CN111237208B - Blade setting angle step length adjustment control method during optimized operation of single unit of pump station - Google Patents
Blade setting angle step length adjustment control method during optimized operation of single unit of pump station Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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Abstract
The invention discloses a method for adjusting and controlling the step length of a blade setting angle during the optimized operation of a single pump station unit, which comprises the following steps: (1) establishing a target function according to the maximum water lifting amount W of a single unit of the blade-adjustable pump station in a certain operation period; (2) setting constraint conditions for solving the objective function; (3) and based on the blade setting angle discrete domain, gradually reducing the uniform discrete blade setting angle step length adjustment control method, and solving the objective function according to the constraint condition. The method takes the maximum total water lifting amount in a certain operation period as a target, is suitable for the maximum water transfer task requirement of a cross-basin water transfer pump station unit in south-to-north water transfer and the like in a certain water transfer period and total operation energy consumption, and is also suitable for the actual requirement of the drainage pump station unit with the blade adjusting function for improving the drainage amount as much as possible in a given period; meanwhile, the method can overcome the defects of the traditional method, and obviously improves the model solving precision and efficiency.
Description
Technical Field
The invention relates to an optimized operation method of a pump station single unit, in particular to a blade setting angle step length adjustment control method during optimized operation of the pump station single unit
Background
The construction and operation of the cross-basin water transfer project play a significant role in relieving uneven space-time distribution of water resources, promoting the development of the economic society and other fields, and the like. The water transfer pump station (group) is used as a key project of the whole water transfer system and has the characteristics of large number of units, large single-machine flow, adjustable working conditions (adjusting the installation angle or the rotating speed of blades of the water pump), long annual operation time, high operation energy consumption and the like. According to the minimum energy consumption or water lifting amount criterion of the pump station (group), energy consumption or flow distribution of each unit and each time period in the operation process of the pump station (group) is reasonably distributed, and the method is practicalThe system optimizes the operation target and has very important theoretical and application values. The existing optimization method directly sets the discrete step length of the blade setting angle in each time interval to be a smaller value, so that H-Q and eta under each blade setting angle are greatly increasedzThe fitting workload of the-Q performance curve is large, the iterative solving workload is greatly increased due to the large number of discrete numbers, the model calculation time is prolonged, and the solving efficiency is reduced.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a blade setting angle step length adjusting control method in optimized operation of a pump station unit, which has high solving efficiency and high precision.
The technical scheme is as follows: the invention discloses a method for adjusting and controlling the step length of a blade setting angle during the optimized operation of a single unit of a pump station, which comprises the following steps:
(1) establishing a target function according to the maximum water lifting amount W of a single unit of the blade-adjustable pump station in a certain operation period;
(2) setting constraint conditions for solving the objective function;
(3) the method for adjusting and controlling the step length of the blade setting angle based on the gradual reduction and uniform dispersion of the discrete domain of the blade setting angle solves an objective function according to constraint conditions, and specifically comprises the following steps:
(31) taking integral uniform discrete step length, solving the model by adopting a one-dimensional dynamic programming method, and obtaining the maximum water extraction W obtained by primary optimization1And optimal blade placement angle path theta at each time interval1 i，i＝1,2，…，SN；
(32) For the obtained optimal blade placement angle path theta in each period1 iReducing the discrete domain of the blade setting angle, taking the discrete step length smaller than that in the previous step, further uniformly dispersing the discrete steps, entering the original model, and optimizing by adopting a one-dimensional dynamic programming method to obtain the maximum water extraction W obtained by the optimizationmAnd optimal blade placement angle path theta at each time intervalm i，i＝1,2，…，SN；
(33) Repeating the step (32) for a plurality of times to successively approximate the objective function until the following formula is satisfied:
in the formula, m is iteration times, epsilon is given model iteration control precision, and SN is the number of time segments divided in the unit operation period.
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages:
(1) as for the model objective function, the maximum total water lifting amount in a certain operation period is the target, so that the method is suitable for the maximum water transfer task requirement of a cross-basin water transfer pump station unit in south-to-north water transfer and the like in a certain water transfer period and total operation energy consumption, and is also suitable for the actual requirement of a drainage pump station unit with a blade adjustable function for improving the water discharge as much as possible in a given period.
(2) For the model constraint condition, considering the safe operation requirement of the unit, the matched power constraint of the unit operation at each time interval is set; considering the efficient operation of the water pump, the operation energy consumption is reduced as much as possible, and the efficiency constraint of the water pump is set; and considering the operation life of the unit, the constraint of the number of times of start-up and shut-down which meets the requirement of not being suitable for frequent start-up and shut-down in the operation period of the unit is set. Therefore, the water lifting total amount maximization of the unit under the safe, stable and efficient operation can be realized.
(3) For the model solution method, two layers are included: and reducing the discrete domain and discrete step length of the blade setting angle in each period, and solving the original model by one-dimensional dynamic programming. Combining the two layers to approach successively until the requirement of iterative control precision is met, and taking the optimal blade placement angle in each period and the corresponding maximum water lifting total amount of the unit obtained by solving the model as the final optimization result of the model for pump station management units to use and reference. On the basis of the blade placement angle optimized path obtained by the previous and second optimization solution, the discrete domain and the discrete step length are directly reduced near the optimized blade placement angle, and then the optimization approximation is dynamically planned in sequence, so that the defects of the traditional method can be overcome, and the model solution precision and efficiency are remarkably improved.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
As shown in fig. 1, the steps of the present invention include:
1. constructing a model:
(1) the maximum water lifting amount of a single unit of the blade-adjustable pump station in a certain operation period is a target, and the following target function is established:
in the formula, W is the maximum total water lifting amount (ten thousand meters) of each time period of a single unit of the blade-adjustable pump station3) (ii) a SN is the number of time segments divided in the unit operation period; i is a period number (i ═ 1,2, …, SN); qi(θi) For the i-th period corresponding to the blade setting angle thetaiFlow (m) of the water pump3/s)；ΔTiIs the period length (h) of the ith period.
(2) Setting constraint conditions
The method comprises the steps of total energy consumption restraint of single unit operation of the blade adjustable pump station, feasible discrete domain restraint of a blade placement angle, power restraint of motor matching, restraint of unit start-up and shut-down, water pump efficiency restraint and the like.
(21) Total energy consumption for running of single unit of blade-adjustable pump station EmAnd (3) constraint:
(22) and (3) motor matching power constraint: the actual power of the unit does not exceed the power N matched with the motor connected with the water pump during operation0：
(23) And (3) restricting the efficiency of the water pump: the water pump is operated in a high-efficiency area, and the following requirements are met:
ηz min≤ηz,i(θi)≤ηzmax
(24) and (3) restraining the start and stop of the unit:
M≤Mmax
wherein ρ is the density of water, and is 103kg/m3G is the acceleration of gravity, and 9.8m/s is taken2，Qi(θi)、ηz,i(θi) Respectively, i-th period corresponding to the blade placement angle thetaiFlow rate (m)3S) and water pump efficiency, HiMean lift (m) at the i-th stage, E0Setting total energy consumption, eta, for the unitz minAnd ηz maxFor water pump efficiency constraints, ηintFor transmission efficiency, ηmotFor the efficiency of the motor, N0For motor matching power (kW), M is the number of start-stop times in the water pump operation period, MmaxThe number of times of starting and stopping of the unit is allowed during the operation.
2. Model solution
(1) The data preparation specifically comprises the following steps:
(11) parameters of the water pump unit: for a given model of pump device, the device model test parameters corresponding to each integer degree of blade setting angle on the model test report are known, i.e., several typical blade setting angle performance characteristic equations can be calculated from the following table. In addition, set water pump efficiency constraint ηz minAnd ηz maxEfficiency η of the transmission mechanismintEfficiency η of the motormotMotor matching power N0。
TABLE 1 Water Pump Performance characteristics equation
(12) Time parameters: the total operation duration T of the unit, the number SN of the time periods divided in the operation period, and the time period length Delta T corresponding to each time periodi(should satisfy
)。
(13) The operation parameters are as follows: total energy consumption for given operation of unit E0Each time period in the operation periodWater pump operating lift HiNumber of allowed start-up and shut-down times M in operation periodmax。
(2) One-dimensional dynamic programming successive approximation optimization method based on successive reduction and uniform dispersion of discrete domain of blade placement angle
Referring to the successive approximation and dynamic programming solving principle, the specific process comprises the following steps:
(21) the original model takes the maximum total water pumping amount of the water pump in a certain operation period as a target, takes a time period i as a stage variable, and takes the placement angle theta of the blades of the water pump in each time periodi,For decision variables, the stage separable one-dimensional dynamic programming model with the total energy consumption of the water pump at the first i stages as the state variable lambda can be solved by adopting a one-dimensional dynamic programming method.
Further, referring to the one-dimensional dynamic programming solution principle, the corresponding recursion equation is obtained as follows:
(a) stage i is 1:
in the formula, the state variable lambda1Represents the operation energy consumption of the water pump unit in the 1 st period, and the energy consumption can be dispersed in a corresponding feasible region: lambda [ alpha ]1＝0,E1,E2,...,Em。g1(λ1) For the water pump set operation energy consumption lambda corresponding to the 1 st time period1The maximum water lifting amount of a single unit of the pumping station is obtained. For each discrete lambda1Decision variable θ1Given blade setting angles for the existing model test data listed in Table 1 can be referenced, and the discrete feasible region lower boundary corresponds to the minimum blade setting angle θi,minThe upper boundary is not more than the matching power N of the unit motor0The corresponding maximum blade setting angle theta is requiredi,maxAnd the discrete step length BC can be an integer number of uniform step lengths, such as-4 degrees, -2 degrees, 0 degrees, +2 degrees and +4 degrees, and the like, and are respectively substituted into the corresponding water pump performance curve equation in the table 1 to calculate the corresponding blade placement angle theta1Flow rate of time Q1(θ1) And water pump efficiency etaz,1(θ1) Should satisfy the constraint condition at the same time, so that each discrete lambda can be obtained separately1When it is at mostExcellent theta1And g corresponding thereto1(λ1)。
(b) Stage i ═ 2,3, …, SN-1:
in the formula, the state variable lambdaiAnd (3) similarly and respectively dispersing the total energy consumption of the operation of the water pump unit in the first i periods: lambda [ alpha ]i＝0,E1,E2,...,Em。gi(λi) For operating the water pump unit corresponding to the first i periods of time, the total energy consumption lambdaiThe maximum total water lifting amount of the single unit of the pumping station is realized. For each discrete lambdaiDecision variable θi,1The dispersion is as above, and should satisfy: etaz min≤ηz,i(θi)≤ηzmax。
At this time, according to the one-dimensional dynamic programming solving step, the state transition equation is obtained as follows:
wherein i is 2,3, …, SN-1.
Uniformly dispersing each theta in integer degree according to the methodiThe values are respectively substituted into the table 1, and the corresponding blade setting angles theta are solvediFlow rate of time Qi(θi) And water pump efficiency etaz,i(θi) (ii) a Then, the obtained Q is calculatedi(θi) Substitution into gi(λi) For each discrete theta according to the state transition equationiLooking up i-1 stage gi-1(λi-1) The values should satisfy:
thereby obtaining
Theta for accomplishing all the above discrepanciesiAfter optimization, the final product can meet the requirements
Required optimum thetaiProcess and corresponding gi(λi)。
(c) And (5) stage SN:
in the formula, QSN(θSN) Corresponding to the blade setting angle theta for the SN th periodSNFlow rate of time, Δ TSNThe period of the SN-th period is long. State variable lambdaSNThe total energy consumption of the water pump unit in the previous SN period is as follows: lambda [ alpha ]SN＝Em(ii) a Decision variable (Water Pump blade setting Angle θ)SN) Uniformly dispersing the integer degrees in the corresponding feasible region by the method of the step (b).
The state transition equation:
adopting the method of step (b), finally obtaining the optimal value of the objective function, which is the first optimization and is marked as W1＝gSN(λSN) And corresponding optimum blade setting angle course theta of water pump1 i(i＝1,2，…，SN)。
(22) The optimal blade placement angle process theta obtained by the optimization solution in the step (21)1 i(i-1, 2, …, SN), determined by the optimization between several typical integer degrees of blade placement angles given by the performance characteristics of the water pump device in table 1. In order to fully utilize the given total energy consumption as much as possible and maximize the water lifting amount as much as possible, the stepless regulation characteristic of the blade adjustable group is considered, and therefore, the optimal water pump blade placement angle process theta in each period obtained in the step (1)1 i(i ═ 1,2, …, SN), further discretized and then one-dimensional dynamic programming is usedAnd (4) optimizing. The method specifically comprises the following steps:
optimally obtained optimal blade placement angle theta in each periodi 1(i ═ 1,2, …, SN), the blade placement angles are further discrete for each period. The discrete domain may be [ theta ]i 1-LS1,θi 1+LS1]，LS12 degrees can be taken as the discrete step BC, 1 degree can be taken as the discrete step BC, the step (1) is also referred, the one-dimensional dynamic programming method is adopted for solving, and the optimal blade placement angle theta in each period is obtainedi 2(i ═ 1,2, …, SN), and the corresponding minimum water lift electricity consumption cost W during the unit operation period2。
(23) The optimal blade placement angle theta in each period obtained in the step (22)i 2(i ═ 1,2, …, SN), the blade placement angles are further discrete for each period. The discrete domain may be [ theta ]i 1-LS2,θi 1+LS2]，LS2Can be 1 degree, the discrete step length BC can be 0.5 degree, and simultaneously, the new discrete blade placement angles correspond to H-Q and etazThe Q performance characteristic curve equation is determined by interpolation according to the existing equation and the size of the blade placement angle; if the blade setting angle of a certain time period or a certain time period obtained after the previous optimization solution is located at the upper (lower) boundary of the feasible discrete domain, the blade setting angle of the time period (or the certain time periods) does not need to be further dispersed during the approximation, and only the blade setting angles of other time periods are dispersed, so that the model solution workload is further reduced. Therefore, the one-dimensional dynamic programming method is also adopted for solving, and the optimal blade placement angle theta in each period is obtainedi 3(i ═ 1,2, …, SN), and the corresponding minimum water lift electricity consumption cost W during the unit operation period3。
(24) Repeating the steps (21) to (23), and reducing the discrete domain LS and the discrete step BC through the decision variables to obtain a successive approximation optimization method (for example, the discrete step BC can be respectively 1 degree, 0.5 degree, 0.2 degree, 0.1 degree and the like in successive approximation) until the steps are finished
It can be considered that the iteration control accuracy epsilon is satisfiedSolving; meanwhile, whether the number M of the startup and shutdown times in the operation period of the water pump meets the requirement that M is less than or equal to M is checked under the condition that the control precision requirement is metmaxW to be obtained therebymThe maximum water lifting total amount of the single unit blade full-adjustment optimized operation and the corresponding blade placement angle thetai m(i ═ 1,2, …, SN) is the optimum blade placement angle combination for each period. In consideration of reducing the workload of optimization solution, the number of times of optimization is controlled to be m-5 at most, or the discrete step length BC of the blade setting angle is 0.1 degrees, the optimization effect can be considered to be achieved, and the solution is finished.
Claims (6)
1. A method for adjusting and controlling the step length of a blade setting angle during the optimized operation of a single unit of a pump station is characterized by comprising the following steps:
(1) establishing a target function according to the maximum water lifting amount W of a single unit of the blade-adjustable pump station in a certain operation period;
(2) setting a constraint condition of the objective function for solving the required constraint parameter;
(3) the method for adjusting and controlling the step length of the blade setting angle based on the gradual reduction and uniform dispersion of the discrete domain of the blade setting angle solves an objective function according to constraint conditions, and specifically comprises the following steps:
(31) taking integral uniform discrete step length, solving the model by adopting a one-dimensional dynamic programming method, and obtaining the maximum water extraction W obtained by primary optimization1And optimal blade placement angle path theta at each time interval1 i，i＝1,2，…，SN；
(32) For the obtained optimal blade placement angle path theta in each period1 iReducing the discrete domain of the blade setting angle, taking the discrete step length smaller than that in the previous step, further uniformly dispersing the discrete steps, entering the original model, and optimizing by adopting a one-dimensional dynamic programming method to obtain the maximum water extraction W obtained by the optimizationmAnd optimal blade placement angle path theta at each time intervalm i，i＝1,2，…，SN；
(33) Repeating the step (32) for a plurality of times to successively approximate the objective function until the following formula is satisfied:
in the formula, m is iteration times, epsilon is given model iteration control precision, and SN is the number of time segments divided in the unit operation period.
2. The method for controlling the step length adjustment of the blade setting angle during the optimized operation of the pump station unit according to claim 1, wherein the objective function is as follows:
in the formula, W is the maximum total water lifting amount of each time period of a single unit of the blade-adjustable pump station; i is a period number, i ═ 1,2, …, SN; qi(θi) For the i-th period corresponding to the blade setting angle thetaiThe flow rate of the water pump; delta TiThe period of the ith period is long.
3. The method for controlling the step length adjustment of the blade setting angle during the optimized operation of the pump station unit according to claim 1, wherein the constraint conditions of the constraint parameters comprise:
(21) total energy consumption for operation of single unit with adjustable blades EmAnd (3) constraint:
(22) and (3) motor matching power constraint: the actual power of the unit does not exceed the matching power of the motor connected with the water pump during operation:
(23) and (3) restricting the efficiency of the water pump: the water pump is operated in a high-efficiency area, and the following requirements are met:
ηz min≤ηz,i(θi)≤ηzmax
(24) and (3) restraining the start and stop of the unit:
M≤Mmax
wherein ρ is the density of water, and is 103kg/m3G is the acceleration of gravity, and 9.8m/s is taken2，ηz,i(θi) For the i-th period corresponding to the blade setting angle thetaiEfficiency of the water pump of HiMean lift at i-th time period, E0Setting total energy consumption, eta, for the unitintFor transmission efficiency, ηmotFor the efficiency of the motor, etazminAnd ηzmaxFor water pump efficiency constraints, N0For the matching power of the motor, M is the number of start-stop times in the operation period of the water pump, MmaxThe number of times of starting and stopping of the unit is allowed during the operation.
4. The method for controlling the step length adjustment of the blade setting angle during the optimal operation of the single unit of the pump station according to claim 1, wherein the step (31) specifically comprises the following steps:
(311) stage i is 1: the lower boundary of the discrete feasible region corresponds to the minimum blade placement angle thetai,minThe upper boundary is not more than the matching power N of the unit motor0The corresponding maximum blade setting angle theta is requiredi,maxRespectively substituting the parameters into corresponding water pump performance curve equations to calculate the corresponding blade placement angles theta1Flow rate of time Q1(θ1) And water pump efficiency etaz,1(θ1) Should satisfy the constraint condition at the same time, each discrete lambda is obtained separately1Optimum theta1And g corresponding thereto1(λ1)：
In the formula, the state variable lambda1Representing the operation energy consumption of the water pump unit in the 1 st period, which can be dispersed in the corresponding feasible region; g1(λ1) For the water pump set operation energy consumption lambda corresponding to the 1 st time period1The maximum water extraction amount of a single unit of a pumping station is calculated;
(312) stage i ═ 2,3, …, SN-1: each thetaiThe values are respectively substituted into a water pump performance characteristic curve equation to solve the corresponding blade placement angle thetaiFlow rate of time Qi(θi) And water pump efficiency etaz,i(θi) (ii) a Then, the obtained Q is calculatedi(θi) Substitution into
From the state transition equation, for each discrete θiLooking up i-1 stage gi-1(λi-1) The value should satisfy the following formula:
in the formula, HiMean lift at i-th time period, Δ TiIs the period of the i-th period, ηintFor transmission efficiency, ηmotFor the efficiency of the motor, state variable lambdaiThe total energy consumption for the operation of the water pump unit in the first i time periods; finally, the optimal theta meeting the requirements can be obtainediProcess and corresponding gi(λi)：
The state transition equation is:
wherein i is 2,3, …, SN-1;
(313) and (5) stage SN: and (3) finally obtaining the optimal value of the objective function by adopting the method of the step (312), wherein the optimal value is primary optimization and is recorded as:
W1＝gSN(λSN)
the optimal blade placement angle of the corresponding primary water pump is theta1 iI ═ 1,2, …, SN; water pump blade setting angle thetaSNThe method of step (312) is also adopted for integral uniform dispersion in the corresponding feasible region, wherein:
in the formula, λSNTotal energy consumption, Q, of water pump unit operation in previous SN time period of state variableSN(θSN) Corresponding to the blade setting angle theta for the SN th periodSNFlow rate of time, Δ TSNThe period of the SN-th period is long;
the state transition equation is:
in the formula, the state variable lambdaSN-1The total energy consumption for the running of the water pump unit in the first SN-1 time periods.
5. The method for controlling the step length adjustment of the blade setting angle during the optimal operation of the single unit of the pump station according to claim 1, wherein m is less than or equal to 5, the discrete step length BC is less than or equal to 0.1 degree, and when m is 5 or the discrete step length BC is 0.1 degree, the solution is finished.
6. The method for controlling the step length adjustment of the blade setting angle during the optimized operation of the pump station unit according to claim 1, wherein the step (3) is followed by the following steps: and (4) replacing the result obtained by the solution with a calculation, and checking whether the constraint parameters meet the constraint conditions set in the step (2).
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| CN113434981B (en) * | 2021-06-30 | 2023-10-27 | 扬州大学 | Multi-objective optimization system, method, computer equipment and storage medium based on blade-adjustable multi-unit pump station |
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