Microgrid voltage control method considering price-type demand response and inverter droop parameter optimization

Abstract

This invention discloses a microgrid voltage control method considering price-based demand response and inverter droop parameter optimization, comprising: a first stage of establishing a day-ahead microgrid voltage control model considering price-based demand response, and solving it using a multi-scenario stochastic optimization method to obtain the hourly electricity price within the microgrid on the second day and the microgrid load forecast curve after the response; a second stage of establishing an intraday microgrid hierarchical coordination model considering dynamic optimization of the reactive power-voltage (Q-V) droop parameter of the photovoltaic inverter; for the nonlinear constraints in the intraday microgrid hierarchical coordination model, a model transformation and reconstruction and a fast solution algorithm based on convex-concave processes are proposed to obtain the reactive power output reference point and Q-V droop curve of the inverter for each scheduling period, and send them to the photovoltaic inverter; a third stage of establishing a real-time control model for the photovoltaic inverter, and adjusting the reactive power output of the inverter in real time according to local real-time voltage measurement information and the optimized Q-V droop curve.

Description

Technical Field

[0001] This invention belongs to the field of power distribution networks, and specifically relates to a microgrid voltage control method that considers price-based demand response and inverter droop parameter optimization. Background Technology

[0002] With the widespread integration of distributed photovoltaic (PV) power into microgrids, the mismatch between its output curve characteristics and microgrid load demand has become increasingly prominent, posing a serious challenge to the microgrid's absorption capacity. Furthermore, the randomness and intermittency of distributed PV output inevitably cause random fluctuations in distribution network voltage and power flow, affecting the safe and stable operation of the system. Traditional solutions involve upgrading the infrastructure and reducing excess PV power generation when operational constraints are exceeded. However, these methods often involve large investments and have low return on investment, resulting in poor economic efficiency.

[0003] To address the aforementioned issues, voltage / reactive power control (VVC) is an economical and effective measure to reduce grid losses and regulate node voltage. However, traditional mechanical VVC resources (such as transformer on-load tap changers and capacitor banks) suffer from discontinuous operation, limited installation quantity, and inability to respond promptly to voltage fluctuations, severely impacting the effectiveness of microgrid regulation. Currently, with the widespread adoption of distributed photovoltaic (PV) power generation, PV inverters possess rapid and continuous reactive power regulation capabilities, making them an effective VVC regulation method. Considering that PV inverters generally have a certain degree of over-limit design, they can generate additional reactive power to participate in regulation during their rated active power output. Currently, the IEEE Standards 1547 working group has developed relevant standards to provide recommendations for VVC strategies for PV inverters.

[0004] Generally speaking, VVC methods can be divided into two types: central control and local control. Central control optimizes the operation of VVC resources by using global information such as network parameters, photovoltaic power generation forecasts, and load demand; local control responds to local measurements (such as node voltage) based on the built-in control strategies of the VVC devices. In recent years, how to optimize local droop curve parameters while realizing central VVC decision-making to achieve coordinated control of central and local VVC has become a research hotspot. However, the current modeling and solving of the inverter linear droop control curve are still insufficient and cannot meet the requirements of coordinated control. Therefore, it is necessary to effectively model the inverter droop control strategy and study a more effective method to solve its parameters.

[0005] Furthermore, active power also has a significant impact on voltage distribution in microgrids. Price-based demand response (PBDR) is a typical demand response mechanism that aims to encourage users to adjust and shift their electricity load by setting different tiered electricity prices. This can effectively achieve load balancing and peak shaving without significantly increasing system operating costs. However, existing PBDR-related work mostly focuses on operating costs and does not consider the linkage with grid voltage control. In addition, to allow users sufficient time to react, PBDR prices usually need to be planned and released one day in advance, while inverter reactive power output is optimized and regulated with a shorter dispatch cycle. Since PBDR and inverter regulation timescales are different, it is necessary to study a new multi-stage hierarchical coordinated dispatch framework based on their different characteristics to achieve coordinated dispatch of PBDR and voltage control. Summary of the Invention

[0006] Purpose of the invention: This invention proposes a microgrid voltage control method that considers price-based demand response and inverter droop parameter optimization. It fully models the parameters of the inverter's linear droop control function and provides a multi-stage hierarchical framework for microgrid operation to coordinate PBDR and inverter voltage control.

[0007] Technical Solution: To achieve the above-mentioned objectives, this invention proposes a microgrid voltage control method that considers price-based demand response and inverter droop parameter optimization, comprising the following steps:

[0008] Step 1: Establish a day-ahead microgrid voltage control model that considers price-based demand response (PBDR), and solve it using a multi-scenario stochastic optimization method to obtain the hourly electricity price within the microgrid on the second day and the microgrid load forecast curve after the response update.

[0009] Step 2: Based on the hourly electricity price and the updated microgrid load curve, establish an intraday microgrid hierarchical coordination model that considers dynamic optimization of the reactive power-voltage QV droop parameter of the photovoltaic inverter.

[0010] Step 3: For the nonlinear constraints in the intraday microgrid hierarchical coordination model, convert them into a linear problem and use a fast solution algorithm based on convex and concave processes to obtain the reactive power output reference point and QV droop curve of the inverter for each scheduling period, and send them to the photovoltaic inverter.

[0011] Step 4: The photovoltaic inverter adjusts the reactive power output in real time based on local real-time voltage measurement information and the optimized QV droop curve.

[0012] Furthermore, in step 1, the steps for establishing the day-ahead microgrid voltage control model considering price-based demand response include:

[0013] (1.1) Construct a demand response model based on electricity price, where the electricity price Pr and the load demand P are related. LD The relationship between them is represented as follows:

[0014] P LD =C·Pr ε (twenty four)

[0015] Where C is a coefficient, and ε is the price elasticity coefficient of load demand;

[0016] (1.2) Based on equation (1), design multiple tiered electricity prices and construct active and reactive power models for PBDR loads:

[0017]

[0018]

[0019] in These represent the active and reactive power of the microgrid load after the implementation of PBDR tiered pricing; These represent the active and reactive power of the microgrid load before the implementation of PBDR tiered pricing, and include its uncertainties; α l,t For PBDR tiered electricity pricing, use binary decision variables; L l Let L be the demand response rate at electricity price level l; L is the set of electricity price levels; t represents the hourly time index in the day-ahead period.

[0020] (1.3) The constraints for implementing PBDR are given:

[0021]

[0022]

[0023]

[0024]

[0025] Where τ is the electricity price time period; Pr l,t For different electricity price levels of PBDR, Pr0 is the original electricity price before PBDR was implemented; I is the set of microgrid nodes; and T is the set of time indices.

[0026] (1.4) To minimize the microgrid's network losses and node voltage deviations, a day-ahead microgrid voltage control model considering electricity price-based demand response is established:

[0027]

[0028] st(2)-(7)

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] Where ω is the weighting factor. For the active power loss of branch ij, V t dev The average voltage deviation at the nodes. This represents the maximum reactive power generated by the inverter during time period t at node i. Considering the uncertainties in the active power generation of photovoltaics at node i during time period t. P represents the reactive power output of the inverter during time period t at node i. ij,t Q ij,t P represents the active and reactive power passing through branch ij during time period t. hi,t Q hi,t These represent the active and reactive power passing through branch hi during time period t, respectively. Let H(i) be the maximum capacity of branch ij, H(i) be the set of parent nodes of node i, J(i) be the set of child nodes of node i, N be the total number of nodes, and V be the maximum capacity of branch ij. i,t V j,t Let Vi be the voltages at nodes i and j, respectively, and V0 be the reference voltage at the root node. i,j x i,j The resistance and reactance between branches ij are respectively, V min V max These define the minimum and maximum voltage values ​​for the nodes, respectively.

[0038] (1.5) Linearize the constraints and combine the day-ahead microgrid voltage control model (2)-(16) considering electricity price demand response into a mixed integer quadratic programming problem, with the decision variable being α. l,t and Uncertain variables include photovoltaic power generation output and microgrid load

[0039] Furthermore, linearizing the constraints includes:

[0040] For the absolute value in formula (13), by introducing the slack variable C, the absolute value expression |AB| is linearized, which is re-expressed as C≥AB and C≥BA, and the objective function will minimize C;

[0041] The quadratic inequality in formula (16) is linearized using the polygonal approximation method, and the feasible region formed by active power and reactive power is approximated by a regular polygon.

[0042] Furthermore, in step 1, the stochastic optimization solution method based on multiple scenarios specifically includes:

[0043] To address the uncertainties in photovoltaic power generation output and load, a sample averaging approximation method is used to represent the probability of the generated scenarios, and a stochastic model for day-ahead microgrid voltage control is constructed:

[0044]

[0045]

[0046]

[0047] In model (17), x represents the day-ahead decision variable α. l,t y s Indicates intraday decision variables, including those under scenario s. Other dependent variables, S represents the set of generated scenarios, D and E are the coefficient matrices of the day-ahead and intraday decision variables in the microgrid voltage control stochastic model, respectively. After solving model (17), only the day-ahead decision variable α l,t It was determined, and The system will be re-optimized based on more accurate forecasts during the intraday phase.

[0048] After determining the decision variable α l,t After finding the optimal value, the microgrid load curve is updated based on equations (2) and (3) and passed to the next stage for optimization in the intraday stage.

[0049] Furthermore, in step 2, the specific construction steps of the intraday microgrid hierarchical coordination model considering the dynamic optimization of the reactive power-voltage QV droop parameter of the photovoltaic inverter are as follows:

[0050] (2.1) Construct an inverter reactive power output model based on a linear droop control function:

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] The subscript t represents the time interval index within each scheduling period of the intraday phase. V is the inverter reactive power setpoint. i exp Let β be the expected value of the node voltage. i For the binary decision of the slope of the sag curve, if β i If the reactive power is zero, the inverter will produce a constant reactive power. λ i The slope of the sag curve;

[0057] (2.2) An intraday microgrid hierarchical coordination model considering the dynamic optimization of the photovoltaic inverter's QV droop parameter is established, as shown below:

[0058]

[0059] st(2)-(3),(10)-(16),(18)-(22)

[0060] Where B represents the set of branches ij.

[0061] The bilinear term in equation (20) makes the intraday microgrid hierarchical coordination model exhibit nonlinear characteristics.

[0062] Furthermore, in step 3, the transformation of the problem includes:

[0063] (3.1) Ignore the subscript of the variable and use ΔV to represent ΔV. i,t Let ΔQ represent ΔQ i,t The bilinear terms in (20) are transformed into their equivalent form as follows:

[0064] λΔV=ΔQ=z1-z2 (24a)

[0065]

[0066] (3.2) Transform the quadratic equality constraint (24b) into the expression (25), where (25a) is a convex constraint and (25b) is a concave constraint:

[0067]

[0068]

[0069] (3.3) Multiply both sides of (25a) by 4 to reconstruct a second-order cone expression:

[0070]

[0071]

[0072] (3.4) Relax the concave constraint (25b) and add a McCormick envelope to tighten the relaxation range, as shown below:

[0073] ΔQ≥ λ ΔV+λ ΔV - λΔV (27a)

[0074]

[0075]

[0076]

[0077] in λ , These represent the lower and upper bounds of the slope of the sag curve, respectively. ΔV These represent the lower and upper bounds of the node voltage offset, respectively.

[0078] By replacing (20) with (24a), (26) and (27), the original nonlinear problem is transformed into a second-order cone relaxation SOCR model, which provides a lower bound for the original problem.

[0079] (3.5) The SOCR model is transformed into a penalized convex-concave model by convexifying the concave constraint of (25b):

[0080] minf0(x)-g0(x) (28)

[0081]

[0082] Where x is the decision variable, f i and g i It is a convex function, -g i (x) is a concave function, and f0(x) and g0(x) are the objective functions in a convex programming problem. Replacing the concave function terms with a convex upper bound transforms the original problem into the following:

[0083] minf0(x)-g0′(x,x k* (29)

[0084]

[0085]

[0086] Where k represents the iteration exponent, g i ′(x,x k* ) is g i (x) in the current solution x k* The linearized function at point g can be regarded as g i The tangent plane of (x), g0′(x,x) k* ) is g0(x) in the current solution x k* The linearized function at the point can be regarded as the tangent plane of g0(x). The solution is obtained by iteratively solving the linearized model (29).

[0087] Furthermore, in step 3, the specific processing steps of the fast solution algorithm based on the convex-concave process CCP are as follows:

[0088] Following the form of (29), the concave constraint (25b) is re-expressed as z 1 / 2 and g 1 / 2 The difference between ′(λ,ΔV) is shown below:

[0089] z1-g1′(λ,ΔV)≤0 (30a)

[0090]

[0091] z²-g²′(λ,ΔV)≤0 (30c)

[0092]

[0093] To reduce relaxation error, relaxation variables s1 and s2 are introduced to represent the difference, as shown below:

[0094] z1-g1′(λ,ΔV)≤s1,s1≥0 (31a)

[0095] z2-g2′(λ,ΔV)≤s2,s2≥0 (31b)

[0096] By adding slack variables as penalty terms to the objective function to tighten the slack error, an intraday microgrid hierarchical coordination penalty convex-concave model is constructed, where s 1,i,t s 2,i,t Let s1 and s2 represent the slack variables s1 and s2 at node i during time period t, respectively.

[0097]

[0098] (2)-(3),(10)-(16),(18),

[0099] st(19),(21),(22),(24a),(26),

[0100] (27),(30b),(30d),(31)

[0101] Solve the updated model (32) to obtain The results and other decision variables are checked against termination criteria C1 and C2. If they are satisfied, the iteration stops and the solution is output; otherwise, the penalty factor π is updated. k And based on the current solution, a penalty concave-convex model (32) is re-established and the solution is continued.

[0102] Furthermore, the termination criteria C1 and C2 are as follows:

[0103]

[0104]

[0105] in and The preset threshold is used, obj0 is the objective function value obtained by solving, C1 determines the difference between the original objective function (23) between the current iteration and the previous iteration, and C2 checks the sum of the introduced slack variables to ensure equal constraints.

[0106] Furthermore, update the penalty factor π. k The update method is as follows:

[0107] π k+1 =min{μπ k ,π max}

[0108] Where μ is a coefficient used to increase the penalty factor, π max The maximum value of the pre-set penalty factor.

[0109] Furthermore, in step 4, the photovoltaic inverter adjusts its reactive power output in real time based on local real-time voltage measurement information and the optimized QV droop curve. The specific adjustment method is as follows:

[0110] Based on the reactive power setting benchmark of the photovoltaic inverter obtained in step 3 Node expected voltage V i exp and the slope parameter λ of the droop curve i The droop control curve of each inverter in the current time period is updated locally. Based on the droop control curve, each photovoltaic inverter is controlled according to the actual local voltage deviation.

[0111] Beneficial effects:

[0112] (1) This invention establishes a three-stage hierarchical coordinated voltage control framework for microgrids, which coordinates the active power regulation of price-based demand response with traditional voltage / reactive power control in multiple stages, multiple time scales and multiple levels, and optimizes the local droop control parameters of the inverter from the central layer of the microgrid system, thereby minimizing the network loss and node voltage deviation of the microgrid operation, and alleviating the impact of the supply and demand mismatch between renewable energy output and load in the microgrid and the uncertainty of renewable energy output.

[0113] (2) This invention proposes a model transformation and reconstruction and a fast solution algorithm based on the convex-concave process, which meets the fast solution requirements of intraday short-cycle scheduling and efficiently obtains the inverter reactive power output reference point and QV droop curve. Attached Figure Description

[0114] Figure 1 This is a diagram of the three-stage hierarchical coordinated voltage / reactive power control framework supported by PBDR in this invention.

[0115] Figure 2 This is a diagram showing the day-ahead PBDR results and expected load demand response in this invention;

[0116] Figure 3 This is a graph of the linear droop control curve in this invention;

[0117] Figure 4 This is a diagram illustrating the solution process of the CCP-based solution algorithm in this invention.

[0118] Figure 5 This is droop control curve A of the PV inverter with set value in this invention;

[0119] Figure 6 This is Graph B, showing the droop control curve of the PV inverter with a set value in this invention. Detailed Implementation

[0120] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0121] This embodiment discloses a three-stage hierarchical coordinated voltage control method for microgrids based on electricity price demand response, the specific framework of which is as follows: Figure 1 As shown, it includes the following steps:

[0122] Step 1:

[0123] A day-ahead microgrid voltage control model considering electricity price-based demand response is established and solved using a multi-scenario stochastic optimization method. The specific process includes:

[0124] (1.1) Construct a demand response model based on electricity price, where the electricity price Pr and the load demand P are related. LD The relationship between them can be represented as:

[0125] PLD =C·Pr ε (1)

[0126] Where C is a coefficient, and ε is the price elasticity coefficient of load demand;

[0127] (1.2) Five tiered electricity prices were designed based on equation (1), as shown in Table 1.

[0128] Table 1. Demand Response Levels Based on Price

[0129]

[0130] (1.3) Based on this tiered electricity pricing, active and reactive power models of PBDR loads can be constructed:

[0131]

[0132]

[0133] in, Active and reactive power of load demand after PBDR implementation; The active and reactive power of the microgrid load before the implementation of PBDR tiered pricing, including its uncertainties, α l,t For PBDR tiered electricity pricing, use binary decision variables; L l Let L be the demand response rate at electricity price level l; L represents the set of electricity price levels; and t represents the hourly time index in the day-ahead phase.

[0134] (1.4) In addition, other operational constraints for implementing PBDR are as follows:

[0135]

[0136]

[0137]

[0138]

[0139] Where τ is the electricity price time period; Pr l,t For different electricity price levels of PBDR; Pr0 is the original electricity price before PBDR was implemented; I is the set of microgrid nodes; T is the set of time indices.

[0140] Equation (4) ensures that only one PBDR electricity price level is activated in each time period; constraint (5) ensures that after the implementation of PBDR tiered pricing, the electricity fee paid by the user cannot be greater than its original electricity fee; constraint (6) indicates that after the implementation of PBDR tiered pricing, the user's overall electricity consumption will not be affected; constraint (7) ensures that after the implementation of PBDR tiered pricing, the microgrid cannot generate new peak loads.

[0141] (1.5) To minimize the microgrid's network losses and node voltage deviations, a day-ahead microgrid voltage control model considering electricity price-based demand response is established:

[0142]

[0143] st(2)-(7)

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152] Where ω is the weighting factor, For the active power loss of branch ij, V t dev The average voltage deviation at the nodes. This represents the maximum reactive power generated by the inverter during time period t at node i. Considering the uncertainties in the active power generation of photovoltaics at node i during time period t. P represents the reactive power output of the inverter during time period t at node i. ij,t Q ij,t P represents the active and reactive power passing through branch ij during time period t. hi,t Q hi,t These represent the active and reactive power passing through branch hi during time period t, respectively. Let H(i) be the maximum capacity of branch ij, H(i) be the set of parent nodes of node i, J(i) be the set of child nodes of node i, N be the total number of nodes, and V be the maximum capacity of branch ij. i,t V j,tLet Vi be the voltages at nodes i and j, respectively, and V0 be the reference voltage at the root node. i,j x i,j The resistance and reactance between branches ij are respectively, V min V max These define the minimum and maximum voltage values ​​for the nodes, respectively.

[0153] Formula (8) is the objective function established under the weighting factor ω, with the goal of minimizing the network loss and node voltage deviation of the microgrid; constraint (9) is used to limit the reactive power output range of the inverter; equations (10)-(12) represent the power flow calculation model; formula (13) is used to calculate the average node voltage deviation; formula (14) is used to calculate the branch power loss; constraint (15) limits the node voltage magnitude; constraint (16) is used to limit the apparent power transmitted on the branch;

[0154] (1.6) Linearize the constraints:

[0155] For the absolute value expression in formula (13), by introducing a slack variable C, the absolute value expression |AB| is linearized. This allows it to be re-expressed as C≥AB and C≥BA, and the objective function will minimize C instead of |AB|.

[0156] The quadratic inequality in formula (16) is linearized using the polygonal approximation method. The feasible region formed by active power and reactive power is approximated by a regular polygon. Taking a regular dodecagon as an example, based on the coordinates of the vertices, formula (16) can be transformed into the following form:

[0157]

[0158]

[0159] Where A v B v and C v For the correlation coefficient, using the above linearization method, the day-ahead microgrid voltage control model (2)-(16) considering electricity price demand response forms a mixed integer quadratic programming problem, with the decision variable being α. l,t and Uncertain variables include photovoltaic power generation output and microgrid load

[0160] (1.7) To address the uncertainties in photovoltaic power generation output and load, a scenario-based stochastic optimization method is adopted. Considering that the probability distribution of the uncertainty may be unknown or inaccurate, a sample average approximation method is used to represent the probability of the generated scenarios. Therefore, the proposed day-ahead microgrid voltage control stochastic model can be expressed as follows:

[0161]

[0162]

[0163]

[0164] In model (17), x represents the day-ahead decision variable α. l,t y s Represents intraday decision variables, including those under scenario s. Other dependent variables, S represents the set of generated scenarios, D and E are the coefficient matrices of the day-ahead and intraday decision variables in the microgrid voltage control stochastic model, respectively. After solving model (17), only the day-ahead decision variable α l,t Being used, and It will be re-optimized based on more accurate forecasts during the intraday phase.

[0165] After determining the decision variable α l,t After finding the optimal value, the microgrid load curve can be updated based on equations (2) and (3) and passed to the next stage for intraday optimization. The final hourly electricity price curve within the microgrid for the second day, and the updated microgrid load curve, are shown below. Figure 2 As shown.

[0166] Step 2:

[0167] Based on the hourly electricity price and the updated microgrid load curve, a hierarchical coordination model for the intraday microgrid is established, considering dynamic optimization of the reactive power-voltage (QV) droop parameter of the photovoltaic inverter. The specific process includes:

[0168] (2.1) As Figure 3 As shown, an inverter reactive power output model based on a linear droop control function is constructed:

[0169]

[0170]

[0171]

[0172]

[0173]

[0174] The subscript t represents the time interval index within each scheduling period (e.g., every hour or every 15 minutes) during the intraday phase. V is the inverter reactive power setpoint. i exp Let β be the expected value of the node voltage. iFor the binary representation of the slope of the sag curve, if β i If the reactive power is zero, the inverter will produce a constant reactive power. λ i denoted as the slope of the sag curve.

[0175] Equation (18) is used to calculate the real-time reactive power output of the inverter; formulas (19)-(22) are used to describe the droop control curve; formula (19) is used to calculate the real-time node voltage V. i,t With the node's expected voltage V i exp The difference; Equation (20) is used to calculate the real-time reactive power adjustment in response to changes in the voltage of the measurement node; Constraint (21) is used to limit the range of the slope of the droop control function.

[0176] (2.2) An intraday microgrid hierarchical coordination model considering the dynamic optimization of the photovoltaic inverter's QV droop parameter is established, as shown below:

[0177]

[0178] st(2)-(3),(10)-(16),(18)-(22)

[0179] Where B represents the set of branches ij.

[0180] The bilinear term in equation (20) makes the intraday microgrid hierarchical coordination model exhibit nonlinear characteristics.

[0181] Step 3:

[0182] To improve the solution rate of the intraday microgrid hierarchical coordination model in step 2, a model transformation and reconstruction algorithm and a fast solution algorithm based on convex-concave process (CCP) are proposed. This algorithm obtains the reactive power output reference point and QV droop curve of the inverter for each scheduling period (e.g., every hour or every 15 minutes) during the day, and sends them to the photovoltaic inverter. The specific steps are as follows:

[0183] (3.1) For ease of description, the variable ΔV is temporarily ignored at this stage. i,t ΔQ i,t The subscript of . Convert the bilinear terms in (20) to their equivalent form as follows:

[0184] λΔV=ΔQ=z1-z2 (24a)

[0185]

[0186] (3.2) The quadratic equality constraint (24b) is transformed into the following expression, where (25a) is a convex constraint and (25b) is a concave constraint:

[0187]

[0188]

[0189] (3.3) Multiply both sides of (25a) by 4 to reconstruct a second-order cone expression:

[0190]

[0191]

[0192] (3.4) Relax the concave constraint (25b) and add a McCormick envelope to tighten the relaxation range, as shown below:

[0193] ΔQ≥ λ ΔV+λ ΔV - λΔV (27a)

[0194]

[0195]

[0196]

[0197] in λ , These represent the lower and upper bounds of the slope of the sag curve, respectively. ΔV These represent the lower and upper bounds of the node voltage offset, respectively.

[0198] By replacing (20) with (24a), (26) and (27), the original nonlinear problem is transformed into a second-order cone relaxation (SOCR) model, which provides a lower bound for the original problem.

[0199] (3.5) Since constraint (26) only constrains one side, a reconstruction method based on CCP is proposed. The SOCR model is transformed into a penalized convex-concave model by convexifying the concave constraint of (25b). The original CCP is used to solve the difference problem in the convex programming problem. This is briefly introduced below.

[0200] minf0(x)-g0(x) (28)

[0201]

[0202] Where x is the decision variable, f i and g i It is a convex function, -g i Let f(x) be a concave function, and f0(x) and g0(x) be the objective functions in a convex programming problem. Replacing the concave function terms with a convex upper bound transforms the original problem into the following:

[0203] minf0(x)-g0′(x,x k* (29)

[0204]

[0205]

[0206] Where k represents the iteration exponent, g i ′(x,x k* ) is g i (x) in the current solution x k* The linearized function at point g can be regarded as g i The tangent plane of (x). g0′(x,x) k* ) is g0(x) in the current solution x k* The linearized function at point X can be considered as the tangent plane of g0(x). The solution can be obtained by iteratively solving this linearized model (29);

[0207] Following the form of (29), the concave constraint (25b) can be re-expressed as z 1 / 2 and g 1 / 2 The difference between ′(λ,ΔV) is shown below:

[0208] z1-g1′(λ,ΔV)≤0 (30a)

[0209]

[0210] z²-g²′(λ,ΔV)≤0 (30c)

[0211]

[0212] (3.6) To reduce relaxation error, relaxation variables s1 and s2 are introduced to represent the difference, as shown below:

[0213] z1-g1′(λ,ΔV)≤s1,s1≥0 (31a)

[0214] z2-g2′(λ,ΔV)≤s2,s2≥0 (31b)

[0215] (3.7) The slack variable is added as a penalty term to the objective function to tighten the slack error, and an intraday microgrid hierarchical coordination penalty convex-concave model is constructed, where s 1,i,t s 2,i,t Let s1 and s2 be the slack variables for node i at time t:

[0216]

[0217] (2)-(3),(10)-(16),(18),

[0218] st(19),(21),(22),(24a),(26),

[0219] (27),(30b),(30d),(31)

[0220] (3.8) Provides a termination condition for iteratively solving this penalty convex-concave model:

[0221]

[0222]

[0223] in and The preset threshold is obj0, which is the objective function value obtained by solving. The C1 condition is used to determine the difference between the original objective function (23) between the current iteration and the previous iteration, while the C2 condition checks the sum of the introduced slack variables to ensure equal constraints.

[0224] In summary, the steps of the CCP-based solution algorithm are shown in Table 2 below:

[0225] Table 2 Solution Algorithm Based on CCP

[0226]

[0227] This scheme enables rapid solution of model (23) in the second stage, and achieves the optimal reactive power setting benchmark for each photovoltaic inverter during each scheduling period within the day. Node expected voltage V i exp and the slope parameter λ of the droop control curve i Update. Figure 4 The solution process of the CCP-based algorithm proposed during this period is shown, with a solution time of 38.7 seconds, which meets the requirement of fast solution for short intraday scheduling cycles.

[0228] Step 4:

[0229] A real-time control model for the photovoltaic inverter is established, and the real-time reactive power output of the inverter is adjusted based on local real-time voltage measurement information and the optimized QV droop curve.

[0230] Based on the reactive power setting benchmark of the photovoltaic inverter obtained in the second stage Node expected voltage V i exp and the slope λ of the droop control curve i During this stage, the droop control curves of each inverter for the current time period can be updated, such as... Figure 5, Figure 6 As shown, through this drooping curve, each photovoltaic inverter can control its reactive power output based on the actual local voltage deviation.

[0231] To verify the effectiveness of the droop control function and the proposed three-stage hierarchical coordinated voltage control method for microgrids that considers electricity price-based demand response, 5000 microgrid photovoltaic output and load scenarios were randomly generated during the periods of 12:00-13:00 and 20:00-21:00 using Monte Carlo sampling to simulate their real-time uncertainties.

[0232] In addition, two other voltage control methods were compared, as shown below.

[0233] Method 1: Hierarchical coordinated voltage control without PBDR implementation. The inverter reactive power setpoint and droop control curve are updated hourly. Through real-time node voltage measurements, the inverter adjusts its reactive power output according to the optimal droop curve.

[0234] Method 2: Two-stage centralized coordination of PBDR and inverter reactive power generation, eliminating the need for local control. The inverter's reactive power distribution is updated and repaired hourly.

[0235] Tables 3 and 4 list the comparison results of different methods during the periods of 12:00-13:00 and 20:00-21:00, respectively.

[0236] Table 3 Comparison results of different methods during the 12:00-13:00 time period

[0237]

[0238] Table 4 Comparison results of different methods during 20:00-21:00

[0239]

[0240] During the peak photovoltaic power generation period from 12:00 to 13:00, Method 1 exhibited the highest average power loss, followed by Method 2, illustrating the significant role of PBDR in reducing power loss. Simultaneously, the voltage range of Method 2 was greater than that of Method 1, but both remained within permissible voltage limits. The method proposed in this invention achieved the lowest average power loss, while maintaining a voltage range similar to Method 1. No voltage exceedances were observed with any of the methods used.

[0241] During peak electricity consumption from 20:00 to 21:00, Method 1 exhibits the highest average power loss, voltage range, and voltage limit violation rate, indicating that inverter reactive power compensation alone cannot completely resolve the voltage issue. In contrast, due to consideration of PBDR, Method 2 significantly reduces average power loss and voltage limit violation rate, but voltage limit violations still occur. The method proposed in this invention not only has slightly lower average power loss and voltage range than Method 2, but also does not exhibit voltage limit violations.

[0242] Overall, the comparison of the three methods demonstrates the effectiveness of PBDR as an active resource-supported voltage control method. More importantly, it verifies the efficiency of the proposed three-stage hierarchical coordinated voltage control method for microgrids, which considers electricity price-based demand response and dynamic optimization of inverter droop parameters. This method fully leverages the advantages of central and local voltage control, as well as the load transfer characteristics of PBDR, to reduce network losses and voltage deviations.

Claims

1. A microgrid voltage control method considering price-based demand response and inverter droop parameter optimization, characterized in that, Includes the following steps: Step 1: Establish a day-ahead microgrid voltage control model that considers price-based demand response (PBDR), and solve it using a multi-scenario stochastic optimization method to obtain the hourly electricity price within the microgrid on the second day and the microgrid load forecast curve after the response update. Step 2: Based on the hourly electricity price and the updated microgrid load curve, establish an intraday microgrid hierarchical coordination model that considers dynamic optimization of the reactive power-voltage QV droop parameter of the photovoltaic inverter, including: (2.1) Constructing an inverter reactive power output model based on a linear droop control function: Subscript This represents the time interval index within each scheduling period of the intraday phase. This is the inverter reactive power setpoint. The expected value of the node voltage. For the binary decision of the slope of the sag curve, if If the reactive power is zero, the inverter will produce a constant reactive power. , The slope of the sag curve; (2.2) Establish an intraday microgrid hierarchical coordination model that considers the dynamic optimization of the QV droop parameter of the photovoltaic inverter, as shown below: s.t. in Indicates a branch A set; The bilinear term in equation (20) causes the intraday microgrid hierarchical coordination model to exhibit nonlinear characteristics; Step 3: For the nonlinear constraints in the intraday microgrid hierarchical coordination model, convert them into a linear problem and use a fast solution algorithm based on convex and concave processes to obtain the reactive power output reference point and QV droop curve of the inverter for each scheduling period, and send them to the photovoltaic inverter. Step 4: The photovoltaic inverter adjusts the reactive power output in real time based on local real-time voltage measurement information and the optimized QV droop curve.

2. The method according to claim 1, characterized in that, In step 1, the steps for establishing the day-ahead microgrid voltage control model considering price-based demand response include: (1.1) Construct a demand response model based on electricity price, where electricity price... With load demand The relationship between them is represented as follows: in It is a coefficient. It is the price elasticity coefficient of load demand; (1.2) Based on equation (1), design multiple tiered electricity prices and construct active and reactive power models for PBDR loads: in These represent the active and reactive power of the microgrid load after the implementation of PBDR tiered pricing; These represent the active and reactive power of the microgrid load before the implementation of PBDR tiered pricing, and include its uncertainties. For PBDR tiered electricity pricing, the binary decision variables are: In order to maintain electricity price levels Demand response rate at that time; L is the set of electricity price levels; The time index representing each hour in the current day period; (1.3) The constraints for implementing PBDR are given: in This refers to the electricity price period. For different electricity price levels of PBDR, The original electricity price before the implementation of PBDR; T represents the set of microgrid nodes; T represents the set of time indices. (1.4) To minimize the microgrid's network losses and node voltage deviations, a day-ahead microgrid voltage control model considering electricity price-based demand response is established: s.t. in As a weighting factor, branch road Active power loss, The average voltage deviation at the nodes. For inverters at nodes Time period The maximum reactive power generated, For photovoltaic at nodes Time period Active power generation considering uncertainty, For inverters at nodes Time period reactive power output, They are respectively in the time period via the side road Active and reactive power, They are respectively in the time period via the side road Active and reactive power on the surface branch road Maximum capacity, For nodes The set of parent nodes, For nodes The set of child nodes The total number of nodes. They are nodes voltage, The reference voltage for the root node is... Branch roads The resistance and reactance between them These define the minimum and maximum voltage values ​​for the nodes, respectively. (1.5) Linearize the constraints and combine the day-ahead microgrid voltage control models (2)-(16) considering electricity price demand response into a mixed integer quadratic programming problem, with the decision variables being... and Uncertain variables include photovoltaic power generation output. and microgrid load .

3. The method according to claim 2, characterized in that, Linearizing the constraints includes: For the absolute value in formula (13), slack variables are introduced. absolute value expression Linearization, which is then re-represented as and And the objective function will be minimized. ; The quadratic inequality in formula (16) is linearized using the polygonal approximation method, and the feasible region formed by active power and reactive power is approximated by a regular polygon.

4. The method according to claim 3, characterized in that, In step 1, the stochastic optimization solution method based on multiple scenarios is specifically as follows: To address the uncertainties in photovoltaic power generation output and load, a sample averaging approximation method is used to represent the probability of the generated scenarios, and a stochastic model for day-ahead microgrid voltage control is constructed: s.t. (17a) In model (17), Represents the day-ahead decision variable , Indicates intraday decision variables, including scenarios. Below Other dependent variables, Represents a set of generated scenes. These are the coefficient matrices of the day-ahead and intraday decision variables in the microgrid voltage control stochastic model, respectively. After solving model (17), only the day-ahead decision variables are represented. It was determined, and The intraday phase will be re-optimized based on more accurate forecasts; After determining the decision variables After finding the optimal value, the microgrid load curve is updated based on equations (2) and (3) and passed to the next stage for optimization in the intraday stage.

5. The method according to claim 4, characterized in that, In step 3, the transformation of the problem includes: (3.1) Ignore the subscript of the variable, and represent ,by represent The bilinear terms in (20) are transformed into their equivalent form as follows: (24a) (24b) (3.2) Transform the quadratic equality constraint (24b) into the expression (25), where (25a) is a convex constraint and (25b) is a concave constraint: (25a) (25b) (3.3) Multiply both sides of (25a) by 4 to reconstruct a second-order cone expression: (26a) (26b) (3.4) Relax the concave constraint (25b) and add a McCormick envelope to tighten the relaxation range, as shown below: (27a) (27b) (27c) (27d) in These represent the lower and upper bounds of the slope of the sag curve, respectively. These represent the lower and upper bounds of the node voltage offset, respectively. By replacing (20) with (24a), (26) and (27), the original nonlinear problem is transformed into a second-order cone relaxation SOCR model, which provides a lower bound for the original problem. (3.5) The SOCR model is transformed into a penalized convex-concave model by convexifying the concave constraint of (25b): (28) s.t. (28a) in It is a decision variable. and It is a convex function. It is a concave function. and For the objective function in the convex programming problem, replace the concave function term with a convex upper bound, and the original problem is replaced by the following problem: （29） s.t. (29a) (29b) in Indicates the iteration index, for In the current solution The linearized function at point can be regarded as The tangent plane, for In the current solution The linearized function at point can be regarded as The tangent plane is obtained by iteratively solving the linearized model (29) to obtain the solution.

6. The method according to claim 5, characterized in that, In step 3, the specific processing steps of the fast solution algorithm based on the convex-concave process CCP are as follows: Following the form of (29), the concave constraint (25b) is re-expressed as follows: and The difference between them is shown below: (30a) (30b) (30c) (30d) To reduce relaxation error, relaxation variables are introduced. and To represent the differences, see below: (31a) (31b) The slack variable is added as a penalty term to the objective function to tighten the slack error, thus constructing an intraday microgrid hierarchical coordination penalty convex-concave model. Representing nodes respectively Time period slack variables and : (32) s.t. Solve the updated model (32) to obtain , Examine the termination criteria for the results and other decision variables. and If the condition is met, stop the iteration and output the solution; Otherwise, update the penalty factor. And based on the current solution, a penalty concave-convex model (32) is re-established and the solution is continued.

7. The method according to claim 6, characterized in that, Termination Criteria and as follows: (33a) (33b) in and It is a preset threshold. To obtain the objective function value, Determine the difference between the original objective function (23) between the current iteration and the previous iteration, and Check the sum of introduced slack variables to ensure equal constraints.

8. The method according to claim 7, characterized in that, Update penalty factor The update method is as follows: in It is a coefficient used to increase the penalty factor. The maximum value of the pre-set penalty factor.

9. The method according to claim 8, characterized in that, In step 4, the photovoltaic inverter adjusts its reactive power output in real time based on local real-time voltage measurement information and the optimized QV droop curve. The specific adjustment method is as follows: Based on the reactive power setting benchmark of the photovoltaic inverter obtained in step 3 Node expected voltage and the slope parameter of the droop curve The droop control curve of each inverter in the current time period is updated locally. Based on the droop control curve, each photovoltaic inverter is controlled according to the actual local voltage deviation.

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