A method for dispatching power systems with wind power reserve and considering wind turbine wake effect

Abstract

The present invention relates to a method for dispatching a power system with wind power reserve and considering the wake effect of wind turbines, including: constructing a wind farm output model considering the wake effect; establishing a dynamic model of power system frequency to obtain the frequency change rate and maximum frequency deviation of the system; constructing a power system frequency safety constraint; establishing a mathematical model for wind farms to provide reserve, and determining the upward and downward reserve of wind farms under prediction scenarios; establishing a connection between wind power reserve under basic scenarios and wind power reserve under uncertain scenarios, and obtaining expressions for upward and downward reserve under uncertain scenarios; constructing a coordinated dispatching model, and solving it. The present invention establishes a power system frequency safety constraint, constructs a coordinated dispatching model in which wind farms provide frequency regulation and reserve for power systems, and solves the model to obtain the optimal unit combination and unit output, thereby ensuring the frequency safety of the power system, improving the stability of the power system, and reducing the operating cost of the power system.

Description

Technical Field

[0001] The present invention belongs to the field of power system dispatching and control, and in particular relates to a power system dispatching method with wind power reserve and taking into account wind turbine wake effect. Background Art

[0002] Low-carbon development has promoted the rapid growth of renewable energy generation such as wind power and solar power. However, large-scale grid-connected renewable energy generation has brought huge challenges to the safe and stable operation of the power system. On the one hand, wind turbines and photovoltaic panels are connected to the power grid through power electronic interfaces. They cannot provide inertia for the system, resulting in a reduction in the system's synchronous inertia, which affects the safe operation of the system. On the other hand, the volatility and uncertainty of renewable energy generation require the power system to provide more backup for real-time power balance to prevent renewable energy generation cuts or large-scale load shedding.

[0003] With the increase of renewable energy power generation, the proportion of synchronous generators has decreased, resulting in insufficient frequency support and flexible adjustment capabilities of the power system.

[0004] The development of power electronics technology has provided more opportunities for renewable energy power generation equipment, and it has become possible for renewable energy to provide virtual inertia for the power system. Wind turbines are able to support primary frequency control and simulate inertia by applying additional control loops. In addition, wind turbines can be operated at locations away from the maximum power tracking point, enabling them to provide operational reserves in a proactive manner. As the installed capacity of wind power generation increases, it has become possible for wind power to provide frequency support and flexible reserves. However, how to introduce the system frequency response model into the power system dispatch model and reasonably quantify the frequency support and reserve of wind turbines remains an issue to be resolved.

[0005] Therefore, a power system dispatching method in which wind farms provide frequency support and wind power reserve is studied to quantify the contribution of wind farms in frequency support and reserve services and fill this gap. Summary of the invention

[0006] The purpose of the present invention is to provide a power system scheduling method with wind power reserve and considering the wind turbine wake effect in view of the above problems, establish a mathematical model for wind farms to provide reserve, and quantify the uncertainty of wind power reserve under uncertain scenarios, use wind power to provide frequency support for the power system, and construct power system frequency security constraints; consider the influence of wind turbine wake effect to improve the calculation accuracy of wind farm output power; construct a collaborative scheduling model for wind farms to provide frequency regulation and reserve for the power system, solve the collaborative scheduling model to obtain the optimal unit combination and unit output, increase the proportion of new energy power generation, ensure the frequency safety of the power system, improve the stability of the power system, and reduce the operating cost and carbon dioxide emissions of the power system.

[0007] The technical solution of the present invention is a method for dispatching a power system with wind power reserve and considering the wind turbine wake effect, comprising the following steps:

[0008] Step 1: Considering the influence of wake effect on wind turbine output, establish a wind farm output model;

[0009] Step 2: Establish a frequency dynamic model of the power system including wind turbines and conventional units, and obtain expressions for the frequency change rate and maximum frequency deviation of the system;

[0010] Step 3: Construct power system frequency security constraints based on the frequency change rate and the maximum frequency deviation;

[0011] Step 4: Establish a mathematical model for the wind farm to provide reserve and determine the upward and downward reserve of the wind farm under the forecast scenario;

[0012] Step 5: Establish the connection between the wind power reserve under the basic scenario and the wind power reserve under the uncertain scenario, and obtain the expressions of the upward reserve and downward reserve under the uncertain scenario;

[0013] Step 6: Establish a coordinated dispatch model for wind farms to provide frequency regulation and backup for the power system;

[0014] Step 7: Use the column and constraint method to solve the collaborative scheduling model, decompose the collaborative scheduling model into a main problem and a sub-problem. The main problem is a mixed integer linear programming problem, and the sub-problem is a Max-Min problem. Solve the sub-problem to obtain the optimal cutting plane, and solve the main problem to obtain the unit combination and unit output;

[0015] In step 1, the output of wind farm wind turbines is:

[0016]

[0017] P w =∑ j μ w,j p w,j (1-κ w ),μ w,j,t ∈{0,1} (2)

[0018] Where p w,j is the output of fan j, f(v w ) is the relationship function between wind turbine output and wind speed, v w is the wind speed captured by the wind turbine, p R Indicates the rated power of the fan, v in 、v out 、v R are the cut-in wind speed, cut-out wind speed and rated wind speed of the fan respectively; μ w,j represents the operating status of wind turbine j in wind farm w, κw Indicates the load reduction ratio of wind turbines in the wind farm; P w represents the output of wind farm w;

[0019] Considering the wake effect of the upstream wind turbines on the downstream wind turbines in the wind farm, and considering the influence of factors such as wind farm distribution, terrain, and average wind speed, the air supply speed of the wind farm wind turbines is as follows:

[0020]

[0021] Where v w,j represents the captured wind speed of wind turbine j under the influence of wake; ω x It represents the ratio of the wake wind speed to the initial wind speed of the fan x; B j,x represents the wake influence coefficient of wind turbine x on wind turbine j;

[0022]

[0023] Where h is the height of the fan; Δh is the height difference between the upstream fan and the downstream fan; C T is the thrust coefficient; r(x) represents the wake influence radius at x; r rot represents the blade radius of the upstream fan;

[0024] B j,x =A shad-jx / A rot-j (5)

[0025] Where B j,x A represents the wake influence coefficient of fan x on fan j; shad-jx is the projected area of ​​wind turbine x at wind turbine j; A rot-j is the swept area of ​​fan j blade;

[0026] Thrust coefficient:

[0027] C T =4a(1-a) (6)

[0028] Where a represents the axial coefficient;

[0029] Combining (3) and (5), we can get

[0030]

[0031]

[0032] In the formula represents the wake reduction factor of wind turbine x on wind turbine j.

[0033] The output power of the w wind farm considering the wake effect is as follows:

[0034] P w =∑ j μ w,j f(v w,j )(1-κ w ) (9).

[0035] In step 2, the dynamic model of power system frequency is as follows:

[0036]

[0037] Where G(s) represents the transfer function; Δf represents the system frequency deviation; ΔP e Represents the unbalanced power of the system; H g , D g They represent the inertia and damping constant of the generator and the operating state u of the generator respectively. i Related; T is the time constant of the steam turbine; R i , K i They represent the droop gain and mechanical power gain coefficient of conventional unit i respectively; F i is the fraction of the total power of the synchronous generator; H v,j , D v,j Respectively represent the inertia and damping of wind turbine j; R d,j , K d,j They represent the droop coefficient and power gain coefficient of wind turbine j respectively; T d , T v are the time constants of the inverter;

[0038] Inertia of wind farm:

[0039]

[0040] Where M W represents the normalized virtual inertia of the wind farm; H v Represents the virtual inertia parameters of the wind turbine;

[0041] Droop gain of wind farm:

[0042]

[0043] Where K d Represents the power gain parameter of the wind turbine; R d represents the droop gain parameter of the wind turbine; R W represents the droop gain of the wind farm;

[0044] Damping of wind farms:

[0045]

[0046] Where Dv Indicates the damping parameter of the wind turbine; D W represents the damping of the wind farm;

[0047] Inertia of the system:

[0048]

[0049] Where P i max Represents the installed capacity of conventional units; M g is the inertia of the conventional unit; M represents the total inertia of the power system;

[0050] Damping of the system:

[0051]

[0052] Where D g The damping provided for conventional units; D represents the total damping of the power system;

[0053] Assuming power deviation ΔP e There is a stepwise disturbance in , and the frequency deviation is as follows:

[0054]

[0055] Where Δf represents the frequency deviation of the system; ω n is the natural frequency; ξ is the damping ratio; t is the time variable; T is the time constant of the steam turbine; ω d represents the damping frequency; φ represents the phase, which can be expressed by the damping ratio;

[0056]

[0057]

[0058] Damping ratio:

[0059]

[0060] Where F g is the total power fraction synthesized by the system; R is the total droop gain synthesized by the system;

[0061] Natural frequency:

[0062]

[0063] According to the time domain expression of frequency deviation, the frequency change rate at the initial moment can be obtained:

[0064]

[0065] In the formula is the frequency change rate of the system;

[0066] Maximum frequency deviation:

[0067]

[0068] Where Δf nadir is the system frequency deviation;

[0069] The time when the system frequency reaches the lowest point:

[0070]

[0071] Where t na dir is the time when the system frequency reaches the lowest point.

[0072] In step 3, the frequency change rate constraint is:

[0073]

[0074] Frequency minimum point constraint:

[0075] f nadir =f0-f0·Δf nadir ≥f min (25)

[0076] Where f0 is the reference frequency of the system, is the frequency change rate limit; f nadir is the lowest frequency point of the system, f min The frequency minimum limit; Δf nadir Indicates the maximum frequency deviation.

[0077] In step 4, the mathematical model of the wind farm providing upward and downward reserves under the forecast scenario is as follows:

[0078]

[0079]

[0080]

[0081]

[0082] in They represent the upward and downward reserve that can be provided by the wind farm under the basic scenario respectively; Respectively represent the upward and downward reserve coefficients of the fan; μ w,j,t is the operating status of wind turbine j in the wind farm at time t, p w,j,t is the predicted output of wind turbine j at time t; κ max is the maximum load reduction ratio of the fan; κw,t It represents the load reduction ratio of wind turbines in wind farm w during period t.

[0083] Wind speed is uncertain, so the actual output and reserve of wind farms are also uncertain. In order to study the uncertainty of wind power reserve, a robust optimization method is used to solve this uncertainty.

[0084] Modeling the predicted wind speed of a wind farm as an uncertainty ensemble

[0085]

[0086] Among them U W represents the wind power uncertainty set, Indicates uncertain wind speed. Both are 0-1 variables of wind speed at the boundary of the uncertainty set, and β represents the uncertainty coefficient of wind speed.

[0087] To ensure that the wind power reserve determined in the wind power forecast scenario can be implemented in the uncertain scenario with wind farm output uncertainty, the wind power reserve coefficient is used to link the reserve in the basic scenario with the reserve in the uncertain scenario;

[0088] When the reserve auxiliary variable is determined, the wind power reserve varies with the uncertainty of wind power output.

[0089] Under the uncertain scenario, the upward and downward reserves provided by wind farms are as follows:

[0090]

[0091]

[0092] In the formula They are the upward and downward reserves that wind farms can provide under uncertain scenarios; is the uncertain output of wind turbine j at time t.

[0093] In step 6, the collaborative scheduling model includes:

[0094] (1) Objective function:

[0095]

[0096] Where c i.k is the power generation cost coefficient of unit i in the kth output interval; are the startup and shutdown costs of conventional units respectively; c e is the price of carbon dioxide emissions; E i,t represents the carbon dioxide emissions of conventional unit i; They are the upward and downward reserve cost coefficients for conventional units respectively; They are the upward and downward reserve cost coefficients of wind farms, respectively; is the output of unit i at time t during period k; They are the upward and downward reserves provided by conventional unit i at time t;

[0097] (2) Constraints in basic scenarios:

[0098] Node power balance constraints:

[0099]

[0100] Wherein the subscripts d and l represent load and line respectively; G(m) Indicates the set of buses where conventional units are located; W(m) represents the set of buses where the wind farm is located; L(m) Represents the set of buses connected to line l; D(m) Indicates the set of buses where the loads are located; Indicates the power of line l; P d,t Indicates load demand; Indicates the planned output of the unit the day before;

[0101] Network constraints:

[0102]

[0103] In the formula represents the voltage phase angle of node m; represents the voltage phase angle of node n; represents the reference node phase angle; x l is the reactance of the line;

[0104]

[0105] Where P l max The capacity limit of the line;

[0106] Output and reserve limits of conventional units:

[0107]

[0108]

[0109]

[0110] Where P i min Indicates the minimum output of the unit; Respectively represent the maximum upward and downward reserves provided by the unit;

[0111] CO2 emission limits:

[0112]

[0113] Where E i,t is the carbon dioxide emission of unit i; e i Indicates the CO2 emission intensity per unit of power output;

[0114] Frequency safety constraints:

[0115]

[0116] f nadir =f0+f0·Δf nadir ≥f min (42)

[0117] Where RoCoF lim Indicates the frequency change rate limit; f nadir The lowest frequency point of the system; f0 is the base frequency of the system; Δf nadir Indicates the maximum frequency deviation; f min Indicates the minimum frequency limit;

[0118] The constraints under the basic scenario also include startup / shutdown costs, start-up and shutdown constraints, ramp restrictions, and wind farm output constraints and reserve constraints.

[0119] (3) Constraints in uncertain scenarios;

[0120] Load uncertainty:

[0121]

[0122]

[0123] Where U D is the load uncertainty set, All are 0-1 variables; are the time and space uncertainty budgets respectively; ΔP d,t represents the load forecast deviation;

[0124] Node power balance constraints:

[0125]

[0126] In the formula Respectively represent the re-dispatching output of conventional units and wind farms; Indicates wind farm redispatching output;

[0127] Network constraints:

[0128]

[0129]

[0130] In the formula They represent the phase angle and power flow of the line under uncertainty respectively; represents the voltage phase angle of the reference node;

[0131] Re-dispatch constraints for conventional units:

[0132]

[0133] In the formula Indicates that conventional units are put on standby; Indicates that conventional units are downgraded to standby;

[0134] Re-dispatch constraints for wind farms:

[0135]

[0136] In the formula They are respectively the upward and downward reserves that wind farms can provide under uncertain scenarios.

[0137] Compared with the prior art, the beneficial effects of the present invention include:

[0138] 1) The present invention establishes a mathematical model of wind power reserve and quantifies the uncertainty of wind power reserve, uses wind power to provide frequency support for the power system, establishes frequency security constraints for the power system, and constructs a collaborative scheduling model for wind farms to provide frequency regulation and backup for the power system. By solving the collaborative scheduling model, the optimal unit combination and unit output are obtained, the proportion of renewable energy power generation is increased, the frequency security of the power system is guaranteed, the stability of the power system is improved, and the operating cost of the power system is reduced.

[0139] 2) The present invention takes into account the impact of wind turbine wake effect on wind farm output, and provides a wind farm inertia, damping, and droop gain parameter model that combines the actual grid-connected wind turbine capacity and quantifies the wake effect, so as to more accurately measure the frequency support capability of the wind farm, which is conducive to reasonably measuring the frequency support capability of the power system and making the power grid more secure and stable.

[0140] 3) The method of the present invention can effectively avoid the redundancy or insufficiency of wind power reserve caused by excessively high or low actual wind power output.

[0141] 4) The present invention effectively reduces carbon dioxide emissions while ensuring the frequency safety of the power system and improving system stability.

[0142] 5) The present invention establishes a connection between the wind power reserve in the basic scenario and the wind power reserve in the uncertain scenario through the wind power reserve coefficient, thereby ensuring that the wind power reserve in the predicted scenario can be implemented in the actual uncertain scenario.

[0143] 6) The collaborative dispatching model proposed in the present invention for wind farms to provide frequency regulation and reserve for the power system is a robust optimization dispatching model that takes into account the uncertainty of wind power and load, and is solved through column and constraint generation methods, thereby realizing the joint dispatching of power generation and reserve, and internalizing the reserve scale problem, and more accurately quantifying the system's reserve demand.

[0144] 7) The present invention adopts the column and constraint method to solve the collaborative scheduling model. Compared with other solution algorithms, the column constraint generation algorithm iteratively optimizes by returning the column and constraint optimal cutting plane, which effectively reduces the number of iterations and improves the solution efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0145] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0146] Figure 1 The figure is a flow chart of a power system dispatching method according to an embodiment of the present invention.

[0147] Figure 2 It is a comparison chart of the dispatching results of the power system dispatching method of the present invention and other methods. DETAILED DESCRIPTION

[0148] like Figure 1 As shown, a power system dispatching method with wind power reserve and considering the wind turbine wake effect includes the following steps:

[0149] Step 1: Considering the influence of wake effect on wind turbine output, establish a wind farm output model;

[0150] Wind farm wind turbine output:

[0151]

[0152] P w =∑ j μ w,j p w,j (1-κ w ),μ w,j,t ∈{0,1} (2)

[0153] Where p w,j is the output of fan j, f(v w ) is the relationship function between wind turbine output and wind speed, v w is the wind speed captured by the wind turbine, p R Indicates the rated power of the fan, v in、v out 、v R are the cut-in wind speed, cut-out wind speed and rated wind speed of the fan respectively; μ w,j represents the operating status of wind turbine j in wind farm w, κ w Indicates the load reduction ratio of wind turbines in the wind farm; P w represents the output of wind farm w;

[0154] Considering the wake effect of the upstream wind turbines on the downstream wind turbines in the wind farm, the air supply speed of the wind turbines in the wind farm is as follows:

[0155]

[0156] Where v w,j represents the captured wind speed of wind turbine j under the influence of wake; ω x It represents the ratio of the wake wind speed to the initial wind speed of the fan x; B j,x represents the wake influence coefficient of wind turbine x on wind turbine j;

[0157]

[0158] Where h is the height of the fan; Δh is the height difference between the upstream fan and the downstream fan; C T is the thrust coefficient; r(x) represents the wake influence radius at x; r ot represents the blade radius of the upstream fan;

[0159] B j,x =A shad-jx / A rot-j (5)

[0160] Where B j,x A represents the wake influence coefficient of fan x on fan j; shad-jx is the projected area of ​​wind turbine x at wind turbine j; A rot-j is the swept area of ​​fan j blade;

[0161] Thrust coefficient:

[0162] C T =4a(1-a)(6)

[0163] Where a represents the axial coefficient;

[0164] Combining (3) and (5), we can get

[0165]

[0166]

[0167] In the formula represents the wake reduction factor of wind turbine x on wind turbine j;

[0168] The output power of the w wind farm considering the wake effect is as follows:

[0169] P w =∑ j μ w,j f(v w,j )(1-κ w ) (9)

[0170] Step 2: Establish a frequency dynamic model of the power system including wind turbines and conventional units, and obtain expressions for the frequency change rate and maximum frequency deviation of the system;

[0171] The dynamic model of power system frequency is as follows:

[0172]

[0173] Where G(s) represents the transfer function; Δf represents the system frequency deviation; ΔP e Represents the unbalanced power of the system; H g , D g They represent the inertia and damping constant of the generator and the operating state u of the generator respectively. i Related; T is the time constant of the steam turbine; R i , K i They represent the droop gain and mechanical power gain coefficient of conventional unit i respectively; F i is the fraction of the total power of the synchronous generator; H v,j , D v,j Respectively represent the inertia and damping of wind turbine j; R d,j , K d,j They represent the droop coefficient and power gain coefficient of wind turbine j respectively; T d , T v are the time constants of the inverter;

[0174] Inertia of wind farm:

[0175]

[0176] Where M W represents the normalized virtual inertia of the wind farm; H v Represents the virtual inertia parameters of the wind turbine;

[0177] Droop gain of wind farm:

[0178]

[0179] Where K d Represents the power gain parameter of the wind turbine; R d represents the droop gain parameter of the wind turbine; RW represents the droop gain of the wind farm;

[0180] Damping of wind farms:

[0181]

[0182] Where D v Indicates the damping parameter of the wind turbine; D W represents the damping of the wind farm;

[0183] Inertia of the system:

[0184]

[0185] Where P i max Represents the installed capacity of conventional units; M g is the inertia of the conventional unit; M represents the total inertia of the power system;

[0186] Damping of the system:

[0187]

[0188] Where D g The damping provided for conventional units; D represents the total damping of the power system;

[0189] Assuming power deviation ΔP e There is a stepwise disturbance in , and the frequency deviation is as follows:

[0190]

[0191] Where Δf represents the frequency deviation of the system; ω n is the natural frequency; ξ is the damping ratio; t is the time variable; T is the time constant of the steam turbine; ω d represents the damping frequency; φ represents the phase, which can be expressed by the damping ratio;

[0192]

[0193]

[0194] Damping ratio:

[0195]

[0196] Where F g is the total power fraction synthesized by the system; R is the total droop gain synthesized by the system;

[0197] Natural frequency:

[0198]

[0199] According to the time domain expression of frequency deviation, the frequency change rate at the initial moment can be obtained:

[0200]

[0201] In the formula is the frequency change rate of the system;

[0202] Maximum frequency deviation:

[0203]

[0204] Where Δf nadir is the system frequency deviation;

[0205] The time when the system frequency reaches the lowest point:

[0206]

[0207] Where t na dir is the time when the system frequency reaches the lowest point.

[0208] Step 3: Construct power system frequency security constraints based on the frequency change rate and the maximum frequency deviation;

[0209] Frequency change rate constraint:

[0210]

[0211] Frequency minimum point constraint:

[0212] f nadir =f0-f0·Δf nadir ≥f min (25)

[0213] Where f0 is the reference frequency of the system, is the frequency change rate limit; f nadir is the lowest frequency point of the system, f min The frequency minimum limit; Δf nadir Indicates the maximum frequency deviation.

[0214] Step 4: Establish a mathematical model for the wind farm to provide reserve, and determine the upward and downward reserve of the wind farm under the forecast scenario; the mathematical model for the wind farm to provide upward and downward reserve under the forecast scenario is as follows:

[0215]

[0216]

[0217]

[0218]

[0219] in They represent the upward and downward reserve that can be provided by the wind farm under the basic scenario respectively; Respectively represent the upward and downward reserve coefficients of the fan; μ w,j,t is the operating status of wind turbine j in the wind farm at time t, p w,j,t is the predicted output of wind turbine j at time t; k max is the maximum load reduction ratio of the fan; κ w,t It represents the load reduction ratio of wind turbines in wind farm w during period t.

[0220] Wind speed is uncertain, so the actual output and reserve of wind farms are also uncertain. In order to study the uncertainty of wind power reserve, a robust optimization method is used to solve this uncertainty.

[0221] Modeling the predicted wind speed of a wind farm as an uncertainty ensemble

[0222]

[0223] Among them U W represents the wind power uncertainty set, Indicates uncertain wind speed. Both are 0-1 variables of wind speed at the boundary of the uncertainty set, and β represents the uncertainty coefficient of wind speed.

[0224] Step 5: Establish the connection between the wind power reserve under the basic scenario and the wind power reserve under the uncertain scenario, and obtain the expressions of the upward reserve and downward reserve under the uncertain scenario;

[0225] To ensure that the wind power reserve determined in the wind power forecast scenario can be implemented in the uncertain scenario with wind farm output uncertainty, the wind power reserve coefficient is used to link the reserve in the basic scenario with the reserve in the uncertain scenario;

[0226] When the reserve auxiliary variable is determined, the wind power reserve varies with the uncertainty of wind power output.

[0227] Under the uncertain scenario, the upward and downward reserves provided by wind farms are as follows:

[0228]

[0229]

[0230] In the formula They are the upward and downward reserves that wind farms can provide under uncertain scenarios; is the uncertain output of wind turbine j at time t.

[0231] Step 6: Establish a coordinated dispatch model for wind farms to provide frequency regulation and backup for the power system;

[0232] The collaborative scheduling model includes:

[0233] (1) Objective function:

[0234]

[0235] Where c i.k is the power generation cost coefficient of unit i and section k; are the startup and shutdown costs of conventional units respectively; c e is the price of carbon dioxide emissions; E i,t represents the carbon dioxide emissions of conventional unit i; They are the upward and downward reserve cost coefficients for conventional units respectively; They are the upward and downward reserve cost coefficients of wind farms, respectively; is the output of unit i at time t during period k; They are the upward and downward reserves provided by conventional unit i at time t;

[0236] (2) Constraints in basic scenarios:

[0237] Node power balance constraints:

[0238]

[0239] Wherein the subscripts d and l represent load and line respectively; G(m) Indicates the set of buses where conventional units are located; W(m) represents the set of buses where the wind farm is located; L(m) Represents the set of buses connected to line l; D(m) Indicates the set of buses where the loads are located; Indicates the power of line l; P d,t Indicates load demand; Indicates the planned output of the unit the day before;

[0240] Network constraints:

[0241]

[0242] In the formula represents the voltage phase angle of node m; represents the voltage phase angle of node n; represents the reference node phase angle; x l is the reactance of the line;

[0243]

[0244] Where P l max The capacity limit of the line;

[0245] Output and reserve limits of conventional units:

[0246]

[0247]

[0248]

[0249] Where P i min Indicates the minimum output of the unit; Respectively represent the maximum upward and downward reserves provided by the unit;

[0250] CO2 emission limits:

[0251]

[0252] Where E i,t is the carbon dioxide emission of unit i; e i Indicates the CO2 emission intensity per unit of power output;

[0253] Frequency safety constraints:

[0254]

[0255] f nadir =f0+f0·Δf nadir ≥f min (42)

[0256] Where RoCoF lim Indicates the frequency change rate limit; f nadir is the lowest frequency point of the system; f0 is the reference frequency of the system; Δf nadir Indicates the maximum frequency deviation; f min Indicates the minimum frequency limit;

[0257] The constraints under the basic scenario also include startup / shutdown costs, start-up and shutdown constraints, ramp restrictions, and wind farm output constraints and reserve constraints.

[0258] (3) Constraints in uncertain scenarios;

[0259] Load uncertainty:

[0260]

[0261]

[0262] Where U D is the load uncertainty set, All are 0-1 variables; are the time and space uncertainty budgets respectively; ΔP d,t represents the load forecast deviation;

[0263] Node power balance constraints:

[0264]

[0265] In the formula Respectively represent the re-dispatching output of conventional units and wind farms; Indicates wind farm redispatching output;

[0266] Network constraints:

[0267]

[0268]

[0269] In the formula They represent the phase angle and power flow of the line under uncertainty respectively; represents the voltage phase angle of the reference node;

[0270] Re-dispatch constraints for conventional units:

[0271]

[0272] In the formula Indicates that conventional units are put on standby; Indicates that conventional units are downgraded to standby;

[0273] Re-dispatch constraints for wind farms:

[0274]

[0275] In the formula They are respectively the upward and downward reserves that wind farms can provide under uncertain scenarios.

[0276] Step 7: Use the column and constraint method to solve the collaborative scheduling model, decompose the collaborative scheduling model into a main problem and a sub-problem. The main problem is a mixed integer linear programming problem, and the sub-problem is a Max-Min problem. Solve the sub-problem to obtain the optimal cutting plane, and solve the main problem to obtain the unit combination and unit output;

[0277] Step 7.1: Write the proposed coordinated dispatch model of wind farms providing frequency support and reserve into matrix form;

[0278] Objective function:

[0279]

[0280] The constraints in the basic scenario include:

[0281]

[0282]

[0283] The constraints in uncertain scenarios include:

[0284]

[0285] The subscript iter indicates the number of iterations; u iter represents the operating status of the iterated conventional unit, Respectively represent the output of conventional units and wind farms; Respectively represent the reserve of conventional units and wind farms; p r represents the generator output under uncertain scenarios; θ r Represents the node phase angle in uncertain scenarios; Indicates wind power output under uncertain scenarios, represents the uncertain variable of wind power; represents the load uncertainty variable;

[0286] a, b, c, e, f, h, z, A, B, E, G, L, N, O, Q, R, X, V, W are all constant coefficient matrices;

[0287] Step 7.2: Decompose the original model of the collaborative scheduling model into a main problem and sub-problems by using a column and constraint generation algorithm, and solve them;

[0288] (1) Solve the main problem;

[0289] Objective function:

[0290]

[0291] The constraints include:

[0292]

[0293] Where F is a constant coefficient matrix;

[0294]

[0295] The columns and constraints returned by the subproblem generate the optimal cutting plane of the algorithm;

[0296] The main problem is a mixed integer linear programming problem, which is solved by Gurobi;

[0297] Solve the main problem to obtain the basic unit combination I b and unit output p b , corresponding to the solution constraints of the base case and all the optimal cutting planes obtained so far;

[0298] (2) Solve the sub-problems;

[0299] The subproblem can be expressed as a Max-Min problem; to ensure that the problem has a feasible solution, the relaxation vector s is introduced;

[0300] Sub-problem objective function:

[0301]

[0302] Constraints:

[0303]

[0304] The subproblem is a Max-Min problem and cannot be solved directly;

[0305] The inner layer Min problem is a linear problem, which can be transformed into a single layer problem by dual transformation.

[0306] Objective function:

[0307]

[0308] Constraints:

[0309] W·n≤0, Q·n≤0, V·n≤0, X·n≤1 (60)

[0310] η≤0orunlimited (61)

[0311] Where η is the dual variable of the subproblem;

[0312] Solve the subproblem to get the optimal solution

[0313] If ψ>ε, ε is the iteration threshold, based on the worst scenario of wind power and load Generate the optimal cutting plane generated by the columns and constraints; otherwise, end the iteration;

[0314] (3) Generate the optimal cutting plane generated by the columns and constraints;

[0315] Create a new variable s iter+1 , and generate the optimal cutting plane generated by the columns and constraints,

[0316]

[0317] Where iter represents the number of iterations;

[0318] (4) Return to the main problem and solve it again.

[0319] The implementation results show that the column constraint generation algorithm is used to solve the collaborative scheduling model of the present invention. Compared with the widely used Benders decomposition algorithm, the column constraint generation algorithm iteratively searches for the optimal solution by returning the optimal cutting plane of the column and constraint, which effectively reduces the number of iterations and improves the solution efficiency.

[0320] In order to verify the effectiveness and superiority of the dispatching method of the present invention, the method of the present invention is compared with other dispatching methods based on the IEEERTS-24 system, as shown in Table 1. Method 1 adopts a frequency security constrained unit combination optimization model. Method 2 adopts a frequency security constrained unit combination optimization model with wind power generation providing frequency support. Method 3 is a power system dispatching method with wind power providing backup. Method 4 is a frequency security constrained power system dispatching method with wind power providing backup and frequency support of the present invention.

[0321] The dispatch results of the four methods shown in Table 1 are analyzed. Method 1 takes into account the system frequency security constraints, but does not take into account the frequency support and backup provided by the wind farm, and its dispatch cost is the highest. In Method 2, the wind farm provides frequency support, thereby reducing the operating time of units with high carbon emissions and power generation costs, thereby reducing the system operating costs. In Method 3, the wind farm provides backup services, which effectively reduces the system's backup costs. Compared with other methods, the system dispatch method in which the wind farm provides frequency support and backup significantly reduces the total cost. Compared with Method 1, the power generation cost and backup cost of the method of the present invention are reduced by 21.9% and 4.1%, respectively. Figure 2 The figure shows the CO2 emissions of all units in the four methods. Unit 3 is a hydroelectric generator, and units 8 and 9 are nuclear generators. Compared with method 1, the CO2 emissions of the entire system in method 4 are reduced by 22.2%.

[0322] Table 1 Comparison of scheduling results of different scheduling methods

[0323]

[0324] Wind turbines provide frequency support and backup services by operating at reduced load, which may affect the profits of wind farms. In the embodiment, the operating profits of wind farms under different methods are analyzed, as shown in Table 2. The on-grid electricity price of wind power generation is set at 10$ / MWh. As can be seen from Table 2, Method 1 does not consider the participation of wind farms in frequency support and backup services, and the profits of wind farms are the lowest. This is because when the penetration rate of wind power is high, the system's flexible adjustment capacity is insufficient, resulting in a decrease in the wind power accommodation ratio, which affects the profits of wind farms. When wind farms provide frequency support and backup services, the system's flexible adjustment capacity is significantly improved, which increases the profits of wind farms. In addition, the auxiliary services provided by wind power generation further increase the profits of wind power generators.

[0325] Table 2 Comparison of wind farm operating profits under different modes

[0326]

[0327] The above embodiments describe the technical solution of the present invention in detail. Obviously, the present invention is not limited to the described embodiments. Based on the embodiments, technicians familiar with the technical field can also make various changes accordingly, but any changes that are equivalent or similar to the present invention belong to the scope of protection of the present invention.

Claims

1. A method for dispatching a power system with wind power reserve and considering the wind turbine wake effect, characterized in that: The following steps are involved: Step 1: Considering the influence of wake effect on wind turbine output, establish a wind farm output model; Step 2: Establish a frequency dynamic model of the power system including wind turbines and conventional units, and obtain expressions for the frequency change rate and maximum frequency deviation of the system; Step 3: Construct power system frequency security constraints based on the frequency change rate and the maximum frequency deviation; Step 4: Establish a mathematical model for the wind farm to provide reserve and determine the upward and downward reserve of the wind farm under the forecast scenario; Step 5: Establish the connection between the wind power reserve under the basic scenario and the wind power reserve under the uncertain scenario, and obtain the expressions of the upward reserve and downward reserve under the uncertain scenario; Step 6: Establish a coordinated dispatch model for wind farms to provide frequency regulation and backup for the power system; Step 7: Use the column and constraint method to solve the collaborative scheduling model, decompose the collaborative scheduling model into a main problem and a sub-problem. The main problem is a mixed integer linear programming problem, and the sub-problem is a Max-Min problem. Solve the sub-problem to obtain the optimal cutting plane, and solve the main problem to obtain the unit combination and unit output; In step 1, the output of wind farm wind turbines is: P w =∑ j m w,j p w,j (1-k w ),m w,j,t ∈{0,1} (2) Where p w,j is the output of fan j, f(v w ) is the relationship function between wind turbine output and wind speed, v w is the wind speed captured by the wind turbine, p R Indicates the rated power of the fan, v in 、v out 、v R are the cut-in wind speed, cut-out wind speed and rated wind speed of the fan respectively; μ w,j represents the operating status of wind turbine j in wind farm w, κ w Indicates the load reduction ratio of wind turbines in the wind farm; P w represents the output of wind farm w; Considering the wake effect of the upstream wind turbines on the downstream wind turbines in the wind farm, the air supply speed of the wind turbines in the wind farm is as follows: Where v w,j represents the captured wind speed of wind turbine j under the influence of wake; ω x It represents the ratio of the wake wind speed to the initial wind speed of the fan x; B j,x represents the wake influence coefficient of wind turbine x on wind turbine j; Where h is the height of the fan; Δh is the height difference between the upstream fan and the downstream fan; C T is the thrust coefficient; r(x) represents the wake influence radius at x; r rot represents the blade radius of the upstream fan; B j,x =A shad-jx / A rot-j (5) Where B j,x A represents the wake influence coefficient of fan x on fan j; shad-jx is the projected area of ​​wind turbine x at wind turbine j; A rot-j is the swept area of ​​fan j blade; Thrust coefficient: C T =4a(1-a) (6) Where a represents the axial coefficient; Combining (3) and (5), we can get In the formula represents the wake reduction factor of wind turbine x on wind turbine j; The output power of the w wind farm considering the wake effect is as follows: P w =∑ j m w,j f(v w,j )(1-k w ) (9); In step 4, the mathematical model of the wind farm providing upward and downward reserves under the forecast scenario is as follows: in They represent the upward and downward reserve that can be provided by the wind farm under the basic scenario respectively; Respectively represent the upward and downward reserve coefficients of the fan; μ w,j,t is the operating status of wind turbine j in the wind farm at time t, p w,j,t is the predicted output of wind turbine j at time t; κ max is the maximum load reduction ratio of the fan; κ w,t It represents the load reduction ratio of wind turbines in wind farm w during period t; Modeling the predicted wind speed of a wind farm as an uncertainty ensemble Among them U W represents the wind power uncertainty set, Indicates uncertain wind speed. They are all 0-1 variables at the boundary of the wind speed uncertainty set, and β represents the wind speed uncertainty coefficient; In step 5, the wind power reserve coefficient is used to link the reserve under the basic scenario with the reserve under the uncertain scenario; Under the uncertain scenario, the upward and downward reserves provided by wind farms are as follows: In the formula They are the upward and downward reserves that wind farms can provide under uncertain scenarios; is the uncertain output of wind turbine j at time t.

2. The power system dispatching method according to claim 1, characterized in that: In step 2, the dynamic model of power system frequency is as follows: Where G(s) represents the transfer function; Δf represents the system frequency deviation; ΔP e Represents the unbalanced power of the system; H g , D g Respectively represent the inertia and damping constant of the generator; T is the time constant of the steam turbine; R i , K i They represent the droop gain and mechanical power gain coefficient of conventional unit i respectively; F i is the fraction of the total power of the synchronous generator; H v,j , D v,j Respectively represent the inertia and damping of wind turbine j; R d,j , K d,j They represent the droop coefficient and power gain coefficient of wind turbine j respectively; T d 、T v are the time constants of the inverter; Inertia of wind farm: Where M W represents the normalized virtual inertia of the wind farm; H v Represents the virtual inertia parameters of the wind turbine; Droop gain of wind farm: Where K d Represents the power gain parameter of the wind turbine; R d is the droop gain parameter of the wind turbine; R W represents the droop gain of the wind farm; Damping of wind farms: Where D v Indicates the damping parameter of the wind turbine; D W represents the damping of the wind farm; Inertia of the system: Where p i max Represents the installed capacity of conventional units; M g is the inertia of the conventional unit; M represents the total inertia of the power system; Damping of the system: Where D g The damping provided for conventional units; D represents the total damping of the power system; Assuming power deviation ΔP e There is a stepwise disturbance in , and the frequency deviation is as follows: Where Δf represents the frequency deviation of the system; ω n is the natural frequency; ξ is the damping ratio; t represents time; T is the time constant of the steam turbine; ω d represents the damping frequency; φ represents the phase, corresponding to the damping ratio; Damping ratio: Where F g is the total power fraction synthesized by the system; R is the total droop gain synthesized by the system; Natural frequency: According to the time domain expression of frequency deviation, the frequency change rate at the initial moment can be obtained: In the formula is the frequency change rate of the system; Maximum frequency deviation: Where Δf nadir is the system frequency deviation; The time when the system frequency reaches the lowest point: Where t nadir The time when the system frequency reaches the lowest point.

3. The power system dispatching method according to claim 2, characterized in that: In step 3, the frequency change rate constraint is: Frequency minimum point constraint: f nadir =f0-f0·Δf nadir ≥f min (25) Where f0 is the reference frequency of the system, is the frequency change rate limit; f nadir is the lowest frequency point of the system, f min The frequency minimum limit; Δf nadir Indicates the maximum frequency deviation.

4. The power system dispatching method according to claim 3, characterized in that: In step 6, the collaborative scheduling model includes: (1) Objective function: Where c i.k is the segmented power generation cost coefficient of unit i; are the startup and shutdown costs of conventional units respectively; c e is the price of carbon dioxide emissions; E i,t represents the carbon dioxide emissions of conventional unit i; They are the upward and downward reserve cost coefficients for conventional units respectively; They are the upward and downward reserve cost coefficients of wind farms, respectively; is the output of unit i at time t during period k; They are the upward and downward reserves provided by conventional unit i at time t; (2) Constraints in basic scenarios: Node power balance constraints: Wherein the subscripts d and l represent load and line respectively; G(m) Indicates the set of buses where conventional units are located; W(m) represents the set of buses where the wind farm is located; L(m) Represents the set of buses connected to line l; D(m) Indicates the set of buses where the loads are located; Indicates the power of line l; P d,t Indicates load demand; Indicates the planned output of the unit the day before; Network constraints: In the formula is the voltage phase angle of node m; represents the voltage phase angle of node n; represents the reference node phase angle; x l is the reactance of the line; Where P l max The capacity limit of the line; Output and reserve limits of conventional units: Where P i min Indicates the minimum output of the unit; Respectively represent the maximum upward and downward reserves provided by the unit; CO2 emission limits: Where E i,t is the carbon dioxide emission of unit i; e i Indicates the CO2 emission intensity per unit of power output; Frequency safety constraints: f nadir =f0+f0·Δf nadir ≥f min (42) Where RoCoF lim Indicates the frequency change rate limit; f nadir The lowest frequency point of the system; f0 is the base frequency of the system; Δf nadir Indicates the maximum frequency deviation; f min Indicates the minimum frequency limit; The constraints in the basic scenario also include startup / shutdown costs, start-up and shutdown constraints, ramp restrictions, and wind farm output constraints and reserve constraints; (3) Constraints in uncertain scenarios; Load uncertainty: Where U D is the load uncertainty set, All are 0-1 variables; are the time and space uncertainty budgets respectively; ΔP d,t represents the load forecast deviation; Node power balance constraints: In the formula Respectively represent the re-dispatching output of conventional units and wind farms; Indicates wind farm redispatching output; Network constraints: In the formula They represent the phase angle and power flow of the line under uncertainty respectively; represents the voltage phase angle of the reference node; Re-dispatch constraints for conventional units: In the formula Indicates that conventional units are put on standby; Indicates that conventional units are downgraded to standby; Re-dispatch constraints for wind farms: In the formula They are respectively the upward and downward reserves that wind farms can provide under uncertain scenarios.

5. The power system dispatching method according to claim 4, characterized in that: Step 7 includes the following sub-steps: Step 7.1: Write the proposed coordinated dispatch model of wind farms providing frequency support and reserve into matrix form; Objective function: The constraints in the basic scenario include: The constraints in uncertain scenarios include: The subscript iter indicates the number of iterations; u iter represents the operating status of the iterated conventional unit, Respectively represent the output of conventional units and wind farms; Respectively represent the reserve of conventional units and wind farms; p r represents the generator output under uncertain scenarios; θ r Represents the node phase angle in uncertain scenarios; Indicates wind power output under uncertain scenarios, represents the uncertain variable of wind power; represents the load uncertainty variable; a, b, c, e, f, h, z, A, B, E, G, L, N, O, Q, R, X, V, W are all constant coefficient matrices; Step 7.2: Decompose the original model of the collaborative scheduling model into a main problem and sub-problems by using a column and constraint generation algorithm, and solve them; (1) Solve the main problem; Objective function: The constraints include: Where F is a constant coefficient matrix; The columns and constraints returned by the subproblem generate the optimal cutting plane of the algorithm; The main problem is a mixed integer linear programming problem, which is solved by Gurobi; Solve the main problem to obtain the basic unit combination I b and unit output p b , and passed to the sub-problem; (2) Solve the sub-problems; The subproblem can be expressed as a Max-Min problem; to ensure that the problem has a feasible solution, the relaxation vector s is introduced; Sub-problem objective function: Constraints: The subproblem is a Max-Min problem and cannot be solved directly; The inner layer Min problem is a linear problem, which can be transformed into a single layer problem by dual transformation. Objective function: Constraints: W·n≤0, Q·n≤0, V·n≤0, X·n≤1 (60) η≤0 or unlimited (61) Where η is the dual variable of the subproblem; Solve the subproblem to get the optimal solution ψ; If ψ>ε, ε is the iteration threshold, based on the worst scenario of wind power and load Generate the optimal cutting plane generated by the columns and constraints; otherwise, end the iteration; (3) Generate the optimal cutting plane generated by the columns and constraints; Create New Variable s iter+1 , and generate the optimal cutting plane generated by the columns and constraints, Where iter represents the number of iterations; (4) Return to the main problem and solve it again.

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