ}}}^{\′\left(m\right)}\]+\[D_G^{\left(nn\right)}\]\[{\widetilde{\mathrm{\δ}}}^{\′\left(n\right)}\])---\left(19\right)$

Formula (19) is substituted into formula (17), the matrix equation obtaining after arranging is as follows：

$\[{\tilde{H}}_{11}\]\[{\widetilde{\mathrm{\δ}}}^{\′\left(m\right)}\]+\[{\tilde{H}}_{12}\]\[{\widetilde{\mathrm{\δ}}}^{\′\left(n\right)}\]=\[{\tilde{P}}^{\left(m\right)}\]-\[{\tilde{P}}_{vQ}^{\left(m\right)}\]---\left(20\right)$

$\[{\tilde{H}}_{21}\]\[{\widetilde{\mathrm{\δ}}}^{\′\left(m\right)}\]+\[{\tilde{H}}_{22}\]\[{\widetilde{\mathrm{\δ}}}^{\′\left(n\right)}\]=\[{\tilde{P}}^{\left(n\right)}\]-\[{\tilde{P}}_{vQ}^{\left(n\right)}\]---\left(21\right)$

Shown in computing formula such as formula (the 22)-formula (25) of four coefficient matrixes occurring in formula (20)-formula (21)；

$\[H_{11}\]=\[C_B^{\left(mm\right)}\]+\[G^{\′\left(mn\right)}\]{\[B^{\′\′\left(nn\right)}\]}^{-1}\[D_G^{\left(nm\right)}\]---\left(22\right)$

$\[H_{12}\]=\[C_B^{\left(mn\right)}\]+\[G^{\′\left(mn\right)}\]{\[B^{\′\′\left(nn\right)}\]}^{-1}\[D_G^{\left(nn\right)}\]---\left(23\right)$

$\[H_{21}\]=\[C_B^{\left(nm\right)}\]+\[G^{\′\left(nn\right)}\]{\[B^{\′\′\left(nn\right)}\]}^{-1}\[D_G^{\left(nm\right)}\]---\left(24\right)$

$\[H_{22}\]=\[C_B^{\left(nn\right)}\]+\[G^{\′\left(nn\right)}\]{\[B^{\′\′\left(nn\right)}\]}^{-1}\[D_G^{\left(nn\right)}\]---\left(25\right)$

Formula (20), formula (21) can be written as after merging：

$\[\tilde{H}\]\[{\widetilde{\mathrm{\δ}}}^{\′}\]=\[\tilde{P}\]-\[{\tilde{P}}_{vQ}\]---\left(26\right)$

In formula：

$\[\tilde{H}\]=\[{\tilde{h}}_{ij}\]=\left[\begin{array}{cc}{\tilde{H}}_{11}& {\tilde{H}}_{12}\\ {\tilde{H}}_{21}& {\tilde{H}}_{22}\end{array}\right]---\left(27\right)$

$\[{\tilde{P}}_{vQ}\]=\left[\begin{array}{cc}{L}_{vm}& L_{Qm}\\ L_{vn}& L_{Qn}\end{array}\right]\left[\begin{array}{c}{v}^{2\left(m\right)}\\ {\tilde{Q}}^{\left(n\right)}\end{array}\right]---\left(28\right)$

In formula, four sub- block matrix calculating formulas of L battle array are as follows：

[L_vm]=[G'^(mm)]-[G'^(mn)][B”⁽ⁿⁿ⁾]^-1[B”^(nm)] (29)

[L_Qm]=- [G'^(mn)][B”⁽ⁿⁿ⁾]^-1(30)

[L_vn]=[G'^(nm)]-[G'⁽ⁿⁿ⁾][B”⁽ⁿⁿ⁾]^-1[B”^(nm)] (31)

[L_Qn]=- [G'⁽ⁿⁿ⁾][B”⁽ⁿⁿ⁾]^-1(32).

6. the DC power flow computational methods of a kind of meter according to claim 1 and charging capacitor are it is characterised in that described profit Calculate circuit complex power with complex power power flow equation as follows：

(1) calculating of node voltage phase angle

Assume balance nodes voltage phase angle δ₁=0, then δ₁'=0, substitutes into formula (26) and obtains：

[H] [δ ']=[P]-[P_vQ] (34)

[δ ']=[H]^-1([P]-[P_vQ]) (35)

Node voltage phase angle is：

${\mathrm{\δ}}_i={{\mathrm{\δ}}_i}^{\′}/v_i^2---\left(36\right)$

(2) calculating of node voltage amplitude

The voltage magnitude that can calculate all PQ nodes after radical sign is opened in δ ' the back substitution that formula (26) is tried to achieve to formula (19)；

(3) calculating of branch road complex power：

Node voltage phasor V is substituted into the Load flow calculation formula of matrixing, can directly try to achieve the complex power of circuit, as formula (37) and Shown in formula (38)：

$S_f={\left(C_{f}V\right)}_d{I}_f^{*}={\left(C_{f}V\right)}_d{Y}_f^{*}{V}^{*}---\left(37\right)$

$S_t={\left(C_{t}V\right)}_d{I}_t^{*}={\left(C_{t}V\right)}_d{Y}_t^{*}{V}^{*}---\left(38\right)$

In formula：S_fFor circuit head end complex power；S_tFor line end complex power；V is the node voltage phasor of nb × 1；C_fAnd C_tFor The incidence matrix (nl is circuitry number, and nb is nodes) of nl × nb；Y_fAnd Y_tBranch admittance matrix for nl × nb；Subscript * represents Conjugate of symbol；Subscript d represents the diagonal matrix of vector composition.

7. the DC power flow computational methods of a kind of meter according to claim 2 and charging capacitor are it is characterised in that described mistake Difference correction factor λ₁And λ₂Value, under different r/x ratios, corresponding value see table：

Wherein, r represents resistance；X represents reactance.