A method and system for power optimization distribution of multi-unit hydroelectric power plant for primary frequency modulation

Abstract

This invention relates to the field of frequency control technology and discloses a method and system for optimizing power allocation among multiple units in a hydropower plant for primary frequency regulation. The method involves collecting grid frequency, guide vane opening, and operating head, converting frequency deviation into frequency regulation power increment commands, and determining the water flow inertia time constant. The rated power of the energy storage converter is used to determine the allowable regulation rate of each unit. Units with larger water flow inertia time constants have lower rate limits, structurally ensuring that the water flow inertia cancellation link always operates in the linear region. The allocation weight is the smaller of capacity and rate, ensuring equal frequency regulation capacity utilization for each unit and simultaneously satisfying both capacity and rate constraints. In case of unit derating or failure, redistribution can be completed through algebraic operations. Slow timescale correction is performed along the zero space, with a constant contribution to the total plant power. Economic optimization and primary frequency regulation response do not interfere with each other. Cross-regional transitions allow optimization to escape the local optimum caused by the vibration zone.

Description

Technical Field

[0001] This invention belongs to the field of frequency control technology for hydropower generation and power systems, specifically relating to a method and system for optimizing the power allocation of multiple units in a hydropower plant for primary frequency regulation. Background Technology

[0002] Frequency regulation is a fundamental obligation of grid-connected power sources, and hydropower plants are considered important frequency regulation resources due to their ability to rapidly adjust loads. However, there is water flow inertia between the turbine and its intake system. When the guide vanes open, the flow cross-section increases, but the water column in the pipe cannot accelerate in time, causing the operating head to drop. The unit's mechanical power initially decreases in the opposite direction, a phenomenon known as water hammer. This reverse regulation phase causes the power at the grid connection point to change in the opposite direction to demand in the initial stage of the event, making it difficult to meet the performance targets for response lag time and frequency regulation integral power. Existing plant power allocation methods often allocate power based on the unit's rated capacity or remaining adjustable capacity, without taking into account the differences in adjustment rates and water flow inertia time constants between units. Slower-speed units may be allocated power they cannot deliver within the performance window, creating a frequency regulation deficit at the plant level. These methods also typically do not consider the vibration zone as a rigid constraint. Existing energy storage-assisted frequency regulation schemes mostly compensate based on frequency deviation droop or unit power deviation feedback: the former's compensation amount is only related to frequency and has no point-to-point correspondence with the hydraulic transition process; the latter requires energy storage to bear all the regulation lag of the governor and relay, resulting in a significant increase in energy demand. In addition, the transmission relationship from turbine guide vane opening to unit active power includes the right half-plane zero point, and the governor power loop can only be set with a very low bandwidth; the plant's economic optimization and the second-level frequency regulation response are superimposed on the same set of power settings and interfere with each other; the vibration zone divides the feasible range of unit power into several unconnected segments, and gradient-type optimization is prone to stagnation at local optima. Summary of the Invention

[0003] The purpose of this invention is to provide a method for optimizing the power allocation of multiple units in a hydropower plant for primary frequency regulation, in order to solve the problems in the prior art such as the mismatch between the compensation amount of water hammer back regulation and the actual hydraulic transition process, the excessive energy demand of energy storage, the lack of physical basis for the power allocation weight between units, the bandwidth limitation of the governor power loop due to the zero point of the right half plane, and the mutual interference between the economic optimization within the plant and the primary frequency regulation response.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows: In a first aspect, the present invention provides a method for optimizing power allocation among multiple generating units in a hydropower plant for primary frequency regulation. The hydropower plant includes multiple generating units operating in parallel, a local control unit corresponding to each generating unit, a plant-wide optimization device, and an energy storage device including an energy storage converter. The method comprises the following steps: Step 1: Collect the grid frequency, unit active power, guide vane opening and unit working head according to the execution cycle, and take the difference between the grid frequency and the rated frequency as the frequency deviation; when the absolute value of the frequency deviation is greater than the artificial frequency dead zone, convert the frequency deviation into the plant-wide frequency regulation power increment command, and determine the water flow inertia time constant of each unit. Step 2: Take the smaller value between the calculated permissible action rate of the relay and the energy storage power constraint rate as the permissible adjustment rate. The energy storage power constraint rate is directly proportional to the rated power of the energy storage converter and inversely proportional to the water flow inertia time constant. Take the smaller value between the product of the remaining adjustable capacity and the permissible adjustment rate and the response window time as the window deliverable power. Step 3: Based on the proportion of the deliverable power of each unit window to the sum of the deliverable power of all unit windows, allocate the plant-wide frequency regulation power increment command as the unit frequency regulation power increment component, and add it to the unit power setpoint as the governor power setpoint. Step 4: Obtain the steady-state power increment of the guide vane opening based on the measured guide vane opening and the guide vane opening-power characteristic curve. Input the steady-state power increment of the guide vane opening into the water flow inertia cancellation link to obtain the water flow inertia cancellation amount. The transfer function of the water flow inertia cancellation link is equal to the difference between the value 1 and the transfer function from the turbine guide vane opening to the active power of the unit. The sum of the water flow inertia cancellation amounts of all units is used as the energy storage compensation power command and sent to the energy storage converter. Step 5: Allocate the actual active power of the energy storage converter according to the ratio of the water flow inertia cancellation amount of each unit to the sum of the water flow inertia cancellation amounts of all units. The allocation result is added to the measured value of the active power of the unit and used as the power feedback amount of the speed governor. Step 6: Correct the unit power setpoint according to the slow timescale execution cycle. The correction amount is equal to the product of the slow timescale optimization step size and the difference. The difference is equal to the difference between the unit's comprehensive cost gradient component and the average value of all units' comprehensive cost gradient components. The unit power setpoint minus the correction amount, and the sum of all unit correction amounts is always equal to 0. The slow timescale execution cycle is greater than the execution cycle.

[0005] Further, in step 1, the grid frequency is obtained by the local control unit corresponding to each unit based on the local measurement of the terminal voltage and then by a moving average. The plant-wide frequency regulation power increment command is calculated locally by the local control unit corresponding to each unit based on the plant-wide equivalent permanent slip coefficient setting value, and the conversion time is recorded as the event start time. Step 1 also collects the effective value of the vibration velocity of the unit roof, the active power at the grid connection point, and the actual active power of the energy storage converter. The pressure pipeline of each unit is taken from the section between the surge tank and the turbine, or from the section between the inlet and the turbine when no surge tank is installed. The one-way propagation time of the water hammer wave is equal to the sum of the ratios of the length of each pipe section to the water hammer wave velocity of each pipe section. The water flow inertial time constant is... =Equals the sum of the ratios of the lengths of each pipe segment to the cross-sectional areas of each pipe segment, multiplied by the unit flow rate, and then divided by the product of the gravitational acceleration and the unit working head. The unit flow rate and the unit working head are the average values ​​within a set time period before the start of the event. The unit flow rate is obtained from the flow-power characteristic curve. The pipe characteristic coefficient is equal to the ratio of the water flow inertial time constant to twice the one-way propagation time of the water hammer wave. The remaining adjustable capacity is the difference between the upper limit of allowable output and the unit power setting value when the plant-wide frequency regulation power increment command is positive, and the difference between the unit power setting value and the lower limit of allowable output when the plant-wide frequency regulation power increment command is negative. For units in derating operation, shutdown, startup, or load shedding state, the remaining adjustable capacity is 0.

[0006] Further, in step 2, the converted value of the relay's allowable operating rate is equal to the product of the relay's allowable operating rate and the slope of the guide vane opening-power characteristic curve at the current guide vane opening; the energy storage power constraint rate is equal to the product of the energy storage converter's rated power and the margin coefficient, divided by the product of the number of units with positive remaining adjustable capacity, the water flow inertia time constant, and the value 1.5; the margin coefficient is taken as 0.7 to 0.8; the allowable adjustment rate and the window deliverable power are latched at the start of the event and remain unchanged during the period when the absolute value of the frequency deviation is greater than the artificial frequency dead zone. After the allowable adjustment rate is converted into the upper limit of the guide vane opening change rate, it is sent to the governor rate limiting link. After the absolute value of the frequency deviation returns to within the artificial frequency dead zone and continues for a set time, it is refreshed according to the latest collected data.

[0007] Further, in step 3, the unit frequency regulation power increment component is the solution that minimizes the sum of the ratios of the squares of the frequency regulation power increment components of each unit to the window deliverable power among all solutions that satisfy the condition that the sum of the frequency regulation power increment components of all units equals the total frequency regulation power increment command of the entire plant. The ratio of the unit frequency regulation power increment component to the window deliverable power is equal for all units. When the absolute value of the total frequency regulation power increment command of the entire plant is greater than the sum of the window deliverable power of all units, the unit frequency regulation power increment component takes the window deliverable power and is oriented according to the positive or negative sign of the total frequency regulation power increment command of the entire plant. When the sum of the window deliverable power of all units is 0, the unit frequency regulation power increment component takes 0. When the plant optimization device is out of operation, the local control unit corresponding to each unit maintains the most recently received unit power setpoint and continues to execute steps 2 to 5 according to the locally measured grid frequency.

[0008] Further, in step 4, the numerator of the transfer function from the turbine guide vane opening to the unit's active power is equal to the value 1 minus the product of twice the pipe characteristic coefficient and the hyperbolic tangent function value, and the denominator is equal to the value 1 plus the product of the pipe characteristic coefficient and the hyperbolic tangent function value. The independent variable of the hyperbolic tangent function is equal to the product of the one-way propagation time of the water hammer wave and the Laplace operator. The numerator of the transfer function of the water flow inertia cancellation link is equal to the product of three times the pipe characteristic coefficient and the hyperbolic tangent function value, and the denominator is the same as the denominator of the transfer function from the turbine guide vane opening to the unit's active power. The value of the water flow inertia cancellation amount in the current execution cycle is equal to the product of three times the pipe characteristic coefficient and difference one, minus the product of difference two and the value of the water flow inertia cancellation amount in the execution cycle of the lag delay step, and then divided by the value 1. The sum of the pipe characteristic coefficients; Difference 1 equals the difference between the value of the guide vane opening-based steady-state power increment in the current execution cycle and the value of the guide vane opening-based steady-state power increment in the execution cycle with a delay step; Difference 2 equals the difference between value 1 and the pipe characteristic coefficient; The delay step is equal to the ratio of twice the one-way propagation time of the water hammer wave to the execution cycle, rounded to the nearest integer; When the pipe characteristic coefficient is greater than or equal to 4, the water flow inertia cancellation link adopts a simplified form, with a margin coefficient of 0.8: First, the guide vane opening-based steady-state power increment is filtered by an inertial link with a time constant equal to half the water flow inertia time constant, and then three times the difference between the guide vane opening-based steady-state power increment and the inertial link filtering result is taken as the water flow inertia cancellation amount; When the pipe characteristic coefficient is less than 4, the margin coefficient is 0.7.

[0009] Further, in step 4, the energy storage compensation power command is equal to the sum of the water flow inertia offset of all units and the sum of the correction term; the correction term is equal to the difference between the sum of the steady-state power increments converted from the guide vane opening of all units and the measured value of the active power increment at the grid connection point, multiplied by the proportional coefficient, which is greater than 0 and less than 1, and the correction term is limited to 20% of the rated power of the energy storage converter; the rated power of the energy storage converter is taken as 1.2 times the maximum design value of the frequency regulation power increment command of the whole plant; the rated capacity of the energy storage device is taken as the product of the value 1.5, the maximum design value of the frequency regulation power increment command of the whole plant, the maximum value of the water flow inertia time constant of all units and the capacity multiple, and the capacity multiple is greater than or equal to 1; when the absolute value of the frequency deviation returns to within the artificial frequency dead zone and continues for a set time, and the absolute value of the difference between the state of charge of the energy storage device and 50% is greater than 10%, the energy storage device is charged and discharged at 2% of the rated power of the energy storage converter until the state of charge is equal to 50%.

[0010] Furthermore, in step 4, the inertia compensation amount is only applied to units that are in grid-connected power generation and have primary frequency regulation enabled; when a unit switches to start-up, shutdown, or load shedding mode, or when the rate of change of the unit's guide vane opening exceeds 1.2 times the allowable regulation rate, the steady-state power increment converted from the guide vane opening is maintained at the value of the most recent execution cycle, and the inertia compensation amount continues to be applied according to step 4 until it decays to 0; when the energy storage converter trips or the state of charge of the energy storage device exceeds the set range, Stop including the water flow inertia compensation amount in the energy storage compensation power command. The allowable adjustment rate is changed to the smaller value between the relay allowable action rate conversion value and the degradation rate. The degradation rate is equal to the allowable reverse adjustment depth setting value divided by 0.45 and the water flow inertia time constant. The allowable reverse adjustment depth setting value is the maximum allowable amplitude of the reverse change of the unit's active power relative to the incremental component of the unit's frequency regulation power. At the same time, the governor power feedback is restored to the measured value of the unit's active power and switched to the governor's standby parameter group.

[0011] Further, in step 5, when the sum of the inertial cancellation amounts of all unit water flow is 0, the governor power feedback is taken as the measured value of the unit's active power; the governor power loop is tuned according to the bandwidth determined by the relay time constant; in step 6, the comprehensive cost gradient component is equal to the sum of the incremental rate of water consumption and the incremental rate of vibration penalty; the incremental rate of water consumption is obtained by numerically differentiating the flow-power characteristic curve at the current unit power setpoint with a step size of 1 MW; in the water intake system with a surge tank, the unit's working head is filtered by a moving average with a window length equal to the surge period of the surge tank before participating in the numerical difference; when the distance between the unit power setpoint and the upper boundary of the vibration zone is less than the set margin... When the distance between the setpoint and the lower boundary of the vibration zone is less than the setpoint, the vibration penalty increment rate is calculated as the product of the penalty coefficient and the setpoint minus the distance, with a negative sign. When the distance between the setpoint and the lower boundary of the vibration zone is less than the setpoint, the vibration penalty increment rate is calculated as the product of the penalty coefficient and the setpoint minus the distance, with a positive sign. When the setpoint is between the upper and lower boundaries of the vibration zone, the vibration penalty increment rate is calculated as the product of the penalty coefficient and the setpoint, with a negative sign when the setpoint is above the midpoint between the upper and lower boundaries of the vibration zone and a positive sign when the setpoint is below the midpoint. When the distance is greater than or equal to the setpoint, the vibration penalty increment rate is 0.

[0012] Further, in step 6, after correcting the unit power setpoint, the unit power setpoint is projected between the lower and upper limits of allowable output. The deviation generated by the projection is allocated proportionally to the window deliverable power of the remaining units. Units responsible for upward adjustment have their window deliverable power determined by the remaining adjustable capacity upwards, while units responsible for downward adjustment have their window deliverable power determined by the remaining adjustable capacity downwards. When the effective value of the vibration velocity of the unit's roof continuously exceeds the set threshold for a set duration, the upper or lower boundary of the vibration zone closest to the current unit power setpoint is moved to the current unit power setpoint. When the unit power setpoint remains unchanged and the effective value of the vibration velocity of the unit's roof continuously falls below 80% of the set threshold for a set duration, the upper or lower boundary of the vibration zone is moved by 1 MW between the upper and lower boundaries of the vibration zone. After the absolute value of the frequency deviation remains within the artificial frequency dead zone for a set duration, a cross-zone jump is initiated. Relocation: After each set number of unit power setpoint corrections is completed, the overall plant cost of moving the unit power setpoint to the boundary on the other side of the vibration zone and having the remaining units bear the cost in the same proportion of the deliverable power within the window is calculated. When the reduction in the overall plant cost is greater than the set threshold, a cross-zone relocation is performed. Only one unit is allowed to be in the cross-zone relocation state at any given time. During the cross-zone relocation, the upper limit of the guide vane opening change rate of all units is taken as 50% of the allowable adjustment rate. When the absolute value of the frequency deviation is greater than the artificial frequency dead zone, the cross-zone relocation is stopped and the upper limit of the guide vane opening change rate is restored to the allowable adjustment rate. The slow timescale execution cycle is greater than or equal to 10 times the stabilization time of the hydraulic transition process. The stabilization time of the hydraulic transition process is the time required for the water hammer component of the unit's working head to enter the steady-state value ±1% band. The value of the slow timescale optimization step size is such that the absolute value of the change in the unit power setpoint in a single correction is less than or equal to 0.5% of the unit's rated power.

[0013] Further, steps 1 to 5 are executed by the local control unit corresponding to each unit, and step 6 is executed by the plant-wide optimization device; each local control unit sends its own window deliverable power and operating status to each other via a dual-ring network using IEEE 1588 time synchronization and GOOSE messages; the energy storage device includes a supercapacitor bank and an energy storage converter, with a capacity multiple of 1; or the energy storage device includes a flywheel energy storage unit and an energy storage converter, with a capacity multiple of 4; the energy storage converter is connected to the low-voltage side bus of the main transformer of the hydropower plant and operates in active power control mode, with an active power step response time of less than or equal to 20 milliseconds; the governor of each unit is equipped with a local frequency loop as a backup channel. If no heartbeat message is received from the local control unit corresponding to the unit within a continuously set time period, the backup channel automatically takes over and sets the permanent slip coefficient to the rated setting value.

[0014] In a second aspect, the present invention provides a power optimization and allocation system for multiple units in a hydropower plant for primary frequency regulation, comprising a water flow inertia determination module, a deliverable power module, a power setting module, a compensation power module, a power feedback module, and an allocation module. The water flow inertia determination module collects the grid frequency, unit active power, guide vane opening and unit working head according to the execution cycle, and takes the difference between the grid frequency and the rated frequency as the frequency deviation; when the absolute value of the frequency deviation is greater than the artificial frequency dead zone, the frequency deviation is converted into the plant-wide frequency regulation power increment command, and the water flow inertia time constant of each unit is determined. The deliverable power module takes the smaller value between the relay's permissible action rate and the energy storage power constraint rate as the permissible adjustment rate. The energy storage power constraint rate is directly proportional to the rated power of the energy storage converter and inversely proportional to the water flow inertia time constant. The smaller value between the remaining adjustable capacity and the product of the permissible adjustment rate and the response window time is taken as the window deliverable power. The power setting module allocates the plant-wide frequency regulation power increment command as a unit frequency regulation power increment component according to the proportion of the deliverable power of each unit window to the sum of the deliverable power of all unit windows, and adds it to the unit power setpoint as the governor power setting. The compensation power module obtains the steady-state power increment of the guide vane opening based on the measured guide vane opening and the guide vane opening-power characteristic curve. The steady-state power increment of the guide vane opening is then input into the water flow inertia cancellation link to obtain the water flow inertia cancellation amount. The transfer function of the water flow inertia cancellation link is equal to the difference between the value 1 and the transfer function from the turbine guide vane opening to the active power of the unit. The sum of the water flow inertia cancellation amounts of all units is used as the energy storage compensation power command and sent to the energy storage converter. The power feedback module allocates the actual active power of the energy storage converter according to the proportion of the water flow inertia cancellation amount of each unit to the sum of the water flow inertia cancellation amounts of all units. The allocation result is added to the measured value of the active power of the unit and used as the power feedback amount of the speed governor. The allocation module corrects the unit power setpoint according to the slow timescale execution cycle. The correction amount is equal to the product of the slow timescale optimization step size and the difference. The difference is equal to the difference between the unit's comprehensive cost gradient component and the average value of all units' comprehensive cost gradient components. The unit power setpoint minus the correction amount, and the sum of all unit correction amounts is always equal to 0. The slow timescale execution cycle is greater than the execution cycle.

[0015] Compared with the prior art, the present invention has the following beneficial technical effects: This invention provides a method for optimizing power allocation among multiple units in a hydropower plant for primary frequency regulation. The inertia compensation stage is composed of a value of 1 and the difference between the turbine guide vane opening and the active power transfer function of the unit, with the measured guide vane opening as the input. The compensation amount corresponds point-by-point to the hydraulic transient process, ensuring that the generator speed limit, governor parameter setting, and guide vane dead travel are all maintained. The power increment at the grid connection point is equal to the sum of the steady-state power corresponding to the guide vane opening of each unit throughout the entire time period. Water hammer back-regulation is completely offset, and the response lag time and frequency regulation integral power index are significantly improved. The DC gain of the inertia compensation stage is zero, and the energy throughput of the closed frequency regulation process after load increase and fall back is automatically zero. The energy storage state of charge can return to the center without external adjustment, and the capacity demand is adjusted accordingly. The rated power of the energy storage converter is reversed to determine the allowable regulation rate of each unit. The unit with a larger water flow inertia time constant has a lower upper limit for its rate, which structurally ensures that the water flow inertia cancellation link always works in the linear region. The allocation weight is taken as the smaller of the capacity and the rate, so that the frequency regulation capacity utilization rate of each unit is equal and the capacity constraint and rate constraint are satisfied at the same time. When the unit is derated or fails, the redistribution can be completed by algebraic calculation only. After the actual power generated by the energy storage is incorporated into the power feedback of the speed governor, the controlled object of the power loop changes from a non-minimum phase to a minimum phase. The slow time scale correction is carried out along the zero space, and its contribution to the total power of the whole plant is always zero. The economic optimization and the primary frequency regulation response do not interfere with each other. The cross-zone transition allows the optimization to jump out of the local optimum caused by the vibration zone. Attached Figure Description

[0016] Figure 1 This is a schematic diagram illustrating the principle of the connection relationship between the hydropower plant water intake system, generating units, and energy storage device, as provided in an embodiment of the present invention.

[0017] Figure 2 This is a schematic diagram illustrating the relationship between the total plant water flow inertia offset and the power increment at the grid connection point, as provided in an embodiment of the present invention.

[0018] Figure 3 This is a schematic diagram of the time process of energy storage compensation power command and energy storage device state of charge provided in the embodiment of the present invention, wherein (a) is the time process of energy storage compensation power command and (b) is the time process of energy storage device state of charge.

[0019] Figure 4 This is a schematic diagram illustrating the relationship between the allowable adjustment rate and the water flow inertia time constant and the rated power of the energy storage converter, as provided in an embodiment of the present invention.

[0020] Figure 5 This is a schematic diagram comparing the step response of the controlled object of the speed controller power loop under two feedback quantity acquisition methods, as provided in an embodiment of the present invention.

[0021] Figure 6This is a schematic diagram illustrating the geometric relationship between zero-space correction and cross-regional transition of the power setpoints of two generating units in the plane, as provided in an embodiment of the present invention.

[0022] Figure 7 A flowchart illustrating the power optimization allocation method for multiple units in a hydropower plant oriented towards primary frequency regulation, provided in an embodiment of the present invention. Detailed Implementation

[0023] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0024] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0025] like Figure 7 As shown, this invention provides a method for optimizing power allocation among multiple units in a hydropower plant for primary frequency regulation. The hydropower plant includes multiple units operating in parallel, a local control unit corresponding to each unit, a plant-wide optimization device, and an energy storage device including an energy storage converter. The method includes the following steps: Step 1: Collect the grid frequency, unit active power, guide vane opening and unit working head according to the execution cycle, and take the difference between the grid frequency and the rated frequency as the frequency deviation; when the absolute value of the frequency deviation is greater than the artificial frequency dead zone, convert the frequency deviation into the plant-wide frequency regulation power increment command, and determine the water flow inertia time constant of each unit. Step 2: Take the smaller value between the calculated permissible action rate of the relay and the energy storage power constraint rate as the permissible adjustment rate. The energy storage power constraint rate is directly proportional to the rated power of the energy storage converter and inversely proportional to the water flow inertia time constant. Take the smaller value between the product of the remaining adjustable capacity and the permissible adjustment rate and the response window time as the window deliverable power. Step 3: Based on the proportion of the deliverable power of each unit window to the sum of the deliverable power of all unit windows, allocate the plant-wide frequency regulation power increment command as the unit frequency regulation power increment component, and add it to the unit power setpoint as the governor power setpoint. Step 4: Obtain the steady-state power increment of the guide vane opening based on the measured guide vane opening and the guide vane opening-power characteristic curve. Input the steady-state power increment of the guide vane opening into the water flow inertia cancellation link to obtain the water flow inertia cancellation amount. The transfer function of the water flow inertia cancellation link is equal to the difference between the value 1 and the transfer function from the turbine guide vane opening to the active power of the unit. The sum of the water flow inertia cancellation amounts of all units is used as the energy storage compensation power command and sent to the energy storage converter. Step 5: Allocate the actual active power of the energy storage converter according to the ratio of the water flow inertia cancellation amount of each unit to the sum of the water flow inertia cancellation amounts of all units. The allocation result is added to the measured value of the active power of the unit and used as the power feedback amount of the speed governor. Step 6: Correct the unit power setpoint according to the slow timescale execution cycle. The correction amount is equal to the product of the slow timescale optimization step size and the difference. The difference is equal to the difference between the unit's comprehensive cost gradient component and the average value of all units' comprehensive cost gradient components. The unit power setpoint minus the correction amount, and the sum of all unit correction amounts is always equal to 0. The slow timescale execution cycle is greater than the execution cycle.

[0026] This embodiment applies to a hydropower plant equipped with four 250 MW mixed-flow turbine units. Each of the four units has its own independent pressure pipeline extending from its surge tank. Each pressure pipeline is 275 meters long, with a cross-sectional area of ​​60.7 square meters and a water hammer velocity of 1100 m / s. Under rated operating conditions, the unit's working head is 80 meters, the unit's flow rate is 346.3 cubic meters per second, and the average flow velocity within the pipeline is 5.71 m / s. The plant is equipped with one energy storage device, consisting of a supercapacitor bank and an energy storage converter. The energy storage converter is composed of multiple power modules connected in parallel to the 15.75 kV busbar on the low-voltage side of the main transformer, operating in active power control mode with an active power step response time of 15 milliseconds. Each unit is equipped with one local control unit, and the entire plant is equipped with one plant-wide optimization device. The execution cycle is set to 20 milliseconds, the slow timescale execution cycle to 60 seconds, the response window time to 15 seconds, and the manual frequency dead zone to 0.05 Hz. The maximum design value of the plant-wide frequency modulation power increment command is 6% of the plant's rated capacity, i.e., 60 megawatts, with a corresponding frequency deviation of 0.17 Hz.

[0027] Figure 1This illustration shows the connection relationship between the water diversion system, generating units, and energy storage device in this embodiment. The reservoir is connected to the surge tank via a water diversion tunnel. Pressure pipelines for each generating unit are led out from the lower part of the surge tank and connected to the turbines of each unit. The turbines drive generators via their main shafts. The generator outputs are fed into the low-voltage busbar of the main transformer. The busbar is connected to the grid connection point via the main transformer and then to the power grid. The supercapacitor bank of the energy storage device is connected to the same low-voltage busbar of the main transformer via an energy storage converter. Therefore, the power output of the energy storage converter and the power output of each generating unit are directly superimposed on this busbar and transmitted through the same main transformer. The power increment at the grid connection point is thus synthesized algebraically, and the energy storage power accurately offsets the mechanical power deficit of the generating units. Figure 1 The required measuring points for this embodiment are also marked: the working head measuring point on the pressure pipeline near the turbine, the guide vane opening measuring point at the turbine inlet, and the generator terminal power measuring point on the generator output line, wherein the guide vane opening is obtained by the servo drive stroke sensor; a power measuring point is also set at the grid connection point. The signals from each measuring point are sent to the local control unit corresponding to the unit, and the local control units exchange data with each other and with the plant-wide optimization device through the station control layer network.

[0028] In step 1, the local control unit corresponding to each unit measures the grid frequency using the secondary signal from the voltage transformer at the unit's terminal. The measurement result is averaged over a 100-millisecond window and subtracted from the rated frequency to obtain the frequency deviation. Local frequency measurement is used instead of being uniformly issued by the plant-wide optimization device because primary frequency regulation is a fundamental grid-connected obligation of the units. If frequency information and power commands are generated by a single device, the plant-wide primary frequency regulation function will fail simultaneously if that device shuts down. Local frequency measurement allows each unit to independently determine the frequency deviation and calculate commands even when the plant-wide optimization device is out of service. When the absolute value of the frequency deviation exceeds the artificial frequency dead zone, [the following applies]. The conversion yields the plant-wide frequency modulation power increment command; where This is a plant-wide frequency modulation power increment command, in megawatts; The portion of the frequency deviation that exceeds the artificial frequency dead zone, measured in Hertz; The rated frequency is 50 Hz. The rated capacity of the entire plant is taken as 1000 megawatts; The equivalent permanent slip coefficient for the entire plant is taken as 0.04. The negative sign in the formula indicates that the frequency regulation power increment command for the entire plant is positive when the grid frequency is lower than the rated frequency. The moment when the frequency regulation power increment command for the entire plant is generated is recorded as the event start time.

[0029] In step 1, the pressure pipeline for each unit is taken from the section between the surge tank and the turbine. In water intake systems without surge tanks, it is taken from the section between the inlet and the turbine. The upstream boundary is taken at the surge tank because the free water surface of the surge tank forms an approximate constant-pressure reflection surface for the water hammer wave, and the water intake tunnel above the surge tank does not participate in the water hammer process within the frequency regulation timescale. The one-way propagation time of the water hammer wave is calculated as follows: Calculations are made based on the inertial time constant of the water flow. Online updates, pipeline characteristic coefficients are based on Calculate; subscripts in the formula Indicates the first Taiwanese unit, subscript Indicates the first pressure pipeline Each pipe section; The one-way propagation time of water shock waves, in seconds; The inertial time constant of the water flow is expressed in seconds. The pipeline characteristic coefficient is dimensionless. This refers to the length of the pipe section, in meters. The water hammer wave velocity of the pipe section is expressed in meters per second. This refers to the cross-sectional area of ​​the pipe section, in square meters. The unit flow rate is expressed in cubic meters per second. The unit's operating head is measured in meters. The acceleration due to gravity is taken as 9.81 meters per second squared.

[0030] The unit flow rate and operating head are taken as the average value within 10 seconds prior to the start of the event. The unit flow rate is obtained from the pre-stored flow-power characteristic curve based on the current unit power setting and the current unit operating head. The average value prior to the start of the event is used here, rather than the instantaneous measured value during the transition process. This is because the frequency regulation process itself causes water hammer fluctuations in the operating head; if the instantaneous head during these fluctuations were used in the calculation, the parameters used to describe the transition process would change with the transition process, forming positive feedback within the flow inertia compensation link and distorting the compensation amount. The flow inertia time constant is directly proportional to the unit flow rate and inversely proportional to the unit operating head. Under partial load or high head conditions, its value can be reduced to about half of the rated value. If the value is fixed according to the factory rating, the time constant of the flow inertia compensation link will be mismatched with the actual hydraulic transition process. In this embodiment, the one-way propagation time of the water hammer wave is calculated to be 0.25 seconds, the water flow inertia time constant is 2.00 seconds, and the pipe characteristic coefficient is 4.00 under rated operating conditions; under operating conditions where the working head rises to 110 meters and the unit flow rate drops to 249.1 cubic meters per second, the water flow inertia time constant is calculated to be 1.05 seconds and the pipe characteristic coefficient is 2.09.

[0031] In step 1, the remaining adjustable capacity is determined by the sign of the plant-wide frequency regulation power increment command: a positive value is the difference between the unit's maximum allowable output at the current operating head and the unit's power setting value; a negative value is the difference between the unit's power setting value and the minimum allowable output limit. The reason for using the directional value is that the margin provided by primary frequency regulation in the upward and downward directions is not symmetrical; if the smaller value is used uniformly without distinguishing the direction, the available frequency regulation capacity will be reduced. Units operating under derating, shut down, starting up, or shedding load have a remaining adjustable capacity of 0, thus these units automatically exit the subsequent allocation without requiring a separate logical branch. In this embodiment, the power setting value for all four units is 150 MW, the maximum allowable output at the current operating head is 240 MW, and the minimum allowable output is 60 MW. Therefore, the remaining adjustable capacity in the upward direction is 90 MW, and the number of units with a positive remaining adjustable capacity is 4.

[0032] In step 2, the allowable adjustment rate is as follows: Values; where For the first The permissible adjustment rate of the unit is measured in megawatts per second. The permissible operating rate of the relay is converted to a value in megawatts per second, which is equal to the product of the permissible operating rate of the relay and the slope of the guide vane opening-power characteristic curve at the current guide vane opening. The margin coefficient is dimensionless. The rated power of the energy storage converter is expressed in megawatts (MW). This represents the number of generating units with positive remaining adjustable capacity. Let be the inertial time constant of the water flow. The second term within the curly braces is called the energy storage power constraint rate.

[0033] The product of 1.5 and the water flow inertia time constant appears in the denominator of the energy storage power constraint rate. This is because when the guide vane opening, converted to steady-state power increment, changes linearly at the allowable adjustment rate, the water flow inertia cancellation amount for this unit can be analytically calculated using the water flow inertia cancellation mechanism given later. Its supremum is precisely the product of the value 1.5 and the allowable adjustment rate and the inertial time constant of the water flow; where For the first The amount of inertial water flow cancellation for the unit, in megawatts; This is the time elapsed since the start of the event, measured in seconds. Therefore, as long as the upper bound of each unit is limited to the rated power of the energy storage converter... Within a factor of 1, the upper limit of the sum of the inertial offsets of all generating units' water flow is maintained at its... Within a factor of two. The rated power of the energy storage converter thus determines the allowable regulation rate of each unit. The larger the water flow inertia time constant of a unit, the lower its allowable regulation rate. The longer the water intake system and the greater the water flow inertia of a unit, the deeper the water hammer back adjustment caused by a unit regulation rate, and the more energy storage power is required. Under the condition that the total energy storage power is given, it should be allocated to a lower rate upper limit; this method of determination is different from the practice of determining the rate upper limit only based on the unit capacity.

[0034] The margin factor is taken as 0.7 to 0.8: 0.8 is used when a simplified form is adopted for the flow inertia compensation stage, with the remaining 0.2 times the rated power of the energy storage converter reserved for the correction term; 0.7 is used when a general form is adopted, with an additional 0.1 times margin used to cover the fluctuation of flow inertia compensation caused by standing wave resonance in the pressure pipeline. The window deliverable power is calculated according to... Values; where For the first The window of power available for the unit is in megawatts; Remaining adjustable capacity, in megawatts; The response window time is measured in seconds. The deliverable power within the window is the power the unit can deliver during the response window time, limited by both capacity and rate. In this embodiment, under rated operating conditions, the pipeline characteristic coefficient is 4.00, the margin coefficient is 0.8, and the rated power of the energy storage converter is 72 MW. Therefore, the energy storage power constraint rate is 0.8 multiplied by 72 and then divided by the product of 1.5, 4, and 2.00, which is 4.8 MW / s. The allowable operating rate of the relay is converted to 25 MW / s, so the allowable adjustment rate is 4.8 MW / s. The product of the allowable adjustment rate and the response window time is 72 MW, which is less than the remaining adjustable capacity of 90 MW; therefore, the deliverable power within the window is 72 MW.

[0035] Figure 4 The relationship between the allowable regulation rate and the time constant of water flow inertia and the rated power of the energy storage converter is shown. Figure 4 The horizontal axis represents the water flow inertia time constant, and the vertical axis represents the regulation rate. The three curves that monotonically decrease as the water flow inertia time constant increases correspond to the energy storage power constraint rates when the rated power of the energy storage converter is 216 MW, 144 MW, and 72 MW, respectively. The horizontal dotted line represents the converted value of the relay's allowable operating rate, and the bold light-colored trajectory represents the smaller envelope of the two values ​​when the rated power of the energy storage converter is 216 MW. In the section where the water flow inertia time constant is less than 1.15 seconds, the allowable regulation rate is limited by the relay's operating capability; in the subsequent section, it is limited by the energy storage power. Figure 4 The marked operating point is the value taken under rated operating conditions in this embodiment, with the horizontal axis being 2.0 seconds and the vertical axis being 4.8 megawatts per second.

[0036] The permissible adjustment rate and window deliverable power are latched at the start of the event and remain unchanged for a period of time during which the absolute value of the frequency deviation exceeds the artificial frequency dead zone. The permissible adjustment rate is converted into the upper limit of the guide vane opening change rate and then sent to the governor rate limiting circuit. After the absolute value of the frequency deviation returns to within the artificial frequency dead zone and remains so for 30 seconds, it is refreshed according to the latest acquired data. After latching, even if the number of units with positive remaining adjustable capacity changes during the event due to the withdrawal of a unit, the permissible adjustment rate will not change abruptly, and the sudden change in the upper limit of the guide vane opening change rate will not cause hydraulic shock on the relay. All local control units share the same set of window deliverable power values ​​during the event. Even if the communication between a local control unit and the station control layer network is interrupted during the event, the sum of the shares calculated by all units will still be exactly equal to 1, and the total power of the entire plant will not deviate due to communication abnormalities.

[0037] In step 3, the total plant power constraint is defined as the sum of the frequency regulation power increment components of each unit equaling the total plant frequency regulation power increment command. A weighted matrix is ​​then used. For a diagonal matrix, its first... The diagonal elements are the reciprocals of the window's deliverable power, taken as... A single row containing only 1s. Column vectors, For the number of generating units, record the frequency regulation power increment components of each unit. dimensional column vector is Then the weighted minimum norm solution of this constraint is ; superscript in the formula Indicates transpose, superscript This indicates finding the inverse. and Substitute the specific form and expand to obtain In the formula For the first The frequency regulation power increment component of the unit, in megawatts.

[0038] The above formula is equivalent to: among all solutions that satisfy the sum of the frequency regulation power increment components of all units equaling the total frequency regulation power increment command of the entire plant, the solution minimizes the sum of the ratios of the squares of the frequency regulation power increment components of each unit to the window deliverable power. In the expansion, the ratio of the unit's frequency regulation power increment component to its window deliverable power is equal for each unit, meaning the frequency regulation capacity utilization is completely equal. Selecting the window deliverable power as the weight makes the allocation result automatically feasible: when the absolute value of the total frequency regulation power increment command of the entire plant is less than or equal to the sum of the window deliverable power of all units, the absolute value of the unit's frequency regulation power increment component must be less than or equal to its window deliverable power. The window deliverable power itself is less than or equal to both the remaining adjustable capacity and the product of the allowable adjustment rate and the response window time. Therefore, the capacity constraint and the rate constraint are satisfied simultaneously, and there is no need for further limiting and iterative redistribution. If the rated capacity or the remaining adjustable capacity is used as the weight instead, units with slower rates may be allocated power that they cannot deliver within the response window time.

[0039] When the absolute value of the plant-wide frequency regulation power increment command is greater than the sum of the deliverable power windows of all units, the frequency regulation power increment component of each unit is taken from the deliverable power window and oriented according to the positive or negative sign of the plant-wide frequency regulation power increment command. At this time, the plant-wide frequency regulation capacity is fully engaged. When the sum of the deliverable power windows of all units is 0, the frequency regulation power increment component of each unit is taken as 0. This branch also avoids the situation where the divisor is 0 in the expansion formula. The unit frequency regulation power increment components are superimposed on the unit power setpoint and then used as the governor power setpoint. When the plant-wide optimization device is out of operation, the local control unit corresponding to each unit maintains the most recently received unit power setpoint and continues to execute steps 2 to 5 according to the locally measured grid frequency. The primary frequency regulation function is fully retained, only the economic optimization of the slow timescale is paused. In this embodiment, the window deliverable power of each of the four generating units is 72 MW, totaling 288 MW. When the plant-wide frequency regulation power increment command is 60 MW, the frequency regulation power increment component of each unit is 72 multiplied by 60 and then divided by 288, which is 15 MW. The frequency regulation capacity utilization rate of each unit is 0.208. Calculated at an allowable regulation rate of 4.8 MW per second, the time required for the guide vane opening to increase the steady-state power increment from 0 to 15 MW is 3.125 seconds, which is much less than the 15-second response window time. When the fourth generating unit fails and exits the system, its remaining adjustable capacity is set to 0, and the window deliverable power is also set to 0. The frequency regulation power increment component of the remaining three generating units changes from 15 MW to 20 MW within the same execution cycle, and the redistribution is completed solely through algebraic operations.

[0040] In step 4, the transfer function from the turbine guide vane opening to the unit's active power is calculated according to... Description; in the formula For the first The transfer function from the turbine guide vane opening to the active power of the unit. For the Laplace operator, The transfer function is a hyperbolic tangent function. When the Laplace operator approaches 0, the value of this transfer function is 1, indicating that the steady-state effect of the guide vane opening on power is not affected by the inertia of the water flow. However, when the Laplace operator takes a large positive real number, its value tends to be negative: 1 minus twice the pipe characteristic coefficient, divided by 1 and added to the pipe characteristic coefficient. This indicates that the unit's mechanical power decreases instantaneously upon a sudden increase in guide vane opening; this is known as water hammer. The physical reason is that at the moment the guide vane opens, the flow cross-section increases, but the water column in the pipe cannot accelerate in time due to inertia, causing the working head to drop. This drop in head initially reduces power more than the increase in flow cross-section. When the pipe characteristic coefficient is much greater than 1, the above ratio tends to negative 2, meaning the initial change in mechanical power is twice the final change and in the opposite direction.

[0041] When the steady-state power increment, calculated from the guide vane opening, increases linearly at the allowable adjustment rate, the unit's mechanical power increment is: In the formula For the first The mechanical power increment of the generator set is expressed in megawatts. Taking the derivative of the above equation and setting it to zero, we find that the extreme point occurs at... Substituting the values, we get the extreme value of the reverse adjustment as the product of -0.4507, the allowable adjustment rate, and the water flow inertia time constant. Setting the above equation to 0, we can obtain the time when the mechanical power increment returns to 0. In this embodiment, for a single unit, the steady-state power increment calculated from the guide vane opening increases from 0 at 4.8 MW / s to 15 MW and remains thereafter. The unit's mechanical power increment reaches a negative extreme of 4.33 MW at 1.10 seconds, only returning to 0 after 2.82 seconds, and then approaching 15 MW around 10 seconds later. With four units superimposed, the grid connection point power will experience a reverse offset of approximately 17.3 MW in the initial stage of the event, lasting for 2.82 seconds. Consequently, the response lag time and frequency regulation integral power of the hydropower unit's primary frequency regulation will be difficult to meet the required standards.

[0042] Step 4 constructs a flow inertia cancellation element, whose transfer function is taken as the difference between the value of 1 and the transfer function from the turbine guide vane opening to the unit's active power, i.e. Here, subtraction is used instead of inversion. The numerator of the transfer function from the turbine guide vane opening to the unit's active power has a zero when the Laplace operator takes a positive real number. If directly inverted, this zero would become the pole of the inverse link, located in the right half of the complex plane, resulting in a divergent link that cannot be realized. The link obtained by subtraction uses the denominator of the original transfer function as its denominator, and its poles are exactly the same as those of the original transfer function. Therefore, as long as the turbine and its water intake system are stable, the flow inertia cancellation link is stable. The numerator of the subtracted link contains a hyperbolic tangent factor, which tends to 0 when the Laplace operator tends to 0. Therefore, the DC gain of the flow inertia cancellation link is always 0, and the self-recovery of the state of charge discussed later is derived from this property. The coefficient 3 in the numerator comes from the subtraction of the numerator: 1 plus the product of the pipeline characteristic coefficient and the hyperbolic tangent function value, minus 1 minus the product of 2 times the pipeline characteristic coefficient and the hyperbolic tangent function value, which gives exactly 3 times the pipeline characteristic coefficient and the hyperbolic tangent function value. This coefficient is independent of the specific value of the pipeline parameters, and therefore holds true for any water diversion system.

[0043] To implement the above steps in the local control unit, the hyperbolic tangent function is expanded according to its exponential definition. That is, the value of the hyperbolic tangent function equals 1 minus the natural exponential function with a negative 2 times the independent variable as the exponent, then divided by 1 and added to the same natural exponential function. After substituting this, both the numerator and denominator of the water flow inertia cancellation step contain only one pure time delay factor. This time delay is twice the one-way propagation time of the water hammer wave, which physically means the time required for the water hammer wave to propagate from the turbine to the surge tank and back to the turbine. This time delay is discretized according to the execution cycle to obtain the number of time delay steps. And organize them to obtain the recurrence relation. In the formula For the first The water flow inertia compensation of the unit is in the first The value for each execution cycle, in megawatts; To calculate the steady-state power increment of the guide vane opening in the first... The value for each execution cycle, in megawatts; The number of delay steps; The execution period is in seconds. This indicates rounding to the nearest integer. The above formula can be completed in the local control unit using only two circular buffers with a length equal to the delay step and four multiply-accumulate operations.

[0044] The feedback coefficient modulus of the above recursive formula is For any positive value of the pipe characteristic coefficient, the modulus is less than 1, therefore the recursion is unconditionally stable and will not become unstable due to online updates of pipe parameters. Furthermore, when both input and output are constant, substituting them into the recursive formula yields an output of 0, indicating that its DC gain is 0, consistent with the continuous form. In this embodiment, the one-way propagation time of the water hammer wave is 0.25 seconds, and the execution cycle is 20 milliseconds, therefore the time delay step is 25, and the feedback coefficient modulus is 0.6 when the pipe characteristic coefficient is 4.00. The steady-state power increment calculated by the guide vane opening is obtained by subtracting the corresponding value on the curve at the start of the event from the steady-state power obtained by looking up the guide vane opening-power characteristic curve corresponding to the working head at the start of the event, based on the measured guide vane opening. The working head at the start of the event is used here instead of the instantaneous measured head to ensure that the steady-state power increment calculated by the guide vane opening only represents the steady-state power excluding the effect of water flow inertia, while all changes in head during the transition process are handled by the water flow inertia cancellation link according to its transmission relationship. Thus, the division of labor between the two does not overlap.

[0045] When the pipe characteristic coefficient is greater than or equal to 4, the hyperbolic tangent function can be replaced by its independent variable within the frequency band of interest, and the flow inertia cancellation element degenerates into... That is, the washing stage with a gain of 3 and a time constant that is half the inertial time constant of the water flow is discretely implemented as follows: first according to An inertial filter is applied to the steady-state power increment calculated from the guide vane opening, where the filter coefficients are... Press again Take three times the difference as the amount of water flow inertia compensation; where For inertial element filtering in the first stage The output per execution cycle, in megawatts; The filter coefficient is dimensionless. In this embodiment, the pipeline characteristic coefficient is 4.00 and the filter coefficient is 0.9802 under rated operating conditions, so a simplified form can be used; under operating conditions where the working head rises to 110 meters and the pipeline characteristic coefficient drops to 2.09, the general form is used.

[0046] Regarding the amplitude-frequency characteristics of the two forms, when the pipe characteristic coefficient is 4.00, both completely overlap in the low-frequency range and simultaneously approach 0 when the frequency approaches 0, indicating that the simplified form is an accurate approximation of the general form in the low-frequency range. In the high-frequency range, the amplitude of the simplified form monotonically approaches 3, while the amplitude of the general form shows a dip at the standing wave frequency of the pressure pipe and approaches 3 at the midpoint of two adjacent standing wave frequencies. In this embodiment, the standing wave frequencies are 2 Hz and 4 Hz. The amplitude dip occurs at the frequency corresponding to an integer multiple of the round-trip propagation time of the water hammer wave. At this time, the incident wave and the reflected wave cancel each other out at the turbine, and the inertia of the water flow has no net effect on the power. The simplified form cannot reflect this phenomenon, and the general form must be used when the pipe characteristic coefficient is small.

[0047] The increase in the unit's mechanical power is equal to the product of the turbine guide vane opening to the unit's active power transfer function and the steady-state power increase calculated based on the guide vane opening. The amount of water flow inertia cancellation is equal to the product of the difference between the value 1 and the transfer function and the steady-state power increase calculated based on the guide vane opening. The sum of these two amounts is exactly equal to the steady-state power increase calculated based on the guide vane opening itself. The sum of the water flow inertia cancellation amounts for all units is then used as the energy storage compensation power command and sent to the energy storage converter. Since the energy storage converter and the generator terminals of each unit are connected to the same low-voltage busbar of the main transformer, the power increase at the grid connection point is equal to the sum of the steady-state power corresponding to the guide vane opening of each unit at any given time, and the water flow inertia is completely canceled out. This relationship holds true for any time waveform of the guide vane opening, and therefore is not affected by the relay speed limit, governor parameter setting, or guide vane dead stroke. The difference between this method and compensation methods based on frequency deviation droop or unit power deviation feedback is that the latter two do not have a point-to-point correspondence between the compensation amount and the hydraulic transition process, while the compensation amount of this method is directly generated from the measured guide vane opening through a determined transmission relationship.

[0048] Figure 2 The above process for the entire plant in this embodiment is illustrated. Figure 2 The horizontal axis represents time, and the vertical axis represents power increment. The thick solid line represents the power increment at the grid connection point, which monotonically increases from time 0, reaching 60 MW at 3.125 seconds and maintaining that level. The dashed line represents the sum of the inertial offset of all units' water flow, which rises from 0 to 55.07 MW at 3.125 seconds and then decays exponentially, returning to 0 around 10 seconds. The dotted line represents the sum of the mechanical power increments of each unit, which initially drops to -17.3 MW before rebounding. The sum of the dashed and dotted lines equals the thick solid line throughout the entire time period. Figure 2 The upper limit of the energy storage power is also marked as 57.6 MW, which is 0.8 times the rated power of the energy storage converter. The peak value of the sum of the water flow inertia offset of all units is 55.07 MW, which is lower than the upper limit, indicating that the margin guaranteed by the method of choosing the allowable adjustment rate is indeed valid in this embodiment.

[0049] The energy storage compensation power command equals the sum of the total water flow inertia compensation of all units plus the sum of the correction terms, with the correction terms calculated as follows: Calculate; where For the correction term in the 1st The value for each execution cycle, in megawatts; The proportionality constant is dimensionless. The measured value of the active power increment at the grid connection point is expressed in megawatts (MW), representing the difference between the active power at the grid connection point and its value at the start of the event. The correction term (within parentheses) is calculated by subtracting the measured value of the active power increment at the grid connection point from the sum of the steady-state power increments converted from the guide vane opening of each unit. This order cannot be reversed. If the difference between the two is a residual without the correction term, adding the correction term increases the active power increment at the grid connection point by the value of this correction term, and the residual decreases accordingly to a multiple of the original residual (1 divided by 1 plus the proportional coefficient). If the two terms within the parentheses are swapped, the residual is amplified to a multiple of the original residual (1 divided by 1 minus the proportional coefficient), and the correction process changes from suppressing error to amplifying error. The proportional coefficient is a value greater than 0 and less than 1, with its upper bound derived from the lag of one execution cycle introduced by the measurement and the energy storage converter response. The convergence condition of the closed loop under this lag is that the absolute value of the proportional coefficient is less than 1. In this embodiment, the proportional coefficient is 0.5, and the residual is compressed to 0.667 times that without the correction term. The correction term is limited to 20% of the rated power of the energy storage converter, i.e., 14.4 MW. This limit corresponds to the 0.2 times margin left in the allowable regulation rate method, so that the upper limit of the energy storage compensation power command remains within the rated power of the energy storage converter.

[0050] The DC gain of the flow inertia cancellation element is 0. For a unidirectional frequency modulation process in which the steady-state power increment, calculated from the guide vane opening, rises from 0 to a certain value and remains thereafter, the integral of the flow inertia cancellation amount over time is: Furthermore, this integral value is independent of the specific waveform change in the guide vane opening; the result is the same regardless of whether the guide vane opens quickly or slowly. This integral value represents the upper bound of the state of charge offset of the energy storage device during this process. For a closed-loop frequency modulation process where the steady-state power increment converted from the guide vane opening increases and then falls back to its original value, the above integral is 0, the energy throughput of the energy storage device automatically becomes 0, and the state of charge returns to its pre-event value without any external adjustment. Accordingly, the rated capacity of the energy storage device is calculated based on... Select; in the formula The rated capacity of an energy storage device is measured in megajoules and is defined as the energy that can be released or absorbed in one direction from a 50% state of charge. This represents the maximum design value of the plant's frequency modulation power increment command, in megawatts. This represents the maximum value of the inertial time constant of the water flow for all units, in seconds. This is a capacity multiple, dimensionless. The rated power of the energy storage converter is taken as 1.2 times the maximum value of the plant's frequency regulation power increment command. Among them, 0.8 times the rated power of the energy storage converter corresponds to the upper limit of the sum of the inertia cancellation of all units' water flow, and 0.2 times the rated power of the energy storage converter corresponds to the limit of the correction term. The sum of the two is exactly the rated power of the energy storage converter.

[0051] In this embodiment, the rated capacity of the energy storage device is the product of 1.5, 60 MW, and 2.00 seconds, which is 180 MJ, equivalent to 50 kWh; the rated power of the energy storage converter is 72 MW. The state of charge is based on the total energy of the energy storage device, and the usable range is 10% to 90%. From 50% state of charge onwards, the energy available in one direction corresponds to 40% of the total energy. Therefore, the total energy of the energy storage device is taken as 2.5 times the rated capacity of the energy storage device, which is 450 MJ, equivalent to 125 kWh. In this embodiment, the ratio of the rated capacity of the energy storage device to the rated power of the energy storage converter is 2.5 seconds, which falls under the application scenario of high power density and low energy density. Therefore, a supercapacitor bank is selected as the energy storage device. The stored energy of the supercapacitor bank is proportional to the square of the terminal voltage. When the operating voltage range is 50% to 100% of the rated voltage, the energy that can be released is 75% of its installed stored energy. Therefore, the installed stored energy of the supercapacitor bank is 450 megajoules divided by 0.75, which is 600 megajoules, equivalent to 167 kilowatt-hours. As an optional implementation, the energy storage device can also be a flywheel energy storage unit. However, the ratio of the rated power to the rated capacity of the flywheel energy storage unit is usually lower than the value required in this embodiment due to rotor design limitations. Therefore, when using a flywheel energy storage unit, the capacity multiple is set to 4 to ensure sufficient energy margin while meeting the rated power requirements of the energy storage converter.

[0052] Figure 3 This embodiment illustrates the energy storage compensation power command and the state of charge of the energy storage device during a complete load increase and decrease process. Figure 3 In (a), the horizontal axis represents time and the vertical axis represents the energy storage compensation power command. At time 0, an upward event of 60 MW occurs, and the energy storage compensation power command reaches a peak of 55.07 MW in 3.125 seconds and then decays exponentially. At time 50, an downward event of equal amplitude occurs, and the energy storage compensation power command shows a symmetrical peak of negative 55.07 MW. Figure 3 In (b), the horizontal axis represents time, and the vertical axis represents the state of charge (SBC) of the energy storage device. The SBC monotonically decreases from 50% to 10%, remains constant between two events, and automatically recovers to 50% after the decrease event, without requiring any charge / discharge control during the entire process. In this embodiment, the rated capacity of the energy storage device is selected based on the maximum design value of the plant's frequency regulation power increment command. Therefore, a unidirectional event under this maximum design value precisely utilizes the available energy in one direction, and the SBC deviation caused by a frequency regulation event with a smaller amplitude is reduced proportionally. Only when the absolute value of the frequency deviation returns to within the artificial frequency dead zone and lasts for 60 seconds, and the absolute value of the difference between the SBC and 50% of the energy storage device is greater than 10%, will the energy storage device be charged and discharged to 50% at 2% of the rated power of the energy storage converter, i.e., 1.44 MW. This duration setting ensures that the charging and discharging action falls outside the primary frequency regulation assessment window, avoiding contamination of the power integral used for assessment.

[0053] In step 4, the inertial offset of the water flow is only applied to units that are in grid-connected power generation and have primary frequency regulation. When a unit enters start-up, shutdown, or load shedding mode, or when the rate of change of the unit's guide vane opening exceeds 1.2 times the allowable regulation rate, the steady-state power increment converted from the guide vane opening is maintained at the value of the most recent execution cycle, and the inertial offset of the water flow continues to be applied recursively until it decays to 0. This rule is determined by the applicable premise of the upper limit of the inertial offset of the water flow: the derivation of the upper limit is based on the premise that the rate of change of the guide vane opening is constrained by the allowable regulation rate. However, the guide vane movement rate during start-up, shutdown, and load shedding is much higher than this constraint. If the recursion continues based on the measured guide vane opening, the inertial offset of the water flow will lose its upper limit, and the energy storage converter will enter saturation or even inject impulse power in the opposite direction into the grid connection point. Freezing the input instead of setting it to 0 allows the inertial compensation of the water flow to decay smoothly along the exponential law of the recursive formula, avoiding a step in the energy storage compensation power command; the 1.2 multiplier in the criterion is used to avoid the measurement noise of the guide vane opening change rate during normal adjustment.

[0054] When the energy storage converter trips or the state of charge of the energy storage device exceeds the set range, the calculation of the water flow inertia compensation amount in the energy storage compensation power command is stopped. Simultaneously, the allowable regulation rate is changed to the smaller value between the calculated allowable operating rate of the relay and the degradation rate. The degradation rate is calculated according to... Values; where The degradation rate is expressed in megawatts per second. The allowable reverse regulation depth setting value, in megawatts, represents the maximum permissible amplitude of the reverse change in the unit's active power relative to the incremental component of the unit's frequency regulation power. The coefficient 0.45 in the formula comes from the analytical result of the aforementioned reverse regulation extreme value, -0.4507, meaning that under uncompensated conditions, the reverse regulation depth is proportional to the product of the allowable regulation rate and the water flow inertia time constant. In this embodiment, the allowable reverse regulation depth setting value is taken as 1% of the unit's rated capacity, i.e., 2.5 megawatts. Therefore, the degradation rate is 2.5 divided by the product of 0.45 and 2.00, i.e., 2.78 megawatts per second, which is lower than the 4.8 megawatts per second under compensation. This means that after the energy storage device is removed, the plant's overall regulation rate automatically decreases, thereby limiting the reverse regulation depth within the allowable range, rather than simply losing compensation. At the same time, the governor power feedback value is restored to the measured value of the unit's active power and switched to the governor's standby parameter group.

[0055] In step 5, the power feedback of the speed controller is calculated according to... Generate; in the formula For the first The power feedback of the governor of the Taiwanese generator set in the first... The value for each execution cycle, in megawatts; The active power of the unit is the measured value, in megawatts; This represents the actual active power of the energy storage converter, measured in megawatts (MW). When the energy storage compensation power command is not subject to amplitude limiting, it is allocated to the [number]th [unit / phase]. The energy storage power of the generator unit is exactly equal to the water flow inertia cancellation amount of the unit. The governor power feedback amount, obtained by adding this to the measured active power of the unit, is exactly equal to the steady-state power increment calculated from the guide vane opening. The controlled object of the governor power loop thus changes from guide vane opening via the turbine transfer function to the unit's active power, to guide vane opening via the guide vane opening-power characteristic curve to the feedback amount. This no longer contains the water flow inertia element; the remaining dynamics are only the inertia element of the relay unit, and the zero point in the right half-plane disappears entirely. The formula uses the actual active power of the energy storage converter instead of the energy storage compensation power command. This is used to ensure that when the energy storage compensation power command is limited or the energy storage converter is partially deactivated, the sum of the governor power feedback amounts of each unit is still precisely equal to the measured active power increment at the grid connection point, thus preventing a situation where the governor believes the power is in place when the grid connection point is not actually in place.

[0056] Figure 5 The step response of the power loop controlled object under two feedback sampling methods was compared. Figure 5 The horizontal axis represents time, and the vertical axis represents the per-unit step response. The dashed line corresponds to the feedback quantity, which is the measured value of the unit's active power. In its initial stage, it dips downwards to -1.01, returns to 0 after 1.43 seconds, and approaches steady state after about 7 seconds. The solid line corresponds to the feedback quantity reconstructed according to this invention. It rises monotonically and approaches steady state in about 1 second. Since the controlled object corresponding to the dashed line contains a zero point in the right half-plane, the open-loop gain of its power loop is limited by the position of this zero point and can only be tuned very low; otherwise, the closed loop will become unstable. The controlled object corresponding to the solid line only contains the relay inertial element, and the power loop can be tuned according to the bandwidth determined by the relay time constant. In this embodiment, the relay time constant is taken as 0.3 seconds. When the sum of the inertial cancellation of all units' water flow is 0, that is, under steady-state conditions without frequency regulation events, the apportionment ratio in the above formula is undefined. At this time, the power feedback of the speed governor is taken as the actual measured value of the active power of the unit. Since the actual active power of the energy storage converter is also 0 at this time, the two methods are consistent in value, and the switching will not cause disturbance.

[0057] In step 6, the plant-wide optimization unit uses a slow timescale execution cycle to correct the unit power setpoint within the zero-space constraint of the total plant power. The zero-space projection matrix is ​​taken as... In the formula The null projection matrix, for An identity matrix of order 1. For elements all equal to 1 A column vector. Multiplying this matrix by the column vector consisting of the combined cost gradient components on the left, the result is the first column vector. Each element represents the sum of the unit's comprehensive cost gradient components minus the average sum of all unit comprehensive cost gradient components. Therefore, the correction is based on... Execution, in which In the formula For the first The unit power setting value of the unit, in megawatts; The step size for slow time-scale optimization is expressed in megawatt-squared seconds per cubic meter. This represents the overall cost gradient component, expressed in cubic meters per second per megawatt. This is the average value of the gradient components of the comprehensive cost of all units. Since the result of left multiplying a row vector with all elements equal to 1 by the null space projection matrix is ​​a zero row vector, the sum of the corrections for all units is always equal to 0 in each iteration. Therefore, the contribution of slow time-scale optimization to the total power of the plant is always 0. The economic optimization process and the primary frequency regulation response are mathematically completely decoupled: even if the slow time-scale optimization has not yet converged or gives an unreasonable gradient direction, the total power of the plant is still determined solely by the algebraic expression in step 3.

[0058] The comprehensive cost gradient component is equal to the sum of the incremental rate of water consumption and the incremental rate of vibration penalty, both measured in cubic meters per second per megawatt. The incremental rate of water consumption is obtained by numerically differentiating the pre-stored flow-power characteristic curve at the current unit power setting with a step size of 1 megawatt. In this embodiment, the incremental rate of water consumption is calculated to be 1.40 cubic meters per second per megawatt when the unit power setting is 150 megawatts and the operating head is 80 meters. In a water intake system with a surge tank, the unit operating head is first filtered by a moving average with a window length equal to the surge period of the surge tank before participating in the numerical difference. This is because the surge period of the surge tank is usually on the order of 100 to 300 seconds, which is on the same order of magnitude as the slow timescale execution period. If it is not filtered out, the incremental rate of water consumption will change back and forth with the surge, and the slow timescale optimization will generate ineffective power back-and-forth adjustments following the surge.

[0059] The rules for determining the vibration penalty increment rate are as follows: When the distance between the unit power setpoint and the upper boundary of the vibration zone is less than the set margin, the product of the penalty coefficient and the set margin minus the distance is taken as negative; when the distance between the unit power setpoint and the lower boundary of the vibration zone is less than the set margin, the same product is taken as positive; when the unit power setpoint is between the upper and lower boundaries of the vibration zone, the product of the penalty coefficient and the set margin is taken, with the sign being negative when the unit power setpoint is above the midpoint of the two boundaries and positive when it is below the midpoint; and 0 when the distance is greater than or equal to the set margin. These sign rules ensure that the correction always pushes the unit power setpoint away from the vibration zone, and when the unit power setpoint falls into the vibration zone, it exits from the nearest side according to the principle of proximity, thus preventing stagnation due to gradient direction cancellation within the vibration zone. In this embodiment, the four units are of the same type, and the vibration zone of each unit is between 95 MW and 145 MW; the set margin is 10 MW, and the penalty coefficient is 0.4 cubic meters per second per square megawatt. Based on the above values, the incremental rate of water consumption is 1.40 cubic meters per second per megawatt-hour, and the range of the comprehensive cost gradient component is from -2.60 to +5.40 cubic meters per second per megawatt. With four generating units, the absolute value of the difference between the comprehensive cost gradient component of any given unit and the average value of all units does not exceed 6.00 cubic meters per second per megawatt. Therefore, the slow timescale optimization step size is 0.2 megawatts squared seconds per cubic meter. The change in the unit power setpoint during a single correction does not exceed 1.20 megawatts, which is less than 0.5% of the unit's rated capacity, i.e., 1.25 megawatts. The linearization upon which the numerical difference is based holds true within this step size.

[0060] After correcting the unit power setpoints according to the above formula, the unit power setpoints are projected between the lower and upper limits of allowable output. The deviation generated by the projection is allocated proportionally to the window deliverable power of the remaining units. Units undertaking upward adjustments have their window deliverable power determined by the remaining adjustable capacity upwards, while units undertaking downward adjustments have their window deliverable power determined by the remaining adjustable capacity downwards. In the slow timescale, the window deliverable power is determined separately according to the direction undertaken. This is because there is no plant-wide frequency regulation power increment command during the slow timescale optimization process, and the direction of the remaining adjustable capacity cannot be determined by the sign of the command; it must be determined according to the actual direction undertaken by each unit in this redistribution. The above projection and redistribution are executed cyclically until the unit power setpoints of all units fall within their allowable output range. Since at least one unit is fixed at the boundary in each cycle, the number of cycles does not exceed the number of units.

[0061] The initial values ​​of the upper and lower boundaries of the vibration zone are obtained from the unit's comprehensive operating characteristic curve under the current operating head and are updated online according to the following rules: When the effective value of the vibration velocity of the unit's top cover continuously exceeds the set threshold for a set duration, the upper or lower boundary of the vibration zone that is closer to the current unit power setting value is moved to the current unit power setting value, i.e., that power point is incorporated into the vibration zone; when the unit power setting value remains unchanged and the effective value of the vibration velocity of the unit's top cover is continuously lower than 80% of the set threshold for a set duration, the upper or lower boundary of the vibration zone is moved 1 MW between the upper and lower boundaries of the vibration zone, i.e., that power point is released. The rule of inward shift allows the vibration zone boundary to change bidirectionally with unit maintenance, runner replacement, and sediment wear, avoiding the boundary from only expanding and never shrinking, which would cause the plant's available regulating capacity to shrink year by year; using 80% of the set threshold as the shift criterion and requiring a continuous set duration leaves a hysteresis zone between expansion and shift, preventing the boundary from jumping back and forth near the threshold. In this embodiment, the threshold is set to 2.5 millimeters per second, the duration of continuous exceeding the threshold is set to 5 seconds, and the duration of the shift criterion is set to 30 minutes.

[0062] The vibration zone divides the allowable range of unit power setpoints into two unconnected segments. Therefore, the overall plant cost becomes a non-convex function under the total plant power constraint, and gradient correction along the null space can only converge to a local optimum within the segment where the starting point is located. To address this, after the absolute value of the frequency deviation remains within the artificial frequency dead zone for a set duration, a cross-zone transition is initiated: after each set number of unit power setpoint corrections, the overall plant cost is calculated one by one after moving the unit power setpoint to the boundary on the other side of the vibration zone, with the remaining units bearing the cost in equal proportions according to the window's deliverable power. A cross-zone transition is executed once when the reduction exceeds a set threshold. The sum of all components of the transition vector is always equal to 0, meaning the transition and gradient correction reside in the same null space, and the total plant power remains unchanged during the transition. Only one unit is allowed to be in the cross-zone transition state at any given time to ensure that pressure pulsations of units on the same water intake system crossing the vibration zone do not superimpose at the same time. During the cross-regional transition, the upper limit of the guide vane opening change rate for all units is set at 50% of the allowable regulation rate, ensuring that the amount of water flow inertia offset during the transition process remains within 0.4 times the rated power of the energy storage converter. The remaining 0.4 times is reserved for possible simultaneous primary frequency regulation. When the absolute value of the frequency deviation exceeds the artificial frequency dead zone, the cross-regional transition is immediately stopped, and the upper limit of the guide vane opening change rate is restored to the allowable regulation rate. In other words, primary frequency regulation always takes precedence over economic optimization. In this embodiment, the start-up condition is taken as 30 seconds within the dead zone, and the trial calculation interval is taken as 20 corrections.

[0063] Figure 6 The above geometric relationship is illustrated using the case of two generating units. Figure 6The horizontal and vertical axes represent the power setpoints of the two generating units, respectively. The thick solid line with a slope of -1 represents the total power constraint of the entire plant. The vertical and horizontal shaded bands represent the vibration zones of Unit 1 and Unit 2, respectively. The dashed ellipse represents the contour line of the overall plant cost. The thick solid line is truncated by the two shaded bands into two unconnected feasible segments, one in the upper left and one in the lower right. The initial working point is located in the upper left segment. Corrections along the zero space cause the working point to move to the lower right along the thick solid line until it reaches the boundary of the vibration zone of Unit 1 and cannot continue. At this point, a cross-zone transition is performed, and the working point moves along... Figure 6 The curved dashed arrow crosses the section covered by two shaded bands to the lower right section, and then continues to correct along the zero space until it reaches the optimization endpoint where the contour line of the comprehensive cost is tangent to the thick solid line. Before and after the transition, the operating point always lies on the same thick solid line, that is, the total power of the entire plant remains unchanged; if there is no cross-regional transition, the optimization will stop at the boundary of the upper left section.

[0064] Slow timescale execution cycle Setting; where The execution period is for the slow timescale, and the unit is seconds. The settling time for the hydraulic transition process, measured in seconds, is the time required for the water hammer component of the unit's operating head to enter the steady-state range within ±1% of its value. This time is obtained from on-site step disturbance tests and is approximately three times the flow inertia time constant. The tuning is based on the hydraulic transition process settling time, not the unit power adjustment time. Since the water consumption increment rate in the comprehensive cost gradient component is calculated at the current unit power setpoint and the current unit operating head, the operating point on which this value difference is based is only true when the unit's operating head enters steady state. If the value is taken before the hydraulic transition process is complete, the gradient direction will carry the instantaneous deviation of the transition process. In step 4, the flow inertia cancellation acts on the grid connection point. The unit's own mechanical power and the flow rate and head in the pressure pipeline still transition according to the flow inertia time constant. Therefore, the hydraulic transition process settling time is not shortened by the introduction of the flow inertia cancellation element. In this embodiment, the inertial time constant of the water flow is 2.00 seconds, and the measured stabilization time of the hydraulic transition process is 6 seconds. Therefore, the slow timescale execution period is 60 seconds.

[0065] Steps 1 to 5 are executed by the local control unit corresponding to each unit, and step 6 is executed by the plant-wide optimization unit. Each local control unit communicates with the others via a dual-ring network using IEEE 1588 time synchronization, sending their window deliverable power and operating status via GOOSE messages. The message period is consistent with the execution period. GOOSE messages are used instead of conventional station control layer polling because the denominator of the allocation method requires the window deliverable power of all units. If forwarded by the host computer, the link delay would reach hundreds of milliseconds to seconds, making it impossible to complete the share update between units within the time scale of a single frequency regulation. Each unit's governor has a local frequency ring set as a backup channel. If no heartbeat message is received from the local control unit corresponding to the unit within a continuously set time period, the backup channel automatically takes over and sets the permanent slip coefficient to the rated setting value. Therefore, a failure of the local control unit itself will not cause the unit to lose its single frequency regulation capability. In this embodiment, the heartbeat message period is 100 milliseconds, and the continuously set time period for the criterion is 1 second.

[0066] As an optional implementation, in addition to obtaining the flow rate from the flow-power characteristic curve, the flow rate can also be obtained online by the differential pressure flow measurement device in the volute. That is, a differential pressure transmitter is installed on the existing pressure taps on the inner and outer sides of the volute, and the flow rate is converted according to the relationship that the differential pressure is proportional to the first power of the two. This method can track the characteristic deviation of the unit caused by erosion and increased clearance without shutdown and modification, making the online update of the water flow inertial time constant more accurate.

[0067] As an optional implementation, the flow inertia time constant can also be corrected online by the difference between the measured value of the active power increment at the grid connection point and the sum of the steady-state power increments calculated from the guide vane opening of each unit. The integral of this difference over a time window of 0.5 to 3 times the flow inertia time constant after the event's inception is taken as the error signal. When the error signal is positive, the flow inertia time constant of each unit is multiplied by 1.05; when it is negative, it is multiplied by 0.95. The cumulative correction coefficient is limited to 0.7 to 1.4. If the selected flow inertia time constant is less than the actual value, the flow inertia cancellation amount decays too quickly, and the difference between the sum of the steady-state power increments calculated from the guide vane opening of each unit and the measured value of the active power increment at the grid connection point is positive within that time window; otherwise, it is negative. This correction differs from the aforementioned correction term in its function. The correction term deals with the instantaneous residuals of each cycle, while this correction deals with the systematic deviations of the model parameters.

[0068] As an optional implementation, the energy storage devices can be distributed among the generating units, with each unit equipped with one energy storage device whose capacity is allocated according to that unit and connected to the unit's terminal. In this case, the water flow inertia compensation of each unit is sent to the energy storage converter of the unit, and the allocation link in the governor power feedback is simplified to directly taking the actual active power of the unit's energy storage converter. Distributed configuration eliminates the allocation calculation between units, but loses the mutual assistance capability of energy storage power between units, and the total rated power of the energy storage converters in the whole plant needs to be increased accordingly. As another optional implementation, the fatigue penalty incremental rate can also be included in the comprehensive cost gradient component of slow time-scale optimization. Its value is obtained by converting the change history of the effective value of the unit top cover vibration velocity and the unit power setpoint into equivalent water consumption after rain flow counting and linear cumulative damage criteria, and then taking the partial derivative with respect to the unit power setpoint, thereby balancing the cumulative damage among multiple units and making the maintenance cycle of all units in the whole plant tend to be consistent.

[0069] According to the above implementation method, in the example where the plant-wide frequency regulation power increment command is 60 MW, the grid-connected power increment monotonically increases from time 0, and the reverse regulation segment is completely canceled out. Without this method, the grid-connected power would first reverse and drop by 17.3 MW for 2.82 seconds; the step response of the governor's power loop controlled object changes from a reverse drop of 1.01 per unit value and a settling time of approximately 7 seconds to a monotonically increasing response and a settling time of approximately 1 second; the rated capacity of the energy storage device is only 50 kWh, and the state-of-charge deviation after the closed frequency regulation process is 0. Those skilled in the art can adjust the above parameter values ​​accordingly based on the actual layout of the on-site water intake system, the number of generating units, and the type of energy storage medium.

[0070] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing power allocation among multiple generating units in a hydropower plant for primary frequency regulation, characterized in that, A hydropower plant comprises multiple generating units operating in parallel, local control units corresponding to each unit, plant-wide optimization devices, and energy storage devices including energy storage converters; specifically, it includes the following steps: The power grid frequency, unit active power, guide vane opening and unit working head are collected according to the execution cycle. The difference between the power grid frequency and the rated frequency is taken as the frequency deviation. When the absolute value of the frequency deviation is greater than the artificial frequency dead zone, the frequency deviation is converted into the plant-wide frequency regulation power increment command, and the water flow inertia time constant of each unit is determined. The smaller of the permissible operating rate of the relay and the energy storage power constraint rate is taken as the permissible adjustment rate. The energy storage power constraint rate is directly proportional to the rated power of the energy storage converter and inversely proportional to the water flow inertia time constant. The smaller of the product of the remaining adjustable capacity, the permissible adjustment rate and the response window time is taken as the window deliverable power. Based on the proportion of the deliverable power of each unit window to the sum of the deliverable power of all units windows, the frequency regulation power increment command of the whole plant is allocated as the frequency regulation power increment component of the units, and then superimposed on the unit power setpoint as the governor power setpoint. The steady-state power increment of the guide vane opening is obtained from the measured guide vane opening according to the guide vane opening-power characteristic curve. The steady-state power increment of the guide vane opening is input into the water flow inertia cancellation link to obtain the water flow inertia cancellation amount. The transfer function of the water flow inertia cancellation link is equal to the difference between the value 1 and the transfer function of the active power of the turbine guide vane opening. The sum of the water flow inertia cancellation amounts of all units is used as the energy storage compensation power command and sent to the energy storage converter. The actual active power of the energy storage converter is allocated according to the proportion of the water flow inertia cancellation amount of each unit to the sum of the water flow inertia cancellation amounts of all units. The allocation result is added to the measured value of the active power of the unit and used as the power feedback amount of the speed governor. The unit power setpoint is corrected according to the slow timescale execution cycle. The correction amount is equal to the product of the slow timescale optimization step size and the difference. The difference is equal to the difference between the unit's comprehensive cost gradient component and the average value of all units' comprehensive cost gradient components. The unit power setpoint minus the correction amount, and the sum of all unit correction amounts is always equal to 0. The slow timescale execution cycle is greater than the execution cycle.

2. The method for optimizing power allocation among multiple units in a hydropower plant for primary frequency regulation according to claim 1, characterized in that, The grid frequency is obtained by the local control unit corresponding to each unit based on the local measurement of the terminal voltage and after moving average. The frequency regulation power increment command of the whole plant is calculated locally by the local control unit corresponding to each unit based on the equivalent permanent slip coefficient setting value of the whole plant. The conversion time is recorded as the event start time. The system also collects the effective value of the vibration velocity of the unit's top cover, the active power at the grid connection point, and the actual active power of the energy storage converter; the pressure pipeline of each unit is taken from the section between the surge tank and the turbine, or from the inlet to the turbine when no surge tank is installed; the one-way propagation time of the water hammer wave is equal to the sum of the ratios of the length of each pipe section to the water hammer wave velocity of each pipe section; the inertial time constant of the water flow is equal to the sum of the ratios of the length of each pipe section to the cross-sectional area of ​​each pipe section, multiplied by the unit flow rate, and then divided by the product of the gravitational acceleration and the unit's operating head, where the unit flow rate and the unit's operating head are... The working head is the average value within a set time period before the start of the event; the unit flow rate is obtained from the flow-power characteristic curve; the pipeline characteristic coefficient is equal to N times the inertial time constant of the water flow and the one-way propagation time of the water hammer wave; the remaining adjustable capacity is the difference between the upper limit of allowable output and the unit power setting value when the plant-wide frequency regulation power increment command is positive, and the difference between the unit power setting value and the lower limit of allowable output when the plant-wide frequency regulation power increment command is negative; the remaining adjustable capacity of the unit in derating operation, shutdown, startup, or load shedding state is 0.

3. The method for optimizing power allocation among multiple units in a hydropower plant for primary frequency regulation according to claim 1, characterized in that, The permissible operating rate of the relay is equal to the product of the permissible operating rate of the relay and the slope of the guide vane opening-power characteristic curve at the current guide vane opening. The energy storage power constraint rate is equal to the product of the rated power of the energy storage converter and the margin coefficient, divided by the product of the number of units with positive remaining adjustable capacity, the water flow inertia time constant, and the value 1.

5. The margin coefficient is taken as 0.7 to 0.

8. The permissible adjustment rate and the window deliverable power are latched at the beginning of the event and remain unchanged during the period when the absolute value of the frequency deviation is greater than the artificial frequency dead zone. The permissible adjustment rate is converted into the upper limit of the guide vane opening change rate and then sent to the governor rate limiting link. After the absolute value of the frequency deviation returns to within the artificial frequency dead zone and continues for a set time, it is refreshed according to the latest collected data.

4. The method for optimizing power allocation among multiple units in a hydropower plant for primary frequency regulation according to claim 1, characterized in that, The unit frequency regulation power increment component is the solution that minimizes the sum of the ratios of the squares of the frequency regulation power increment components of each unit to the window deliverable power among all solutions that satisfy the condition that the sum of the frequency regulation power increment components of all units equals the total frequency regulation power increment command of the entire plant. The ratio of the unit frequency regulation power increment component to the window deliverable power is equal for all units. When the absolute value of the total frequency regulation power increment command of the entire plant is greater than the sum of the window deliverable power of all units, the unit frequency regulation power increment component takes the window deliverable power and is oriented according to the positive or negative sign of the total frequency regulation power increment command of the entire plant. When the sum of the window deliverable power of all units is 0, the unit frequency regulation power increment component takes 0. When the plant optimization device is out of operation, the local control unit corresponding to each unit maintains the most recently received unit power setpoint and continues to execute the above power feedback acquisition steps according to the locally measured grid frequency.

5. The method for optimizing power allocation among multiple units in a hydropower plant for primary frequency regulation according to claim 3, characterized in that, The numerator of the transfer function from the turbine guide vane opening to the unit's active power is equal to the value 1 minus the product of the pipe characteristic coefficient and the hyperbolic tangent function value. The denominator is equal to the value 1 plus the product of the pipe characteristic coefficient and the hyperbolic tangent function value. The independent variable of the hyperbolic tangent function is equal to the product of the one-way propagation time of the water hammer wave and the Laplace operator. The numerator of the transfer function for the water flow inertia cancellation element is equal to the product of three times the pipe characteristic coefficient and the hyperbolic tangent function value. The denominator is the same as that of the transfer function from the turbine guide vane opening to the unit's active power. The value of the water flow inertia cancellation amount in the current execution cycle is equal to the product of three times the pipe characteristic coefficient and difference one, minus the product of difference two and the value of the water flow inertia cancellation amount in the execution cycle with the lag time delay step, divided by the value 1 and the pipe characteristic coefficient. The sum of the numbers; Difference 1 equals the difference between the value of the guide vane opening-based steady-state power increment in the current execution cycle and the value of the guide vane opening-based steady-state power increment in the execution cycle with a delay step; Difference 2 equals the difference between value 1 and the pipe characteristic coefficient; The delay step is equal to the ratio of twice the one-way propagation time of the water hammer wave to the execution cycle, rounded to the nearest integer; When the pipe characteristic coefficient is greater than or equal to 4, the water flow inertia cancellation link adopts a simplified form, with a margin coefficient of 0.8: First, the guide vane opening-based steady-state power increment is filtered by an inertial link with a time constant equal to half the water flow inertia time constant, and then three times the difference between the guide vane opening-based steady-state power increment and the inertial link filtering result is taken as the water flow inertia cancellation amount; When the pipe characteristic coefficient is less than 4, the margin coefficient is 0.

7.

6. The method for optimizing power allocation among multiple units in a hydropower plant for primary frequency regulation according to claim 1, characterized in that, The energy storage compensation power command is equal to the sum of the inertia compensation of all units' water flow and the sum of the correction term; the correction term is equal to the difference between the sum of the steady-state power increments converted from the guide vane opening of all units and the measured value of the active power increment at the grid connection point, multiplied by the proportional coefficient, which is greater than 0 and less than 1, and the correction term is limited to 20% of the rated power of the energy storage converter; the rated power of the energy storage converter is taken as 1.2 times the maximum design value of the frequency regulation power increment command of the whole plant; the rated capacity of the energy storage device is taken as the product of the value 1.5, the maximum design value of the frequency regulation power increment command of the whole plant, the maximum value of the water flow inertia time constant of all units, and the capacity multiple, and the capacity multiple is greater than or equal to 1; when the absolute value of the frequency deviation returns to within the artificial frequency dead zone and continues for a set time, and the absolute value of the difference between the state of charge of the energy storage device and 50% is greater than 10%, the energy storage device is charged and discharged at 2% of the rated power of the energy storage converter until the state of charge is equal to 50%.

7. The method for optimizing power allocation among multiple units in a hydropower plant for primary frequency regulation according to claim 1, characterized in that, The inertia compensation amount is only applied to units that are in grid-connected power generation and have primary frequency regulation enabled. When a unit enters start-up, shutdown, or load shedding mode, or when the rate of change of the unit's guide vane opening exceeds 1.2 times the allowable regulation rate, the steady-state power increment converted from the guide vane opening is maintained at the value of the most recent execution cycle, and the inertia compensation amount continues to be applied until it decays to 0. When the energy storage converter trips or the state of charge of the energy storage device exceeds the set range, the inertia compensation amount is no longer included in the energy storage compensation power command. The allowable regulation rate is changed to the smaller value between the converted value of the relay's allowable action rate and the degradation rate. The degradation rate is equal to the allowable reverse regulation depth setting value divided by the product of 0.45 and the inertia time constant. The allowable reverse regulation depth setting value is the maximum allowable amplitude of the reverse change of the unit's active power relative to the unit's frequency regulation power increment component. At the same time, the governor power feedback amount is restored to the measured value of the unit's active power and switched to the governor's standby parameter group.

8. The method for optimizing power allocation among multiple units in a hydropower plant for primary frequency regulation according to claim 1, characterized in that, When the sum of the inertial cancellation amounts of all unit water flows is 0, the governor power feedback is taken as the measured value of the unit's active power; the governor power loop is tuned according to the bandwidth determined by the relay time constant; the comprehensive cost gradient component is equal to the sum of the incremental rate of water consumption and the incremental rate of vibration penalty; the incremental rate of water consumption is obtained by numerically differentiating the flow-power characteristic curve at the current unit power setpoint with a step size of 1 MW; in the water intake system with a surge tank, the unit's working head is filtered by a moving average with a window length equal to the surge period of the surge tank before participating in the numerical difference; when the distance between the unit power setpoint and the upper boundary of the vibration zone is less than the set margin, the vibration penalty incremental rate is... The vibration penalty increment rate is calculated as the product of the penalty coefficient and the set margin minus the distance, with a negative sign. When the distance between the unit power setpoint and the lower boundary of the vibration zone is less than the set margin, the vibration penalty increment rate is calculated as the product of the penalty coefficient and the set margin minus the distance, with a positive sign. When the unit power setpoint is located between the upper and lower boundaries of the vibration zone, the vibration penalty increment rate is calculated as the product of the penalty coefficient and the set margin, with a negative sign when the unit power setpoint is higher than the midpoint between the upper and lower boundaries of the vibration zone and a positive sign when the unit power setpoint is lower than the midpoint. When the distance is greater than or equal to the set margin, the vibration penalty increment rate is 0.

9. The method for optimizing power allocation among multiple units in a hydropower plant for primary frequency regulation according to claim 1, characterized in that, After correcting the unit power setpoint, the unit power setpoint is projected between the lower and upper limits of allowable output. The deviation generated by the projection is allocated proportionally to the window deliverable power of the other units. Units responsible for upward adjustments have their window deliverable power determined by the remaining adjustable capacity upwards, while units responsible for downward adjustments have their window deliverable power determined by the remaining adjustable capacity downwards. When the effective value of the vibration velocity of the unit's roof continuously exceeds the set threshold for a set duration, the upper or lower boundary of the vibration zone closest to the current unit power setpoint is moved to the current unit power setpoint. When the unit power setpoint remains unchanged and the effective value of the vibration velocity of the unit's roof continuously falls below 80% of the set threshold for a set duration, the upper or lower boundary of the vibration zone is moved by 1 MW between the upper and lower boundaries of the vibration zone. After the absolute value of the frequency deviation remains within the artificial frequency dead zone for a set duration, a cross-zone transition is initiated: after each completion... After the set number of unit power setpoint corrections, the overall plant cost is calculated one by one after moving the unit power setpoint to the boundary on the other side of the vibration zone, with the remaining units bearing the cost in the same proportion of the deliverable power within the window. When the reduction in the overall plant cost is greater than the set threshold, a cross-zone transition is performed. Only one unit is allowed to be in the cross-zone transition state at any given time. During the cross-zone transition, the upper limit of the guide vane opening change rate of all units is taken as 50% of the allowable adjustment rate. When the absolute value of the frequency deviation is greater than the artificial frequency dead zone, the cross-zone transition is stopped and the upper limit of the guide vane opening change rate is restored to the allowable adjustment rate. The slow timescale execution cycle is greater than or equal to 10 times the stabilization time of the hydraulic transition process. The stabilization time of the hydraulic transition process is the time required for the water hammer component of the unit's working head to enter the steady-state value ±1% band. The value of the slow timescale optimization step size is such that the absolute value of the change in the unit power setpoint in a single correction is less than or equal to 0.5% of the unit's rated power.

10. A power optimization and allocation system for multiple units in a hydropower plant oriented towards primary frequency regulation, characterized in that, It includes a water flow inertia determination module, a deliverable power module, a power setting module, a compensation power module, a power feedback module, and an allocation module; The water flow inertia determination module collects the grid frequency, unit active power, guide vane opening and unit working head according to the execution cycle, and takes the difference between the grid frequency and the rated frequency as the frequency deviation; when the absolute value of the frequency deviation is greater than the artificial frequency dead zone, the frequency deviation is converted into the plant-wide frequency regulation power increment command, and the water flow inertia time constant of each unit is determined. The deliverable power module takes the smaller value between the relay's permissible action rate and the energy storage power constraint rate as the permissible adjustment rate. The energy storage power constraint rate is directly proportional to the rated power of the energy storage converter and inversely proportional to the water flow inertia time constant. The smaller value between the remaining adjustable capacity and the product of the permissible adjustment rate and the response window time is taken as the window deliverable power. The power setting module allocates the plant-wide frequency regulation power increment command as a unit frequency regulation power increment component according to the proportion of the deliverable power of each unit window to the sum of the deliverable power of all unit windows, and adds it to the unit power setpoint as the governor power setting. The compensation power module obtains the steady-state power increment of the guide vane opening based on the measured guide vane opening and the guide vane opening-power characteristic curve. The steady-state power increment of the guide vane opening is then input into the water flow inertia cancellation link to obtain the water flow inertia cancellation amount. The transfer function of the water flow inertia cancellation link is equal to the difference between the value 1 and the transfer function from the turbine guide vane opening to the active power of the unit. The sum of the inertial compensation of all units' water flow is used as the energy storage compensation power command and sent to the energy storage converter. The power feedback module allocates the actual active power of the energy storage converter according to the proportion of the water flow inertia cancellation amount of each unit to the sum of the water flow inertia cancellation amounts of all units. The allocation result is added to the measured value of the active power of the unit and used as the power feedback amount of the speed governor. The allocation module corrects the unit power setpoint according to the slow timescale execution cycle. The correction amount is equal to the product of the slow timescale optimization step size and the difference. The difference is equal to the difference between the unit's comprehensive cost gradient component and the average value of all units' comprehensive cost gradient components. The unit power setpoint minus the correction amount, and the sum of all unit correction amounts is always equal to 0. The slow timescale execution cycle is greater than the execution cycle.

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