CN103441518B

CN103441518B - Three-phase Power Flow distribution determination method in single-phase load and alternate load mixing situation

Info

Publication number: CN103441518B
Application number: CN201310338526.6A
Authority: CN
Inventors: 胡丽娟; 盛万兴; 宋晓辉; 孟晓丽; 李建芳; 史常凯
Original assignee: State Grid Corp of China SGCC; Electric Power Research Institute of State Grid Shanxi Electric Power Co Ltd; China Electric Power Research Institute Co Ltd CEPRI
Current assignee: State Grid Corp of China SGCC; Electric Power Research Institute of State Grid Shanxi Electric Power Co Ltd; China Electric Power Research Institute Co Ltd CEPRI
Priority date: 2013-08-06
Filing date: 2013-08-06
Publication date: 2016-04-20
Anticipated expiration: 2033-08-06
Also published as: CN103441518A

Abstract

The present invention proposes the Three-phase Power Flow distribution determination method in a kind of single-phase load and alternate load mixing situation, first network topology, the low-pressure side payload of each node and load access way is obtained, then according to different access way, by low-pressure side load Equivalent Conversion, obtain the power output of each phase of medium voltage side, finally adopt the Three Phase Power Flow based on neutral point voltage skew, obtain Three-phase Power Flow distribution.The present invention is by the Load flow calculation problem in the inconsistent situation of load access way in equivalent transformation process power distribution network, propose the power distribution network Three-phase Power Flow distribution acquiring method in a kind of applicable single-phase load and alternate load mixing situation, make power distribution network operating analysis result more accurate.

Description

Three-phase power flow distribution determination method under the condition of single-phase load and mixed inter-phase load

技术领域technical field

本发明属于配电网运行控制技术领域，具体涉及一种单相负荷和相间负荷混合情况下的三相潮流分布确定方法。The invention belongs to the technical field of distribution network operation control, and in particular relates to a method for determining three-phase power flow distribution in the case of mixed single-phase load and interphase load.

背景技术Background technique

潮流计算是配电网规划、运行分析、控制与优化的基础，是配电网最基本、最重要的计算。随着我国国民经济的蓬勃发展、负荷各样性增长以及分布式电源接入配电网方式的不一致，配电网三相潮流计算研究越来越受到关注。Power flow calculation is the basis of distribution network planning, operation analysis, control and optimization, and is the most basic and important calculation of distribution network. With the vigorous development of my country's national economy, the increase of load diversity and the inconsistency of distributed power access to distribution network, the research on three-phase power flow calculation of distribution network has attracted more and more attention.

配电网具有诸多不同于输电网络的特征，如开环运行（闭环设计、辐射状运行）、三相不平衡情况突出、线路电阻和电抗比值大、节点数目大等，另外，随着分布式电源入网方式的不同、单相和三相等不同供电模式的广泛应用，配电网三相潮流不宜采用等效成单相的传统处理方式进行计算。为了提高配电网的自动化管理水平、保障配电网的安全可靠运行，必需对配电网进行及时、准确的三相潮流计算，因而有必要研究适于配电网的三相潮流计算方法。根据配电网的特征，不少专家学者提出了多种三相潮流计算方法，如改进牛拉法，回路阻抗法，前推回代法等。针对这些方法的优缺点，专利“一种基于中性点偏移的配电网三相潮流计算方法”提出了一种快速有效准确的三相潮流计算方法，所提方法能很好的处理各节点的负荷输出功率已知的网络。而实际配电网，低压侧负荷接入中压配电网的方式不尽相同，可能接入某一相，也可能接入某两相间，也可能三相均接入，中压配电网既包括接入某一相上的单相负荷，也包括接入某个相间或多个相间的相间负荷，在因而有必要研究在已知低压侧负荷情况下，负荷接入方式不一的三相潮流计算方法，即单相与相间负荷混合情况下的潮流计算方法。The distribution network has many characteristics different from the transmission network, such as open-loop operation (closed-loop design, radial operation), prominent three-phase unbalance, large ratio of line resistance to reactance, large number of nodes, etc. In addition, with the distributed Due to the different ways of power grid connection and the wide application of different power supply modes of single-phase and three-phase, the three-phase power flow of the distribution network should not be calculated by the traditional processing method equivalent to single-phase. In order to improve the automatic management level of distribution network and ensure the safe and reliable operation of distribution network, it is necessary to carry out timely and accurate three-phase power flow calculation for distribution network, so it is necessary to study the three-phase power flow calculation method suitable for distribution network. According to the characteristics of the distribution network, many experts and scholars have proposed a variety of three-phase power flow calculation methods, such as the improved cow-pull method, the loop impedance method, and the push-back method. Aiming at the advantages and disadvantages of these methods, the patent "A Three-phase Power Flow Calculation Method for Distribution Network Based on Neutral Point Offset" proposes a fast, effective and accurate three-phase power flow calculation method, which can handle various A network in which the load output power of the nodes is known. In the actual distribution network, the way that the low-voltage side load is connected to the medium-voltage distribution network is different. It may be connected to a certain phase, it may be connected to a certain two-phase, or it may be connected to all three phases. The medium-voltage distribution network It includes not only the single-phase load connected to a certain phase, but also the phase-to-phase load connected to a certain phase or multiple phases. Therefore, it is necessary to study the three-phase load with different load connection methods under the known low-voltage side load. Phase power flow calculation method, that is, the power flow calculation method in the case of single-phase and inter-phase load mixing.

发明内容Contents of the invention

针对现有技术的不足，本发明提出一种单相负荷和相间负荷混合情况下的三相潮流分布确定方法，通过等效变换将低压侧负荷等效成中压侧各相的功率输出，可有效处理负荷接入方式不一致的情况，适用于即有接入中压侧的某一相上、又有接入中压侧的某个相间或多个相间的负荷的单三相混合供电模式的配电网，也适用于分布式电源单相、相间混合接入配电网情况下的潮流计算。Aiming at the deficiencies of the prior art, the present invention proposes a method for determining the distribution of three-phase power flow in the case of mixed single-phase load and interphase load. Through equivalent transformation, the load on the low-voltage side is equivalent to the power output of each phase on the medium-voltage side, which can Effectively deal with inconsistent load connection methods, suitable for single-phase and three-phase hybrid power supply modes where loads are connected to a certain phase on the medium-voltage side and connected to a certain phase or multiple phases on the medium-voltage side The distribution network is also suitable for the power flow calculation in the case of single-phase and inter-phase hybrid access to the distribution network of distributed power.

本发明提供的单相负荷和相间负荷混合情况下的三相潮流分布确定方法，其改进之处在于，首先获取网络拓扑、各节点的低压侧负荷大小及负荷接入方式，然后根据不同接入方式，将低压侧负荷等效换算，得到中压侧各相的输出功率，最后采用基于中性点电压偏移的三相潮流计算方法，计算三相潮流分布。The improvement of the method for determining the three-phase power flow distribution in the case of mixed single-phase loads and interphase loads provided by the present invention is that firstly, the network topology, the load size of the low-voltage side of each node and the load access mode are obtained, and then according to different access In this way, the load on the low-voltage side is equivalently converted to obtain the output power of each phase on the medium-voltage side. Finally, the three-phase power flow calculation method based on the neutral point voltage offset is used to calculate the three-phase power flow distribution.

其中，所述负荷接入方式包括星形接线与三角形接线两种方式；其中，Wherein, the load connection method includes star connection and delta connection; wherein,

配电变压器中压接线方式为星形时，通过单相变压器接入中压侧某一相上、或者通过三相变压器分别接入到中压侧各相上的负荷称为单相负荷；When the medium-voltage wiring mode of the distribution transformer is star-shaped, the load connected to a phase of the medium-voltage side through a single-phase transformer, or connected to each phase of the medium-voltage side through a three-phase transformer is called a single-phase load;

配电变压器中压接线方式为三角形时，通过单相变压器接入中压侧的相间或者通过三相变压器接入中压侧各相间的负荷均称为相间负荷。When the medium-voltage connection mode of the distribution transformer is a triangle, the load connected to the phase-to-phase of the medium-voltage side through a single-phase transformer or connected to each phase of the medium-voltage side through a three-phase transformer is called an inter-phase load.

其中，所述根据不同接入方式，将低压侧负荷等效换算，得到中压侧各相的输出功率的步骤包括：Wherein, the step of obtaining the output power of each phase of the medium-voltage side by equivalently converting the load on the low-voltage side according to different access modes includes:

配电变压器中压接线方式为星形时，若单相负荷通过单相变压器接入中压侧的任意一相，则该相输出的等效功率为低压侧单相负荷大小，该节点其它两相的输出功率为0；When the medium-voltage wiring mode of the distribution transformer is star-shaped, if the single-phase load is connected to any phase of the medium-voltage side through the single-phase transformer, the equivalent power output by this phase is the size of the single-phase load on the low-voltage side, and the other two phases of the node The output power of the phase is 0;

配电变压器中压接线方式为星形时，三相间通过三相变压器均接入单相负荷，则经等效换算，三相输出的功率为各相上的单相负荷大小；When the medium-voltage wiring mode of the distribution transformer is star-shaped, the three-phases are all connected to the single-phase load through the three-phase transformer, then after equivalent conversion, the three-phase output power is the size of the single-phase load on each phase;

配电变压器中压接线方式为三角形时，若通过单相变压器在三相的任意一个相间接入相间负荷，则各相输出功率为：When the medium-voltage connection mode of the distribution transformer is triangle, if the interphase load is connected between any phase of the three phases through a single-phase transformer, the output power of each phase is:

对于接入A相和B相相间： $\{\begin{matrix} S_{A} = V_{A} {I_{A}}^{*} = V_{A} * S_{a} / (V_{B} - V_{A}) \\ S_{B} = V_{B} {I_{B}}^{*} = - V_{B} * S_{a} / (V_{B} - V_{A}) \\ S_{C} = 0 \end{matrix};$ For access between phase A and phase B: $\{\begin{matrix} S_{A} = V_{A} {I_{A}}^{*} = V_{A} * S_{a} / (V_{B} - V_{A}) \\ S_{B} = V_{B} {I_{B}}^{*} = - V_{B} * S_{a} / (V_{B} - V_{A}) \\ S_{C} = 0 \end{matrix};$

对于接入B相和C相相间： $\{\begin{matrix} S_{B} = V_{B} {I_{B}}^{*} = V_{B} * S_{b} / (V_{C} - V_{B}) \\ S_{C} = V_{C} {I_{C}}^{*} = - V_{C} * S_{b} / (V_{C} - V_{B}) \\ S_{A} = 0 \end{matrix};$ For access between Phase B and Phase C: $\{\begin{matrix} S_{B} = V_{B} {I_{B}}^{*} = V_{B} * S_{b} / (V_{C} - V_{B}) \\ S_{C} = V_{C} {I_{C}}^{*} = - V_{C} * S_{b} / (V_{C} - V_{B}) \\ S_{A} = 0 \end{matrix};$

对于接入C相和A相相间： $\{\begin{matrix} S_{C} = V_{C} {I_{C}}^{*} = V_{C} * S_{c} / (V_{A} - V_{C}) \\ S_{A} = V_{A} {I_{A}}^{*} = - V_{A} * S_{c} / (V_{A} - V_{C}) \\ S_{B} = 0 \end{matrix};$ For access between phase C and phase A: $\{\begin{matrix} S_{C} = V_{C} {I_{C}}^{*} = V_{C} * S_{c} / (V_{A} - V_{C}) \\ S_{A} = V_{A} {I_{A}}^{*} = - V_{A} * S_{c} / (V_{A} - V_{C}) \\ S_{B} = 0 \end{matrix};$

配电变压器中压接线方式为三角形时，若通过单相变压器在三相的任意两相相间接入相间负荷，则各相输出功率为：When the medium-voltage connection mode of the distribution transformer is a triangle, if the interphase load is connected between any two phases of the three phases through a single-phase transformer, the output power of each phase is:

对于A-B相和B-C相两相间： $\{\begin{matrix} S_{A} = V_{A} {I_{A}}^{*} = V_{A} * \frac{S_{a}}{V_{B} - V_{A}} \\ S_{B} = V_{B} {I_{B}}^{*} = V_{B} (- \frac{S_{a}}{V_{B} - V_{A}} + \frac{S_{b}}{V_{C} - V_{B}}) \\ S_{C} = V_{C} {I_{C}}^{*} = - V_{C} \frac{S_{b}}{V_{C} - V_{B}} \end{matrix};$ For phases AB and BC: $\{\begin{matrix} S_{A} = V_{A} {I_{A}}^{*} = V_{A} * \frac{S_{a}}{V_{B} - V_{A}} \\ S_{B} = V_{B} {I_{B}}^{*} = V_{B} (- \frac{S_{a}}{V_{B} - V_{A}} + \frac{S_{b}}{V_{C} - V_{B}}) \\ S_{C} = V_{C} {I_{C}}^{*} = - V_{C} \frac{S_{b}}{V_{C} - V_{B}} \end{matrix};$

对于B-C相和C-A相两相间： $\{\begin{matrix} S_{A} = V_{A} {I_{A}}^{*} = - V_{A} * \frac{S_{c}}{V_{A} - V_{C}} \\ S_{B} = V_{B} {I_{B}}^{*} = V_{B} * \frac{S_{b}}{V_{C} - V_{B}} \\ S_{C} = V_{C} {I_{C}}^{*} = V_{C} (- \frac{S_{b}}{V_{C} - V_{B}} + \frac{S_{c}}{V_{A} - V_{C}}) \end{matrix};$ For the two phases between BC phase and CA phase: $\{\begin{matrix} S_{A} = V_{A} {I_{A}}^{*} = - V_{A} * \frac{S_{c}}{V_{A} - V_{C}} \\ S_{B} = V_{B} {I_{B}}^{*} = V_{B} * \frac{S_{b}}{V_{C} - V_{B}} \\ S_{C} = V_{C} {I_{C}}^{*} = V_{C} (- \frac{S_{b}}{V_{C} - V_{B}} + \frac{S_{c}}{V_{A} - V_{C}}) \end{matrix};$

对于C-A相和A-B相两相间： $\{\begin{matrix} S_{A} = V_{A} {I_{A}}^{*} = V_{A} * \frac{S_{a} - S_{c}}{V_{B} - V_{A}} + S_{c} \\ S_{B} = V_{B} {I_{B}}^{*} = V_{B} (- \frac{S_{a} - S_{c}}{V_{B} - V_{A}} + \frac{S_{b} - S_{c}}{V_{C} - V_{B}}) + S_{c} \\ S_{C} = V_{C} {I_{C}}^{*} = - V_{C} \frac{S_{b} - S_{c}}{V_{C} - V_{B}} + S_{c} \end{matrix};$ For CA phase and AB phase between two phases: $\{\begin{matrix} S_{A} = V_{A} {I_{A}}^{*} = V_{A} * \frac{S_{a} - S_{c}}{V_{B} - V_{A}} + S_{c} \\ S_{B} = V_{B} {I_{B}}^{*} = V_{B} (- \frac{S_{a} - S_{c}}{V_{B} - V_{A}} + \frac{S_{b} - S_{c}}{V_{C} - V_{B}}) + S_{c} \\ S_{C} = V_{C} {I_{C}}^{*} = - V_{C} \frac{S_{b} - S_{c}}{V_{C} - V_{B}} + S_{c} \end{matrix};$

配电变压器中压接线方式为三角形时，若三相均接入相间负荷且三相负荷平衡，则三相输出的功率为各相上的单相负荷大小；When the medium-voltage connection mode of the distribution transformer is a triangle, if all three phases are connected to the interphase load and the three-phase load is balanced, the output power of the three phases is the size of the single-phase load on each phase;

配电变压器中压接线方式为三角形时，若三相均接入相间负荷且三相负荷不平衡，则当三相均接入相间负荷但三相负荷不平衡时，各相间负荷大小分别为S_a，S_b，S_c，将各相相间负荷分为相等的与不相等的两部分，相等的部分各相相间负荷大小为S_c，不相等的部分接入到A-B、B-C两相相间负荷分别为S_a-S_c、S_b-S_c，不相等的部分按两相接入相间负荷的处理方法，可得中压侧各相的等效输出S_A，S_B，S_C，When the medium-voltage connection mode of the distribution transformer is triangle, if all three phases are connected to the interphase load and the three-phase load is unbalanced, then when the three phases are connected to the interphase load but the three-phase load is unbalanced, the magnitude of the interphase load is S _a , S _b , S _c , divide the interphase load of each phase into equal and unequal parts, the equal part of the interphase load of each phase is S _c , and the unequal part is connected to the interphase load of AB and BC They are S _a -S _c , S _b -S _c , respectively, and the unequal parts are treated as two phases connected to the interphase load, and the equivalent output S _A , S _B , S _C of each phase on the medium voltage side can be obtained,

$\{\begin{matrix} {S S}_{A A} = = {V V}_{A A} {I I}_{A A}^{* *} = = {V V}_{A A} * * \frac{{S S}_{a a} - - {S S}_{c c}}{{V V}_{B B} - - {V V}_{A A}} + + {S S}_{c c} \\ {S S}_{B B} = = {V V}_{B B} {I I}_{B B}^{* *} = = {V V}_{B B} ((- - \frac{{S S}_{a a} - - {S S}_{c c}}{{V V}_{B B} - - {V V}_{A A}} + + \frac{{S S}_{b b} - - {S S}_{c c}}{{V V}_{C C} - - {V V}_{B B}})) + + {S S}_{c c} \\ {S S}_{C C} = = {V V}_{C C} {I I}_{C C}^{* *} = = - - {V V}_{C C} \frac{{S S}_{b b} - - {S S}_{c c}}{{V V}_{C C} - - {V V}_{B B}} + + {S S}_{c c} \end{matrix};;$

其中，所述采用基于中性点电压偏移的三相潮流计算方法，计算三相潮流分布的步骤包括：Wherein, the step of calculating the three-phase power flow distribution using the three-phase power flow calculation method based on the neutral point voltage offset includes:

（1）根据中压配电网网络拓扑，对馈线上各个节点和各条支路进行编号；(1) According to the network topology of the medium voltage distribution network, number each node and each branch on the feeder;

（2）引入各节点中性点电压偏移量 (2) Introduce the neutral point voltage offset of each node

（3）采用节点i的中性点偏移量对节点i的计算相电压值进行修正：(3) Use the neutral point offset of node i Correct the calculated phase voltage value of node i:

（4）计算各支路的三相电流值及各节点的三相电压值；(4) Calculate the three-phase current value of each branch and the three-phase voltage value of each node;

（5）采用牛顿-拉夫逊法进行迭代，修正中性点电压偏移量；(5) The Newton-Raphson method is used to iterate to correct the neutral point voltage offset;

（6）采用混合迭代法对三相电压进行求解，直至满足迭代终止条件，得到三相潮流分布。(6) The mixed iterative method is used to solve the three-phase voltage until the termination condition of the iteration is satisfied, and the three-phase power flow distribution is obtained.

其中，步骤（3）采用节点i的中性点偏移量对节点i的计算相电压值进行修正，其表达式为：Among them, step (3) uses the neutral point offset of node i Correct the calculated phase voltage value of node i, and its expression is:

$[\begin{matrix} {\overset{\cdot &Center Dot;}{U u}}_{Ai Ai} \\ {\overset{\cdot &Center Dot;}{U u}}_{Bi Bi} \\ {\overset{\cdot &Center Dot;}{U u}}_{Ci Ci} \end{matrix}] = = [\begin{matrix} {\overset{\cdot &Center Dot;}{V V}}_{Ai Ai} - - {\overset{\cdot &Center Dot;}{V V}}_{Ni Ni} \\ {\overset{\cdot &Center Dot;}{V V}}_{Bi Bi} - - {\overset{\cdot &Center Dot;}{V V}}_{Ni Ni} \\ {\overset{\cdot &Center Dot;}{V V}}_{Ci Ci} - - {\overset{\cdot &Center Dot;}{V V}}_{Ni Ni} \end{matrix}];;$

式中，分别为节点i处A相、B相、C相三相的计算相电压值；分别为节点i处A相、B相、C相三相电位值。In the formula, are the calculated phase voltage values of phase A, phase B and phase C at node i respectively; are the three-phase potential values of phase A, phase B and phase C at node i, respectively.

其中，步骤（4）计算各支路的三相电流值及各节点的三相电压值的表达式包括；Wherein, the expressions for calculating the three-phase current value of each branch and the three-phase voltage value of each node in step (4) include;

节点i的A相、B相、C相三相的等效输出功率分别为输出功率S_Ai、输出功率S_Bi、输出功率S_Ci，采用修正后的计算相电压值计算节点i的等效输出负荷电流为：The equivalent output power of A phase, B phase and C phase of node i are respectively output power S _Ai , output power S _Bi , output power S _Ci , and the equivalent output of node i is calculated by using the corrected calculated phase voltage value The load current is:

$[\begin{matrix} {\overset{\cdot &Center Dot;}{I I}}_{ai ai} \\ {\overset{\cdot \cdot}{I I}}_{bi bi} \\ {\overset{\cdot &Center Dot;}{I I}}_{ci ci} \end{matrix}] = = [\begin{matrix} \frac{{S S}_{Ai Ai}}{{\overset{\cdot &Center Dot;}{U u}}_{Ai Ai}} \\ \frac{{S S}_{Bi Bi}}{{\overset{\cdot &Center Dot;}{U u}}_{Bi Bi}} \\ \frac{{S S}_{Ci Ci}}{{\overset{\cdot &Center Dot;}{U u}}_{Ci Ci}} \end{matrix}];;$

其中：分别为节点i处的负荷在节点i处A相、B相、C相三相的等效输出负荷电流；根据基尔霍夫电流定律的推论有：in: Respectively, the load at node i is the equivalent output load current of phase A, phase B, and phase C at node i; the inferences according to Kirchhoff’s current law are:

${\overset{\cdot &Center Dot;}{I I}}_{ai ai} + + {\overset{\cdot &Center Dot;}{I I}}_{bi bi} + + {\overset{\cdot \cdot}{I I}}_{ci ci} = = 00;;$

采用前推法计算各支路的三相支路电流为：Calculate the three-phase branch current of each branch by using the forward push method for:

$[\begin{matrix} {\overset{\cdot &Center Dot;}{I I}}_{Ai Ai} \\ {\overset{\cdot \cdot}{I I}}_{Bi Bi} \\ {\overset{\cdot &Center Dot;}{I I}}_{Ci Ci} \end{matrix}] = = [\begin{matrix} {\overset{\cdot &Center Dot;}{I I}}_{ai ai} + + \underset{j j &Element; &Element; M m}{Σ Σ} {\overset{\cdot &Center Dot;}{I I}}_{Aj Aj} \\ {\overset{\cdot &Center Dot;}{I I}}_{bi bi} + + \underset{j j &Element; &Element; M m}{Σ Σ} {\overset{\cdot &Center Dot;}{I I}}_{Bj bj} \\ {\overset{\cdot \cdot}{I I}}_{ci ci} + + \underset{j j &Element; &Element; M m}{Σ Σ} {\overset{\cdot \cdot}{I I}}_{Cj C j} \end{matrix}];;$

式中，M为与节点i直接相连的所有下层支路集；对于辐射状馈线，上下层按电流流向划分，对于节点i和节点j，若实际电源是从i流向j，则i为j的上层节点；若实际电源从j流向i，则i为j的下层节点；分别表示节点j在A相、B相、C相三相支路电流；In the formula, M is the set of all lower branches directly connected to node i; for radial feeders, the upper and lower layers are divided according to the current flow direction, for node i and node j, if the actual power flow is from i to j, then i is j The upper node; if the actual power flows from j to i, then i is the lower node of j; Respectively represent the three-phase branch current of node j in phase A, phase B and phase C;

采用回代法计算节点i的三相电压值，为：Using the back substitution method to calculate the three-phase voltage value of node i, it is:

$[\begin{matrix} {\overset{\cdot \cdot}{U u}}_{Ai Ai} \\ {\overset{\cdot &Center Dot;}{U u}}_{Bi Bi} \\ {\overset{\cdot \cdot}{U u}}_{Ci Ci} \end{matrix}] = = [\begin{matrix} {\overset{\cdot \cdot}{U u}}_{Ah Ah} - - {\overset{\cdot &Center Dot;}{I I}}_{Ai Ai} * * {Z Z}_{Ai Ai} \\ {\overset{\cdot \cdot}{U u}}_{Bh Bh} - - {\overset{\cdot &Center Dot;}{I I}}_{Bi Bi} * * {Z Z}_{Bi Bi} \\ {\overset{\cdot &Center Dot;}{U u}}_{Ch Ch} - - {\overset{\cdot &Center Dot;}{I I}}_{Ci Ci} * * {Z Z}_{Ci Ci} \end{matrix}];;$

式中，节点h为与节点直接相连的上层节点；分别为节点h在A相、B相、C相三相电压值；In the formula, node h is the upper layer node directly connected to the node; are the three-phase voltage values of node h in phase A, phase B and phase C respectively;

对于首端节点的三相电压值，用下式表示：For the three-phase voltage value of the head-end node, it is expressed by the following formula:

$[\begin{matrix} {\overset{\cdot &Center Dot;}{U u}}_{Ai Ai} \\ {\overset{\cdot &Center Dot;}{U u}}_{Bi Bi} \\ {\overset{\cdot &Center Dot;}{U u}}_{Ci Ci} \end{matrix}] = = [\begin{matrix} {\overset{\cdot &Center Dot;}{U u}}_{A A 00} - - {\overset{\cdot \cdot}{I I}}_{Ai Ai} * * {Z Z}_{Ai Ai} \\ {\overset{\cdot &Center Dot;}{U u}}_{B B 00} - - {\overset{\cdot \cdot}{I I}}_{Bi Bi} * * {Z Z}_{Bi Bi} \\ {\overset{\cdot &Center Dot;}{U u}}_{C C 00} - - {\overset{\cdot &Center Dot;}{I I}}_{Ci Ci} * * {Z Z}_{Ci Ci} \end{matrix}];;$

式中，分别为首端节点在A相、B相、C相三相电压值。In the formula, are the three-phase voltage values of the head-end node in phase A, phase B and phase C respectively.

其中，步骤（5）采用牛顿-拉夫逊法进行迭代，修正中性点电压偏移量的表达式为；Among them, step (5) uses the Newton-Raphson method to iterate, and the expression of the corrected neutral point voltage offset is;

采用牛顿-拉夫逊法，得中性点电压偏移量的迭代公式，用下式表示：Using the Newton-Raphson method, the iterative formula of the neutral point voltage offset is obtained, which is expressed by the following formula:

$\begin{matrix} {\overset{\cdot &Center Dot;}{V V}}_{Ni Ni}^{((k k))} = = {\overset{\cdot \cdot}{V V}}_{Ni Ni}^{((k k - - 11))} - - \frac{{(({\overset{\cdot &Center Dot;}{V V}}_{Ai Ai}^{((k k))} - - {\overset{\cdot \cdot}{V V}}_{Ni Ni}^{((k k - - 11))}))}^{22}}{{S S}_{ai ai}} \\ * * ((\frac{{S S}_{ai ai}}{{\overset{\cdot \cdot}{V V}}_{Ai Ai}^{((k k - - 11))} - - {\overset{\cdot &Center Dot;}{V V}}_{Ni Ni}^{((k k - - 11))}} + + \frac{{S S}_{bi bi}}{{\overset{\cdot \cdot}{V V}}_{Bi Bi}^{((k k - - 11))} - - {\overset{\cdot \cdot}{V V}}_{Ni Ni}^{((k k - - 11))}} + + \frac{{S S}_{ci ci}}{{\overset{\cdot \cdot}{V V}}_{Ci Ci}^{((k k - - 11))} - - {\overset{\cdot \cdot}{V V}}_{Ni Ni}^{((k k - - 11))}})) \end{matrix};;$

式中，分别为第k次迭代时节点i中性点电压偏移量和A相电位，分别为第k-1次迭代时所得的节点i处的中性点电压偏移量及A相、B相、C相三相的电位。In the formula, are the neutral point voltage offset of node i and phase A potential at the kth iteration, respectively, are the neutral point voltage offset at node i and the potentials of phase A, phase B, and phase C obtained in the k-1 iteration, respectively.

与现有技术比，本发明的有益效果为：Compared with the prior art, the beneficial effects of the present invention are:

1．本发明提供单相负荷和相间负荷混合情况下的三相潮流分布确定方法，经过严格理论推导，用有效解决在负荷已知条件下的三相潮流计算问题；1. The invention provides a method for determining the distribution of three-phase power flow under the condition of single-phase load and interphase load mixing, and through strict theoretical derivation, it can effectively solve the problem of three-phase power flow calculation under the condition of known load;

2．本发明提供的将低压侧负荷大小等效成中压侧各相输出功率值的方法，等效结果可用于各相三相潮流算法中，可以直接利用低压侧负荷实测或预测结果，而无需在中压侧测量各节点的负荷输出，适合实际应用；2. The method provided by the present invention to equate the load on the low-voltage side to the output power value of each phase on the medium-voltage side, the equivalent result can be used in the three-phase power flow algorithm of each phase, and the measured or predicted results of the load on the low-voltage side can be directly used without having to The medium-voltage side measures the load output of each node, which is suitable for practical applications;

3．本发明在处理三相相间负荷时，采用了将负荷分解的方法，将三相相间负荷分解成平衡部分与不平衡部分，可快速计算各相的等效输出，避免了三相耦合问题；3. When dealing with the three-phase interphase load, the present invention adopts the method of decomposing the load, and decomposes the three-phase interphase load into a balanced part and an unbalanced part, so that the equivalent output of each phase can be quickly calculated, and the three-phase coupling problem is avoided;

4．本发明采用的基于中性点偏移的配电网三相潮流计算方法，采用混合迭代法进行求解，综合了前推回代与牛顿拉夫逊法的优化，原理直观，计算三相潮流时迭代收敛性好，计算速度快；4. The method for calculating the three-phase power flow of the distribution network based on the neutral point offset adopted by the present invention adopts a hybrid iterative method to solve the problem, and integrates forward-backward generation and optimization of the Newton-Raphson method. The principle is intuitive and iterative when calculating the three-phase power flow Good convergence and fast calculation speed;

5．本发明提供的单相负荷和相间负荷混合情况下的三相潮流分布确定方法，既适应于辐射状配电网，也适应于弱环配电网的潮流计算。5. The method for determining the three-phase power flow distribution in the case of mixed single-phase load and interphase load provided by the invention is not only suitable for the radial distribution network, but also suitable for the power flow calculation of the weak ring distribution network.

6．本发明通过等效变换处理配电网中负荷接入方式不一致情况下的潮流计算问题，提出一种适合单相负荷和相间负荷混合情况下的配电网三相潮流分布获取方法，使配电网运行分析结果更加精确。6. The invention handles the power flow calculation problem in the case of inconsistent load access modes in the distribution network through equivalent transformation, and proposes a distribution network three-phase power flow distribution acquisition method suitable for single-phase loads and phase-to-phase loads, so that power distribution The network operation analysis results are more accurate.

附图说明Description of drawings

图1为本发明提供的单相负荷与相间负荷混合情况下的三相潮流计算流程图。Fig. 1 is a flow chart of three-phase power flow calculation in the case of mixed single-phase load and inter-phase load provided by the present invention.

图2为本发明提供的中压侧星形接线示意图。Fig. 2 is a schematic diagram of star connection on the medium voltage side provided by the present invention.

图3为本发明提供的中压侧三角形接线示意图。Fig. 3 is a schematic diagram of a delta connection on the medium voltage side provided by the present invention.

图4为本发明提供的单相负荷接入A相示意图。Fig. 4 is a schematic diagram of a single-phase load connected to phase A provided by the present invention.

图5为本发明提供的中压侧各相均接入单相负荷示意图。Fig. 5 is a schematic diagram of a single-phase load connected to each phase of the medium-voltage side provided by the present invention.

图6为本发明提供的中压侧一相接入相间负荷示意图。Fig. 6 is a schematic diagram of a phase-to-phase load on the medium-voltage side provided by the present invention.

图7为本发明提供的中压侧三相均接入相间负荷示意图。Fig. 7 is a schematic diagram of all three phases on the medium voltage side being connected to interphase loads provided by the present invention.

图8为本发明提供的馈线节点、支路编号示意图。Fig. 8 is a schematic diagram of the numbering of feeder nodes and branches provided by the present invention.

具体实施方式detailed description

下面结合附图对本发明的具体实施方式作进一步的详细说明。The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings.

针对配电网中负荷接入方式多样化的情况，本实施例提出的一种单相负荷和相间负荷混合情况下的三相潮流分布确定方法，是在在已知低压侧负荷实测结果或预测结果以及各节点的负荷接入方式的情况下，采用等效变换的方法，得到中压侧各相的等效输出功率，再采用基于中性点电压偏移的三相潮流计算方法，得到潮流分布。其总体思路如图1所示。In view of the diversification of load access modes in the distribution network, this embodiment proposes a method for determining the three-phase power flow distribution in the case of mixed single-phase load and inter-phase load. In the case of the results and the load connection mode of each node, the equivalent transformation method is used to obtain the equivalent output power of each phase on the medium voltage side, and then the three-phase power flow calculation method based on the neutral point voltage offset is used to obtain the power flow distributed. Its overall idea is shown in Figure 1.

首先获取网络拓扑、各节点的低压侧负荷大小及负荷接入方式，然后根据不同接入方式，将低压侧负荷等效换算，得到中压侧各相的输出功率，最后采用基于中性点电压偏移的三相潮流计算方法，计算三相潮流分布。具体的，First obtain the network topology, the load size of the low-voltage side of each node, and the load connection method, and then convert the load equivalent of the low-voltage side according to different connection methods to obtain the output power of each phase of the medium-voltage side. Offset three-phase power flow calculation method to calculate three-phase power flow distribution. specific,

（一）负荷接入方式：(1) Load access method:

中压配电网通常采用三相三线制，配电变压器中压侧包括星形接线与三角形接线两种方式，如附图2和附图3所示。The medium-voltage distribution network usually adopts a three-phase three-wire system, and the medium-voltage side of the distribution transformer includes star connection and delta connection, as shown in Figure 2 and Figure 3.

低压配电网包括单相供电与三相供电模式两种，单相供电模式采用单相变压器，三相供电模式采用三相变压器。配电变压器中压接线方式为星形时，通过单相变压器接入中压侧某一相上、或者通过三相变压器分别接入到中压侧各相上的负荷统称为单相负荷；配电变压器中压接线方式为三角形时，通过单相变压器接入中压侧的相间或者通过三相变压器接入中压侧各相间的负荷均称为相间负荷。在通过监测或负荷预测获取了低压侧的负荷数据后，采用下述换算方法分别将单相和相间负荷进行等效换算，得到中压侧各相的输出功率大小。The low-voltage distribution network includes two modes of single-phase power supply and three-phase power supply. The single-phase power supply mode uses a single-phase transformer, and the three-phase power supply mode uses a three-phase transformer. When the medium-voltage connection mode of distribution transformer is star-shaped, the load connected to a phase of the medium-voltage side through a single-phase transformer, or connected to each phase of the medium-voltage side through a three-phase transformer is collectively referred to as a single-phase load; When the medium-voltage connection mode of the electric transformer is a triangle, the load connected to the phase-to-phase of the medium-voltage side through a single-phase transformer or connected to each phase of the medium-voltage side through a three-phase transformer is called an inter-phase load. After obtaining the load data on the low-voltage side through monitoring or load forecasting, the following conversion methods are used to perform equivalent conversion of the single-phase and inter-phase loads to obtain the output power of each phase on the medium-voltage side.

（二）低压侧负荷到高压侧输出功率的等效换算：(2) Equivalent conversion from low-voltage side load to high-voltage side output power:

1、单相负荷；1. Single-phase load;

以负荷接入A相为例，如图4所示，配电变压器中压接线方式为星形时，单相负荷S_a通过单相变压器接入中压侧的A相，中压侧A相输出的等效功率为低压侧负荷大小S_a，该节点其它两相的输出功率为0，即：Taking the load connected to phase A as an example, as shown in Figure 4, when the medium-voltage connection mode of the distribution transformer is star-shaped, the single-phase load S _a is connected to the A-phase on the medium-voltage side through the single-phase transformer, and the A-phase on the medium-voltage side The output equivalent power is the load S _a of the low-voltage side, and the output power of the other two phases of this node is 0, namely:

$\{\begin{matrix} {S S}_{A A} {= = S S}_{a a} \\ {S S}_{B B} = = 00 \\ {S S}_{C C} = = 00 \end{matrix} - - - - - - ((11))$

其中，S_a为低压侧单相负荷的大小，S_A，S_B，S_C分别为S_A等效换算后A、B、C各相输出的功率。负荷接入B相与C相时与A相类似。Among them, S _a is the size of the single-phase load on the low-voltage side, S _A , S _B , and S _C are the output powers of A, B, and C phases after equivalent conversion of S _A , respectively. When the load is connected to phase B and phase C, it is similar to phase A.

配电变压器中压接线方式为星形时，A、B、C三相间通过三相变压器均接入单相负荷S_A，S_B，S_C，如附图5所示，经等效换算，A、B、C各相输出的功率S_A，S_B，S_C为：When the medium-voltage connection mode of the distribution transformer is star-shaped, the three phases A, B, and C are all connected to the single-phase loads S _A , S _B , and S _C through the three-phase transformer, as shown in Figure 5. After equivalent conversion, The output power S _A , S _B , and S _C of each phase of A, B, and C are:

$\{\begin{matrix} {S S}_{A A} {= = S S}_{a a} \\ {S S}_{B B} = = {S S}_{b b} \\ {S S}_{C C} = = {S S}_{c c} \end{matrix} - - - - - - ((22))$

2、相间负荷；2. Interphase load;

1）一相相间；1) One phase alternates with the other;

以A、B相间为例，配电变压器中压接线方式为三角形时，通过单相变压器在A、B相间接入相间负荷S_a，如附图6所示。Taking phase A and phase B as an example, when the medium-voltage connection mode of the distribution transformer is a triangle, the phase-to-phase load S _a is connected between phases A and B through a single-phase transformer, as shown in Figure 6.

不计变压器损耗，Ignoring transformer losses,

$\{\begin{matrix} {S S}_{AB AB} {= = S S}_{a a} \\ {S S}_{BC BC} = = 00 \\ {S S}_{CA CA} = = 00 \end{matrix} - - - - - - ((33))$

其中，S_a低压侧接入的相间负荷大小，S_AB、S_BC、S_CA分别中压侧A-B、B-C、C-A相等效输出功率。Among them, S _a is the magnitude of the phase-to-phase load connected to the low-voltage side, and S _AB , S _BC , and S _CA are the equivalent output powers of the medium-voltage sides AB, BC, and CA, respectively.

根据基尔霍夫电流定律有：According to Kirchhoff's current law:

$\{\begin{matrix} {I I}_{A A} + + {I I}_{CA CA} = = {I I}_{AB AB} \\ {I I}_{B B} + + {I I}_{AB AB} = = {I I}_{BC BC} \\ {I I}_{C C} + + {I I}_{BC BC} = = {I I}_{CA CA} \\ {I I}_{A A} + + {I I}_{B B} + + {I I}_{C C} = = 00 \end{matrix} - - - - - - ((44))$

其中，I_A、I_B、I_C分别为中压侧各相的负荷电流，I_AB、I_BC、I_CA分别中压侧A-B、B-C、C-A相的相间电流。Among them, I _A , I _B , and I _C are the load currents of each phase on the medium-voltage side, respectively, and I _AB , I _BC , and I _CA are the phase-to-phase currents of phases AB, BC, and CA on the medium-voltage side, respectively.

不计变压器损耗时，理论上，I_BC=0，I_CA=0，由此可得：When the transformer loss is not considered, theoretically, I _BC =0, I _CA =0, thus:

$\{\begin{matrix} {I I}_{A A} = = {I I}_{AB AB} \\ {I I}_{B B} = = {- - I I}_{AB AB} \\ {I I}_{C C} = = {I I}_{BC BC} = = 00 \end{matrix} - - - - - - ((55))$

设变压器中压侧各相的电位为V_A、V_B、V_C，有：Assuming the potentials of each phase on the medium voltage side of the transformer are V _A , V _B , V _C , there are:

S_AB＝S_a＝(V_B-V_A)I_AB ^*（6）S _AB ＝S _a ＝(V _B -V _A )I _AB ^* (6)

结合式（3）、（5）和（6）可得A、B、C各相输出的功率S_A，S_B，S_C为：Combining formulas (3), (5) and (6), the output power S _A , S _B , and S _C of each phase of A, B, and C can be obtained as:

$\{\begin{matrix} {S S}_{A A} = = {V V}_{A A} {I I}_{A A}^{* *} = = {V V}_{A A} * * {S S}_{a a} / / (({V V}_{B B} - - {V V}_{A A})) \\ {S S}_{B B} = = {V V}_{B B} {I I}_{B B}^{* *} = = - - {V V}_{B B} * * {S S}_{a a} / / (({V V}_{B B} - - {V V}_{A A})) \\ {S S}_{C C} = = 00 \end{matrix} - - - - - - ((77))$

2）两相相间；2) Alternating between two phases;

以A-B、B-C两相间为例，同理，当A-B、B-C两相间接入相间负荷时：Take A-B, B-C two phases as an example, similarly, when A-B, B-C two phases are connected to the interphase load:

$\{\begin{matrix} {S S}_{AB AB} {= = S S}_{a a} \\ {S S}_{BC BC} = = {S S}_{b b} \\ {S S}_{CA CA} = = 00 \end{matrix} - - - - - - ((88))$

S_b低压侧接入B-C相间的相间负荷大小。S _b The magnitude of the phase-to-phase load between the BC phases connected to the low-voltage side.

根据基尔霍夫电流定律有：According to Kirchhoff's current law:

$\{\begin{matrix} {I I}_{A A} = = {I I}_{AB AB} \\ {I I}_{B B} = = {- - I I}_{A A} - - {I I}_{C C} \\ {I I}_{C C} = = {- - I I}_{BC BC} \end{matrix} - - - - - - ((99))$

忽略变电器损耗有：Neglecting transformer losses are:

$\{\begin{matrix} {S S}_{AB AB} = = {S S}_{a a} = = (({V V}_{B B} - - {V V}_{A A})) {I I}_{AB AB}^{* *} \\ {S S}_{BC BC} = = {S S}_{b b} = = (({V V}_{C C} - - {V V}_{B B})) {I I}_{BC BC}^{* *} \end{matrix} - - - - - - ((1010))$

结合式（8）、（9）和（10）可得A、B、C各相输出的功率S_A，S_B，S_C为：Combining formulas (8), (9) and (10), the output power S _A , S _B , and S _C of each phase of A, B, and C can be obtained as:

$\{\begin{matrix} {S S}_{A A} = = {V V}_{A A} {I I}_{A A}^{* *} = = {V V}_{A A} * * \frac{{S S}_{a a}}{{V V}_{B B} - - {V V}_{A A}} \\ {S S}_{B B} = = {V V}_{B B} {I I}_{B B}^{* *} = = {V V}_{B B} ((- - \frac{{S S}_{a a}}{{V V}_{B B} - - {V V}_{A A}} + + \frac{{S S}_{b b}}{{V V}_{C C} - - {V V}_{B B}})) \\ {S S}_{C C} = = {V V}_{C C} {I I}_{C C}^{* *} = = - - {V V}_{C C} \frac{{S S}_{b b}}{{V V}_{C C} - - {V V}_{B B}} \end{matrix} - - - - - - ((1111))$

3、三相负荷3. Three-phase load

1）三相平衡1) Three-phase balance

如附图7所示，当三相均接入相间负荷且三相负荷平衡时，各相间负荷大小分别为S_a，S_b，S_c，中压侧各相的等效输出S_A，S_B，S_C为：As shown in Figure 7, when all three phases are connected to interphase loads and the three phase loads are balanced, the magnitudes of the interphase loads are S _a , S _b , S _c , and the equivalent outputs S _A , S _B , S _C is:

$\{\begin{matrix} {S S}_{A A} {= = S S}_{a a} \\ {S S}_{B B} = = {S S}_{b b} \\ {S S}_{C C} = = {S S}_{c c} \end{matrix} - - - - - - ((1212))$

2）三相不平衡2) Three-phase unbalance

如附图7所示，当三相均接入相间负荷但三相负荷不平衡时，各相间负荷大小分别为S_a，S_b，S_c，将各相相间负荷分为相等的与不相等的两部分，，相等的部分各相相间负荷大小为S_c，不相等的部分接入到A-B、B-C两相相间负荷分别为S_a-S_c、S_b-S_c，不相等的部分按两相接入相间负荷的处理方法，可得中压侧各相的等效输出S_A，S_B，S_C，As shown in Figure 7, when all three phases are connected to interphase loads but the three phase loads are unbalanced, the magnitudes of the interphase loads are S _a , S _b , S _c , and the interphase loads of each phase are divided into equal and unequal The two parts, the equal part is S _c between phases, the unequal part is connected to AB and BC, and the interphase load is S _a -S _c , S _b -S _c The processing method of two phases connected to the interphase load can obtain the equivalent output S _A , S _B , S _C of each phase on the medium voltage side,

$\{\begin{matrix} {S S}_{A A} = = {V V}_{A A} {I I}_{A A}^{* *} = = {V V}_{A A} * * \frac{{S S}_{a a} - - {S S}_{c c}}{{V V}_{B B} - - {V V}_{A A}} + + {S S}_{c c} \\ {S S}_{B B} = = {V V}_{B B} {I I}_{B B}^{* *} = = {V V}_{B B} ((- - \frac{{S S}_{a a} - - {S S}_{c c}}{{V V}_{B B} - - {V V}_{A A}} + + \frac{{S S}_{b b} - - {S S}_{c c}}{{V V}_{C C} - - {V V}_{B B}})) + + {S S}_{c c} \\ {S S}_{C C} = = {V V}_{C C} {I I}_{C C}^{* *} = = - - {V V}_{C C} \frac{{S S}_{b b} - - {S S}_{c c}}{{V V}_{C C} - - {V V}_{B B}} + + {S S}_{c c} \end{matrix} - - - - - - ((1313))$

（三）基于中性点电压偏移的三相潮流计算；(3) Three-phase power flow calculation based on neutral point voltage offset;

采用上述等效变换得到中压侧各相的等效输出功率后，采用基于中性点电压偏移的三相潮流计算方法，计算三相潮流分布，方法如下：After the equivalent output power of each phase on the medium voltage side is obtained by using the above equivalent transformation, the three-phase power flow calculation method based on the neutral point voltage offset is used to calculate the three-phase power flow distribution. The method is as follows:

（1）根据中压配电网网络拓扑，如图8所示，对馈线上各个节点和各条支路进行编号；(1) According to the network topology of the medium-voltage distribution network, as shown in Figure 8, number each node and each branch on the feeder;

（3）采用节点i的中性点偏移量对节点i的计算相电压值进行修正；(3) Use the neutral point offset of node i Correct the calculated phase voltage value of node i;

$[\begin{matrix} {\overset{\cdot \cdot}{U u}}_{Ai Ai} \\ {\overset{\cdot \cdot}{U u}}_{Bi Bi} \\ {\overset{\cdot \cdot}{U u}}_{Ci Ci} \end{matrix}] = = [\begin{matrix} {\overset{\cdot \cdot}{V V}}_{Ai Ai} - - {\overset{\cdot \cdot}{V V}}_{Ni Ni} \\ {\overset{\cdot \cdot}{V V}}_{Bi Bi} - - {\overset{\cdot \cdot}{V V}}_{Ni Ni} \\ {\overset{\cdot \cdot}{V V}}_{Ci Ci} - - {\overset{\cdot \cdot}{V V}}_{Ni Ni} \end{matrix}] - - - - - - ((1414))$

其中：分别为节点i处A、B、C三相的计算相电压值；分别为节点i处A、B、C三相电位值。in: are the calculated phase voltage values of the three phases A, B, and C at node i, respectively; are the three-phase potential values of A, B, and C at node i, respectively.

节点i的A、B、C三相的等效输出功率分别为S_Ai，S_Bi，S_Ci，采用修正后的计算相电压值计算节点i的等效输出负荷电流为：The equivalent output power of three phases A, B, and C of node i are S _Ai , S _Bi , S _Ci , respectively, and the equivalent output load current of node i is calculated by using the corrected calculated phase voltage value as:

$[\begin{matrix} {\overset{\cdot \cdot}{I I}}_{ai ai} \\ {\overset{\cdot \cdot}{I I}}_{bi bi} \\ {\overset{\cdot \cdot}{I I}}_{ci ci} \end{matrix}] = = [\begin{matrix} \frac{{S S}_{Ai Ai}}{{\overset{\cdot \cdot}{U u}}_{Ai Ai}} \\ \frac{{S S}_{Bi Bi}}{{\overset{\cdot \cdot}{U u}}_{Bi Bi}} \\ \frac{{S S}_{Ci Ci}}{{\overset{\cdot \cdot}{U u}}_{Ci Ci}} \end{matrix}] - - - - - - ((1515))$

其中：分别为节点i处的负荷在节点i处A、B、C三相的等效输出负荷电流。根据基尔霍夫电流定律的推论有：in: Respectively, the load at node i is the equivalent output load current of the three phases A, B, and C at node i. The corollary from Kirchhoff's current law is:

${\overset{\cdot \cdot}{I I}}_{ai ai} + + {\overset{\cdot \cdot}{I I}}_{bi bi} + + {\overset{\cdot &Center Dot;}{I I}}_{ci ci} = = 00 - - - - - - ((1616))$

采用前推法计算各支路的三相支路电流用下述式（17）表示：Calculate the three-phase branch current of each branch by using the forward push method Expressed by the following formula (17):

$[\begin{matrix} {\overset{\cdot &Center Dot;}{I I}}_{Ai Ai} \\ {\overset{\cdot &Center Dot;}{I I}}_{Bi Bi} \\ {\overset{\cdot &Center Dot;}{I I}}_{Ci Ci} \end{matrix}] = = [\begin{matrix} {\overset{\cdot &Center Dot;}{I I}}_{ai ai} + + \underset{j j &Element; &Element; M m}{Σ Σ} {\overset{\cdot &Center Dot;}{I I}}_{Aj Aj} \\ {\overset{\cdot &Center Dot;}{I I}}_{bi bi} + + \underset{j j &Element; &Element; M m}{Σ Σ} {\overset{\cdot &Center Dot;}{I I}}_{Bj bj} \\ {\overset{\cdot &Center Dot;}{I I}}_{ci ci} + + \underset{j j &Element; &Element; M m}{Σ Σ} {\overset{\cdot &Center Dot;}{I I}}_{Cj C j} \end{matrix}] - - - - - - ((1717))$

其中：M为与节点i直接相连的所有下层支路集；对于辐射状馈线，上下层是按电流流向划分的，对于节点i和节点j，若实际电源是从i流向j，则i为j的上层节点；若实际电源从j流向i，则i为j的下层节点；分别表示节点j在A、B、C三相支路电流。Where: M is the set of all lower branches directly connected to node i; for radial feeders, the upper and lower layers are divided according to the current flow direction, for node i and node j, if the actual power flow is from i to j, then i is j if the actual power flows from j to i, then i is the lower node of j; Respectively represent node j in A, B, C three-phase branch current.

采用回代法计算节点i的三相电压值，用下述（18）式表示：The three-phase voltage value of node i is calculated by the back substitution method, which is expressed by the following formula (18):

$[\begin{matrix} {\overset{\cdot &Center Dot;}{U u}}_{Ai Ai} \\ {\overset{\cdot &Center Dot;}{U u}}_{Bi Bi} \\ {\overset{\cdot &Center Dot;}{U u}}_{Ci Ci} \end{matrix}] = = [\begin{matrix} {\overset{\cdot &Center Dot;}{U u}}_{Ah Ah} - - {\overset{\cdot &Center Dot;}{I I}}_{Ai Ai} * * {Z Z}_{Ai Ai} \\ {\overset{\cdot &Center Dot;}{U u}}_{Bh Bh} - - {\overset{\cdot &Center Dot;}{I I}}_{Bi Bi} * * {Z Z}_{Bi Bi} \\ {\overset{\cdot &Center Dot;}{U u}}_{Ch Ch} - - {\overset{\cdot &Center Dot;}{I I}}_{Ci Ci} * * {Z Z}_{Ci Ci} \end{matrix}] - - - - - - ((1818))$

其中：节点h为与节点直接相连的上层节点；分别为节点h在A、B、C三相电压值；Among them: node h is the upper layer node directly connected to the node; are the three-phase voltage values of node h at A, B, and C respectively;

对于首端节点的三相电压值，用下述（19）式表示：For the three-phase voltage value of the head-end node, it is expressed by the following formula (19):

$[\begin{matrix} {\overset{\cdot &Center Dot;}{U u}}_{Ai Ai} \\ {\overset{\cdot &Center Dot;}{U u}}_{Bi Bi} \\ {\overset{\cdot &Center Dot;}{U u}}_{Ci Ci} \end{matrix}] = = [\begin{matrix} {\overset{\cdot &Center Dot;}{U u}}_{A A 00} - - {\overset{\cdot &Center Dot;}{I I}}_{Ai Ai} * * {Z Z}_{Ai Ai} \\ {\overset{\cdot &Center Dot;}{U u}}_{B B 00} - - {\overset{\cdot &Center Dot;}{I I}}_{Bi Bi} * * {Z Z}_{Bi Bi} \\ {\overset{\cdot &Center Dot;}{U u}}_{C C 00} - - {\overset{\cdot &Center Dot;}{I I}}_{Ci Ci} * * {Z Z}_{Ci Ci} \end{matrix}] - - - - - - ((1919))$

其中：分别为首端节点在A、B、C三相电压值。in: are the three-phase voltage values of the head-end nodes at A, B, and C, respectively.

采用牛顿-拉夫逊法，得中性点电压偏移量的迭代公式，用下述（20）式表示：Using the Newton-Raphson method, the iterative formula of the neutral point voltage offset is obtained, which is expressed by the following formula (20):

$\begin{matrix} {\overset{\cdot &Center Dot;}{V V}}_{Ni Ni}^{((k k))} = = {\overset{\cdot &Center Dot;}{V V}}_{Ni Ni}^{((k k - - 11))} - - \frac{{(({\overset{\cdot \cdot}{V V}}_{Ai Ai}^{((k k))} - - {\overset{\cdot \cdot}{V V}}_{Ni Ni}^{((k k - - 11))}))}^{22}}{{S S}_{ai ai}} \\ * * ((\frac{{S S}_{ai ai}}{{\overset{\cdot \cdot}{V V}}_{Ai Ai}^{((k k - - 11))} - - {\overset{\cdot \cdot}{V V}}_{Ni Ni}^{((k k - - 11))}} + + \frac{{S S}_{bi bi}}{{\overset{\cdot \cdot}{V V}}_{Bi Bi}^{((k k - - 11))} - - {\overset{\cdot \cdot}{V V}}_{Ni Ni}^{((k k - - 11))}} + + \frac{{S S}_{ci ci}}{{\overset{\cdot \cdot}{V V}}_{Ci Ci}^{((k k - - 11))} - - {\overset{\cdot \cdot}{V V}}_{Ni Ni}^{((k k - - 11))}})) \end{matrix} - - - - - - ((2020))$

其中：分别为第k次迭代时节点i中性点电压偏移量和A相电位，分别为第k-1次迭代时所得的节点i处的中性点电压偏移量及A、B、C三相的电位。in: are the neutral point voltage offset of node i and phase A potential at the kth iteration, respectively, are the neutral point voltage offset at node i and the potentials of A, B, and C phases obtained at the k-1th iteration, respectively.

（6）采用混合迭代法对三相电压进行求解，直至满足迭代终止条件，得到三相潮流分布(6) Use the hybrid iterative method to solve the three-phase voltage until the iteration termination condition is satisfied, and the three-phase power flow distribution is obtained

最后应当说明的是：以上实施例仅用以说明本发明的技术方案而非对其限制，尽管参照上述实施例对本发明进行了详细的说明，所属领域的普通技术人员应当理解：依然可以对本发明的具体实施方式进行修改或者等同替换，而未脱离本发明精神和范围的任何修改或者等同替换，其均应涵盖在本发明的权利要求范围当中。Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: the present invention can still be Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention shall be covered by the scope of the claims of the present invention.

Claims

1. The method for determining the distribution of three-phase power flow in the case of mixed single-phase load and interphase load is characterized in that firstly, the network topology, the load size of the low-voltage side of each node and the load connection method are obtained, and then the low-voltage The side load equivalent conversion is used to obtain the output power of each phase on the medium voltage side, and finally the three-phase power flow calculation method based on the neutral point voltage offset is used to calculate the three-phase power flow distribution;

The load connection method includes star connection and delta connection; wherein,

When the medium-voltage wiring mode of the distribution transformer is star-shaped, the load connected to a phase of the medium-voltage side through a single-phase transformer, or connected to each phase of the medium-voltage side through a three-phase transformer is called a single-phase load;

When the medium-voltage connection mode of the distribution transformer is a triangle, the load connected to the phase-to-phase of the medium-voltage side through a single-phase transformer or connected to each phase of the medium-voltage side through a three-phase transformer is called an inter-phase load;

The step of obtaining the output power of each phase of the medium-voltage side by equivalently converting the load on the low-voltage side according to different access modes includes:

When the medium-voltage wiring mode of the distribution transformer is star-shaped, if the single-phase load is connected to any phase of the medium-voltage side through the single-phase transformer, the equivalent power output by this phase is the size of the single-phase load on the low-voltage side, and the other two phases of the node The output power of the phase is 0;

When the medium-voltage wiring mode of the distribution transformer is star-shaped, the three-phases are all connected to the single-phase load through the three-phase transformer, then after equivalent conversion, the three-phase output power is the size of the single-phase load on each phase;

When the medium-voltage connection mode of the distribution transformer is triangle, if the interphase load is connected between any phase of the three phases through a single-phase transformer, the output power of each phase is:

For access between phase A and phase B:

For access between Phase B and Phase C:

For access between phase C and phase A:

When the medium-voltage connection mode of the distribution transformer is a triangle, if the interphase load is connected between any two phases of the three phases through a single-phase transformer, the output power of each phase is:

For phases AB and BC:

For the two phases between BC phase and CA phase:

For CA phase and AB phase between two phases:

When the medium-voltage connection mode of the distribution transformer is a triangle, if all three phases are connected to the interphase load and the three-phase load is balanced, the output power of the three phases is the size of the single-phase load on each phase;

When the medium-voltage connection mode of the distribution transformer is triangle, if all three phases are connected to the interphase load and the three-phase load is unbalanced, then when the three phases are connected to the interphase load but the three-phase load is unbalanced, the magnitude of the interphase load is S _a , S _b , S _c , divide the interphase load of each phase into equal and unequal parts, the equal part of the interphase load of each phase is S _c , and the unequal part is connected to the interphase load of AB and BC They are S _a -S _c , S _b -S _c , respectively, and the unequal parts are treated as two phases connected to the interphase load, and the equivalent output S _A , S _B , S _C of each phase on the medium voltage side can be obtained,

2. The method for determining three-phase power flow distribution as claimed in claim 1, wherein the step of calculating the three-phase power flow distribution by using a three-phase power flow calculation method based on neutral point voltage offset comprises:

(1) According to the network topology of the medium voltage distribution network, number each node and each branch on the feeder;

(2) Introduce the neutral point voltage offset of each node

(3) Using the neutral point voltage offset of node i Correct the calculated phase voltage value of node i:

(4) Calculate the three-phase current value of each branch and the three-phase voltage value of each node;

(5) The Newton-Raphson method is used to iterate, and the neutral point voltage offset is corrected;

(6) The hybrid iterative method is used to solve the three-phase voltage until the iteration termination condition is satisfied, and the three-phase power flow distribution is obtained.

3. the three-phase power flow distribution determination method as claimed in claim 2, is characterized in that, step (3) adopts the neutral point voltage offset of node i Correct the calculated phase voltage value of node i, and its expression is:

In the formula, are the calculated phase voltage values of phase A, phase B and phase C at node i respectively; are the three-phase potential values of phase A, phase B and phase C at node i, respectively.

4. three-phase power flow distribution determining method as claimed in claim 2, is characterized in that, the expression of step (4) calculating the three-phase current value of each branch and the three-phase voltage value of each node comprises;

The equivalent output power of A phase, B phase and C phase of node i are respectively output power S _Ai , output power S _Bi , output power S _Ci , and the equivalent output of node i is calculated by using the corrected calculated phase voltage value The load current is:

in: Respectively, the load at node i is the equivalent output load current of phase A, phase B and phase C at node i; are the calculated phase voltage values of phase A, phase B, and phase C at node i respectively; the inferences according to Kirchhoff’s current law are:

Calculate the three-phase branch current of each branch by using the forward push method for:

In the formula, M is the set of all lower branches directly connected to node i; for radial feeders, the upper and lower layers are divided according to the current flow direction, for node i and node j, if the actual power flow is from i to j, then i is j The upper node; if the actual power flows from j to i, then i is the lower node of j; Respectively represent the three-phase branch current of node j in phase A, phase B and phase C;

Using the back substitution method to calculate the three-phase voltage value of node i, it is:

In the formula, node h is the upper layer node directly connected to node i; are the three-phase voltage values of node h in phase A, phase B, and phase C respectively; Z _Ai , Z _Bi , and Z _Ci are the three-phase loads of A, B, and C at node i respectively. For the three-phase voltage values of the head-end node, Expressed in the following formula:

In the formula, are the three-phase voltage values of the head-end node in phase A, phase B and phase C respectively.

5. the method for determining three-phase power flow distribution as claimed in claim 2, is characterized in that, step (5) adopts Newton-Raphson method to iterate, and the expression of correcting neutral point voltage offset is;

Using the Newton-Raphson method, the iterative formula of the neutral point voltage offset is obtained, which is expressed by the following formula:

In the formula, and are the neutral point voltage offset of node i and phase A potential at the kth iteration, respectively, are the neutral point voltage offset at node i and the potentials of phase A, phase B, and phase C obtained in the k-1 iteration, respectively.