CN116047915B - Self-adaptive control method for full-load working condition of water turbine - Google Patents
Self-adaptive control method for full-load working condition of water turbine Download PDFInfo
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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Abstract
The invention discloses a full-load working condition self-adaptive control method of a water turbine, which comprises the following steps: step 1, a generalized Smith predictor is adopted in a speed regulator to predict the working condition of a control object, mathematical models of a water diversion system, a water turbine and a generator are built, a whole control object model is built, and a mathematical model without a non-minimum phase item with steady-state gain of 1 is built; and 2, aiming at a mathematical model which does not consider a non-minimum phase item with steady-state gain of 1, adopting a shortest time controller to control, measuring the rotating speed of the unit, comparing the rotating speed with the output value of the whole control object model, correcting by utilizing a rotating speed set value, and simultaneously considering the differential regulation requirement when the unit is operated in parallel. The method of the invention achieves the best control effect of the unit under any working condition, and solves the problems of insufficient stability and reduced adjustment quality of the adjustment system when the existing unit operates within the full-load working condition range.
Description
Technical Field
The invention belongs to the technical field of hydroelectric generating set adjustment, and relates to a full-load working condition self-adaptive control method of a water turbine.
Background
Currently, under the background of solar power generation and wind power generation with strong randomness and high gap property and a large number of grid connection, the power balance adjustment effect of the hydroelectric generating set on the power grid is particularly important. The conventional hydroelectric generating set only carries out small-range power adjustment near the design working condition, when the set deeply participates in power grid adjustment, the set needs to operate in a wider working condition range especially when the set operates at variable speed and participates in power grid adjustment, and at the moment, the traditional PID control method is difficult to integrate relevant parameters which can meet the requirements of the set on the adjustment quality under different load working conditions, so that the problems of insufficient stability and reduced adjustment quality of an adjustment system when the set operates in the full load working condition range are caused.
Disclosure of Invention
The invention aims to provide a full-load working condition self-adaptive control method for a water turbine, which solves the problems of insufficient stability and reduced regulation quality of a regulating system when a PID control method unit operates in a full-load working condition range in the prior art.
The technical scheme adopted by the invention is that the full-load working condition self-adaptive control method of the water turbine is implemented according to the following steps:
step 1, a generalized Smith predictor is adopted in a speed regulator to predict the working condition of a control object, mathematical models of a water diversion system, a water turbine and a generator are built, a whole control object model is built, and a mathematical model without a non-minimum phase item with steady-state gain of 1 is built;
and 2, aiming at a mathematical model without a non-minimum phase item with steady-state gain of 1, adopting a shortest time controller to control, measuring the rotating speed of the unit, comparing the rotating speed with the output value of the whole control object model, correcting by utilizing a rotating speed set value, and simultaneously considering the differential regulation requirement when the unit is operated in parallel.
The method has the advantages that the generalized Smith predictor is adopted to predict the working condition of the adjusting object, the shortest time controller is adopted to control the non-minimum phase link, the measured rotating speed and the predicted rotating speed of the unit are adopted to carry out comparison and correction, meanwhile, the differential adjusting requirement of parallel operation of the unit is considered, so that the optimal control effect of the unit under any working condition is achieved, meanwhile, the parameter setting of the regulator is not needed, and the problems of insufficient stability and reduced adjusting quality of an adjusting system when the hydraulic unit adopting the traditional PID control strategy operates in the full-load working condition range are solved.
Drawings
FIG. 1 is a block diagram of a governor control object model in the method of the present invention;
FIG. 2 is a block diagram of a conditioning system in the method of the present invention;
FIG. 3 is a family of system state phase trajectory graphs in the method of the present invention;
FIG. 4 is a graph of discriminant functions in the method of the present invention;
FIG. 5a is a graph of the flow characteristics of a turbine in accordance with an embodiment of the method of the present invention;
FIG. 5b is a graph of torque characteristics of a hydraulic turbine according to an embodiment of the method of the present invention;
FIG. 6a shows the coefficient of transfer e of the turbine according to an embodiment of the method of the present invention y A graph changing along with working conditions;
FIG. 6b shows the coefficient of transfer e of the turbine according to an embodiment of the method of the present invention ab A graph changing along with working conditions;
FIG. 6c shows the coefficient of transfer e of the turbine according to an embodiment of the method of the present invention x A graph changing along with working conditions;
FIG. 6d is a graph showing the characteristic coefficient e of the water turbine according to the working condition of the method embodiment of the present invention;
fig. 7 is a graph showing the motor rotation speed according to the embodiment of the method of the present invention.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The invention relates to a full-load working condition self-adaptive control method of a water turbine, which is implemented according to the following steps:
and 1, predicting the working condition of a control object by adopting a generalized Smith predictor in a speed regulator, establishing mathematical models of a water diversion system, a water turbine and a generator, establishing a whole control object model, and establishing a mathematical model without a non-minimum phase item with a steady-state gain of 1.
The operation mode of the open-loop speed regulator servomotor is adopted, namely, the servomotor stroke is not output to the servomotor input end as feedback quantity, the output value of the controller is output to the servomotor after passing through the electrohydraulic conversion module, and the set parameters are as follows: y is the opening of a guide vane of the water turbine; u is the regulator output value; t (T) y Is a servomotor response time constant; s is a pull-type calculationAnd (5) a seed. The transfer function expression for the servomotor is:
ignoring the influence of the rotation speed of the water turbine on the flow, adopting a rigid water hammer mode for the pipeline, m t Is the moment of the water turbine; y is the opening of a guide vane of the water turbine; e, e y The transmission coefficient of the torque of the water turbine to the opening of the guide vane; e, e qh The transfer coefficient of the flow of the water turbine to the water head; e, e qy The transmission coefficient of the flow of the water turbine to the opening of the guide vane; e, e h The transfer coefficient of the torque of the water turbine to the water head is used; t (T) w Is the inertial time constant of the water flow. The transfer function expression of the diversion system and the water turbine is as follows:
wherein ,
because the transfer coefficients can correspondingly change along with the working condition change of the water turbine, the change relation of each parameter is obtained by inquiring the relation between the preset transfer coefficients and the working condition parameters of the water turbine, and the expression is as follows:
in formula (4), x' is the generator speed; h is the working water head of the water turbine; f (f) x For the transfer coefficient e x Relationship with the operating mode parameters; f (f) y For the transfer coefficient e y Relationship with the operating mode parameters; f (f) h For the transfer coefficient e h Relationship with the operating mode parameters; f (f) qy For the transfer coefficient e qy Relationship with the operating mode parameters; f (f) qh Transfer coefficient e qh Relation of working condition parameters.
Neglecting the electromagnetic process of the generator, the transfer function expression of the generator and the load is as follows:
wherein ,en ＝e g -e x (6)
In the formula (5) and the formula (6), m g0 A load disturbance torque; t (T) a Is the inertial time constant of the unit; e, e n The coefficient is comprehensively self-adjusted for the unit; e, e g Self-regulating the factor for the load.
According to equations (2) to (6), the whole control object model and the mathematical model without the non-minimum phase term with the steady-state gain of 1 are respectively established, and as shown in fig. 1, the output value of the whole control object model is x', and the output value of the mathematical model without the non-minimum phase term with the steady-state gain of 1 is x 1 。
And 2, aiming at a mathematical model which does not consider a non-minimum phase item with steady-state gain of 1, adopting a shortest time controller to control, measuring the rotating speed of the unit, comparing the rotating speed with the output value of the whole control object model, correcting by utilizing a rotating speed set value, and simultaneously considering the differential regulation requirement when the unit is operated in parallel.
Setting a shortest time controller for the minimum phase link, and neglecting the load moment m g0 The state equation for the minimum phase link of the regulation system is obtained as:
wherein the state quantity x 2 Is the state quantity x 1 Is a rate of change of (2); u is the servomotor input value.
Considering the motion speed constraint of the servomotor, the conditions required to be met by the input value u of the servomotor are as follows:
v c T y ≤u≤v o T y (8)
wherein ,vc Is relay forceThe fastest closing speed of the device; v o The highest opening speed of the servomotor is achieved;
in order for the regulation system to meet the standard form of the shortest time controller, let:
at the moment, the I U I is less than or equal to 1, and the state equation (7) is rewritten as follows:
the functional expression of the regulation time of the regulation system is:
in equation (11), T is the time required for the state of the system equation (10) to return to the origin.
At this time, the hamiltonian expression of the adjustment system is:
in the formula (12), lambda 1 and λ2 Are all the accompanying coefficients.
The accompanying equation from the hamiltonian is:
further, the solution for obtaining the accompanying coefficient is:
in the formula (14), a 1 And a 2 Are all arbitrary constants.
As can be seen from equation (14), equation (14) is a monotonic function with respect to time t, so that the optimal control u= -sign (λ 2 ) The output of (1) needs to be converted at most once between 1 and-1 in one control process. The regulation system phase trajectory profile family is shown as a dotted line in fig. 3 when u=1, and the regulation system phase trajectory profile family is shown as a solid line in fig. 3 when u= -1. As can be seen from the phase trajectory curve family of fig. 3, the discriminant function when the state of the system is restored to the origin is shown in fig. 4, that is, the operating point needs to move along the solid line in fig. 3 to the discriminant function, that is, u= -1 when the state point is located on the left side of the curve in fig. 4, and similarly, the state point is first transferred to the curve shown in fig. 4 and then restored to the origin along the curve, so that the output discriminant function can be obtained according to fig. 4.
As can be taken from fig. 4, the expression of the regulation system discriminant function is:
consider a rotation speed given as x r The output function expression of the regulating system is as follows:
and (3) combining the formula (9) and the formula (16), and taking the error between the actual measurement value and the predicted value of the rotating speed into consideration to obtain the output value of the water turbine regulator, wherein the output value is as follows:
as seen by the formula (17), the output of the system in the dynamic process is always the input extremum of the servomotor, and the output of the water turbine regulator has the same control effect when the following formula is satisfied due to the limited movement speed of the guide vane:
wherein R is not less than |v max |T y (19)
In the formula (18) and the formula (19), v max The opening is positive and the closing is negative for the fastest movement speed of the opening of the guide vane of the water turbine.
Considering that the hydropower unit needs to meet the differential regulation requirement during grid-connected operation, x is adopted r -e p Rotation speed set value x in p substitution type (18) r Meanwhile, the deviation part of the rotation speed estimation and the rotation speed measurement is considered, and the output of the shortest time controller is obtained as follows:
in the formula (20), e p And p is the relative value of the power deviation for the unit deviation rate.
To this end, a block diagram of the final regulating system as a whole is obtained, as shown in fig. 2.
And (3) experimental verification:
in order to verify the effectiveness of the method, a certain power station is taken as an example for simulation verification, a control object in the simulation is simulated by adopting a more accurate mathematical model, a water diversion system adopts a characteristic line method to solve a water hammer basic equation, a water turbine adopts a model comprehensive characteristic curve to interpolate, a motor adopts a 5-order mathematical model considering electromechanical transient, a load adopts an index model of the load, and a controller adopts the full-load working condition self-adaptive control method of the water turbine.
The diameter of the rotating wheel of the power station is 4.36m, the rated output force of the unit is 266.7MW, the rated rotating speed is 214.3r/min, the rated water head is 202m, and the rated flow is 145.7m 3 And/s, response time of the servomotor is 0.2s, resistive load is adopted, and the load self-adjustment coefficient e g =0. The length of the power station reservoir to the volute section is 683.8m, the diameter is 5.6m, the water hammer wave speed is 1000m/s, the local loss coefficient is 0.274, and the pipe wall roughness is 0.012; the length of the equivalent circular straight pipe of the volute is 20m, and the diameter is 4.36m, the water hammer wave speed is 1200m/s, the local loss coefficient is 0, and the wall roughness is 0.012; the length from the draft tube to the outlet section of the power station is 34.87m, the tube diameter is 4.97m, the water hammer wave speed is 1200m/s, the local loss coefficient is 1, and the tube wall roughness is 0.0001; water flow inertia time constant T w =2.27 s, generator flywheel moment 20000t·m 2 . Mechanical inertia time constant T a System margin b =9.68 s p The hydraulic turbine model synthesis characteristic curves are shown in fig. 5a and 5b, and the hydraulic turbine model correlation coefficients obtained by the hydraulic turbine model synthesis characteristic curves are shown in fig. 6a, 6b, 6c and 6 d.
The dynamic process of 10% load disturbance reduction of the water turbine under different load working conditions can be obtained by the method, the dynamic process is shown by a thick line in the figure 7, a thin line curve is compared with the thick line, and the optimal PID parameter is set under the rated working condition P 2.4, K I 0.35, K D And 3.5, the simulation result shows that the water turbine can show a better adjusting process under the full-load working condition, the stability of the full-load operation of the unit is enhanced, and the adjusting quality of the unit is improved.
Claims (2)
1. The full-load working condition self-adaptive control method of the water turbine is characterized by comprising the following steps of:
step 1, a generalized Smith predictor is adopted in a speed regulator to predict the working condition of a control object, mathematical models of a water diversion system, a water turbine and a generator are built, a whole control object model is built, and a mathematical model without a non-minimum phase item with a steady-state gain of 1 is built, wherein the specific process is as follows:
the operation mode of the open-loop speed regulator servomotor is adopted, namely, the servomotor stroke is not output to the servomotor input end as feedback quantity, the output value of the controller is output to the servomotor after passing through the electrohydraulic conversion module, and the set parameters are as follows: y is the opening of a guide vane of the water turbine; u is the input value of the servomotor; t (T) y Is a servomotor response time constant; s is a pull operator, and the transfer function expression of the servomotor is:
ignoring the influence of the rotation speed of the water turbine on the flow, adopting a rigid water hammer mode for the pipeline, m t Is the moment of the water turbine; y is the opening of a guide vane of the water turbine; e, e y The transmission coefficient of the torque of the water turbine to the opening of the guide vane; e, e qh The transfer coefficient of the flow of the water turbine to the water head; e, e qy The transmission coefficient of the flow of the water turbine to the opening of the guide vane; e, e h The transfer coefficient of the torque of the water turbine to the water head is used; t (T) w And the transfer function expression of the diversion system and the water turbine is as follows:
wherein ,
because the transfer coefficients can correspondingly change along with the working condition change of the water turbine, the change relation of each parameter is obtained by inquiring the relation between the preset transfer coefficients and the working condition parameters of the water turbine, and the expression is as follows:
in formula (4), x' is the generator speed; h is the working water head of the water turbine; f (f) x For the transfer coefficient e x Relationship with the operating mode parameters; f (f) y For the transfer coefficient e y Relationship with the operating mode parameters; f (f) h For the transfer coefficient e h Relationship with the operating mode parameters; f (f) qy For the transfer coefficient e qy Relationship with the operating mode parameters; f (f) qh Transfer coefficient e qh Relation of working condition parameters;
neglecting the electromagnetic process of the generator, the transfer function expression of the generator and the load is as follows:
wherein ,en ＝e g -e x (6) In the formula (5) and the formula (6), m g0 A load disturbance torque; t (T) a Is the inertial time constant of the unit; e, e n The coefficient is comprehensively self-adjusted for the unit; e, e g Self-regulating the coefficient for the load;
step 2, aiming at a mathematical model which does not consider a non-minimum phase item with steady-state gain of 1, adopting a shortest time controller to control, measuring the rotating speed of a unit, comparing the rotating speed with the output value of a whole control object model, correcting by utilizing a rotating speed set value, and simultaneously considering the differential regulation requirement when the unit is operated in parallel, wherein the specific process is as follows:
setting a shortest time controller for the minimum phase link, and neglecting the load disturbance moment m g0 The state equation for the minimum phase link of the regulation system is obtained as:
wherein the state quantity x 2 Is the state quantity x 1 Is a rate of change of (2); u is the input value of the servomotor;
considering the motion speed constraint of the servomotor, the conditions required to be met by the input value u of the servomotor are as follows:
v c T y ≤u≤v o T y (8)
wherein ,vc The highest closing speed of the servomotor; v o The highest opening speed of the servomotor is achieved;
in order for the regulation system to meet the standard form of the shortest time controller, let:
at this time |U| is less than or equal to 1, and the state equation (7) is rewritten as:
the functional expression of the regulation time of the regulation system is:
in the formula (11), T is the time required for the state of the system equation (10) to return to the original point;
at this time, the hamiltonian expression of the adjustment system is:
in the formula (12), lambda 1 and λ2 All are accompanying coefficients;
the accompanying equation from the hamiltonian is:
further, the solution for obtaining the accompanying coefficient is:
in the formula (14), a 1 And a 2 Are all arbitrary constants;
the expression of the regulating system discriminant function is:
consider a rotation speed given as x r Rear adjustment systemThe output function expression is:
and (3) combining the formula (9) and the formula (16), and taking the error between the actual measurement value and the predicted value of the rotating speed into consideration to obtain the output value of the water turbine regulator, wherein the output value is as follows:
as seen by the formula (17), the output of the system in the dynamic process is always the input extremum of the servomotor, and the output of the water turbine regulator has the same control effect when the following formula is satisfied due to the limited movement speed of the guide vane:
wherein R is not less than |v max |T y (19)
In the formula (18) and the formula (19), v max The opening is positive and the closing is negative for the fastest movement speed of the opening of the guide vane of the water turbine;
considering that the hydropower unit needs to meet the differential regulation requirement during grid-connected operation, x is adopted r -e p Rotation speed set value x in p substitution type (18) r Meanwhile, the deviation part of the rotation speed estimation and the rotation speed measurement is considered, and the output of the shortest time controller is obtained as follows:
in the formula (20), e p And p is the relative value of the power deviation for the unit deviation rate.
2. The method for adaptively controlling full-load conditions of a water turbine according to claim 1, which is characterized in thatCharacterized in that the formula (14) is a monotonic function with respect to time t, so that the optimal control u= -sign (λ) 2 ) The output of (1) needs to be converted at most once between 1 and-1 in one control process,
when the state of the regulating system is recovered to the original point, the working condition point needs to move to a discrimination function U= -1 along a solid line, and similarly, the working condition point is located at the left side of the curve, and at the moment, the working condition point is firstly transferred to the curve and then recovered to the original point along the curve, so that the output discrimination function is obtained.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH03245201A (en) * | 1990-02-23 | 1991-10-31 | Katsuhisa Furuta | Shortest time controller |
| CN104503228A (en) * | 2014-11-19 | 2015-04-08 | 国家电网公司 | Primary frequency modulation stability domain determination method of water turbine speed regulator under power mode |
| CN107168103A (en) * | 2017-06-22 | 2017-09-15 | 南方电网科学研究院有限责任公司 | Hydropower Unit speed regulating control emulation mode and system |
| CN111237116A (en) * | 2020-01-14 | 2020-06-05 | 河海大学 | Nonlinear non-salient pole hydraulic generator water gate and excitation combined adjusting method and system |
| CN113471988A (en) * | 2021-06-30 | 2021-10-01 | 武汉大学 | Active-frequency coupling control method based on double-fed variable-speed pump-storage unit electromechanical transient model under pumping working condition |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8260440B2 (en) * | 2008-12-05 | 2012-09-04 | The Regents Of The University Of Michigan | Adaptive control based on retrospective cost optimization |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH03245201A (en) * | 1990-02-23 | 1991-10-31 | Katsuhisa Furuta | Shortest time controller |
| CN104503228A (en) * | 2014-11-19 | 2015-04-08 | 国家电网公司 | Primary frequency modulation stability domain determination method of water turbine speed regulator under power mode |
| CN107168103A (en) * | 2017-06-22 | 2017-09-15 | 南方电网科学研究院有限责任公司 | Hydropower Unit speed regulating control emulation mode and system |
| CN111237116A (en) * | 2020-01-14 | 2020-06-05 | 河海大学 | Nonlinear non-salient pole hydraulic generator water gate and excitation combined adjusting method and system |
| CN113471988A (en) * | 2021-06-30 | 2021-10-01 | 武汉大学 | Active-frequency coupling control method based on double-fed variable-speed pump-storage unit electromechanical transient model under pumping working condition |
Non-Patent Citations (1)
| Title |
|---|
| Study on Primary Frequency Regulation Capability and System Stability of Hydropower Units;Chunyang Gao 等;2022 5th International Conference on Renewable Energy and Power Engineering (REPE);全文 * |
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Application publication date: 20230502 Assignee: Xi'an Boer Industrial Automation Technology Co.,Ltd. Assignor: SHAANXI RAILWAY INSTITUTE Contract record no.: X2024980002032 Denomination of invention: Adaptive Control Method for Full Load Operating Conditions of Hydraulic Turbines Granted publication date: 20230815 License type: Common License Record date: 20240208 |