Inertia and primary frequency regulation pricing method considering wind turbine generator electrical power loss

Abstract

The application discloses an inertia and primary frequency modulation pricing method considering wind turbine electric power loss, and the method comprises the following steps: acquiring power grid basic data, which is used for quantifying system frequency response characteristics, and establishing frequency safety constraints based on the system frequency response characteristics; a joint clearing model considering wind turbine electric power loss is established, the joint clearing model comprises a target function and constraint conditions, the constraint conditions comprise power balance constraints, unit constraints and frequency safety constraints, and the power balance constraints consider wind turbine electric power loss; the conventional units and the wind turbines are jointly optimized based on the joint clearing model, and joint clearing results are obtained; and the marginal price of inertia and primary frequency modulation is calculated by using the Lagrange multiplier method based on the joint clearing results. The application can realize explicit measurement of the opportunity cost of wind turbine electric power loss, and improve the frequency safety and operation economy of a power system containing a high proportion of new energy.

Description

Technical Field

[0001] This invention relates to power technology, and more specifically to an inertia and primary frequency regulation pricing method that takes into account the power loss of wind turbine generators. Background Technology

[0002] As the penetration rate of new energy sources continues to increase, the inertia level of the power system continues to decline, posing a more severe challenge to frequency security. With technological advancements, inertia has transformed from an "auxiliary capability" of traditional synchronous generators into an independent, tradable resource. However, the current spot market and ancillary service market have not yet established a complete inertia pricing mechanism. In particular, the power losses associated with new energy generators providing virtual inertia and primary frequency regulation services are not explicitly factored in, leading to the following key issues:

[0003] 1) Insufficient cost compensation for new energy units. Wind turbines provide virtual inertia through power electronic interfaces. When inertial response occurs, the rotor decelerates and deviates from the maximum power point, directly causing a deviation between mechanical power and electrical power, i.e., electrical power loss. However, the existing pricing mechanism does not take this loss into account, resulting in insufficient enthusiasm for participation.

[0004] 2) The coupling relationship between energy, inertia, and frequency regulation is not reflected in the pricing. Inertia response changes the available frequency regulation capability of a wind turbine, but the existing mechanism still prices energy, inertia, and primary frequency regulation separately, lacking a unified optimization and joint clearing framework, and failing to truly reflect the coupling relationship between the three and their impact on system frequency security. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies by providing a pricing method for inertia and primary frequency regulation that considers the power loss of wind turbine generators.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A pricing method for inertia and primary frequency regulation that considers the power loss of wind turbine generators includes the following steps: Acquire basic power grid data to quantify system frequency response characteristics, and establish frequency security constraints based on system frequency response characteristics; A joint clearing model is established that coordinates energy, inertia, and primary frequency regulation. The joint clearing model includes an objective function and constraints, including power balance constraints, turbine constraints, and frequency security constraints. The power balance constraints take into account the power loss of the wind turbine. Based on the joint clearing model, conventional units and wind turbine units are jointly optimized to obtain joint clearing results; Based on the joint clearing results, the inertia and marginal price of primary frequency modulation are calculated using the Lagrange multiplier method.

[0007] To optimize the above technical solution, the specific measures also include: Furthermore, the basic power grid data includes generating unit data, load data, renewable energy data, load forecasting error data, and renewable energy forecasting error data.

[0008] Furthermore, the frequency response characteristics of the quantization system specifically include: quantizing three features: maximum frequency change rate, inertia response time, and maximum frequency difference; The maximum rate of frequency change is specifically the maximum value of the rate of frequency change of the power system at the moment the disturbance occurs, and its calculation formula is as follows:

[0009] In the formula, Indicates the maximum rate of change of frequency. Represents the change in frequency The differential, Δ represents the derivative of time t. P This indicates the power of the disturbance experienced by the system; H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. The inertia response time is specifically the time it takes for the system frequency to drop to its lowest point. It is calculated based on the equivalent inertia of the power system after the wind turbine is connected to the grid, the equivalent damping of the system, and the equivalent gain of the speed governor. The calculation formula is as follows:

[0010] In the formula, t nadir Indicates the inertia response time. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. D eq Indicates the equivalent damping of the system; K eq This represents the equivalent gain of the speed controller. a eq Indicates the equivalent parameter one. T eq Indicates the second equivalent parameter; The maximum frequency difference is specifically the frequency difference caused by Δ in the system. P The maximum frequency deviation is determined by the disturbance power, and its calculation formula is as follows:

[0011] In the formula, Δf max Indicates the maximum frequency difference. K eq Δ represents the equivalent gain of the speed controller. P This indicates the power of the disturbance experienced by the system; D eq Indicates the equivalent damping of the system. aeq Indicates the equivalent parameter one. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. T eq This represents the equivalent parameter two.

[0012] Furthermore, the establishment of frequency security constraints based on system frequency response characteristics specifically refers to: Frequency safety constraints include maximum frequency difference constraints, frequency change rate constraints, and quasi-steady-state constraints; The maximum frequency difference constraint is that the frequency difference of the system during the inertial response time does not exceed the maximum frequency difference, and the specific formula is as follows:

[0013] In the formula, H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. Δf max Indicates the maximum frequency difference. f N Indicates the system's rated frequency. R G This indicates the combined frequency regulation capability of all thermal power units. R I This represents the combined frequency regulation capability of all wind turbine units. T PFR This indicates the full-power response time of the synchronous generator frequency regulation service; T EFR Δ represents the full-power response time of frequency modulation services for power electronic equipment; P This indicates the power of the disturbance experienced by the system; The frequency change rate constraint is specifically as follows:

[0014] In the formula, H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. f N Indicates the system's rated frequency, Δ P This represents the power of the disturbance experienced by the system. Indicates the maximum rate of change of frequency; The quasi-steady-state constraint is that the sum of the aggregated frequency regulation capabilities of all thermal power units and the aggregated frequency regulation capabilities of all wind power units is not less than the disturbance power experienced by the system. The specific formula is as follows:

[0015] In the formula, R G This indicates the combined frequency regulation capability of all thermal power units.R I Δ represents the combined frequency regulation capability of all wind turbine units. P This indicates the power of the disturbance experienced by the system.

[0016] Furthermore, the objective function of the joint clearing model is as follows:

[0017] In the formula, T represents the scheduling period, and N represents the number of synchronous generators. This represents the unit cost function, which includes start-up, shutdown, and operating costs. P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; C i PFR This indicates the price quoted for a single frequency modulation operation of the synchronous machine. R G,i,t This indicates the primary frequency regulation quantity of the synchronous machine; M represents the number of wind turbine units. C i W This indicates the electricity price quoted for wind turbine units. P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period; C i EFR This indicates the price quote for primary frequency regulation of wind turbine units; R I,i,t This indicates the amount won in the primary frequency regulation of the wind turbine. C i H Indicates virtual inertia pricing; H w,i,t Indicates the scalar value of virtual inertia; The constraints of the joint clearing model include power balance constraints, unit constraints, and frequency security constraints. The power balance constraint takes into account the power loss of the wind turbine generator, and the specific formula is as follows:

[0018] In the formula, P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period P curtThis indicates the power loss of the wind turbine generator. express t Load during the period; The unit constraints include wind turbine output constraints, conventional unit output constraints, synchronous unit ramping constraints, synchronous unit start-stop constraints, synchronous unit frequency regulation constraints, wind turbine frequency regulation constraints, wind turbine virtual inertia constraints, and power flow safety constraints. The frequency security constraints include maximum frequency difference constraints, frequency change rate constraints, and quasi-steady-state constraints.

[0019] Furthermore, the formula for calculating the power loss of the wind turbine is as follows:

[0020] In the formula, P curt This indicates the power loss of the wind turbine generator. H w This represents the virtual inertia provided by the wind turbine. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. This indicates the combined frequency regulation capability of all thermal power units. t nadir For inertial response time, T PFR This indicates the full-power response time of the synchronous generator frequency regulation service. R I This indicates the combined frequency regulation capability of all wind turbine units; T EFR This indicates the full-power response time of frequency regulation services for power electronic equipment.

[0021] Furthermore, the specific constraints on the wind turbine output are as follows:

[0022] In the formula, P W,i,min Indicates the first i Minimum output of each wind turbine unit P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period P W,i,max Indicates the first i Maximum output of each wind turbine R i,I Indicates the full power of the fan frequency modulation; The specific output constraints of the conventional generating units are as follows:

[0023] In the formula,u i,t Indicates the first i Taiwan synchronous generator unit t Start / stop status during a time period Indicates the first i Each synchronous unit in t Minimum output during the time period P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; Indicates the first i Each synchronous unit in t Maximum output during the period R i,G Indicates the first i The full power of the primary frequency modulation of the synchronous machine; The specific ramp-up constraints for the synchronous generator units are as follows:

[0024]

[0025] In the formula, P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period Indicates the first i Each synchronous unit in t Output during the -1 time period Indicates the first i Taiwan synchronous generator unit t Start-stop status during the -1 time period R u This indicates the ramp-up rate of the synchronous machine. S i,u Indicates the first i The synchronous generator unit starts at maximum lifting capacity. u i,t Indicates the first i Taiwan synchronous generator unit t Start / stop status during a time period R d This indicates the ramp-down rate of the synchronous machine. S i,d Indicates the first i The maximum output reduction when the synchronous generator unit is shut down; The specific start-up and shutdown constraints of the synchronous generator units are as follows:

[0026]

[0027] In the formula, Indicates the firsti Taiwan synchronous generator unit k Start / stop status during a time period TS Indicates the minimum shutdown time. Indicates the first i Taiwan synchronous generator unit t Start-stop status during the -1 time period u i,t Indicates the first i Taiwan synchronous generator unit t Start / stop status during a time period TO Indicates the minimum boot time; The frequency regulation constraints of the synchronous generator unit are as follows:

[0028] In the formula, R i,G Indicates the first i The full power of the primary frequency regulation of the synchronous generator unit; r i This indicates the speed limiter of the synchronous generator unit. u i,t Indicates the first i Taiwan synchronous generator unit t Start / stop status during a time period Indicates the first i The maximum output of each synchronous generator unit; The specific frequency regulation constraints of the wind turbine generator are as follows:

[0029] In the formula, R i,I Indicates the first i FM full power of typhoon generator unit; r e This indicates the speed limiter of the wind turbine generator. P W,i,max Indicates the first i Maximum output of each wind turbine unit; The specific virtual inertia constraint of the wind turbine is as follows:

[0030] In the formula, Let represent the virtual inertia of the i-th wind turbine. H w,max This represents the maximum value of the inertia level; The specific power flow safety constraints are as follows:

[0031] In the formula, P i Indicates the line iThe transmission power; P i,max Indicates the line i Maximum permissible transmission power; V q Indicates the first q The voltage amplitude at each node, V min and V max These represent the maximum and minimum allowable values ​​for the voltage amplitude, respectively.

[0032] Furthermore, the joint clearing result specifically refers to the unit scheduling result, including the unit output, inertia level, and primary frequency regulation magnitude of the synchronous unit at 24 time points.

[0033] Furthermore, the calculation of inertia and the marginal price of primary frequency modulation using the Lagrange multiplier method based on the joint clearing results specifically involves: By using Lagrange multipliers, the objective function and constraints of the joint clearing model are transformed into Lagrange functions. The partial derivatives of the Lagrange functions are then used to obtain the marginal price calculation formulas for inertia and frequency modulation. The joint clearing results are then substituted into the marginal price calculation formulas for inertia and frequency modulation to obtain the marginal prices for inertia and frequency modulation.

[0034] Furthermore, the Lagrange function is specifically:

[0035] In the formula, L represents the Lagrange function, T represents the scheduling period, and N represents the number of synchronous generators. This represents the unit cost function, which includes start-up, shutdown, and operating costs. P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; C i PFR This indicates the price quoted for a single frequency modulation operation of the synchronous machine. R G,i,t This indicates the primary frequency regulation quantity of the synchronous machine; M represents the number of wind turbine units. C i W This indicates the electricity price quoted for wind turbine units. P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period; C i EFR This indicates the price quote for primary frequency regulation of wind turbine units; R I,i,t This indicates the amount won in the primary frequency regulation of the wind turbine. Ci H Indicates virtual inertia pricing; H w,i,t Indicates the scalar value of virtual inertia; α 1 represents the dual multiplier of the power balance constraint; P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period P curt This indicates the power loss of the wind turbine output. P sys express t Load during the period; l RoCoF Represents the dual multiplier of the frequency change rate constraint. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. f N Indicates the system's rated frequency, Δ P This represents the power of the disturbance experienced by the system. Indicates the maximum rate of change of frequency; l q-s-s Denotes the dual multipliers of quasi-steady-state constraints. R G This indicates the combined frequency regulation capability of all thermal power units. R I Δ represents the combined frequency regulation capability of all wind turbine units. P This represents the power of the disturbance experienced by the system. l 1. l 2. m Represents the dual multiplier of the maximum frequency difference constraint; T PFR This indicates the full-power response time of the synchronous generator frequency regulation service; T EFR Indicates the full-power response time of frequency modulation services for power electronic equipment; Δf max Indicates the maximum frequency difference. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. The marginal price calculation formulas for inertia and frequency modulation are as follows: The specific formula for calculating the marginal price of frequency modulation is as follows:

[0036] In the formula, l PFR This represents the marginal price of primary frequency regulation for a synchronous generator unit. α 1 represents the dual multiplier of the power balance constraint. H w This represents the virtual inertia provided by the wind turbine. t nadir For inertial response time, This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. T PFR This indicates the full-power response time of the synchronous generator frequency regulation service; l 1. l 2. m Represents the dual multipliers of the maximum frequency difference constraint. l q-s-s Denotes the dual multipliers of quasi-steady-state constraints. This represents the marginal price of primary frequency regulation for wind turbine units. T EFR Indicates the full-power response time of frequency regulation services for power electronic equipment. Δf max Indicates the maximum frequency difference; The specific formula for calculating the marginal price of inertia is as follows:

[0037] In the formula, l sys This represents the marginal price of the inertia of a synchronous generator unit. l w This represents the marginal price of the virtual inertia of a wind turbine. This indicates the capacity percentage of thermal power units in the system.

[0038] The beneficial effects of this invention are: To address the current lack of mechanisms in the spot market to incentivize the supply of inertial resources, this invention presents a pricing method for inertia and primary frequency regulation that considers the power loss of wind turbine generators. This method calculates the price of system inertia and frequency regulation, thereby guiding dispatching agencies to fully incentivize renewable energy manufacturers to provide inertial resources. This effectively expands the advantages of renewable energy virtual inertia compensation control in ancillary services and its impact on the market. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating an inertia-based pricing method for primary frequency regulation that considers power loss in wind turbine generators, provided by the present invention. Figure 2 This is a schematic diagram of a simplified model of the frequency response of a power system provided by the present invention; Figure 3 This is a diagram of an IEEE-30 node network. Figure 4 This is a graph showing the output results of thermal power units for each time period.

[0040] Figure 5 This is a graph showing the virtual inertia and power output reduction of the wind turbine at each time period; Figure 6 This is a graph showing the calculation results of the virtual inertia price of wind turbines for each time period. Detailed Implementation

[0041] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0042] Example 1 This invention proposes a pricing method for wind turbine inertia and primary frequency regulation that considers power loss. The process of this method is as follows: Figure 1 As shown, it includes the following steps: S1. Obtain basic power grid data, including generating unit data, load data, renewable energy data, load forecasting error data, and renewable energy forecasting error data. This data is used to quantify the system's frequency response characteristics and establish frequency security constraints based on these characteristics. The specific frequency response characteristics of the quantized system are as follows: A power system frequency response model with virtual inertia control capability is constructed for wind turbines and synchronous generators. The simplified power system frequency response model in this embodiment is as follows: Figure 2 Based on this model, three characteristics were quantified: maximum frequency change rate, inertia response time, and maximum frequency difference. The formula for calculating the maximum rate of change of frequency is as follows:

[0043] In the formula, Indicates the maximum rate of change of frequency. Represents the change in frequency The differential, Δ represents the derivative of time t. P This indicates the power of the disturbance experienced by the system; H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid; the maximum rate of frequency change is generally taken as 0.5 Hz / s. The formula for calculating inertia response time is as follows:

[0044] In the formula, tnadir Indicates the inertia response time. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. D eq Indicates the equivalent damping of the system; K eq This represents the equivalent gain of the speed controller. a eq Indicates the equivalent parameter one. T eq Indicates the second equivalent parameter; The formula for calculating the maximum frequency difference is as follows:

[0045] In the formula, Δf max Indicates the maximum frequency difference. K eq Δ represents the equivalent gain of the speed controller. P This indicates the power of the disturbance experienced by the system; D eq Indicates the equivalent damping of the system. a eq Indicates the equivalent parameter one. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. T eq This represents equivalent parameter two. The maximum frequency deviation of a typical system is 1 Hz.

[0046] The frequency security constraints established based on the system's frequency response characteristics are as follows: Constructing the frequency response equation for a power system with a high proportion of renewable energy connected to the grid:

[0047] H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. EFR(t) Indicates the frequency regulation power of the new energy unit; PFR (t) Indicates the frequency regulation power of the synchronous generator unit; Δ P This indicates the power of the disturbance experienced by the system; P res (t) This represents the power generated by the "restoration effect" in the renewable energy unit. The power signal model of the unit is expressed as follows: Frequency modulation response model of power electronic equipment:

[0048] T EFR R represents the full-power response time of frequency regulation services for power electronic equipment.i This represents the frequency droop coefficient of new energy power generation units.

[0049] Frequency regulation response model of synchronous generator units:

[0050] T PFR This indicates the full-power response time of the synchronous generator frequency regulation service; R g This represents the frequency droop coefficient of a thermal power unit.

[0051] The "restoration effect" model of wind turbines:

[0052] k rec Indicates the recovery factor; T rec Indicates the time when the recovery effect occurs. This indicates the magnitude of the virtual inertia level of the wind turbine.

[0053] Frequency security constraints are obtained by integral transformation of the frequency response equation of a power system with a high proportion of renewable energy connected to the grid.

[0054] Frequency safety constraints include maximum frequency difference constraints, frequency change rate constraints, and quasi-steady-state constraints; The maximum frequency difference constraint is as follows:

[0055] Its integral term is expanded as follows:

[0056] After rearranging and substituting these values, we obtain the final maximum frequency difference constraint:

[0057] In the formula, H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. Δf max Indicates the maximum frequency difference. f N Indicates the system's rated frequency. R G This indicates the combined frequency regulation capability of all thermal power units. R I ∑ represents the aggregate frequency regulation capability of all wind turbine units. R i = R I ;∑ R g =R G . T PFR This indicates the full-power response time of the synchronous generator frequency regulation service; T EFR Δ represents the full-power response time of frequency modulation services for power electronic equipment; P This indicates the power of the disturbance experienced by the system; The frequency change rate constraint is as follows:

[0058] In the formula, H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. f N Indicates the system's rated frequency, Δ P This represents the power of the disturbance experienced by the system. Indicates the maximum rate of change of frequency; The quasi-steady-state constraints are as follows:

[0059] In the formula, R G This indicates the combined frequency regulation capability of all thermal power units. R I Δ represents the combined frequency regulation capability of all wind turbine units. P This indicates the power of the disturbance experienced by the system.

[0060] S2. Establish a joint clearing model that considers the power loss of wind turbine units. The joint clearing model includes an objective function and constraints, including power balance constraints, unit constraints, and frequency security constraints. The power balance constraints consider the power loss of wind turbine units. The objective function of the joint clearing model is as follows:

[0061] In the formula, T represents the scheduling period, and N represents the number of synchronous generators. This represents the unit cost function, which includes start-up, shutdown, and operating costs. P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; C i PFR This indicates the price quoted for a single frequency modulation operation of the synchronous machine. R G,i,t This indicates the primary frequency regulation quantity of the synchronous machine; M represents the number of wind turbine units. C i WThis indicates the electricity price quoted for wind turbine units. P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period; C i EFR This indicates the price quote for primary frequency regulation of wind turbine units; R I,i,t This indicates the amount won in the primary frequency regulation of the wind turbine. C i H Indicates virtual inertia pricing; H w,i,t Indicates the scalar value of virtual inertia; The constraints of the joint clearing model include power balance constraints, unit constraints, and frequency security constraints. The power balance constraint is specifically as follows:

[0062] In the formula, P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period P curt This indicates the power loss of the wind turbine output. express t Load during the period; The formula for calculating the power loss of the wind turbine output is as follows:

[0063] In the formula, P curt This indicates the power loss of the wind turbine output. H w This represents the virtual inertia provided by the wind turbine. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. This indicates the combined frequency regulation capability of all thermal power units. t nadir For inertial response time, T PFR This indicates the full-power response time of the synchronous generator frequency regulation service. R I This indicates the combined frequency regulation capability of all wind turbine units; T EFR This indicates the full-power response time of frequency regulation services for power electronic equipment.

[0064] The unit constraints include wind turbine output constraints, conventional unit output constraints, synchronous unit ramping constraints, synchronous unit start-stop constraints, synchronous unit frequency regulation constraints, wind turbine frequency regulation constraints, wind turbine virtual inertia constraints, and power flow safety constraints. The specific constraints on the wind turbine output are as follows:

[0065] In the formula, P W,i,min Indicates the first i Minimum output of each wind turbine unit P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period P W,i,max Indicates the first i Maximum output of each wind turbine R i,I Indicates the full power of the fan frequency modulation; The specific output constraints of conventional generating units are as follows:

[0066] In the formula, u i,t Indicates the first i Taiwan synchronous generator unit t Start / stop status during a time period Indicates the first i Each synchronous unit in t Minimum output during the time period P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; Indicates the first i Each synchronous unit in t Maximum output during the period R i,G Indicates the first i The full power of the primary frequency modulation of the synchronous machine; The specific ramp-up constraints for synchronous generator units are as follows:

[0067]

[0068] In the formula, P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period Indicates the first iEach synchronous unit in t Output during the -1 time period Indicates the first i Taiwan synchronous generator unit t Start-stop status during the -1 time period R u This indicates the ramp-up rate of the synchronous machine. S i,u Indicates the first i The synchronous generator unit starts at maximum lifting capacity. u i,t Indicates the first i Taiwan synchronous generator unit t Start / stop status during a time period R d This indicates the ramp-down rate of the synchronous machine. S i,d Indicates the first i The maximum output reduction when the synchronous generator unit is shut down; The specific start-up and shutdown constraints for synchronous generator units are as follows:

[0069]

[0070] In the formula, Indicates the first i Taiwan synchronous generator unit k Start / stop status during a time period TS Indicates the minimum shutdown time. Indicates the first i Taiwan synchronous generator unit t Start-stop status during the -1 time period u i,t Indicates the first i Taiwan synchronous generator unit t Start / stop status during a time period TO Indicates the minimum boot time; The frequency regulation constraints of synchronous generator units are as follows:

[0071] In the formula, R i,G Indicates the first i The full power of the primary frequency regulation of the synchronous generator unit; r i This indicates the speed limiter of the synchronous generator unit. u i,t Indicates the first i Taiwan synchronous generator unit t Start / stop status during a time period Indicates the first i The maximum output of each synchronous generator unit; The specific frequency regulation constraints for wind turbine generators are as follows:

[0072] In the formula, R i,I Indicates the first i FM full power of typhoon generator unit; r e This indicates the speed limiter of the wind turbine generator. P W,i,max Indicates the first i Maximum output of each wind turbine unit; The specific virtual inertia constraints for wind turbine units are as follows:

[0073] In the formula, Let represent the virtual inertia of the i-th wind turbine. H w,max This represents the maximum value of the inertia level; The specific power flow safety constraints are as follows:

[0074] In the formula, P i Indicates the line i The transmission power; P i,max Indicates the line i Maximum permissible transmission power; V q Indicates the first q The voltage amplitude at each node, V min and V max These represent the maximum and minimum allowable values ​​for the voltage amplitude, respectively.

[0075] The frequency security constraints include maximum frequency difference constraints, frequency change rate constraints, and quasi-steady-state constraints.

[0076] The form of frequency security constraints is shown in S1.

[0077] S3. Based on the joint clearing model, the conventional units and wind turbines are jointly optimized to obtain the joint clearing results. The joint clearing results are specifically the unit scheduling results, including the unit output, inertia level and primary frequency regulation magnitude of the synchronous units at 24 time points.

[0078] S4. Based on the joint clearing results, calculate the inertia and the marginal price of primary frequency modulation using the Lagrange multiplier method. Specifically: The objective function and constraints of the joint clearing model are transformed into Lagrange functions using Lagrange multipliers. The specific Lagrange functions are as follows:

[0079] In the formula, L represents the Lagrange function, T represents the scheduling period, and N represents the number of synchronous generators. This represents the unit cost function, which includes start-up, shutdown, and operating costs. P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; C i PFR This indicates the price quoted for a single frequency modulation operation of the synchronous machine. R G,i,t This indicates the primary frequency regulation quantity of the synchronous machine; M represents the number of wind turbine units. C i W This indicates the electricity price quoted for wind turbine units. P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period; C i EFR This indicates the price quote for primary frequency regulation of wind turbine units; R I,i,t This indicates the amount won in the primary frequency regulation of the wind turbine. C i H Indicates virtual inertia pricing; H w,i,t Indicates the scalar value of virtual inertia; α 1 represents the dual multiplier of the power balance constraint; P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period P curt This indicates the power loss of the wind turbine output. P sys express t Load during the period; l RoCoF Represents the dual multiplier of the frequency change rate constraint. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. f N Indicates the system's rated frequency, Δ P This represents the power of the disturbance experienced by the system. Indicates the maximum rate of change of frequency; lq-s-s Denotes the dual multipliers of quasi-steady-state constraints. R G This indicates the combined frequency regulation capability of all thermal power units. R I Δ represents the combined frequency regulation capability of all wind turbine units. P This represents the power of the disturbance experienced by the system. l 1. l 2. m Represents the dual multiplier of the maximum frequency difference constraint; T PFR This indicates the full-power response time of the synchronous generator frequency regulation service; T EFR Indicates the full-power response time of frequency modulation services for power electronic equipment; Δf max Indicates the maximum frequency difference. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid.

[0080] The marginal price calculation formulas for inertia and frequency modulation are obtained by taking the partial derivative of the Lagrange function. Substituting the joint clearing results into the marginal price calculation formulas for inertia and frequency modulation, the marginal prices of inertia and frequency modulation are obtained.

[0081] The specific formula for calculating the marginal price of frequency modulation is as follows:

[0082] In the formula, l PFR This represents the marginal price of primary frequency regulation for a synchronous generator unit. α 1 represents the dual multiplier of the power balance constraint. H w This represents the virtual inertia provided by the wind turbine. t nadir For inertial response time, This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. T PFR This indicates the full-power response time of the synchronous generator frequency regulation service; l 1. l 2. m Represents the dual multipliers of the maximum frequency difference constraint. l q-s-s Denotes the dual multipliers of quasi-steady-state constraints. This represents the marginal price of primary frequency regulation for wind turbine units. T EFR Indicates the full-power response time of frequency regulation services for power electronic equipment. Δf max Indicates the maximum frequency difference; The specific formula for calculating the marginal price of inertia is as follows:

[0083] In the formula, l sys This represents the marginal price of the inertia of a synchronous generator unit. l w This represents the marginal price of the virtual inertia of a wind turbine. This indicates the capacity percentage of thermal power units in the system.

[0084] The following specific examples will be used for verification.

[0085] Choose an IEEE-30 node network, such as Figure 3 As shown in Table 1, the generator data and the output curve of the thermal power unit are shown in Table 2. Figure 4 As shown, the virtual inertia results of the wind turbine are as follows: Figure 5 As shown.

[0086] Table 1 Generator Data

[0087] The power output of the thermal power unit obtained by the present invention under the two methods is compared as follows: Figure 4 As shown; the virtual inertia results provided by the wind turbine are as follows Figure 5 As shown; the virtual inertia price calculation results are as follows. Figure 6 As shown, the realization of virtual inertia in wind turbines causes temporary power losses. If the optimization model does not consider this loss, the marginal cost of wind turbines providing inertia to the system will be underestimated, resulting in a low price for virtual inertia. When power losses are accurately modeled, the reduction in wind turbine output will no longer be "zero cost," and its corresponding opportunity cost will be reflected in the market clearing results, thereby pushing up the price level of inertia, making it more in line with actual operating economics, and effectively stimulating the supply of inertial resources.

[0088] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0089] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A pricing method for inertia and primary frequency regulation that considers the power loss of wind turbine generators, characterized in that, Includes the following steps: Acquire basic power grid data to quantify system frequency response characteristics, and establish frequency security constraints based on system frequency response characteristics; A joint clearing model is established that coordinates energy, inertia, and primary frequency regulation. The joint clearing model includes an objective function and constraints, including power balance constraints, turbine constraints, and frequency security constraints. The power balance constraints take into account the power loss of the wind turbine. Based on the joint clearing model, conventional units and wind turbine units are jointly optimized to obtain joint clearing results; Based on the joint clearing results, the inertia and marginal price of primary frequency modulation are calculated using the Lagrange multiplier method.

2. The inertia and primary frequency regulation pricing method considering power loss of wind turbine generators as described in claim 1, characterized in that, The basic power grid data includes generating unit data, load data, renewable energy data, load forecasting error data, and renewable energy forecasting error data.

3. The pricing method for inertia and primary frequency regulation considering power loss of wind turbine generators as described in claim 1, characterized in that, The frequency response characteristics of the quantization system are specifically: the maximum frequency change rate, inertia response time and maximum frequency difference are quantized. The maximum rate of frequency change is specifically the maximum value of the rate of frequency change of the power system at the moment the disturbance occurs, and its calculation formula is as follows: In the formula, Indicates the maximum rate of change of frequency. Represents the change in frequency The differential, Δ represents the derivative of time t. P This indicates the power of the disturbance experienced by the system; H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. The inertia response time is specifically the time it takes for the system frequency to drop to its lowest point. It is calculated based on the equivalent inertia of the power system after the wind turbine is connected to the grid, the equivalent damping of the system, and the equivalent gain of the speed governor. The calculation formula is as follows: In the formula, t nadir Indicates the inertia response time. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. D eq Indicates the equivalent damping of the system; K eq This represents the equivalent gain of the speed controller. a eq Indicates the equivalent parameter one. T eq Indicates the second equivalent parameter; The maximum frequency difference is specifically the frequency difference caused by Δ in the system. P The maximum frequency deviation is determined by the disturbance power, and its calculation formula is as follows: In the formula, Δf max Indicates the maximum frequency difference. K eq Δ represents the equivalent gain of the speed controller. P This indicates the power of the disturbance experienced by the system; D eq Indicates the equivalent damping of the system. a eq Indicates the equivalent parameter one. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. T eq This represents the equivalent parameter two.

4. The inertia and primary frequency regulation pricing method considering power loss of wind turbine generators as described in claim 1, characterized in that, The establishment of frequency security constraints based on system frequency response characteristics specifically refers to: Frequency safety constraints include maximum frequency difference constraints, frequency change rate constraints, and quasi-steady-state constraints; The maximum frequency difference constraint is that the frequency difference of the system during the inertial response time does not exceed the maximum frequency difference, and the specific formula is as follows: In the formula, H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. Δf max Indicates the maximum frequency difference. f N Indicates the system's rated frequency. R G This indicates the combined frequency regulation capability of all thermal power units. R I This represents the combined frequency regulation capability of all wind turbine units. T PFR This indicates the full-power response time of the synchronous generator frequency regulation service; T EFR Δ represents the full-power response time of frequency modulation services for power electronic equipment; P This indicates the power of the disturbance experienced by the system; The frequency change rate constraint is specifically as follows: In the formula, H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. f N Indicates the system's rated frequency, Δ P This represents the power of the disturbance experienced by the system. Indicates the maximum rate of change of frequency; The quasi-steady-state constraint is that the sum of the aggregated frequency regulation capabilities of all thermal power units and the aggregated frequency regulation capabilities of all wind power units is not less than the disturbance power experienced by the system. The specific formula is as follows: In the formula, R G This indicates the combined frequency regulation capability of all thermal power units. R I Δ represents the combined frequency regulation capability of all wind turbine units. P This indicates the power of the disturbance experienced by the system.

5. The inertia and primary frequency regulation pricing method considering the power loss of wind turbine generators as described in claim 4, characterized in that, The objective function of the joint clearing model is as follows: In the formula, T represents the scheduling period, and N represents the number of synchronous generators. This represents the unit cost function, which includes start-up, shutdown, and operating costs. P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; C i PFR This indicates the price quoted for a single frequency modulation operation of the synchronous machine. R G,i,t This indicates the primary frequency regulation quantity of the synchronous machine; M represents the number of wind turbine units. C i W This indicates the electricity price quoted for wind turbine units. P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period; C i EFR This indicates the price quote for primary frequency regulation of wind turbine units; R I,i,t This indicates the amount won in the primary frequency regulation of the wind turbine. C i H Indicates virtual inertia pricing; H w,i,t Indicates the scalar value of virtual inertia; The constraints of the joint clearing model include power balance constraints, unit constraints, and frequency security constraints. The power balance constraint takes into account the power loss of the wind turbine generator, and the specific formula is as follows: In the formula, P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period P curt This indicates the power loss of the wind turbine generator. express t Load during the period; The unit constraints include wind turbine output constraints, conventional unit output constraints, synchronous unit ramping constraints, synchronous unit start-stop constraints, synchronous unit frequency regulation constraints, wind turbine frequency regulation constraints, wind turbine virtual inertia constraints, and power flow safety constraints. The frequency security constraints include maximum frequency difference constraints, frequency change rate constraints, and quasi-steady-state constraints.

6. The inertia and primary frequency regulation pricing method considering the power loss of wind turbine generators as described in claim 5, characterized in that, The formula for calculating the power loss of the wind turbine is as follows: In the formula, P curt This indicates the power loss of the wind turbine generator. H w This represents the virtual inertia provided by the wind turbine. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. This indicates the combined frequency regulation capability of all thermal power units. t nadir For inertial response time, T PFR This indicates the full-power response time of the synchronous generator frequency regulation service. R I This indicates the combined frequency regulation capability of all wind turbine units; T EFR This indicates the full-power response time of frequency regulation services for power electronic equipment.

7. The inertia and primary frequency regulation pricing method considering power loss of wind turbine generators as described in claim 5, characterized in that, The specific constraints on the wind turbine output are as follows: In the formula, P W,i,min Indicates the first i Minimum output of each wind turbine unit P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period P W,i,max Indicates the first i Maximum output of each wind turbine R i,I Indicates the full power of the fan frequency modulation; The specific output constraints of the conventional generating units are as follows: In the formula, u i,t Indicates the first i Taiwan synchronous generator unit t Start / stop status during a time period Indicates the first i Each synchronous unit in t Minimum output during the time period P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; Indicates the first i Each synchronous unit in t Maximum output during the period R i,G Indicates the first i The full power of the primary frequency modulation of the synchronous machine; The specific ramp-up constraints for the synchronous generator units are as follows: In the formula, P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period Indicates the first i Each synchronous unit in t Output during the -1 time period Indicates the first i Taiwan synchronous generator unit t Start-stop status during the -1 time period R u This indicates the ramp-up rate of the synchronous machine. S i,u Indicates the first i The synchronous generator unit starts at maximum lifting capacity. u i,t Indicates the first i Taiwan synchronous generator unit t Start / stop status during a time period R d This indicates the ramp-down rate of the synchronous machine. S i,d Indicates the first i The maximum output reduction when the synchronous generator unit is shut down; The specific start-up and shutdown constraints of the synchronous generator units are as follows: In the formula, Indicates the first i Taiwan synchronous generator unit k Start / stop status during a time period TS Indicates the minimum shutdown time. Indicates the first i Taiwan synchronous generator unit t Start-stop status during the -1 time period u i,t Indicates the first i Taiwan synchronous generator unit t Start / stop status during a time period TO Indicates the minimum boot time; The frequency regulation constraints of the synchronous generator unit are as follows: In the formula, R i,G Indicates the first i The full power of the primary frequency regulation of the synchronous generator unit; r i This indicates the speed limiter of the synchronous generator unit. u i,t Indicates the first i Taiwan synchronous generator unit t Start / stop status during a time period Indicates the first i The maximum output of each synchronous generator unit; The specific frequency regulation constraints of the wind turbine generator are as follows: In the formula, R i,I Indicates the first i FM full power of typhoon generator unit; r e This indicates the speed limiter of the wind turbine generator. P W,i,max Indicates the first i Maximum output of each wind turbine unit; The specific virtual inertia constraint of the wind turbine is as follows: In the formula, Let represent the virtual inertia of the i-th wind turbine. H w,max This represents the maximum value of the inertia level; The specific power flow safety constraints are as follows: In the formula, P i Indicates the line i The transmission power; P i,max Indicates the line i Maximum permissible transmission power; V q Indicates the first q The voltage amplitude at each node, V min and V max These represent the maximum and minimum allowable values ​​for the voltage amplitude, respectively.

8. The inertia and primary frequency regulation pricing method considering power loss of wind turbine generators as described in claim 1, characterized in that, The joint clearing results specifically refer to the unit scheduling results, including unit output, inertia level, and primary frequency regulation magnitude of synchronous units at 24 time points.

9. The pricing method for inertia and primary frequency regulation considering power loss of wind turbine generators as described in claim 1, characterized in that, The calculation of inertia and the marginal price of primary frequency modulation using the Lagrange multiplier method based on the joint clearing results is as follows: By using Lagrange multipliers, the objective function and constraints of the joint clearing model are transformed into Lagrange functions. The partial derivatives of the Lagrange functions are then used to obtain the marginal price calculation formulas for inertia and frequency modulation. The joint clearing results are then substituted into the marginal price calculation formulas for inertia and frequency modulation to obtain the marginal prices for inertia and frequency modulation.

10. The inertia and primary frequency regulation pricing method considering the power loss of wind turbine generators as described in claim 9, characterized in that, The Lagrange function is specifically: In the formula, L represents the Lagrange function, T represents the scheduling period, and N represents the number of synchronous generators. This represents the unit cost function, which includes start-up, shutdown, and operating costs. P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; C i PFR This indicates the price quoted for a single frequency modulation operation of the synchronous machine. R G,i,t This indicates the primary frequency regulation quantity of the synchronous machine; M represents the number of wind turbine units. C i W This indicates the electricity price quoted for wind turbine units. P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period; C i EFR This indicates the price quote for primary frequency regulation of wind turbine units; R I,i,t This indicates the amount won in the primary frequency regulation of the wind turbine. C i H Indicates virtual inertia pricing; H w,i,t Indicates the scalar value of virtual inertia; α 1 represents the dual multiplier of the power balance constraint; P G,i,t Indicates the first i Each synchronous unit in t Efforts during the time period; P W,i,t Indicates the first i Each wind turbine unit t Efforts during the time period P curt This indicates the power loss of the wind turbine output. P sys express t Load during the period; λ RoCoF Represents the dual multiplier of the frequency change rate constraint. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. f N Indicates the system's rated frequency, Δ P This represents the power of the disturbance experienced by the system. Indicates the maximum rate of change of frequency; λ q-s-s Represents the dual multipliers of quasi-steady-state constraints. R G This indicates the combined frequency regulation capability of all thermal power units. R I Δ represents the combined frequency regulation capability of all wind turbine units. P This represents the power of the disturbance experienced by the system. λ 1. λ 2. μ Represents the dual multiplier of the maximum frequency difference constraint; T PFR This indicates the full-power response time of the synchronous generator frequency regulation service; T EFR Indicates the full-power response time of frequency modulation services for power electronic equipment; Δf max Indicates the maximum frequency difference. H eq This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. The marginal price calculation formulas for inertia and frequency modulation are as follows: The specific formula for calculating the marginal price of frequency modulation is as follows: In the formula, λ PFR This represents the marginal price of primary frequency regulation for a synchronous generator unit. α 1 represents the dual multiplier of the power balance constraint. H w This represents the virtual inertia provided by the wind turbine. t nadir For inertial response time, This represents the equivalent inertia of the power system after the wind turbine is connected to the grid. T PFR This indicates the full-power response time of the synchronous generator frequency regulation service; λ 1. λ 2. μ Represents the dual multipliers of the maximum frequency difference constraint. λ q-s-s Represents the dual multipliers of quasi-steady-state constraints. This represents the marginal price of primary frequency regulation for wind turbine units. T EFR Indicates the full-power response time of frequency regulation services for power electronic equipment. Δf max Indicates the maximum frequency difference; The specific formula for calculating the marginal price of inertia is as follows: In the formula, λ sys This represents the marginal price of the inertia of a synchronous generator unit. λ w This represents the marginal price of the virtual inertia of a wind turbine. This indicates the capacity percentage of thermal power units in the system.

Images