Photovoltaic power station double-layer optimization method considering unit voltage droop characteristic

Abstract

The invention discloses a photovoltaic power station double-layer optimization method considering a unit voltage droop characteristic, and the method comprises the steps: firstly building a photovoltaic power station model which comprises a plurality of groups of photovoltaic power generation units composed of photovoltaic arrays and inverters, and enabling the photovoltaic power generation units to be connected to a common connection point bus through a medium-voltage current collection line, and to be connected to a power grid through a booster station; a double-layer optimization model of the photovoltaic power station is constructed, the upper layer model aims at optimizing the operating voltage of the power station, and the in-station voltage deviation is reduced by adjusting the reactive power output of the photovoltaic unit; the lower layer model takes optimization of unit active power output as a target, and the active power utilization rate is improved by adjusting the voltage droop characteristic of the photovoltaic unit; and finally, on the basis of the double-layer optimization model, constructing a Lagrange function of a lower-layer model, writing KTT conditions in parallel, taking the KKT conditions of the lower-layer model as constraint conditions of an upper-layer model, and converting the double-layer optimization model into a single-layer optimization model for solving. The photovoltaic power station double-layer optimization method has the advantages of being small in calculation burden, high in adaptability and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of photovoltaic power stations, and in particular to a double-layer optimization method for photovoltaic power stations taking into account the voltage droop characteristics of generator sets. Background Art

[0002] In recent years, the pursuit of the "dual carbon goals" has driven the development of new energy sources, leading to a continuous expansion in the scale of renewable energy development and utilization. As a leading form of new energy, photovoltaic power generation has seen its installed capacity continue to expand. While this large-scale development improves the energy mix, it also poses new challenges to the safe and stable operation of the power grid. Influenced by natural factors such as sunlight, photovoltaic power generation exhibits significant time-varying, fluctuating, and intermittent characteristics. If operational control measures are inadequate, the grid-connected integration of large-scale photovoltaic power stations can impact the power grid, affecting its stable operation.

[0003] During grid-connected operation, the dynamic reactive power regulation capability of photovoltaic power stations has a significant impact on system voltage stability. By studying the issue of photovoltaic power stations participating in grid voltage control, the risk of voltage instability caused by large-scale photovoltaic access can be effectively mitigated, further improving the economy and stability of power system operation. A more common control method is based on a dynamic reactive power compensation mechanism, which coordinates the reactive power output of photovoltaic inverters with the coordinated operation of reactive power compensation devices at the collection station. The reactive power compensation of existing photovoltaic systems is mainly controlled independently by photovoltaic power stations, with reactive power support provided by the station's automatic voltage control system (AVC) and reactive power compensation equipment installed at the collection station. A centralized control method is used, with system parameters acquired and optimized by a central controller.

[0004] However, for large-scale, complex photovoltaic power plants, centralized control approaches, which rely on a single controller for independent control, are characterized by incoordination and complexity. Furthermore, they have limited computing power, are prone to single points of failure, and cannot guarantee the voltage regulation requirements of the overall system. Distributed control methods can effectively address these issues, but they also suffer from a lack of global coordination, high information sharing requirements, and insufficient collaborative optimization. Therefore, studying hierarchical coordinated optimization strategies for photovoltaic power generation system voltage control has important theoretical and practical significance.

[0005] Currently, research on the application of two-tier optimization in photovoltaic systems focuses primarily on economic dispatch, the coordinated optimization of photovoltaic power plants and energy storage systems, and the site selection and sizing optimization of photovoltaic power plants. The optimization objectives of these models are often to maximize profits, maximize the value of power transmission and reception, and minimize system losses. While some research has explored reactive power optimization in photovoltaic power plants and established a two-tier model for reactive power optimization based on voltage regulation characteristics, the application of two-tier optimization to optimal voltage control in photovoltaic power plants is still understudied. Therefore, the construction of a two-tier optimization control strategy that considers the voltage droop characteristics of photovoltaic units remains a pressing technical challenge. Summary of the Invention

[0006] In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is: how to provide a two-layer optimization method for photovoltaic power stations with low computational burden and strong adaptability.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] A two-layer optimization method for a photovoltaic power station considering the voltage droop characteristics of a generator set includes the following steps:

[0009] S1. Establish a photovoltaic power station model, including multiple photovoltaic power generation units consisting of photovoltaic arrays and inverters. The photovoltaic power generation units are connected to the common connection point bus through medium-voltage collector lines and connected to the power grid through a booster station;

[0010] S2. Construct a two-layer optimization model for the photovoltaic power station. The upper layer model aims to optimize the operating voltage of the power station by adjusting the reactive power output of the photovoltaic units to reduce the voltage deviation within the station. The lower layer model aims to optimize the active power output of the units by adjusting the voltage droop characteristics of the photovoltaic units to improve the active power utilization rate.

[0011] S3. Based on the two-layer optimization model, construct the Lagrangian function of the lower model, write the KTT conditions, use the KKT conditions of the lower model as the constraints of the upper model, and convert the two-layer optimization model into a single-layer optimization model for solution.

[0012] Furthermore, in step S2, the objective function of the upper model is:

[0013]

[0014] Where: V i is the node voltage amplitude; V ref is the reference voltage; is the set of nodes within the station;

[0015] The constraints of the upper model include the QV droop control of the PV unit and the power flow constraints of the upper collector line;

[0016] The reactive output of the photovoltaic unit in the QV droop control satisfies the following formula:

[0017]

[0018] Where: The reactive power output of the unit corresponding to the dead zone; The upper and lower limits of the voltage amplitude corresponding to the dead zone; is the left and right droop slope of the droop zone; is the node set where the photovoltaic unit is located; It is the reactive power output of the unit when it is working in the saturated area. and Satisfy the constraints:

[0019]

[0020] Where: P PV,i is the active power output of the photovoltaic unit on node i; is the rated capacity of the photovoltaic generator set at node i;

[0021] The upper collector line power flow constraint is:

[0022]

[0023] Where: Q li is the reactive power flowing through branch li; R li 、X li is the resistance and reactance of the branch; k T is the transformer ratio on the branch; Q i Inject reactive power into the node; It is the set of all nodes in the grid-connected model of large-scale photovoltaic power stations; is the set of all branches, They are the grid-connected side node set and branch set respectively.

[0024] Furthermore, in step S2, the objective function of the lower model is:

[0025]

[0026] The constraints of the lower model include the lower collector line power flow constraint, PV unit capacity constraint and PV droop control of PV units;

[0027] The power flow constraint of the lower collector line is:

[0028]

[0029] Where: 1,l,i,j and λ2,r,t is the Lagrange multiplier corresponding to the collector line power flow constraint; is the set of branches within the station; the active power injection constraint of the node is:

[0030]

[0031] Where: 3,i Inject the Lagrange multiplier corresponding to the active power constraint into the node;

[0032] The photovoltaic unit capacity constraint is:

[0033]

[0034] Where: is the Lagrange multiplier corresponding to the inequality constraint;

[0035] The active power processing of the photovoltaic unit in the PV droop control satisfies the following formula:

[0036]

[0037] Where: is the active power output of the photovoltaic unit corresponding to the saturation zone and dead zone, k i is the droop slope of the droop zone, are the upper and lower limits of the voltage in the droop region; is the Lagrange multiplier corresponding to the inequality constraint.

[0038] Furthermore, the large M scaling method is used to process the QV droop control of the photovoltaic unit to obtain:

[0039]

[0040] Among them, the voltage condition is:

[0041]

[0042] In the formula, ε is a small constant, is a binary variable, an auxiliary variable They are bilinear terms

[0043] Furthermore, the large M scaling method is used to process the PV droop control of the photovoltaic unit to obtain:

[0044]

[0045] Among them, the voltage condition is:

[0046]

[0047] Where: are the Lagrange multipliers corresponding to the inequality constraints.

[0048] Furthermore, in step S3, the KTT conditions include original feasibility conditions, optimality conditions and complementary relaxation conditions;

[0049] The original feasibility condition is the operation constraint of the lower model;

[0050] The optimality condition is formed by performing partial derivative operations on each variable in the lower model according to the Lagrangian function and setting the partial derivatives to zero;

[0051] The complementary relaxation condition is formed by the product of the inequality constraint of the lower model and the corresponding Lagrange multiplier being equal to zero.

[0052] Furthermore, for the nonlinear terms in the complementary relaxation conditions, the Big-M method is used to introduce 0-1 variables for linearization.

[0053] In summary, the photovoltaic power station double-layer optimization method of the present invention has the advantages of low computational burden and strong adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is the grid-connected topology diagram of a large photovoltaic power station.

[0055] Figure 2 Schematic diagram of QV droop control for photovoltaic units.

[0056] Figure 3 Schematic diagram of PV droop control for photovoltaic units.

[0057] Figure 4 Schematic diagram of the solution process.

[0058] Figure 5 Schematic diagram for comparing voltage control effects.

[0059] Figure 6 This is the voltage distribution in scenario 1.

[0060] Figure 7 This is the voltage distribution in scenario 2.

[0061] Figure 8 This is the voltage distribution in scenario 3.

[0062] Figure 9 This is a schematic diagram of the unit power-voltage distribution. DETAILED DESCRIPTION

[0063] The present invention will be further described in detail below with reference to the embodiments.

[0064] Large-scale photovoltaic power stations are characterized by centralized grid connection and long-distance power consumption. They have internal trunk-type collection lines, and the voltage difference between the busbar at the head-end grid connection point and the terminal unit access node is large. Fluctuations in photovoltaic output can easily cause voltage over-limit problems. Therefore, an effective voltage optimization control strategy is required. Traditional centralized control has the disadvantages of heavy computational burden and poor adaptability when dealing with complex problems. To this end, this embodiment proposes a two-layer optimization control strategy for photovoltaic power stations that considers the voltage droop characteristics of the units. The piecewise linearized P / QV droop characteristic constraint is embedded in the voltage control model, and a two-layer optimization model considering two different optimization objectives is established. The upper model optimizes the voltage deviation within the station, and the lower model optimizes the active power output of the photovoltaic units. The Karush-Kuhn-Tucker (KKT) condition is used to transform and solve the model. Finally, the applicability of the proposed control strategy is verified through numerical analysis of a case study.

[0065] Specifically, this embodiment proposes a two-layer optimization control strategy for a large photovoltaic power station that takes into account the P / QV droop characteristics of photovoltaic units. A typical large photovoltaic power station example model is used and different scenarios are set to verify the effectiveness of the proposed control strategy.

[0066] Figure 1 The topology of a large-scale photovoltaic power station system is shown in the figure. As can be seen, a photovoltaic power station consists of multiple photovoltaic power generation units, each composed of a photovoltaic array and an inverter. The output of the photovoltaic power generation units is collected by a combiner box and then connected to a medium-voltage collector line, which typically adopts a radial structure. Multiple collector lines converge and connect to a point of common coupling (PCC) busbar. After being boosted by a booster station, the power is transmitted to the external grid via high-voltage transmission lines. Uncertainty in photovoltaic output can cause random voltage fluctuations. When a large amount of energy is concentrated in the grid, there is a risk of voltage exceeding the limit, affecting the stability and safety of system operation. Therefore, it is necessary to study voltage optimization control strategies that address both safety and economic objectives to ensure the stable operation of photovoltaic power stations.

[0067] Bi-level optimization refers to an optimization problem consisting of two hierarchical systems. Its significance lies in simultaneously considering the interests of both the upper and lower levels. The upper and lower models have their own decision variables, objective functions, and constraints, and are coupled. The upper model makes decisions first, passing the values ​​of its decision variables to the lower model. The lower model determines the feasible region based on the upper-level decision, performs optimization through computational solution, and obtains the optimal value of the objective function. The lower-level optimization results are then fed back to the upper model, and finally, an iterative process yields the optimal solution and its corresponding optimal value. The upper-level problem depends on the optimal solution to the lower-level problem, which is in turn influenced by the decision variables of the upper problem. Bi-level optimization problems are characterized by hierarchy, independence, conflict, priority, and autonomy. When optimizing voltage control for large-scale photovoltaic power plants, the primary considerations are system safety and economic efficiency.

[0068] The optimization model for the upper-level photovoltaic grid-connected system focuses on the overall performance of the photovoltaic grid-connected system, optimizing the economic efficiency and voltage quality of the grid operation. Considering that the uncertainty of photovoltaic output leads to voltage fluctuations within the station, which affects the safety of the system, to prevent the risk of voltage over-limit, reactive power compensation is required to offset the internal voltage fluctuations caused by the fluctuation of photovoltaic active power output. Therefore, the optimization goal of the upper-level photovoltaic grid-connected system optimization model is to minimize the voltage deviation within the station. Its objective function is:

[0069]

[0070] Where: V i is the node voltage amplitude; V ref is the reference voltage; A collection of nodes within the station.

[0071] The constraints of the upper photovoltaic grid-connected system optimization model include the QV droop control of the photovoltaic unit and the upper collector line power flow constraints.

[0072] PV unit QV droop control: PV unit QV droop control curve is as follows Figure 2 , the relationship between the node voltage and reactive output of the unit is given in detail, which can be divided into three working states: saturation zone, droop zone and dead zone. Therefore, the expression of the reactive output of the unit can be obtained as:

[0073]

[0074] Where: The reactive power output of the unit corresponding to the dead zone; The upper and lower limits of the voltage amplitude corresponding to the dead zone; is the left and right droop slope of the droop zone; It is the node set where the photovoltaic unit is located.

[0075] When the unit operates in the drooping area and When the voltage deviation decreases, the reactive power output decreases and enters the dead zone When the unit applies constant reactive compensation, the reactive output is When the voltage reaches the upper and lower limits or exceeds the limit, the unit works in the saturation zone, and the reactive output is Therefore, the reactive output of the unit satisfies:

[0076]

[0077] To process formula (2), we introduce auxiliary variables The construction formula is as follows:

[0078]

[0079] Furthermore, formula (2) can be expressed as a combination of bilinear terms:

[0080]

[0081]

[0082] in, For binary variables, the bilinear term Use auxiliary variables Instead, we can get the following relationship:

[0083]

[0084] Introducing auxiliary variables Processing the bilinear term in Equation (6) And use the large M scaling method to process it as follows:

[0085]

[0086] Similarly, the voltage condition in equation (5b) can be expressed as:

[0087]

[0088] A smaller constant ε is introduced to transform the “<” in equation (5b) into “≤”, satisfying the standard form of the inequality constraint.

[0089] It should be noted that and The constraints should be satisfied:

[0090]

[0091] Where: P PV,i is the active power output of the photovoltaic unit on node i; is the rated capacity of the photovoltaic generator set at node i.

[0092] Distflow constraints on upper-level collector lines: Distflow constraints on branch lines require that the power (including active and reactive power) transmitted by each branch in a power system meet certain constraints to ensure safe and stable operation of the power system. This constraint is often used in optimal power flow problems involving radial topologies. Therefore, it is also applicable to collector lines in large photovoltaic power plants with similar radial topologies. The mathematical expression is:

[0093]

[0094] Where: P li , Q li is the active power and reactive power flowing through branch li; R li 、X li is the resistance and reactance of the branch; k T is the transformer ratio on the branch; P i , Q i Inject active power and reactive power into the node; It is the set of all nodes in the grid-connected model of large-scale photovoltaic power stations; is the set of all branches.

[0095] Now we need to linearize the Distflow model shown in Equation (10) and express the optimization model as a linear programming (LP) problem, which can be better solved by existing optimization algorithms. Considering that in actual operation, the power loss on the transmission line of a large photovoltaic power station is much smaller than the total power output of the photovoltaic unit, the power loss part in Equation (10), that is, the quadratic part, can be ignored. At the same time, the voltage fluctuation range allowed within the photovoltaic power station is between [0.95 1.05] pu, and most branches do not have transformers, so k T is 1, it can be approximately considered that k T V i ≈1, V l +(k T V i )≈2. Finally, the linearized Distflow model is as follows:

[0096]

[0097] Among them, the node injected reactive power and voltage amplitude satisfy the following relationship:

[0098]

[0099] Where: Q PV,i is the reactive power output of the photovoltaic unit on node i; V i maxand V i min Vmaxiand Vminiare the upper and lower limits of voltage amplitude of node i.

[0100] In addition, for the linearized Distflow model shown in equation (11), the branch active power loss can be approximated as When the branch contains a transformer, the bilinear term k T V i exists for equation (11) and needs to be handled. Let k T take values in the set {K1, K2, …, K n}, and introduce binary variable b k , the following relationship can be obtained:

[0101]

[0102] Introduce auxiliary variable σ k , and then through the big M relaxation method, the constraint can be constructed:

[0103]

[0104] In the formula: M is a large enough constant.

[0105] According to the difference of upper and lower layer decision variables, the collection line power flow constraints need to be processed in layers. The upper layer collection line power flow constraint is:

[0106]

[0107] Where, is the set of nodes and branches on the grid side, V u and V v are the voltages of nodes u and v, P uv , Q uv , R uv and X uv are the active power, reactive power, resistance and reactance of branch uv, respectively.

[0108] The objective function of the lower layer photovoltaic unit optimization operation model: the lower layer problem focuses on the operation of photovoltaic units. By reasonably adjusting the voltage droop characteristic of the unit, the unit output more active power as much as possible while making the photovoltaic unit meet the voltage droop characteristic, so as to improve its power generation efficiency and utilization. Therefore, the optimization goal is:

[0109]

[0110] The constraint conditions of the lower layer photovoltaic unit optimization operation model include the lower layer collection line power flow constraint, photovoltaic unit capacity constraint and photovoltaic unit P-V droop control.

[0111] Lower collector line power flow constraint: According to the linearized Distflow model and the difference between the upper and lower decision variables, in addition, there is no transformer branch on the collector side, k T is 1, the power flow constraint of the lower collector line is:

[0112]

[0113] Where: 1,l,i,j and λ 2,r,t is the Lagrange multiplier corresponding to the collector line power flow constraint; is the set of branches within the station. At the same time, the active power injected by the node satisfies:

[0114]

[0115] Where: 3,i The Lagrange multiplier corresponding to the active power constraint (19) injected into the node.

[0116] PV unit capacity constraints: PV power station generators use constant power control, replaced by equivalent PQ nodes, without considering the impact within the PV inverter access point. The output reference power value is calculated using the voltage optimization control model and meets the unit capacity constraints. In addition, the unit's output active power is limited by maximum power point tracking (MPPT). Therefore, the unit's active and reactive output limits can be determined by the following constraints:

[0117]

[0118] Where: is the MPPT power of the photovoltaic generator set at node i; is the Lagrange multiplier corresponding to the inequality constraint in equation (20).

[0119] The capacity constraint (21) can be understood as the size of a complex-valued function, which can be expressed as:

[0120]

[0121] Assume P PV,i and Q PV,i are all controllable, then (21) is a non-convex constraint. It can be approximated by constructing a series of linear inequalities for the real and imaginary parts through the polyhedron norm. Here, multi-vertex polygons (k = 16, 32, etc.) are used for convexification and approximation:

[0122]

[0123] Where: is the Lagrange multiplier corresponding to the inequality constraint in equation (23).

[0124] PV droop control of photovoltaic units: The PV droop control curve of photovoltaic units is as follows: Figure 3 , similar to QV droop control, the operating state can also be divided into saturation zone, droop zone and dead zone. Therefore, the expression of the unit active output can be obtained as:

[0125]

[0126] Where: is the active power output of the photovoltaic unit corresponding to the saturation zone and dead zone, k i is the droop slope of the droop zone, are the upper and lower limits of the voltage in the droop region.

[0127] When the unit voltage operates in the saturation region When the unit output active power is saturated When the voltage is in the droop region When the active power output of the unit gradually decreases until the voltage reaches the dead zone After that, the unit output active power is minimum.

[0128] In addition, in order to achieve the goal of taking into account the voltage deviation within the station and making the unit's active output as large as possible, the unit's active output should be greater than the minimum active power Even reaching the maximum power tracking point Therefore, the active power output of the unit satisfies:

[0129]

[0130] Where: is the Lagrange multiplier corresponding to the inequality constraint in equation (25).

[0131] Depend on Figure 3 The PV droop control curve can be used to obtain the active power output in the saturation zone. Similarly, the auxiliary variable is introduced The PV droop control relationship is expressed as:

[0132]

[0133] Where: 4,i ,λ 5,i ,λ 6,i are the Lagrange multipliers corresponding to the constraints in equation (26).

[0134] By introducing binary variables The active output can be expressed as:

[0135]

[0136]

[0137] Where: 7,i,n is the Lagrange multiplier corresponding to the constraint in equation (27a).

[0138] Further introduction of variables Handling bilinear terms At the same time, the auxiliary variable δ is introduced i ,make When is 0, the inequality constraint still holds, and the following formula can be obtained:

[0139]

[0140] Under extreme voltage regulation conditions, individual units must fully output reactive power, and active power output may drop to zero. Can be set to zero. Introduce auxiliary variables Processing the bilinear term in Equation (28) Therefore, formula (28) can be expressed as:

[0141]

[0142] Where: is the Lagrange multiplier corresponding to the inequality constraint in equation (29).

[0143] Further processing by the large M scaling method yields the following formula:

[0144]

[0145] Where: is the Lagrange multiplier corresponding to the inequality constraints in equations (30a) and (30b).

[0146] Similarly, the voltage condition in equation (27b) can be expressed as:

[0147]

[0148] Where: is the Lagrange multiplier corresponding to the inequality constraints in Equations (31a) to (31c).

[0149] Bi-level optimization problem usually involves complex non-convex constraints, and there are interrelated decision variables between upper level and lower level. Therefore, the solution methods are also different. Common methods include intelligent optimization algorithm and transformation into a single optimization problem. When intelligent optimization algorithm is used to solve bi-level optimization problem, there are problems such as complex solving process, easy to fall into local optimum and greatly affected by parameter setting. According to the structure of bi-level optimization model and transformation method, the upper level variable can be considered as the parameter of the lower level problem. For a given variable, the lower level problem is a linear optimization problem, which is continuous and convex in structure. Therefore, this paper transforms the lower level model through KKT (Karush-Kuhn-Tucker) condition, so as to convert the bi-level model into a single level model for solving.

[0150] The solving process is shown in Figure 4 First, the Lagrangian function of the lower level optimization model is constructed, and the KKT condition is listed. Then, the KKT condition of the lower level optimization model is added to the upper level optimization problem as a constraint condition, so as to transform it into a single level nonlinear model. For the nonlinear term in the single level nonlinear model, the big M method can be used for linearization processing, and finally a single level mixed integer linear programming problem is formed, which is solved by the solver.

[0151] Lower level model transformation: for the lower level model, the KKT condition is listed, which includes the original feasibility condition, optimality condition and complementary relaxation condition.

[0152] The original feasibility condition is the equality and inequality constraint condition related to the original lower level model, that is, equations (18)-(31c) still hold.

[0153] Optimality condition: according to the KKT condition, the derivative of the lower level model is 0 at the extreme point. Therefore, according to the objective function and constraint condition of the lower level model, the Lagrangian function is constructed, and then the derivative of each variable involved in the lower level model is obtained to get the optimality condition.

[0154] Complementary relaxation condition: the complementary relaxation constraint is constructed according to the inequality constraint of the lower level model and the corresponding Lagrange multiplier.

[0155] The steps for determining the optimality condition and the complementary relaxation condition are as follows: first, construct the Lagrangian function of the lower level model.

[0156]

[0157] Take the derivative of each variable to get the optimality condition as follows:

[0158]

[0159]

[0160] It is particularly important to note that in the lower level power flow constraint, P li is the active power of the entire photovoltaic system branch, which includes the active power P of the branch on the collector side of the station rt Therefore, the derivative of the active power of the branch on the collector side of the station is:

[0161]

[0162] In addition, for the variable V r 、V t 、V i , the derivative needs to be calculated according to different situations.

[0163] When the derivative of the first-end node voltage V1 is taken:

[0164]

[0165] The voltage at the end node V e When taking the derivative:

[0166]

[0167] For other node voltages V i When taking the derivative:

[0168]

[0169] The complementary relaxation conditions constructed are:

[0170]

[0171]

[0172] Here, for the formula “0≤a⊥b≥0”, it can be expressed as a≥0, b≥0 and ab=0.

[0173] After obtaining the KKT conditions of the lower-layer model, they are added to the upper-layer optimization problem as additional constraints, thereby converting the two-layer model into a single-layer model.

[0174] Linearization of single-layer problems: When using KKT conditions for single-layer transformation, there are nonlinear terms in the complementary relaxation conditions introduced in the constraints, that is, there are nonlinear terms in Equations (17F) to (42F). The Big-M method can be used to linearize them by introducing several 0-1 variables.

[0175] Taking Equation (17F) as an example, there are bilinear terms in the form of multiplication of variables and Lagrange multipliers. The linearization process transforms it into:

[0176]

[0177] Where: M is a sufficiently large constant, and ν is a 0-1 variable.

[0178] The complementary slack conditions (18F) to (42F) are similar to the linearization process of Equation (17F). This process effectively linearizes the nonlinear terms in the lower-level model after the KKT transformation, thereby transforming the two-level optimization programming model into a single-level mixed-integer linear program, which can be effectively solved using commercial solvers such as GUROBI.

[0179] Case Analysis: The example parameters for a photovoltaic power plant, as shown in Table 1, were selected for analysis to verify the effectiveness of the two-tier optimization control strategy for large-scale photovoltaic power plants. The photovoltaic power plant is equipped with three identical collector lines, each connected to 12 photovoltaic generators with a rated power of 2 MW. The collector lines are connected to the main power grid via long-distance high-voltage transmission lines. The on-load tap regulator (OLTC) on the grid side has 17 tap positions and a voltage regulation range of ±1.25% × 8. The simulation model was built in the YALMIP environment on the MATLAB platform, and the mixed integer optimization problem was solved using the GUROBI solver.

[0180] Table 1 Parameters of photovoltaic power station example

[0181]

[0182] By changing the maximum power point tracking power, three different scenarios are set as follows: Scenario 1: 1.2MW; Scenario 2: 1.6MW; Scenario 3: 1.8MW.

[0183] Comparison of Optimization Control Strategies: For the optimization of large-scale photovoltaic power plants, traditional control strategies often assume that the active output of the unit is achieved at the maximum power output point and that the reactive output is adjusted within the unit's available reactive power range to optimize system operation. This strategy is overly idealistic and has limitations. It fails to consider the relationship between the unit's export power and voltage, assuming that the unit is always operating at full capacity. Therefore, by introducing the unit's voltage droop characteristic, it fully considers the unit's available capacity and the power and voltage distribution relationship at the unit's ports, making it more applicable.

[0184] The centralized optimization control strategy is a single-level global optimization, which regards the system as a whole and solves the global optimal solution directly through mathematical model in the same optimization model. The double-layer optimization control strategy is a hierarchical decision structure, which processes the single optimization problem in layers and realizes the multi-objective coordinated optimization through principal-agent game. Assuming that the active and reactive capacity of each unit in the photovoltaic power station is sufficient, this paper optimizes the photovoltaic power station considering the voltage droop characteristics of the unit by using the centralized optimization control and the double-layer optimization control strategies. To verify the effectiveness of the double-layer optimization strategy, it is compared with the centralized optimization strategy. Under the centralized optimization strategy, different optimization target weights are set as shown in Table 2:

[0185] Table 2 Centralized optimization target weights

[0186]

[0187] The optimization results of the centralized optimization and double-layer optimization strategies are analyzed for different scenarios. Tables 3-5 show the active power output optimization results and the maximum and minimum node voltage amplitude of the centralized optimization and double-layer optimization strategies with different weights under three different scenarios. It can be seen that under the centralized optimization strategy, the setting of the optimization target weight has a great influence on the optimization results. When the optimization target weight is biased towards voltage deviation, the voltage control effect is very good, while the active power output effect is poor. Similarly, when the weight is biased towards active power output, the active power output effect is good, and the voltage control effect is poor. This is the disadvantage of handling multi-objective optimization problems under the centralized control framework, which is strongly subjective and lacks objectivity. The weight distribution depends on the subjective judgment or experience knowledge of the decision maker, and the randomness is too strong, making it difficult to quantify the actual importance of different objectives. While the double-layer optimization strategy handles multi-objective optimization problems, it processes the optimization problem in layers. The upper layer optimizes globally to provide a stable operation framework for the lower layer, and each unit adjusts dynamically based on the upper layer optimization variables. Under the voltage safety constraint, the active power output is improved, and the influence of the weight is not considered, which can better balance the optimization objectives.

[0188] Table 3 Optimization results of scenario 1

[0189]

[0190] Table 4 Optimization results of scenario 2

[0191]

[0192] Table 5 Optimization results of scenario 3

[0193]

[0194] Further analysis is conducted based on the specific node optimization effect diagrams of the two strategies. Taking scenario 3 as an example, the voltage control effects of the centralized optimization and double-layer optimization strategies under different weights are compared. Figure 5 As shown in Figure 2 , the node voltage distributions under the two strategies show a significant difference in the performance of centralized optimization when weights 2 and 3 are used, indicating that the weight of the optimization objective has a significant impact. When centralized optimization control uses weight 1 for optimization, the optimization objectives are more balanced. In this case, the voltage deviation of the two-tier optimization is slightly larger than that of centralized optimization, but still within a safe range. Centralized optimization, through regulation by a central controller, focuses more on global voltage deviation, enabling more efficient coordination of OLTC adjustment and PV droop control, achieving global synergy and minimizing voltage deviation. However, two-tier optimization, in hierarchical control, prioritizes local voltage uniformity, sacrificing some voltage regulation performance. This adjustment improves active power output, achieving a reasonable allocation of reactive resources while increasing active power output. Due to its hierarchical structure, complex duality processing, and potential conflicting objectives, two-tier optimization is subject to hierarchical constraints. When optimizing multiple objectives simultaneously, it is necessary to balance the game between objectives.

[0195] Optimization Results Analysis: To analyze the optimization situation, reactive power compensation was not performed, and the reactive power output of each unit was set to 0 MVar. Tables 6 through 8 show the voltage deviation and active power output optimization results for three different scenarios, using a two-tier optimization strategy and without reactive power compensation. It can be seen that the two-tier optimization control achieves reactive power compensation without sacrificing active power output, and achieves an increase in active power output while optimizing voltage, effectively balancing system safety and economic efficiency.

[0196] Table 6 Optimization results of scenario 1

[0197]

[0198] Table 7 Optimization results of scenario 2

[0199]

[0200] Table 8 Optimization results of scenario 3

[0201]

[0202] Figures 6 to 8 The results show line voltages under three scenarios, using two-tier optimization for voltage control and without reactive power compensation. The figures show that without reactive power compensation, the voltage distribution fluctuates significantly, with node voltages close to the safe voltage range. The two-tier optimization strategy achieves a more uniform voltage distribution, with node voltages within the range of [0.986, 1.02] pu, validating the strategy's ability to globally optimize intra-station voltage deviations.

[0203] Figure 9 The figure shows the P / QV distribution of the units after voltage droop control under the two strategies. The blue line represents the droop control characteristic curve, the blue scattered points represent the unit output under the centralized optimization strategy, and the red scattered points represent the unit output under the dual-tier optimization strategy. As can be seen from the figure, under both strategies, the unit's active output mostly operates in the saturation zone, outputting as much active power as possible, while the unit's reactive output is mostly distributed near the dead zone, demonstrating good optimization control results.

[0204] This paper proposes a two-tier optimization strategy for large-scale photovoltaic power plant operations that considers the voltage droop characteristics of the generator units. This strategy addresses the optimization problem at both the system safety and the economic efficiency of the generator units. The two-tier optimization model is transformed into a mixed-integer linear programming problem using KKT conditions and the Big-M method. A case study is presented, comparing this strategy with a centralized optimization control strategy and a scenario without reactive power compensation.

[0205] Case studies show that when dealing with multi-objective optimization problems, two-layer optimization control effectively addresses the drawbacks of centralized control, which suffers from the human intervention of weight dependence and lacks adaptability in dynamic environments. This approach addresses multi-objective problems in a hierarchical manner, enabling dynamic interaction through hierarchical decoupling of upper and lower-level problems. In particular, for uncertain scenarios such as photovoltaic output, two-layer optimization control exhibits strong adaptability, reducing line active power losses and increasing unit active power output while ensuring the operational safety of the photovoltaic power station. Its advantage lies in the combination of a hierarchical control structure and droop characteristics: the upper-layer model globally optimizes voltage, while the lower-layer model dynamically adjusts unit power based on the droop characteristics, achieving global and local coordinated optimization, thereby achieving coordinated optimization of safety and economy. This strategy provides an efficient and feasible solution for voltage control in large-scale photovoltaic power stations.

[0206] The above description is only a preferred embodiment of the present invention and does not limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A two-layer optimization method for photovoltaic power stations considering the voltage droop characteristics of the units, characterized in that: The steps include: S1. Establish a photovoltaic power station model, including multiple photovoltaic power generation units consisting of photovoltaic arrays and inverters. The photovoltaic power generation units are connected to the common connection point bus through medium-voltage collector lines and connected to the power grid through a booster station; S2. Construct a two-layer optimization model for the photovoltaic power station. The upper layer model aims to optimize the operating voltage of the power station by adjusting the reactive power output of the photovoltaic units to reduce the voltage deviation within the station. The lower layer model aims to optimize the active power output of the units by adjusting the voltage droop characteristics of the photovoltaic units to improve the active power utilization rate. S3. Based on the two-layer optimization model, construct the Lagrangian function of the lower model, write the KTT conditions, use the KKT conditions of the lower model as the constraints of the upper model, and convert the two-layer optimization model into a single-layer optimization model for solution.

2. The double-layer optimization method for a photovoltaic power station considering the voltage droop characteristics of a generator set according to claim 1, characterized in that: In step S2, the objective function of the upper model is: Where: V i is the node voltage amplitude; V ref is the reference voltage; is the set of nodes within the station; The constraints of the upper model include the QV droop control of the PV unit and the power flow constraints of the upper collector line; The reactive output of the photovoltaic unit in the QV droop control satisfies the following formula: Where: The reactive power output of the unit corresponding to the dead zone; The upper and lower limits of the voltage amplitude corresponding to the dead zone; is the left and right droop slope of the droop zone; is the node set where the photovoltaic unit is located; It is the reactive power output of the unit when it is working in the saturation zone. and Satisfy the constraints: Where: P PV,i is the active power output of the photovoltaic unit on node i; is the rated capacity of the photovoltaic generator set at node i; The upper collector line power flow constraint is: Where: Q li is the reactive power flowing through branch li; R li 、X li is the resistance and reactance of the branch; k T is the transformer ratio on the branch; Q i Inject reactive power into the node; It is the set of all nodes in the grid-connected model of large-scale photovoltaic power stations; is the set of all branches, They are the grid-connected side node set and branch set respectively.

3. The double-layer optimization method for a photovoltaic power station considering the voltage droop characteristics of a generator set according to claim 2, characterized in that: In step S2, the objective function of the lower model is: The constraints of the lower model include the lower collector line power flow constraint, PV unit capacity constraint and PV droop control of PV units; The power flow constraint of the lower collector line is: Where: 1,l,i,j and λ 2,r,t is the Lagrange multiplier corresponding to the collector line power flow constraint; is the set of branches within the station; the active power injection constraint of the node is: Where: 3,i Inject the Lagrange multiplier corresponding to the active power constraint into the node; The photovoltaic unit capacity constraint is: Where: is the Lagrange multiplier corresponding to the inequality constraint; The active power processing of the photovoltaic unit in the PV droop control satisfies the following formula: Where: is the active power output of the photovoltaic unit corresponding to the saturation zone and dead zone, k i is the droop slope of the droop zone, are the upper and lower limits of the voltage in the droop region; is the Lagrange multiplier corresponding to the inequality constraint.

4. The double-layer optimization method for a photovoltaic power station considering the voltage droop characteristics of a generator set according to claim 3, characterized in that: The large M scaling method is used to process the QV droop control of the photovoltaic unit to obtain: Among them, the voltage condition is: In the formula, ε is a small constant, is a binary variable, an auxiliary variable They are bilinear terms 5. The double-layer optimization method for a photovoltaic power station considering the voltage droop characteristics of a generator set according to claim 3, characterized in that: The large M scaling method is used to process the PV droop control of the photovoltaic unit to obtain: Among them, the voltage condition is: Where: are the Lagrange multipliers corresponding to the inequality constraints.

6. The double-layer optimization method for a photovoltaic power station considering the voltage droop characteristics of a generator set according to claim 1, characterized in that: In step S3, the KTT conditions include original feasibility conditions, optimality conditions and complementary relaxation conditions; The original feasibility condition is the operation constraint of the lower model; The optimality condition is formed by performing partial derivative operations on each variable in the lower model according to the Lagrangian function and setting the partial derivatives equal to zero; The complementary relaxation condition is formed by the product of the inequality constraint of the lower model and the corresponding Lagrange multiplier being equal to zero.

7. The double-layer optimization method for a photovoltaic power station considering the voltage droop characteristics of a generator set according to claim 6, characterized in that: For the nonlinear terms in the complementary relaxation conditions, the Big-M method is used to introduce 0-1 variables for linearization.

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