Linear Optimal Power Flow Method for DC Power Grids

Abstract

The present invention discloses a linear optimal power flow method for a DC power grid, which includes the following steps: performing per-unit processing on the system; listing the objective function of the optimal power flow problem; converting the nonlinear power flow equation constraint of the optimal power flow problem into a linear power flow equation constraint; forming a simplified optimal power flow problem; obtaining a linear expression of a DC voltage deviation; deriving the power command value of each power-controllable converter station to achieve regulation of the operating state of the DC system; its transmission system and its transmission and distribution network have a linear optimal power flow algorithm. The present invention utilizes a fast linear power flow algorithm for a DC power grid to convert the nonlinear equation constraint in the optimal power flow problem into a linear equation constraint. For the optimal power flow problem with the DC voltage deviation and the converter power deviation as the objective function, a linear expression of the optimal power flow solution is obtained by Lagrange number multiplication.

Description

Technical Field

[0001] The invention belongs to the technical field of direct current transmission, and in particular relates to a linear optimal power flow method for a direct current power grid. Background Art

[0002] Fully developing and utilizing renewable energy is an important way and means to achieve carbon peak and carbon neutrality. Thanks to the advantages of voltage source converter (VSC) in realizing active power and reactive power decoupling control and the absence of commutation failure and other problems, DC transmission technology has developed rapidly. Compared with AC system, DC system alleviates the adverse effects of intermittent and volatile renewable energy, while improving power conversion efficiency.

[0003] Therefore, the DC system is an effective solution for large-scale grid connection of renewable energy and increasing the penetration rate of new energy.

[0004] Multi-terminal direct current (MTDC) systems bring more flexible and economical operation modes, but also make the system control strategy more complex. The hierarchical control of DC systems evolved from the hierarchical control of AC systems. Usually, there are local control layers and upper secondary optimization control layers, and the action time scale of the secondary optimization control layer is mostly in the minute level. This is because in the optimal power flow calculation of multi-terminal DC systems or DC power grids, the optimal power flow problem is a non-convex nonlinear optimization problem with complex inequality constraints and equality constraints and many optimization variables. Among them, the power flow equation is a set of nonlinear equations that need to be solved iteratively, which further leads to the relatively complex optimization procedure of the optimal power flow and the relatively long calculation time, which cannot be timely involved in the control of the converter level in the DC system. If the optimal power flow calculation speed is fast enough, the optimization results can be combined with the local control of the converter to participate in the real-time control of the system.

[0005] Since there are significant differences between DC and AC systems in the power flow equation, that is, there is no concept of reactive power and phase angle in the DC system, the DC power flow equation can be further simplified and linearized by ignoring high-order terms and ensuring sufficient accuracy. In addition, since all power-controllable converter stations in the DC system can be regarded as droop-controlled converter stations with different droop gains, the power instructions or voltage instructions of all droop-controlled converter stations will also be calculated by the fast linear power flow algorithm. This will improve the defects of the optimal power flow of the DC power grid in terms of complex calculation methods and long calculation time. Summary of the invention

[0006] The present invention is proposed to solve the problems of complex solution algorithm and slow solution speed in the prior art of the optimal power flow of a DC system due to its nonlinear power flow equation constraints, and its purpose is to provide a linear optimal power flow method for a DC power grid.

[0007] The technical solution of the present invention is: a linear optimal power flow method for a DC power grid, comprising the following steps:

[0008] ⅰ.Perform standard processing on the system S1

[0009] ⅱ. List the objective function S2 of the optimal power flow problem

[0010] ⅲ. Convert the nonlinear power flow equation constraint of the optimal power flow problem into a linear power flow equation constraint S3

[0011] ⅳ. Formation of simplified optimal power flow problem S4

[0012] ⅴ. Obtain the linear expression of DC voltage deviation S5

[0013] ⅵ. Derive the power command value of each power-controllable converter station to realize the regulation of the operating state of the DC system S6.

[0014] Furthermore, when the system is calibrated in step i, the voltage base value is the rated DC voltage, and the power base value is the maximum converter capacity of the DC system.

[0015] Furthermore, step ii lists the objective function of the optimal power flow problem, which is a quadratic function of the DC voltage deviation and the power deviation, as follows:

[0016]

[0017] Among them, α is the weight factor;

[0018] Vector ΔV dc is the DC voltage deviation of the DC grid node, which is the difference between the DC voltage of each node and the rated value;

[0019] The vector ΔP is the power deviation;

[0020] Vector P c Inject power into power-controllable converter station nodes;

[0021] P t The target value of the power injected into the power-controllable converter station.

[0022] Furthermore, step iii transforms the nonlinear power flow equation constraint of the optimal power flow problem into a linear power flow equation constraint. The specific process is as follows:

[0023] First, the nonlinear power flow equation constraint of the optimal power flow problem is transformed into a linear power flow equation constraint, and the following equation is obtained:

[0024] P=YΔV dc

[0025] Among them, vector P is the DC grid node injection power;

[0026] Y is the admittance matrix of the DC power grid system;

[0027] Then, the linear power flow equation is written in block matrix form to distinguish between power controllable and power uncontrolled converter stations, and the following equation is obtained:

[0028]

[0029] Among them, the vector P n Inject power into nodes of uncontrolled power converter stations.

[0030] Furthermore, step iv forms a simplified optimal power flow problem, and the specific process is as follows:

[0031] The optimal power flow is obtained by simplifying it as follows:

[0032]

[0033] Y 2 ΔV dc =P n

[0034] And its Lagrangian function:

[0035]

[0036] Where E is the identity matrix;

[0037] L(ΔV dc ,λ) and λ are the Lagrangian function and Lagrangian multiplier respectively.

[0038] Furthermore, in step V, a linear expression of the DC voltage deviation is obtained, and the specific process is as follows:

[0039] make and Equal to 0, the linear expression of DC voltage deviation is obtained as follows:

[0040]

[0041] Furthermore, step ⅵ derives the power command value of each power-controllable converter station to realize the regulation of the operating state of the DC system. The specific process is as follows:

[0042] Using ΔV dcThe power command value of each power-controllable converter station is derived, and the operation state of the DC system is regulated by adjusting the power command, thereby achieving the optimal power flow.

[0043] P ref =ΑΔV dc

[0044] Α=Y+diag(β)

[0045] Among them, the vector P ref is the power command value of the power controllable converter station, and the vector β is the droop gain of the droop control converter station.

[0046] Furthermore, the control rate of the power controllable converter station is:

[0047] P ref -P+βΔV dc =0.

[0048] A DC power grid is a multi-terminal DC power grid, and its nodes are composed of flexible DC converter stations, conventional DC converter stations and DC transformers.

[0049] The beneficial effects of the present invention are as follows:

[0050] The present invention uses a fast linear power flow algorithm for DC power grid to convert the nonlinear equality constraints in the optimal power flow problem into linear equality constraints. For the optimal power flow problem with DC voltage deviation and converter power deviation as the objective function, a linear expression of the optimal power flow solution is obtained by Lagrange number multiplication.

[0051] Compared with the traditional DC grid optimal power flow algorithm, the present invention simplifies the calculation method, accelerates the calculation speed, shortens the calculation time, makes the calculation time scale of the DC grid optimal power flow consistent with the local control time scale of the converter station, and retains considerable calculation accuracy and optimization performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is a flow chart of the method of the present invention;

[0053] Figure 2 is a schematic diagram of the topology of a CIGRE B4 DC system in an embodiment of the present invention;

[0054] Figure 3 It is the theoretical value of the objective function in the embodiment of the present invention under the linear optimization method of the present invention and the traditional optimization method. DETAILED DESCRIPTION

[0055] Hereinafter, the present invention will be described in detail with reference to the accompanying drawings and embodiments:

[0056] like Figures 1 to 3As shown, a linear optimal power flow method for a DC power grid includes the following steps:

[0057] ⅰ.Perform standard processing on the system

[0058] ii. List the objective function of the optimal power flow problem

[0059] ⅲ. Convert the nonlinear power flow equation constraints of the optimal power flow problem into linear power flow equation constraints

[0060] ⅳ. Forming a simplified optimal power flow problem

[0061] ⅴ. Obtain the linear expression of DC voltage deviation

[0062] ⅵ. Derive the power command value of each power-controllable converter station to realize the regulation of the operating status of the DC system.

[0063] When the system is calibrated in step i, the voltage base value is the rated DC voltage, and the power base value is the maximum converter capacity in the DC system.

[0064] Step ii lists the objective function of the optimal power flow problem, which is a quadratic function of DC voltage deviation and power deviation, as follows:

[0065]

[0066] Among them, α is the weight factor;

[0067] Vector ΔV dc is the DC voltage deviation of the DC grid node, which is the difference between the DC voltage of each node and the rated value;

[0068] The vector ΔP is the power deviation;

[0069] Vector P c Inject power into power-controllable converter station nodes;

[0070] P t The target value of the power injected into the power-controllable converter station.

[0071] Step iii: Convert the nonlinear power flow equation constraint of the optimal power flow problem into a linear power flow equation constraint. The specific process is as follows:

[0072] First, the nonlinear power flow equation constraint of the optimal power flow problem is transformed into a linear power flow equation constraint, and the following equation is obtained:

[0073] P=YΔV dc

[0074] Among them, vector P is the DC grid node injection power;

[0075] Y is the admittance matrix of the DC power grid system;

[0076] Then, the linear power flow equation is written in block matrix form to distinguish between power controllable and power uncontrolled converter stations, and the following equation is obtained:

[0077]

[0078] Among them, the vector P n Inject power into nodes of uncontrolled power converter stations.

[0079] Step ⅳ forms a simplified optimal power flow problem, and the specific process is as follows:

[0080] The optimal power flow is obtained by simplifying it as follows:

[0081]

[0082] Y 2 ΔV dc =P n

[0083] And its Lagrangian function:

[0084]

[0085] Where E is the identity matrix;

[0086] L(ΔV dc ,λ) and λ are the Lagrangian function and Lagrangian multiplier respectively.

[0087] Step V obtains the linear expression of the DC voltage deviation. The specific process is as follows:

[0088] make and Equal to 0, the linear expression of DC voltage deviation is obtained as follows:

[0089]

[0090] Step VI derives the power command value of each power-controllable converter station to achieve regulation of the DC system operation state. The specific process is as follows:

[0091] Using ΔV dc The power command value of each power-controllable converter station is derived, and the operation state of the DC system is regulated by adjusting the power command, thereby achieving the optimal power flow.

[0092] P ref =ΑΔV dc

[0093] Α=Y+diag(β)

[0094] Among them, the vector Pref is the power command value of the power controllable converter station, and the vector β is the droop gain of the droop control converter station.

[0095] The control rate of the power controllable converter station is:

[0096] P ref -P+βΔV dc =0.

[0097] In the objective function, P t The target value of the injected power for the power controllable converter station, P t Usually comes from the scheduling layer.

[0098] In step ⅵ, using ΔV dc The power command value of each power-controllable converter station is derived, and the operating state of the DC system is ultimately regulated by adjusting the power command, thereby achieving the optimal power flow.

[0099] The power controllable converter station in the present invention is a droop control converter station.

[0100] More preferably, the DC voltage command value of each power-controllable converter station, i.e., the droop control converter station, is the rated DC voltage value.

[0101] Based on step ⅵ, if the calculation result does not meet the optimal power flow inequality constraint, it is necessary to fix the power of the off-limit converter station, regard this power-controllable converter station as a power-uncontrolled converter station, and recalculate a new optimal solution.

[0102] The present invention linearizes the equality constraints in the optimal power flow problem by using a fast linear power flow algorithm of a DC power grid on the basis that the objective function is a quadratic function of the DC voltage deviation and the power deviation, further uses Lagrange number multiplication to solve the linear solution of the optimal power flow, and transforms the traditional optimal power flow problem into a linear expression.

[0103] A DC power grid is a multi-terminal DC power grid, and its nodes are composed of flexible DC converter stations, conventional DC converter stations and DC transformers.

[0104] Yet another embodiment

[0105] This embodiment uses the CIGRE B4 DC system to compare and analyze the linear optimization method proposed in the present invention and the traditional DC optimal power flow algorithm. The simulation topology diagram used is as follows: Figure 2 The detailed system parameters adopted are shown in the following table. The rated DC voltage of the system is ±200kV. In addition, the direction in which the converter station power is injected into the DC side is defined as the positive direction.

[0106] Basic parameters of multi-terminal DC system

[0107]

[0108]

[0109] A linear optimal power flow method for a DC power grid is proposed. On the basis of an objective function being a quadratic function of DC voltage deviation and power deviation, a fast linear power flow algorithm for a DC power grid is used to linearize the equality constraints in the optimal power flow problem. The linear solution of the optimal power flow is further solved by Lagrange number multiplication, and the traditional optimal power flow problem is converted into a linear expression.

[0110] The specific steps of this embodiment are as follows:

[0111] ⅰ.Perform standard processing on the system

[0112] The voltage base value is the rated DC voltage (400kV), the power base value can be set to the maximum converter capacity in the DC system, or it can be set to other values ​​according to conditions. In this example, the power base value is the maximum converter capacity (600MVA).

[0113] ⅱ. List the objective function of the optimal power flow problem, that is, the quadratic function of DC voltage deviation and power deviation, and obtain the following objective function:

[0114]

[0115] Among them, α is the weight factor, and the vector ΔV dc is the DC voltage deviation of the DC grid node, which is the difference between the DC voltage of each node and the rated value. The vector ΔP is the power deviation, and the vector P c Inject power into the power controllable converter station node, P t The target value of the power injected into the power-controllable converter station is usually derived from the dispatching layer.

[0116] According to the above table, the target value vector of injected power of the power controllable converter station is obtained:

[0117] P t =[250-250-500-250-400] T (MW)

[0118] ⅲ. Convert the nonlinear power flow equation constraint of the optimal power flow problem into a linear power flow equation constraint, that is:

[0119] P=YΔV dc

[0120] Among them, vector P is the DC grid node injection power, and Y is the DC grid system admittance matrix. Figure 1 , write the linear power flow equation in block matrix form to distinguish between power controllable and power uncontrolled converter stations, namely:

[0121]

[0122]

[0123] Among them, the vector P n Inject power into the nodes of the power uncontrolled converter station, specifically:

[0124] P n =[200500150300] T (MW)

[0125] iv. Combining the objective function proposed in step ii and the linear power flow equation equality constraint obtained in step iii, a simplified optimal power flow problem is formed, namely:

[0126]

[0127] sP n =Y 2 ΔV dc

[0128] This optimization problem contains only one variable, namely, the DC grid node DC voltage deviation ΔV dc .

[0129] Furthermore, the Lagrangian function is obtained by Lagrangian number multiplication:

[0130]

[0131] Where E is the unit matrix, L(ΔV dc ,λ) and λ are the Lagrangian function and Lagrangian multiplier respectively.

[0132] ⅴ. Order and Equal to 0, the linear expression of DC voltage deviation is obtained, namely:

[0133]

[0134] Let the weight factor α = 1, and substitute the above parameters to obtain

[0135] ΔV dc =[3.999-0.062-3.333-7.805-5.8095.7656.0132.179-0.615-0.331](kV)

[0136] ⅵ. Using ΔV dc The power command value of each power-controllable converter station is derived, and the operating state of the DC system is ultimately regulated by adjusting the power command, thereby achieving the optimal power flow.

[0137] P ref =ΑΔV dc

[0138] Α=Y+diag(β)

[0139] Among them, the vector P ref is the power command value of the power controllable converter station, and the vector β is the droop gain of the droop control converter station. Substituting the above data, we get the matrix A

[0140]

[0141] The final power command value of the power controllable converter station is shown in the following table:

[0142] The optimization result of the method proposed in the present invention, P VSC8 =150MW

[0143]

[0144] In addition, this embodiment adopts the injection power P of VSC8 VSC8 The power is increased to 400MW to simulate the situation after power disturbance. The same calculation method is used to obtain the power command value of the converter station in this case.

[0145] The optimization result of the method proposed in the present invention, P VSC8 =400MW

[0146]

[0147] The theoretical values ​​of the objective functions of the linear optimization method proposed in the present invention and the traditional optimization method vary with the weight factors as shown in Figure 3 As shown in the figure, the two have similar performance. Taking the weight factor α = 1 as an example, the digital simulation (software: PSCAD / EMTDC, indicated by superscript *) results and estimated calculation time (software: MATLAB) are shown in the following table.

[0148] When α=1, the digital simulation results, P VSC8 =150MW

[0149]

[0150]

[0151] When α=1, the digital simulation results, P VSC8 =150MW

[0152]

[0153] The above chart shows that, between α=0 and 5, the theoretical values ​​of the objective functions of the linear optimization method proposed in the present invention and the traditional optimization method are almost the same, and the method proposed in the present invention greatly simplifies the optimization process and shortens the calculation time.

[0154] The method proposed in the present invention is dozens of times faster than the traditional method, and the increase in voltage index and power index does not exceed 2%. Therefore, the proposed method achieves similar effects to the traditional method while greatly improving the calculation speed.

[0155] The present invention linearizes the equality constraints in the optimal power flow problem of multi-terminal DC power grid and proposes a new linear method to simplify the optimization process. The numerical simulation results show that compared with the traditional optimization method, the proposed method has fast calculation speed and good performance.

[0156] In addition, the rapidity achieved through linearization makes the proposed method applicable to the real-time control of DC systems to achieve integrated regulation and control development.

[0157] At this point, the tasks of the linear optimal power flow method applicable to a multi-terminal DC power grid proposed in the present invention are all completed.

[0158] The present invention uses a fast linear power flow algorithm for DC power grid to convert the nonlinear equality constraints in the optimal power flow problem into linear equality constraints. For the optimal power flow problem with DC voltage deviation and converter power deviation as the objective function, a linear expression of the optimal power flow solution is obtained by Lagrange number multiplication.

[0159] Compared with the traditional DC grid optimal power flow algorithm, the present invention simplifies the calculation method, accelerates the calculation speed, shortens the calculation time, makes the calculation time scale of the DC grid optimal power flow consistent with the local control time scale of the converter station, and retains considerable calculation accuracy and optimization performance.

Claims

1. A linear optimal power flow method for a DC power grid, characterized by: The following steps are involved: (i) Standardize the system (ii) List the objective function of the optimal power flow problem (iii) Convert the nonlinear power flow equation constraints of the optimal power flow problem into linear power flow equation constraints (iv) Forming a simplified optimal power flow problem (v) Obtain the linear expression of DC voltage deviation: (vi) deriving the power command value of each power-controllable converter station to achieve regulation of the operating state of the DC system; Step (ii) lists the objective function of the optimal power flow problem, which is a quadratic function of the DC voltage deviation and the power deviation, as follows: Among them, α is the weight factor; Vector ΔV dc is the DC voltage deviation of the DC grid node, which is the difference between the DC voltage of each node and the rated value; The vector ΔP is the power deviation; Vector P c Inject power into power-controllable converter station nodes; P t A target value of power injected into the power controllable converter station; Step (iv) forms a simplified optimal power flow problem, and the specific process is as follows: The optimal power flow is obtained by simplifying it as follows: s.t.Y2ΔV dc =P n And its Lagrangian function: Where E is the identity matrix; L(ΔV dc ,λ) and λ are the Lagrangian function and Lagrangian multiplier respectively; Step (v) obtains the linear expression of the DC voltage deviation, and the specific process is as follows: make and Equal to 0, the linear expression of DC voltage deviation is obtained as follows: Step (vi) derives the power command value of each power-controllable converter station to achieve regulation of the operating state of the DC system. The specific process is as follows: Using ΔV dc The power command value of each power-controllable converter station is derived, and the operation state of the DC system is regulated by adjusting the power command, thereby achieving the optimal power flow. P ref =ADV dc Α=Y+diag(β) Among them, the vector P ref is the power command value of the power controllable converter station, and the vector β is the droop gain of the droop control converter station.

2. The linear optimal power flow method for a DC power grid according to claim 1, characterized in that: When the system is calibrated in step (i), the voltage base value is the rated DC voltage, and the power base value is the maximum converter capacity of the DC system.

3. The linear optimal power flow method for a DC power grid according to claim 1, characterized in that: Step (iii) converts the nonlinear power flow equation constraint of the optimal power flow problem into a linear power flow equation constraint. The specific process is as follows: First, the nonlinear power flow equation constraint of the optimal power flow problem is transformed into a linear power flow equation constraint, and the following equation is obtained: P=YΔV dc Among them, vector P is the DC grid node injection power; Y is the admittance matrix of the DC power grid system; Then, the linear power flow equation is written in block matrix form, distinguishing between power controllable and power uncontrolled converter stations, and the following equation is obtained: Among them, the vector P n Inject power into nodes of uncontrolled power converter stations.

4. The linear optimal power flow method for a DC power grid according to claim 1, characterized in that: The control rate of the power controllable converter station is: P ref -P+βΔV dc =0。 5. A DC power grid according to the linear optimal power flow method of a DC power grid according to claim 1, characterized in that: The DC grid is a multi-terminal DC grid, whose nodes are composed of flexible DC converter stations, conventional DC converter stations and DC transformers.

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