CN101325336A

CN101325336A - Method for matching multi-region electric network swim based on belt restriction state estimation

Info

Publication number: CN101325336A
Application number: CNA200810117176XA
Authority: CN
Inventors: 吴文传; 张伯明; 蔡斌; 孙宏斌; 吴素农; 曾兵; 万源
Original assignee: JIANGXI POWER DISPATCHING CENTER; Tsinghua University
Current assignee: JIANGXI POWER DISPATCHING CENTER; Tsinghua University
Priority date: 2008-07-25
Filing date: 2008-07-25
Publication date: 2008-12-17
Anticipated expiration: 2028-07-25
Also published as: CN101325336B

Abstract

The invention relates to a multiregion power network current matching method based on the estimation with the constrained state, and belongs to the automation field of electric power system management. The method includes the following steps: according to the power network real time data, superior and subordinate power network dispatching centers generate internal power network models and current distribution of the region, and build corresponding external power network equivalent models; the models and the current data of the subordinate power network are sent to the superior power network dispatching center which connects and combines the superior and the subordinate power network models into a total power network model through connecting lines or transformers; and the total power network current distribution can be obtained by applying the estimation method with the constrained state to the total power network model. The method can ensure that the current distribution of the superior power network part in the total power network model which is obtained after the combination of the multiregion power network models remains the same, and the boundary current mismatches of the superior and the subordinate power networks are distributed to the subordinate power network. The method ensures that the interconnected network on-line safety analysis and the results of simulation computation are accurate, thereby having important significance for ensuring the safe operation of the power networks.

Description

Multi-region power grid power flow matching method based on constrained state estimation

Technical Field

The invention relates to a multi-region power grid power flow matching method based on constrained state estimation, and belongs to the technical field of power system dispatching automation and power grid simulation.

Background

The power grid is formed by interconnecting a plurality of regional power grids and is an integral body, and the influence on the power grid after an accident occurs is global. In an interconnected power grid, a power grid governed by each scheduling center is generally only one part of a large power grid, an EMS system of the scheduling center only models the governed power grid part, and an external power grid is replaced by an equivalent power grid made offline, so that the accuracy is poor, the development and the change of the power grid cannot be adapted, and the problem in the practicability of the traditional EMS is solved.

In order to solve the problem, a global power grid model is established on line through model exchange between the upper and lower power grid longitudinal directions and through model combination. The existing method takes the tidal current estimated value of each subarea power grid as measurement, and establishes a state estimation model of the global power grid, so that the tidal current distribution matched with the global power grid is obtained. However, this method distributes the power flow mismatch between the power grids of the respective partitions into the respective partitions, and it cannot be guaranteed that the power flow distribution of the higher-level power grid or the power grid requiring detailed analysis remains unchanged before and after model merging, and thus cannot meet the actual demand.

Disclosure of Invention

The invention aims to provide a multi-region power grid flow matching method based on belt constraint state estimation, wherein each region power grid establishes power grid models in respective administration regions in each scheduling center, the power grid models are transmitted to a superior scheduling center by using a high-speed data communication network established between the current power grid scheduling centers, the superior scheduling center forms a global power grid model through the combination of the models, so that the multi-region power grid flow models in a power system are combined on line, the real-time state of the superior power grid flow in the combined global power grid model is consistent with the real-time state of the superior power grid, and the superior power grid flow is kept unchanged before and after the combination.

The invention provides a multi-region power grid power flow matching method based on constrained state estimation, which comprises the following steps of:

(1-1) automatically generating an internal power grid model and power flow distribution of a region by a superior power grid dispatching center according to real-time data of a power grid under jurisdiction, and simultaneously establishing an external power grid equivalent model connected with the internal power grid model, wherein the internal power grid model and the external power grid equivalent model are connected with each other through a connecting line or a transformer to form a superior power grid model;

(1-2) automatically generating an internal power grid model and a power flow distribution of a local area by each subordinate power grid dispatching center according to real-time data of a power grid under jurisdiction, simultaneously establishing an external power grid equivalent model connected with the internal power grid model, mutually connecting the internal power grid model and the external power grid equivalent model through a connecting line or a transformer to form a subordinate power grid model, and sending the power flow data of the subordinate power grid model and the subordinate power grid to a superior power grid dispatching center through a wide area network;

(1-3) the superior power grid dispatching center connects the superior power grid model and the received subordinate power grid models with each other through a connecting line or a transformer, and external power grid equivalent models in the superior power grid model and the subordinate power grid models are deleted and combined into a whole local power grid model when the superior power grid model and the subordinate power grid models are connected;

and (1-4) estimating the power flow of the global power grid model by using a constrained state estimation method.

In the method, a process of estimating the load flow of the global power grid model by using a constrained state estimation method specifically comprises the following steps:

(2-1) constructing a weighted two-multiplication state estimation model containing a power flow equality constraint and a node injection inequality constraint for the global power grid:

the following constraints are satisfied:

P_{ij} = P_{ij}^{0},

i∈A，j∈A

Q_{ij} = Q_{ij}^{0},

i∈A，j∈A

P _j＜P_j＜P_j，j∈A

Q _j＜Q_j＜Q_j，j∈A

wherein Z is_iThe state estimation value before the merging of the upper and lower power grid models comprises the active power P of a power grid line or a transformer_ijAnd reactive power Q_ijVoltage amplitude V of the bus_iAnd the active injection power P of the bus_iAnd reactive injection power Q_i，h_i(V, theta) is the measurement equation, w_iFor weighting the weighting coefficients in the two-multiplication state estimation, A is the node set of the upper level grid, A is the node set of all the lower level grids, P_ij、P_ij ⁰The active power after combination and the active power before combination of the upper-level power grid side of the junctor between the upper-level power grid and the lower-level power grid are Q_ij、Q_ij ⁰The connecting line between the upper and lower electric networks is the combined reactive power and the combined reactive power on the upper electric network side, P_j、P _j、P_jRespectively the injected active power, the lower limit of the active power and the upper limit of the active power, Q, of the lower-level power grid node j_j、Q _j、Q_jRespectively the injected reactive power, the lower reactive power limit and the upper reactive power limit of a lower-level power grid node j, and respectively V and theta are the voltage amplitude and the phase angle of all nodes of the power grid;

the above measurement equation h_i(V, θ) is defined as:

the measurement equation of the line or the transformer is as follows:

in the above formula, P_ijIs the active power of the line or transformer, Q_ijIs the reactive power of the line or transformer;

the voltage measurement equation of any bus i of the global power grid is as follows:

V_i＝V_i

the injection measurement equation of any bus i of the global power grid is as follows:

<math> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>P</mi> <mi>i</mi> </msub> <mo>=</mo> <msubsup> <mi>V</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msub> <mi>G</mi> <mi>ii</mi> </msub> <mo>+</mo> <munderover> <mi>Σ</mi> <mrow> <mi>j</mi> <mo>&Element;</mo> <mi>i</mi> </mrow> <mrow> <mi>j</mi> <mo>&NotEqual;</mo> <mi>i</mi> </mrow> </munderover> <msub> <mi>V</mi> <mi>i</mi> </msub> <msub> <mi>V</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mi>ij</mi> </msub> <mi>cos</mi> <msub> <mi>θ</mi> <mi>ij</mi> </msub> <mo>+</mo> <msub> <mi>B</mi> <mi>ij</mi> </msub> <mi>sin</mi> <msub> <mi>θ</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>Q</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>-</mo> <msubsup> <mi>V</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msub> <mi>B</mi> <mi>ii</mi> </msub> <mo>+</mo> <munderover> <mi>Σ</mi> <mrow> <mi>j</mi> <mo>&Element;</mo> <mi>i</mi> </mrow> <mrow> <mi>j</mi> <mo>&NotEqual;</mo> <mi>i</mi> </mrow> </munderover> <msub> <mi>V</mi> <mi>i</mi> </msub> <msub> <mi>V</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mi>ij</mi> </msub> <mi>sin</mi> <msub> <mi>θ</mi> <mi>ij</mi> </msub> <mo>-</mo> <msub> <mi>B</mi> <mi>ij</mi> </msub> <mi>cos</mi> <msub> <mi>θ</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>

in the above formula, P_i、Q_iActive injection power and reactive injection power of any generator or load i in the global power grid;

(2-2) solving the weighted two-multiplication state estimation model by adopting an interior point method;

and (2-3) obtaining the load flow distribution of the global power grid according to the solved voltage amplitude V and phase angle theta of all nodes of the global power grid.

The invention provides a multi-region power grid power flow matching method based on constrained state estimation, which is characterized by comprising the following steps: and the upper-level power grid dispatching center and each lower-level subarea power grid dispatching center respectively establish and maintain the current models of the local-level power grid and the local-area power grid so as to accord with the existing management mode of grading and subarea dispatching. The lower-level power grid dispatching center needs to send the real-time power flow model of the power grid of the local jurisdiction to the upper-level dispatching center, and after the upper-level dispatching center collects the power flow models of the power grids of the lower-level sub-areas, the power grid models of the lower-level sub-areas and the upper-level power grid model are combined to form a global power grid model. And releasing the constraint of partial measurement, and performing state estimation on the global power grid model combined for calculation to obtain the matched load flow distribution of the upper and lower power grids. The whole process is automatically completed, and the method is suitable for online safety analysis, scheduling decision and analog simulation of a large-scale interconnected power grid. Therefore, the method of the invention has the following advantages:

1. each level of power grid dispatching center only needs to maintain the power grid flow model of each level, and the maintenance workload is not increased;

2. automatically realizing online combination of the multi-region power grid load flow models through the collection and state estimation of each region power grid model to form globally matched load flow distribution;

3. after the combination, the upper-level power grid part in the overall power grid flow model is consistent with the actual condition, and the safety analysis, control decision and simulation precision of the interconnected power grid are ensured, so that the safe operation of the power grid is ensured.

4. After the combination, important generators and loads of lower-level power grids in the global power grid flow model do not change greatly after the combination, and meanwhile, the output of all the generators is kept in a limited range.

Drawings

FIG. 1 is a schematic diagram of an online merging method of power flow models of a power grid according to the present invention;

fig. 1(a) is a lower-level power grid power flow model, fig. 1(b) is a higher-level power grid power flow model, and fig. 1(c) is a combined global power grid power flow model.

Fig. 2 is a schematic diagram of a global power grid power flow model merged by the method of the present invention.

In fig. 1 and 2, 1 is a local area internal power grid model automatically generated by a lower power grid dispatching center, 2 is a connection line or transformer connected with the internal power grid model and the external power grid equivalent model, 3 is an external power grid equivalent model connected with the internal power grid model, 4 is an external power grid equivalent model connected with the internal power grid model, 5 is a connection line or transformer connected with the internal power grid model and the external power grid equivalent model, 6 is a local area internal power grid model automatically generated by a higher power grid dispatching center, 7 is a higher power grid model, 8 is a tidal current measurement of a higher power grid side of the connection line or the connection transformer, 9 is a connection transformer, 10 is a connection line, 11 is a lower power grid, 12 is a tidal current measurement of a lower power grid side of the connection line or the connection transformer, and 13 is an injection tidal current measurement of a bus in the lower power grid.

Detailed Description

The following describes a multi-region grid power flow matching method based on constrained state estimation in detail with reference to the accompanying drawings and an embodiment of the invention.

The specific implementation method of the invention is shown in fig. 1, and comprises the following steps:

step one, as shown in fig. 1(b), a superior power grid dispatching center automatically generates a local internal power grid model 6 and a current distribution by using a known power grid state estimation method according to real-time data of a power grid under jurisdiction, wherein the power grid model 6 and the current distribution comprise a power grid topological structure, active power, reactive power or generator-side bus voltage of a power grid generator, active power and reactive power of a power grid load, active power and reactive power of a power grid bus voltage and a line, active power and reactive power of a transformer, tap positions of the transformer and the like; meanwhile, an external power grid equivalent model 4 connected with the internal power grid is established, and the internal model and the external model are connected through a connecting line 5 actually existing between the internal model and the external model to form a superior power grid model;

step two, as shown in fig. 1(a), each sub-regional power grid dispatching center automatically generates a local internal power grid model 1 and a power flow distribution by using a known state estimation method according to the real-time data of the power grid under jurisdiction, wherein the power grid model 1 and the power flow distribution comprise a power grid topological structure, the active power and the reactive power of a power grid generator or the voltage of a generator-side bus, the active power and the reactive power of a power grid load, the active power and the reactive power of a power grid bus voltage and a line, the active power and the reactive power of a transformer, the tap position of the transformer and the like, meanwhile, an external power grid equivalent model 3 connected with the internal power grid is established, the internal model and the external model are connected through a connecting line 2 actually existing between the internal model and the external model to form a lower-level power grid model, sending the lower-level power grid model and the tidal current data to a higher-level power grid dispatching center through a wide area network;

and step three, the superior power grid dispatching center receives the inferior power grid models and the tidal current data sent by the sub-area power grid dispatching centers, firstly, the external network equivalent model (dotted line) parts in the respective power grid models are removed, then, the superior power grid models and the inferior power grid models are in butt joint through the tie lines 5 between the superior power grid models and the inferior power grid models (the

tie lines

2 and 5 represent the same group of tie lines, and the superior power grid side 5 is adopted here), so that the superior power grid models and the inferior power grid models can be combined into a global power grid model for calculation, as shown in fig. 1(c), the global power grid model is obtained by respectively removing the dotted line part areas of the models in fig. 1(a) and fig. 1(b) and then connecting the models together through the tie lines.

And step four, measuring the respective estimation results of the upper and lower power grids as equipment, and carrying out whole-grid estimation by a constrained state estimation method. The state estimation method with the constraint can estimate and obtain new full-network load flow distribution matched with the upper and lower-level power networks, and can ensure that the state of the upper-level power network is kept unchanged before and after estimation. The method comprises the following specific steps:

(1) firstly, a weighted two-multiplication state estimation model containing a connecting line between an upper power grid and a lower power grid, a connecting transformer power flow equality constraint and a node injection inequality constraint is constructed, namely an optimization model of a group of power grid state variables (including voltage amplitude values V and phase angles theta of all nodes of a power grid) under the condition of meeting the constraints is solved:

the following constraints are satisfied:

P_{ij} = P_{ij}^{0},

i∈A，j∈A

Q_{ij} = Q_{ij}^{0},

i∈A，j∈A(1)

P _j＜P_j＜P_j，j∈A

Q _j＜Q_j＜Q_j，j∈A

wherein Z is_iThe state estimation value before the merging of the upper and lower power grid models comprises the active power P of a power grid line or a transformer_ijAnd reactive power Q_ijVoltage amplitude V of the bus_iAnd the active injection power P of the bus_iAnd reactive injection power Q_i，h_i(V, theta) is the measurement equation, w_iTo weight the weighting coefficients in the two-multiplication state estimation, A is the node set of the upper level grid, A is all the lower levelsNode set of the grid, P_ij、P_ij ⁰The active power after combination and the active power before combination of the upper-level power grid side of the junctor between the upper-level power grid and the lower-level power grid are Q_ij、Q_ij ⁰The connecting line between the upper and lower electric networks is the combined reactive power and the combined reactive power on the upper electric network side, P_j、P _j、P_jRespectively the injected active power, the lower limit of the active power and the upper limit of the active power, Q, of the lower-level power grid node j_j、Q _j、Q_jRespectively the injected reactive power, the lower reactive power limit and the upper reactive power limit of a lower-level power grid node j, and respectively V and theta are the voltage amplitude and the phase angle of all nodes of the power grid;

measurement equation h_i(V, θ) is defined as follows:

line or transformer measurement equation:

V_i＝V_i (3)

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>P</mi> <mi>i</mi> </msub> <mo>=</mo> <msubsup> <mi>V</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msub> <mi>G</mi> <mi>ii</mi> </msub> <mo>+</mo> <munderover> <mi>Σ</mi> <mrow> <mi>j</mi> <mo>&Element;</mo> <mi>i</mi> </mrow> <mrow> <mi>j</mi> <mo>&NotEqual;</mo> <mi>i</mi> </mrow> </munderover> <msub> <mi>V</mi> <mi>i</mi> </msub> <msub> <mi>V</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mi>ij</mi> </msub> <mi>cos</mi> <msub> <mi>θ</mi> <mi>ij</mi> </msub> <mo>+</mo> <msub> <mi>B</mi> <mi>ij</mi> </msub> <mi>sin</mi> <msub> <mi>θ</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>Q</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>-</mo> <msubsup> <mi>V</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msub> <mi>B</mi> <mi>ii</mi> </msub> <mo>+</mo> <munderover> <mi>Σ</mi> <mrow> <mi>j</mi> <mo>&Element;</mo> <mi>i</mi> </mrow> <mrow> <mi>j</mi> <mo>&NotEqual;</mo> <mi>i</mi> </mrow> </munderover> <msub> <mi>V</mi> <mi>i</mi> </msub> <msub> <mi>V</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mi>ij</mi> </msub> <mi>sin</mi> <msub> <mi>θ</mi> <mi>ij</mi> </msub> <mo>-</mo> <msub> <mi>B</mi> <mi>ij</mi> </msub> <mi>cos</mi> <msub> <mi>θ</mi> <mi>ij</mi> </msub> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>

(2) solving the constrained state estimation problem represented by equation (1) using an interior point method

The following non-linear programming standard can be written for equation (1):

minimize f(x)

subject to h(x)＝0 (5)

g≤g(x)≤g

wherein: x is formed by R⁽ⁿ⁾，h(x)≡[h₁(x)，…，h_m(x)]^T，g(x)≡[g₁(x)，…，g_r(x)]^T。

Introducing relaxation variable (l, u) epsilon R^(r)The non-linear programming form for transforming equation (5) into a constraint of equality and a simple variable is as follows:

minimize f(x)

subjectto h(x)＝0

g(x)-l-g＝0 (6)

g(x)+u-g＝0

(l，u)≥0

the lagrange function defining equation (6) is:

<math> <mrow> <mi>L</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>l</mi> <mo>,</mo> <mi>u</mi> <mo>;</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>,</mo> <mi>w</mi> <mo>;</mo> <mover> <mi>z</mi> <mo>~</mo> </mover> <mo>,</mo> <mover> <mi>w</mi> <mo>~</mo> </mover> <mo>)</mo> </mrow> <mo>&equiv;</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <msup> <mrow> <mo>-</mo> <mi>y</mi> </mrow> <mi>T</mi> </msup> <mi>h</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <msup> <mi>z</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>l</mi> <mo>-</mo> <munder> <mi>g</mi> <mo>&OverBar;</mo> </munder> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mo>-</mo> <msup> <mi>w</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>u</mi> <mo>-</mo> <mover> <mi>g</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <msup> <mover> <mi>z</mi> <mo>~</mo> </mover> <mi>T</mi> </msup> <mi>l</mi> <mo>-</mo> <msup> <mover> <mi>w</mi> <mo>~</mo> </mover> <mi>T</mi> </msup> <mi>u</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>

here, y ∈ R^(m)And

<math> <mrow> <mrow> <mo>(</mo> <mi>z</mi> <mo>,</mo> <mi>w</mi> <mo>,</mo> <mover> <mi>z</mi> <mo>~</mo> </mover> <mo>,</mo> <mover> <mi>w</mi> <mo>~</mo> </mover> <mo>)</mo> </mrow> <mo>&Element;</mo> <msup> <mi>R</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </msup> </mrow> </math>

is a lagrange multiplier.

According to the Karush-Kuhn-Tucker theorem, the optimal solution must satisfy the following KKT system:

<math> <mrow> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> <mi>L</mi> <mo>&equiv;</mo> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> <mi>h</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mi>y</mi> <mo>-</mo> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>z</mi> <mo>+</mo> <mi>w</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msub> <mo>&dtri;</mo> <mi>y</mi> </msub> <mi>L</mi> <mo>&equiv;</mo> <mi>h</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msub> <mo>&dtri;</mo> <mi>z</mi> </msub> <mi>L</mi> <mo>&equiv;</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>l</mi> <mo>-</mo> <munder> <mi>g</mi> <mo>&OverBar;</mo> </munder> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msub> <mo>&dtri;</mo> <mi>w</mi> </msub> <mi>L</mi> <mo>&equiv;</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>u</mi> <mo>-</mo> <mover> <mi>g</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msub> <mo>&dtri;</mo> <mi>l</mi> </msub> <mi>L</mi> <mo>&equiv;</mo> <mi>z</mi> <mo>-</mo> <mover> <mi>z</mi> <mo>~</mo> </mover> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msub> <mo>&dtri;</mo> <mi>u</mi> </msub> <mi>L</mi> <mo>&equiv;</mo> <mi>w</mi> <mo>+</mo> <mover> <mi>w</mi> <mo>~</mo> </mover> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> </math>

L \tilde{Z} e = 0 - - - (14)

U \tilde{W} e = 0 - - - (15)

<math> <mrow> <mrow> <mo>(</mo> <mi>l</mi> <mo>,</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>&GreaterEqual;</mo> <mn>0</mn> <mo>,</mo> <mrow> <mo>(</mo> <mover> <mi>z</mi> <mo>~</mo> </mover> <mo>,</mo> <mover> <mi>w</mi> <mo>~</mo> </mover> <mo>)</mo> </mrow> <mo>&GreaterEqual;</mo> <mn>0</mn> <mo>,</mo> <mi>y</mi> <mo>&NotEqual;</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein (L, U, Z, W) belongs to R^(r×r)According to convention in mathematical programming, a diagonal matrix, e ≡ 1, …, 1, representing elements l, u, z, w]^T∈R^(r)。

Combining the formulas (12) and (13) and the complementary conditions (14) and (15), introducing a perturbation parameter mu > 0 according to perturbation KKT theory, relaxing the combined complementary conditions, and replacing the formulas (12) to (15) with the following steps:

<math> <mrow> <msubsup> <mo>&dtri;</mo> <mi>l</mi> <mi>μ</mi> </msubsup> <mi>L</mi> <mo>&equiv;</mo> <mi>LZe</mi> <mo>-</mo> <mi>μe</mi> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mo>&dtri;</mo> <mi>u</mi> <mi>μ</mi> </msubsup> <mi>L</mi> <mo>&equiv;</mo> <mi>UWe</mi> <mo>+</mo> <mi>μe</mi> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow> </math>

solving the above perturbation KKT systems (8) - (11), (17) - (18) by directly applying Newton method to obtain the following correction systems:

wherein,

is the residual of the perturbed KKT system.

And

hessian matrices of f (x), h (x), and g (x).

Simplification (19-24), elimination of Δ l, Δ u, Δ z, Δ w, yields the final simplified KKT system as follows:

wherein:

<math> <mrow> <mi>J</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>&equiv;</mo> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> <mi>h</mi> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>27</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mo>+</mo> <msup> <mi>L</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>Z</mi> <mrow> <mo>(</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>l</mi> <mo>-</mo> <munder> <mi>g</mi> <mo>&OverBar;</mo> </munder> <mo>)</mo> </mrow> <mo>-</mo> <msup> <mi>U</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>W</mi> <mrow> <mo>(</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>u</mi> <mo>-</mo> <mover> <mi>g</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </math>

and after elimination, the expressions of Δ l, Δ u, Δ z, Δ w:

<math> <mrow> <mi>Δl</mi> <mo>=</mo> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> <msup> <mrow> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mi>T</mi> </msup> <mi>Δx</mi> <mo>+</mo> <mrow> <mo>(</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>l</mi> <mo>-</mo> <munder> <mi>g</mi> <mo>&OverBar;</mo> </munder> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>29</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mi>Δu</mi> <mo>=</mo> <mo>-</mo> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> <mi>g</mi> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mi>Δx</mi> <mo>-</mo> <mrow> <mo>(</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>u</mi> <mo>-</mo> <mover> <mi>g</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>30</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mi>Δz</mi> <mo>=</mo> <mo>-</mo> <msup> <mi>L</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>Z</mi> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> <mi>g</mi> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mi>Δx</mi> <mo>-</mo> <msup> <mi>L</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mo>(</mo> <mi>LZe</mi> <mo>-</mo> <mi>μe</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>Z</mi> <mrow> <mo>(</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>l</mi> <mo>-</mo> <munder> <mi>g</mi> <mo>&OverBar;</mo> </munder> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>31</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mi>Δw</mi> <mo>=</mo> <msup> <mi>U</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>W</mi> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> <msup> <mrow> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mi>T</mi> </msup> <mi>Δx</mi> <mo>-</mo> <msup> <mi>U</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mo>(</mo> <mi>UWe</mi> <mo>+</mo> <mi>μe</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>W</mi> <mrow> <mo>(</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>u</mi> <mo>-</mo> <mover> <mi>g</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>32</mn> <mo>)</mo> </mrow> </mrow> </math>

(26) in the formula, H (□) is composed of two parts: h_hIs a linear combination of f (x), h (x), and g (x) a hessian matrix; h_gReferred to as Barrier Matrix (Barrier Matrix). H_gTerms prevent inequality constraints g (x) from violating their bilateral limits.

The resulting path-tracing-method interior point iteration format is as follows:

(0) and (5) initializing. K is 0, K_maxCenter parameter (centering parameter) σ ∈ (0, 1)]Convergence accuracy ε is 10^-6. Selecting [ l, u ]]^T＞0，[z＞0，w＜0，y＝0]^THere, K, K_maxAre respectively an iteration meterNumber and maximum allowed number of iterations;

(1) if K < K_maxContinuing; otherwise, the printing does not converge;

(2) calculating complementary gap (complementary gap) C_Gap：

<math> <mrow> <msub> <mi>C</mi> <mi>Gap</mi> </msub> <mo>&equiv;</mo> <munderover> <mi>Σ</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>r</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>l</mi> <mi>i</mi> </msub> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>u</mi> <mi>i</mi> </msub> <msub> <mi>w</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>33</mn> <mo>)</mo> </mrow> </mrow> </math>

If C is present_GapStopping when the value is less than epsilon, and outputting an optimal solution;

(3) solving the correction systems (25) - (32) to obtain correction quantities [ delta x, delta y ], [ delta l, delta u ] and [ delta z, delta w ];

(4) ratio tests, determining the maximum step size in the original and dual spaces:

i＝1，2，…，r

(5) update original and dual variables:

(6) k +1, go back to (1);

(3) by solving the state variables of the system (including the voltage amplitude V and the phase angle theta of all nodes of the power grid) in the last step, the power flow distribution of the whole power grid can be solved. The equation (1) contains the equality constraint that the active power and the reactive power of all the connecting lines and the connecting transformers between the upper-level power grid and the lower-level power grid are kept unchanged, and meanwhile, the power flow distribution of the upper-level power grid is converged before combination, so that the power flow distribution of the upper-level power grid can be kept unchanged after combination. In addition, the deviation amount of the lower-level power grid from the upper-level power grid is distributed in the current-level power grid according to the principle of weighted least squares, and meanwhile, the inequality constraint injected by the nodes in the formula (1) is utilized to be suitable for ensuring that important generators and loads of the lower-level power grid do not have large changes after being combined, and meanwhile, the output of all the generators is kept in a limited range.

Claims

1. The multi-region power grid flow matching method based on the constrained state estimation is characterized by comprising the following steps of:

2. The method according to claim 1, wherein the step (1-4) of estimating the power flow of the global grid model by using a constrained state estimation method specifically comprises the following steps:

the following constraints are satisfied:

P_{ij} = P_{ij}^{0},

i∈A，j∈A

Q_{ij} = Q_{ij}^{0},

i∈A，j∈A

P _j＜P_j＜P_j，j∈A

Q _j＜Q_j＜Q_j，j∈A

wherein Z is_iThe state estimation value before the merging of the upper and lower power grid models comprises the active power P of a power grid line or a transformer_ijAnd reactive power Q_ijVoltage amplitude V of the bus_iAnd the active injection power P of the bus_iAnd reactive injection power Q_i，h_i(V, theta) is the measurement equation, w_iFor weighting the weighting coefficients in the two-multiplication state estimation, A is the node set of the upper level grid, A is the node set of all the lower level grids, P_ij、P_ij ⁰The active power after combination and the active power before combination of the upper-level power grid side of the junctor between the upper-level power grid and the lower-level power grid are Q_ij、Q_ij ⁰The connecting line between the upper and lower power grids has no reactive power after combination and no reactive power before combination on the upper power grid sideWork power, P_j、P _j、P_jRespectively the injected active power, the lower limit of the active power and the upper limit of the active power, Q, of the lower-level power grid node j_j、Q _j、Q_jRespectively the injected reactive power, the lower reactive power limit and the upper reactive power limit of a lower-level power grid node j, and respectively V and theta are the voltage amplitude and the phase angle of all nodes of the power grid;

the above measurement equation h_i(V, θ) is defined as follows:

line or transformer measurement equation:

in the above formula, P_ijIs the active power of the line or transformer, Q_ijIs the reactive power of the line or transformer; the voltage measurement equation of any bus i of the global power grid is as follows:

V_i＝V_i