Linear power flow model, its optimization method and distribution network operation stability evaluation method

Abstract

The present invention discloses a linear power flow model, an optimization method thereof, and a method for evaluating the operation stability of a distribution network. The optimization method of the distribution network power flow model includes the following steps: establishing a distribution network power flow model starting from branch power, and establishing a linear approximation model of the distribution network power flow model according to the distribution network power flow model, including a voltage drop equation and a branch power balance equation; adding a coefficient composed of line impedance admittance parameters to the voltage drop equation to modify the node branch matrix in the voltage drop equation, so as to establish a linear distribution network power flow model considering the shunt branch to the ground of the line. By adding a coefficient composed of line impedance admittance parameters to the voltage drop equation to modify the node branch matrix in the voltage drop equation, the present invention can solve the model error caused by the capacitance susceptance of the shunt branch to the ground, thereby significantly improving the accuracy and accuracy rate of the distribution network power flow model.

Description

Technical Field

[0001] The present invention relates to the technical field of optimizing power flow models of distribution networks, in particular to linear power flow models, their optimization methods, and methods for evaluating the operating stability of distribution networks. Background Art

[0002] Power flow models are the most important components in issues in the fields of power system operation, planning, control, etc. In transmission and distribution systems, transmission lines are generally modeled using the π-type equivalent circuit model, and its shunt branch elements are usually assumed to be zero in many cases, which is acceptable when most of the transmission lines in the distribution network system are overhead lines. However, according to the on-site test report of Shenzhen Power Supply Company, as the distribution network is gradually modernized, overhead lines are gradually replaced by underground cables, and their shunt admittances are 5-10 times larger, and submarine cables even have larger admittance values. Therefore, the "charging effect" caused by the capacitive susceptance of the line shunt admittance will bring model errors to the traditional power flow model that ignores the shunt of parallel lines, raise the voltage amplitude of the end node, cause voltage over-limit, and affect the stability and reliability of the distribution system.

[0003] Therefore, for the accurate calculation of voltage in modern distribution systems, the shunt branch elements in the π-type equivalent circuit line model cannot be ignored. The AC power flow model (ACPF) is a general power factor model that comprehensively considers system parameters. However, due to its complexity and non-convexity, the AC power flow model cannot be directly applied to calculate power flow. Foreign scholars have proposed a simplified Distflow model (a power flow model) of an AC model applied to a radial distribution system. How to approximate the AC power flow model in a distribution network is the focus and difficulty of current research. There are generally two approximation methods in the current academic and industrial circles. The first approximation method is to linearize the Distflow model. When the network loss is small, the linear Distflow model is widely used. Foreign scholars have proposed another commonly used linear decoupled power flow model (LCPF). There are also studies that provide an implicit linearization method using the unit voltage assumption, which can obtain the above-mentioned linear Distflow and LCPF models. Some scholars in the United States have proposed a linear power flow model for a three-phase unbalanced system based on the Distflow model. Another approximation method is the approximate relaxation of the Distflow model. Previous studies have proposed a second-order cone programming (SOCP) for the optimal power flow (OPF) problem that ignores the parallel branch to the ground of the line, and proved the accuracy of the convex relaxation. However, all of the above models have large and unacceptable model errors due to the "charging effect" of underground / submarine power cables, and may not be able to provide sufficient conditions to prove the accuracy of the convex relaxation.

[0004] To solve this problem, three recent studies have proposed second-order cone programming approximation methods for the nonlinear branch flow model (BFM) considering the shunt branches between the line and the ground. The first study obtained a local solution to the optimal power flow problem based on the branch flow model with shunt branches between the line and the ground. Another study considered the "charging effect" of the line, proposed a nonlinear branch flow model as an alternative to the second-order cone relaxation, and proved the accuracy of the relaxation. However, if there is a large part of reverse power flow from distributed generators in the urban distribution network, the relaxation error will become non-negligible.

[0005] It should be noted that the information disclosed in the above background art section is only used for understanding the background of the present application, and thus may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0006] The object of the present invention is to solve the problem of improving the accuracy of the distribution network power flow model, and to provide a linear power flow model, its optimization method and a method for evaluating the operation stability of the distribution network.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] An optimization method for a power flow model, comprising the following steps:

[0009] S1: Establish a distribution network power flow model starting from branch power, and establish a linear approximation model of the distribution network power flow model according to the distribution network power flow model. The linear approximation model of the distribution network power flow model includes a voltage drop equation and a branch power balance equation;

[0010] S2: Add coefficients composed of line impedance admittance parameters to the voltage drop equation to modify the node branch matrix in the voltage drop equation, and establish a linear distribution network power flow model considering the shunt branches between the line and the ground.

[0011] In some embodiments, the distribution network power flow model is a Distflow model.

[0012] In some embodiments, step S2 further includes: introducing the voltage drop phasor angle difference and the ZIP load model in the form of active power and reactive power into the linear distribution network power flow model considering the shunt branches between the line and the ground.

[0013] In some embodiments, the linear distribution network power flow model considering the shunt branches between the line and the ground introduces the voltage drop phasor angle difference and the ZIP load model in the form of active power and reactive power, and is expressed by the following formula:

[0014]

[0015]

[0016] Among them, is the active power of the receiving-end power flow at node l, is the reactive power of the receiving-end power flow at node l, is the active power injected at node l represented by the ZIP load model, is the reactive power injected at node l represented by the ZIP load model, is the active power of the receiving-end power flow at node k, is the reactive power of the receiving-end power flow at node k, Bs lk is the shunt susceptance of branch lk, v l is the square of the voltage magnitude at node l, v k is the square of the voltage magnitude at node k, is a coefficient, r lk is the series resistance of branch lk, x lk is the series reactance of branch lk, is the active power of the receiving-end power flow at node k, is the reactive power of the receiving-end power flow at node k, θ lk is the phase angle difference of the voltage drop phasor, Gs lk is the shunt conductance of branch lk, p l is the active power injected at node l represented in the form of fixed power, a p is the corresponding active power coefficient of the fixed impedance, b p is the corresponding active power coefficient of the fixed current, c p is the corresponding active power coefficient of the fixed power.

[0017] In some embodiments, the linear approximation model of the distribution network power flow model is represented by the following formula:

[0018]

[0019] Among them, is the complex power of the receiving-end power flow at node l, s l is the complex power injected at node l, is the complex power of the receiving-end power flow at node k, v l is the square of the voltage magnitude at node l, v k is the square of the voltage magnitude at node k, z lk is the series impedance of branch lk, and the symbol * indicates the conjugate complex number of this complex number, is the complex power of the receiving-end power flow at node k.

[0020] In some embodiments, the linear distribution network power flow model considering the line-to-ground shunt branch applied to a single-phase system is expressed by the following formula:

[0021]

[0022] Among them, is the receiving-end power flow complex power of node l, s l is the complex power injected at node l, is the receiving-end power flow complex power of node k, v l is the square of the voltage magnitude at node l, v k is the square of the voltage magnitude at node k, z lk is the series impedance of branch lk, is the shunt admittance of branch lk, and the symbol * represents the conjugate complex number of the complex number, is the receiving-end power flow complex power of node k, is the coefficient.

[0023] In some embodiments, the linear distribution network power flow model considering the shunt branch to ground of the line applied to a three-phase system is represented by the following formula:

[0024]

[0025] Among them, the symbol is a matrix containing the physical quantities of the abc three phases, is the receiving-end power flow complex power of node l, s l represents the complex power injected at node l, is the receiving-end power flow complex power of node k, v l is the square of the voltage magnitude at node l, v k is the square of the voltage magnitude at node k, is the shunt admittance of branch lk, is the coefficient, z lk is the series impedance of branch lk, and the symbol * represents the conjugate complex number of the complex number.

[0026] In some embodiments, when the linear distribution network power flow model considering the shunt branch to ground of the line is applied to an unbalanced three-phase system, it includes the linear distribution network power flow model considering the shunt branch to ground applied to the three-phase system and the power of the three-phase star-connected electrical load.

[0027] The present invention also provides a linear power flow model, which is characterized in that it is established by using the above method.

[0028] The present invention also provides a method for evaluating the operation stability of a distribution network, including the following steps:

[0029] A1: Establish a linear distribution network power flow model considering the shunt branch to ground of the line according to the above method;

[0030] A2: Evaluate the operation stability of the distribution network according to the linear distribution network power flow model considering the shunt branch to the ground of the line.

[0031] The present invention has the following beneficial effects:

[0032] By establishing a distribution network power flow model starting from the branch power and establishing a linear approximation model of the distribution network power flow model according to the distribution network power flow model, the model can always remain linear, thereby improving the calculation efficiency of the model; by adding a coefficient composed of line impedance admittance parameters to the voltage drop equation of the linear approximation model of the distribution network power flow model to modify the node branch matrix in the voltage drop equation, the model error caused by the capacitance susceptance of the shunt branch to the ground can be solved, thereby significantly improving the accuracy and accuracy rate of the distribution network power flow model, and further improving the evaluation efficiency and accuracy rate of the operation stability of the distribution network.

[0033] Other beneficial effects in the embodiments of the present invention will be further described below. Description of the Drawings

[0034] Figure 1 It is a flowchart of the optimization method of the linear power flow model in the embodiment of the present invention;

[0035] Figure 2 It is a schematic diagram of the π-type equivalent circuit line model of the radial distribution network in the embodiment of the present invention;

[0036] Figure 3 It is a schematic diagram of the distribution network operation stability evaluation method in the embodiment of the present invention. Detailed Embodiments

[0037] The following makes a detailed description of the embodiments of the present invention. It should be emphasized that the following description is merely exemplary and not intended to limit the scope of the present invention and its applications.

[0038] Since the admittance of the shunt branch to the ground in the existing technology is assumed to be 0 in the power flow model, the model error caused by the "charging effect" of the underground / undersea power cable is very large and unacceptable. In order to improve the accuracy of the power flow model of the distribution network, a linear model is highly needed to achieve higher efficiency, stronger duality and better accuracy in the case of reverse power flow, considering the influence of reverse power flow. Therefore, the embodiment of the present invention provides an optimization method for the power flow model of the distribution network. The approximate power flow model of the distribution network considering the shunt branch to the ground can provide a power flow calculation method for power companies, offshore power systems, such as offshore wind farm collection systems, offshore oil and gas development platforms, etc., which is applicable to large urban distribution networks with mainly underground cables as the main transmission lines in China and offshore distribution systems with undersea cables with large charging power. Power flow calculation of the power system is the basis for problems in the fields of power system operation, planning, control, etc.

[0039] As Figure 1 shown, the optimization method of the linear power flow model in the embodiment of the present invention includes the following steps:

[0040] S1: Establish a power flow model of the distribution network starting from the branch power, and establish a linear approximation model of the power flow model of the distribution network according to the power flow model of the distribution network. The linear approximation model of the power flow model of the distribution network includes a voltage drop equation and a branch power balance equation;

[0041] S2: Add a coefficient composed of line impedance admittance parameters to the voltage drop equation to modify the node branch matrix in the voltage drop equation, and establish an approximate power flow model of the distribution network considering the shunt branch to the ground;

[0042] The following are the specific steps of the optimization method of the linear power flow model:

[0043] (1) Establish a power flow model of the distribution network starting from the branch power, and establish a linear approximation model of the power flow model of the distribution network according to the power flow model of the distribution network:

[0044] The power flow model of the distribution network in this embodiment is the Distflow model: Foreign scholars Baran and Wu proposed a power flow model widely used in radial distribution networks, that is, the Distflow model, assuming that the shunt element is zero, that is, y m =0. Referring to the schematic diagram of the simplified radial network shown by Figure 2 , the Distflow model can be expressed by the following equation:

[0045]

[0046] Among them, s l :=p l +iq l represents the complex power injected at node l, are the active and reactive powers injected at node l, are the receiving - end and sending - end power - flow complex powers at node l respectively, is the receiving - end power - flow complex power at node l, respectively represent the squares of the voltage magnitudes at nodes l and k, and indicates the square of the current magnitude of branch lk. is the series impedance of branch lk, r lk / x lk are the series resistance and reactance of branch lk respectively, is the series admittance of branch lk, is the shunt admittance of branch lk, Gs lk / Bs lk are the shunt conductance and susceptance of branch lk respectively. The symbol * indicates the conjugate complex number of this complex number, and i is the imaginary - part identifier of the complex number. Note that due to equation (3), the Distflow model is non - linear and non - convex, so it cannot be solved directly, which is also the basic problem that this embodiment wants to solve. According to the following assumptions, simplifying equations (1)-(3) can obtain the linear Distflow equation, that is, the linear approximation model (LinDist) of the distribution - network power - flow model:

[0047] 1) For each line, the losses of the series impedance and shunt admittance are ignored;

[0048] 2) Assume that the shunt admittance of each line is zero;

[0049] The obtained linear approximation model of the distribution - network power - flow model is as follows:

[0050]

[0051]

[0052] (II) Establish a linear distribution - network power - flow model considering the shunt branch to the ground of the line:

[0053] 2.1. Linear distribution - network power - flow model considering the shunt branch to the ground of the line applied to a single - phase system

[0054] In this embodiment, both the distribution - network power - flow model and its linear approximation model, that is, the Distflow model and its linear approximation model, ignore the shunt admittance of the line. If the shunt - admittance value of the line cannot be ignored in the system, the model - calculation error will increase a lot, affecting the accuracy, reliability, and stability of the power - system power - flow calculation. Therefore, this embodiment proposes a linear distribution - network power - flow model (LinDistS) considering the shunt branch to the ground of the line to improve this problem.

[0055] Based on formulas (1)-(3), considering non-zero shunt branches to the ground in this embodiment, it is difficult to form a linear mathematical structure of the Pi circuit model with non-zero shunt elements in the voltage drop equation (2). Therefore, this embodiment starts the derivation from the Figure 2 two-node system in

[0056] Since there is no transformer in the two-node system, assume that the shunt admittances at both ends of the same branch shown in Figure 2 are the same According to Figure 2 the two-node system in lk (the network between nodes l and k), the current I lk through the series impedance z

[0057]

[0058] where, I lk represents the current of line lk, is the receiving-end current at node k, V k is the voltage at node k, is the conjugate complex of the shunt admittance of branch lk. Then, the power flow through the same impedance is:

[0059]

[0060] where, V l is the voltage at node l, represents the conjugate complex of the current of line lk, and the voltage at node l is the sum of the voltage at the other node and the voltage drop across the series impedance:

[0061] V l = V k + z lk I lk (8)

[0062] Take formula (8) and multiply each side by its complex conjugate:

[0063]

[0064]

[0065] where, is the conjugate complex of the voltage at node k. The linear approximation of the voltage drop equation can be obtained by taking the lower limit of the inequality equation in formula (13) and ignoring the two parts in formula (14), and It is achieved as follows. Assumption 1: Assuming that the angles of the current phasors are equal, the approximate values of Formulas (12) to (13) can be obtained. Taking the 33-bus system described in Section 4 as an example, this assumption is based on the following findings: The average angle difference between and is approximately 19.36°, while the average error between and is 1.32%. (The error of the IEEE 123-bus system is 0.4%). is the shunt branch current to the ground near the node k end in the line lk. Assumption 2: Both and in Formula (14) essentially contain the mathematical property of the product of the square of the impedance value and the square of the current value. In per-unit values, compared with the square of the voltage magnitude, the square value of the impedance magnitude can be ignored, so these two parts can be ignored in the linear approximation.

[0066] Regarding the branch power balance equation (1), the power injection on the shunt admittance of both sides of the line should be considered. The linear approximation of the branch power balance equation is achieved by ignoring the series admittance loss . Then, according to the circuit model in Figure 2 , the linear distribution network power flow model formula for the single-phase system considering the shunt branch to the ground in this embodiment is shown in Formulas (17)-(19):

[0067]

[0068] The mathematical structure of LinDistS is similar to that of LinDist, and an additional coefficient composed of the impedance admittance parameters of the line lk is used to modify the node branch matrix in the voltage drop equation.

[0069] 2.2. Linear Distribution Network Power Flow Model Considering Weak Ring Network Topology and ZIP Load Model with Shunt Branch to the Ground

[0070] In this embodiment, the voltage drop phasor angle difference θ lk is introduced in the following equation (20) to consider the influence of the weak grid topology and can be further approximated as equation (21):

[0071] |V l ||V k |sinθ lk =x lk P lk -r lk Q lk (20)

[0072] θ lk =x lk Plk -r lk Q lk (21)

[0073] Among them, P lk / Q lk are the power flows of line lk respectively. In addition, the following ZIP load model (referring to the physical simulation or mathematical description of load characteristics in power system analysis and calculation) (in the form of active and reactive power) is considered in the formula of LinDistS:

[0074]

[0075] Among them, is the active and reactive power injected at node l represented by the ZIP load model, p l / q l is the active and reactive power injected at node l represented in the form of fixed power, a p , a q \b p , b q \c p , c q are the corresponding active and reactive power coefficients of fixed impedance, current, and power respectively, and h is 1 in the per-unit system. Taking the active power equation as an example, it can be rewritten as:

[0076]

[0077] Except for the constant current load (p l *b p ), the ZIP model is linear. By defining v = 1 + Δv and ignoring the high-order terms of the Taylor series near zero, the linear approximation (the reactive power part is the same) can be achieved:

[0078]

[0079] The error of this approximation is calculated by defining a function, For example, the error when v l = 1.05 2 is about 0.12%, and the error will decrease when v l is close to 1. Therefore, the LinDistS formula considering weak grid topology and ZIP load model is given:

[0080]

[0081] Among them, is the active and reactive power of the receiving-end power flow at node l.

[0082] 2.3 Linear Distribution Network Power Flow Model Considering Shunt Branches to Ground Applied to Three-Phase Systems

[0083] For a three-phase system, Kirchhoff's voltage law formula (8) can be rewritten as:

[0084]

[0085] is the node voltage of the three phases a, b, and c, is the branch current of the three phases a, b, and c. The symbol is a matrix containing physical quantities of the three phases a, b, and c, is the total line series impedance matrix. The branch current through the line impedance is:

[0086]

[0087] where, ⊙ and respectively represent element-by-element multiplication and division in the matrix, is the three-phase power flow power of branch lk. Take formula (32) and multiply each side by its complex conjugate:

[0088]

[0089] where, is the line shunt branch matrix to ground, that is, the diagonal term of the admittance matrix. represents the square of the element modulus value. For example According to the approximate assumption of voltage balance of the three-phase bus, α is defined as:

[0090]

[0091] Together with the branch power balance equation, the linear distribution network power flow considering line shunt branches to ground applied to a three-phase system can be expressed as:

[0092]

[0093] The power of a three-phase star-connected electrical load can be described as:

[0094]

[0095] The ZIP parameter settings are the same as those of the single-phase model, is the active and reactive power of the ZIP load of the three phases a, b, and c. A delta-connected load can be converted into an approximately star-connected load:

[0096]

[0097] Among them, is the approximate three-phase star-connected load power after conversion, is the equivalent load power between every two phases among the three phases of the delta connection. Equations (41)-(45) constitute a linear distribution network power flow model considering the shunt branches between the line and the ground and applied to unbalanced three-phase systems.

[0098] An embodiment of the present invention also provides a linear power flow model, which is established by using the above method.

[0099] As Figure 3 shown, the method for evaluating the operation stability of the distribution network in the embodiment of the present invention includes the following steps:

[0100] A1: Establish a linear distribution network power flow model considering the shunt branches between the line and the ground according to the above method;

[0101] A2: Evaluate the operation stability of the distribution network according to the linear distribution network power flow model considering the shunt branches between the line and the ground.

[0102] This embodiment can quickly and accurately calculate whether the voltage amplitude, power flow, etc. exceed the limit, and improve the evaluation efficiency and accuracy of the operation stability of the distribution network.

[0103] Experimental example

[0104] (1) Measure the basic situation of the system

[0105] This experimental example uses the IEEE 33-bus system and the 69-bus system and modifies the test system: the shunt conductance of the entire system is the same and is 0.0005 p.u.; the shunt susceptance Bs is 1 / 4 of the magnitude of the series impedance in the same branch. The influence is also measured in the IEEE 123-bus system: the line shunt admittance value is expanded by 5 times to represent the replacement of overhead lines with underground cables. In the single-phase calculation error analysis, the IEEE 123-bus system is converted into a single-phase system through positive-sequence equivalence, and Kron reduction is applied in the neutral case. The four test systems are extended to 100 scenarios with randomly different load levels to verify the calculation performance of the mentioned model in large-scale distribution systems. The calculation error is calculated as ∈ = |Test - Real| / Real (Test represents the test value, Real represents the true value, and the true value is solved by the AC power flow model). The example is based on the YALMIP toolbox in Matlab R 2019B for modeling, and the commercial solver Gurobi 9.0.0 is used for solving.

[0106] This experimental example also introduced four linear models to test the performance of the proposed model: (1) Linear Branch Flow Model LBFS; (2) Linear Branch Flow Model without Squared Current Terms LBFMS; (3) Linear Load Flow Model LLFS by Modifying the Admittance Matrix; (4) Linear AC Power Flow Model LACS extracted from the Optimal Power Flow Problem and Modified to Consider Shunt Branches to Ground with Updated Admittance Submatrices and Related Equations.

[0107] (2) Analysis of Single-Phase Power Flow Calculation Errors

[0108] Table 1 below shows the average error (%) of the four linear models.

[0109] Table 1

[0110]

[0111] As can be seen from Table 1, LinDistS in the embodiments of the present invention improves the accuracy of the node voltage amplitude by 80% compared to LinDist, which is very important in large distribution systems. Compared with other linear models, LinDistS has better computational performance. Both LPFS and LBFMS modify the power flow using line parameters in the voltage drop equation, which may affect the accuracy of the voltage amplitude. Because the feeders between nodes in the 33-node system are relatively long and the magnitudes of series impedance and shunt admittance are large, the errors are large. For reactive power, LinDistS, LPFS, and LBFMS have similar errors and are much smaller than LBFS. Compared with LinDist, LinDistS still significantly improves the accuracy of branch currents, and thus also improves the power loss. An error of about 10% is acceptable because it is not so important in a distribution system with a large enough line capacity, and reducing line losses is not the main concern. Since the current error varies between positive and negative values, the error of power loss may be less than the error of current amplitude. The overall computational time of LinDistS is almost the same as that of LBFS (and other linear models). Therefore, compared with BFMS and ACPF, the linear distribution network power flow model considering shunt branches to ground proposed in the embodiments of the present invention significantly reduces the computational time, thereby improving the evaluation efficiency of the operation stability of the distribution network.

[0112] Table 2 below shows the average error (%) considering the ZIP load model in the weak loop system.

[0113] Table 2

[0114]

[0115] Refer to Table 2. In the 33-node system, reconnect four disconnected branches and assign appropriate line parameters to form a weak-loop network topology. The ZIP load parameters are set to 3:4:3 and remain unchanged in the three-phase analysis. This experimental example also conducts error analysis at different load levels. The voltage magnitude error and power loss of LinDistS are not significantly affected by the network topology type and load level. However, when the system is at the maximum load point (the maximum feeder capacity of the 33-bus system is approximately 10 MW, around 300%), the calculation accuracy decreases. The voltage magnitude accuracy for different line impedance ratios R / X is similar, while the accuracy of power loss decreases with the increase of the ratio. For example, the voltage magnitude error and network loss error increase from 0.12% and 9.38% (average R / X = 0.7) to 0.14% and 13.24% (average R / X = 2.0). LLFS shows slightly higher accuracy than LinDistS in terms of the voltage magnitude for constant power loads and ZIP loads, but due to its load flow nature, it has lower power loss accuracy in the weak-loop network system. For radial systems other than case33, the voltage magnitude error (0.09% for the 69-node system and 0.08% for the 123-node system) and power loss (13.46%, 9.32%) of LLFS are higher than those of LinDistS. The calculation accuracy of LACS is opposite to that of LLFS.

[0116] (3) Three-phase power flow calculation error analysis

[0117] In the three-phase system calculation error analysis, a linear three-phase power flow model (LPF) and a three-phase extended model of LLF are introduced to more comprehensively evaluate the performance of LinDistS power flow calculation. The power injection of distributed resources in the 123-node system is calculated by BFM after semi-definite programming. The true power flow and voltage magnitude of the modified 123-node system are solved by the forward-backward sweep algorithm (FBS), so as to compare LPF, LLFS, and LinDistS under the same benchmark.

[0118] The following Table 3 shows the average error (%) of the three-phase 123-node system

[0119] Table 3

[0120]

[0121] As can be seen from Table 3, after considering the shunt branches to ground in the three-phase unbalanced system, the LinDistS has significantly improved accuracy in terms of voltage magnitude and branch power flow network loss compared to the original linear Distflow model (LPF), which is consistent with the conclusion drawn from the single-phase error analysis. In addition, the calculation accuracy of LinDistS in three-phase analysis is higher than that in single-phase analysis. For example, the calculation error of the voltage magnitude is 0.0684%, which is lower than the error of 0.0902% equivalent to the ZIP load of the 123-bus system. In addition, LinDistS shows higher calculation accuracy than LLFS in both voltage magnitude and power loss, thus reflecting the calculation accuracy of LinDistS in the three-phase unbalanced system.

[0122] The improved linear distribution network power flow model (LinDistS) considering shunt branches to ground proposed in this embodiment has good calculation accuracy, can solve the model error caused by the capacitive susceptance of the shunt branches to ground, and can thereby improve the accuracy rate of the operation stability assessment of the distribution network. The superiority of LinDistS lies in retaining the structure of the original LinDist model (a linearized power flow model) and adding a correction factor (a coefficient composed of line impedance admittance parameters) to the voltage drop equation to consider the influence of shunt branches to ground. The simulation results show that the calculation efficiency of LinDistS is higher than that of the non-linear model, and the voltage magnitude and power flow power accuracy are higher than those of the original LinDist model and other linear models. LinDistS is further extended to consider the ZIP load model, weak loop network topology, and three-phase unbalanced system. The advantage of LinDistS is that it can always remain linear, so it still maintains a high calculation efficiency after these extensions. By comparing with a sufficient number of control models in the simulation, the importance of introducing the shunt branches to ground into the linear approximation model of the distribution network power flow model and performing these extensions is highlighted.

[0123] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0124] The present invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each flow and / or block in the flowchart illustrations and / or block diagrams, and combinations of flows and / or blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions executed by the processor of the computer or other programmable data processing device create means for implementing the functions specified in the flow Figure 1 one or more flows and / or blocks Figure 1 or means for implementing the functions specified in a block or blocks.

[0125] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means that implement the functions specified in the flow Figure 1 one or more flows and / or blocks Figure 1 or means for implementing the functions specified in a block or blocks.

[0126] These computer program instructions may also be loaded onto a computer or other programmable data processing device, such that a series of operational steps are performed on the computer or other programmable device to produce a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in the flow Figure 1 one or more flows and / or blocks Figure 1 or means for implementing the functions specified in a block or blocks.

[0127] The above content is a further detailed description of the present invention in combination with specific / preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several alternatives or modifications can be made to these described embodiments, and these alternative or modified forms should all be regarded as belonging to the protection scope of the present invention. In the description of this specification, the description with reference to terms such as "an embodiment", "some embodiments", "preferred embodiment", "example", "specific example", or "some examples" means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. Without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples. Although the embodiments of the present invention and their advantages have been described in detail, it should be understood that various changes, substitutions, and alterations can be made herein without departing from the scope of protection of the patent application.

Claims

1. An optimization method for a linear power flow model, characterized in that, Including the following steps: S1: Establish a distribution network power flow model starting from branch power, and establish a linear approximation model of the distribution network power flow model according to the distribution network power flow model. The linear approximation model of the distribution network power flow model includes a voltage drop equation and a branch power balance equation; S2: Add coefficients composed of line impedance admittance parameters to the voltage drop equation to modify the node branch matrix in the voltage drop equation, and establish a linear distribution network power flow model considering the shunt branch to the ground of the line; Among them, step S2 further includes: introducing the voltage drop phasor angle difference and the ZIP load model in the form of active power and reactive power in the linear distribution network power flow model considering the shunt branch to the ground of the line, and expressed by the following formula: Among them, is the active power of the receiving-end power flow of node l, is the reactive power of the receiving-end power flow of node l, is the active power injected at node l represented by the ZIP load model, is the reactive power injected at node l represented by the ZIP load model, is the active power of the receiving-end power flow of node k, is the reactive power of the receiving-end power flow of node k, Bs lk is the shunt susceptance of branch lk, v l is the square of the voltage magnitude at node l, v k is the square of the voltage magnitude at node k, is a coefficient, r lk is the series resistance of branch lk, x lk is the series reactance of branch lk, is the active power of the receiving-end power flow of node k, is the reactive power of the receiving-end power flow of node k, θ lk is the phase angle difference of the voltage drop phasor, Gs lk is the shunt conductance of branch lk, p l is the active power injected at node l represented in the form of fixed power, a p is the corresponding active power coefficient of the fixed impedance, b p is the corresponding active power coefficient of the fixed current, c p is the corresponding active power coefficient of the fixed power.

2. The method according to claim 1, wherein The distribution network power flow model is the Distflow model.

3. The method according to claim 1, wherein The linear approximation model of the distribution network power flow model is represented by the following formula: Among them, is the receiving-end power flow complex power of node l, s l is the complex power injected at node l, is the receiving-end power flow complex power of node k, v l is the square of the voltage magnitude at node l, v k is the square of the voltage magnitude at node k, z lk is the series impedance of branch lk, and the symbol * indicates the conjugate complex number of this complex number, is the receiving-end power flow complex power of node k.

4. The method according to claim 1, wherein The linear distribution network power flow model considering the shunt branch to the ground of the line applied to a single-phase system is expressed by the following formula: wherein, is the receiving-end power flow complex power of node l, s l is the complex power injected at node l, is the receiving-end power flow complex power of node k, v l is the square of the voltage magnitude at node l, v k is the square of the voltage magnitude at node k, z lk is the series impedance of branch lk, is the shunt admittance of branch lk, and the symbol * represents the conjugate complex number of the complex number, is the receiving-end power flow complex power of node k, is a coefficient.

5. The method according to claim 1, characterized in that, The linear distribution network power flow model considering the shunt branch to the ground of the line applied to a three-phase system is represented by the following formula: Among them, the symbol is a matrix containing the physical quantities of three phases a, b, and c. is the receiving - end power - flow complex power at node l, s l represents the complex power injected at node l. is the receiving - end power - flow complex power at node k, v l is the square of the voltage magnitude at node l, v k is the square of the voltage magnitude at node k. is the shunt admittance of branch lk. is a coefficient, z lk is the series impedance of branch lk, and the symbol * represents the conjugate complex number of a complex number.

6. The method according to claim 5, wherein When the linear distribution network power flow model considering the shunt branch to the ground of the line is applied to an unbalanced three-phase system, it includes the linear distribution network power flow model considering the shunt branch to the ground applied to a three-phase system and the power of a three-phase star-connected electrical load.

7. A linear power flow model, characterized in that, Established by using the method described in claims 1-6.

8. A method for evaluating the operation stability of a distribution network, characterized in that, Including the following steps: A1: Establish a linear distribution network power flow model considering the shunt branch to the ground of the line according to the method described in any one of claims 1-6; A2: Evaluate the operation stability of the distribution network according to the linear distribution network power flow model considering the shunt branch to the ground of the line.

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