JPS6132683B2 - - Google Patents

Description

[Detailed description of the invention]

The present invention can be used for any object that requires control of the number of pumps. For example, water supply, sewerage, irrigation,
Can be used for pump equipment such as drainage. When controlling the flow rate based on the number of pumps, sequence control is simple and economical, but since the control is discontinuous, the following method has been adopted. One is a method based on the reservoir water level, in which the flow rate is controlled by increasing or decreasing the number of pumps in operation according to the water level. To switch the number of pumps, start and stop the pumps by setting the upper and lower water level limits for the number of pumps. This is shown in FIG. In addition, in the same figure, 1
00, 101, 102 are the stop water levels of pumps 1, 2, and 3, and 100', 101', 102'
is the starting water level of pumps No. 1, No. 2, and No. 3. Another method is to start as infrequently as possible,
For the purpose of improving operational efficiency, there is a program control method that increases or decreases the number of water pumps according to a pre-predicted load flow curve. This is shown in FIG. In this method, the discrepancy between the amount of water pumped under program control and the actual load flow rate is absorbed by the capacity of the reservoir. From a minor point of view, these systems are devised to reduce the frequency of switching while making effective use of the capacity of the reservoir, but when viewed from the perspective of the water system as a whole, they cannot necessarily be said to be optimal operation. In the conventional feedback control method, the scale of the system becomes large, and if the pump facility is installed as one key point in the entire facility, there is a risk that the entire system may not operate smoothly. For this reason, predictive control different from feedback control, that is, number control based on an operation plan, has become necessary. The newly invented operation plan for controlling the number of pumps determines how to optimally switch the number of pumps in response to changes in pump load, reservoir water storage, etc. over time. In this case, optimization means minimizing the switching frequency of the pump, maximizing the storage capacity of the reservoir, and minimizing the operating cost of the pump. An object of the present invention is to provide a control method that allows an operator to freely select one of these operating methods depending on the time and situation and realizes an operation that suits these purposes. To explain the present invention, a typical water system diagram is shown in Figure 3.
As shown in the figure. The figure shows a representative model that accounts for up to 80% of water systems. There is a water intake limit at the water intake, and there is a flow delay in the irrigation canal between the water intake and the pumping well. This model uses agricultural irrigation as an example;
It can also be applied to water supply and sewerage systems. In the case of water supply, the pumping well is the receiving well, and the reservoir can be thought of as a pond within the water treatment plant. In the case of sewage systems, irrigation canals can be thought of as sewage pipe beams, and reservoirs can be thought of as ponds within sewage plants. The original purpose of pump operation in a water system is to control the reservoir so that it does not overflow or the supply does not become insufficient for the load, but if you can create a distribution plan for the entire water system and operate based on this, The operation of the entire water system becomes smoother and more desirable. Using the representative model shown in FIG. 3 as an example, consider the problem of minimizing the frequency of switching the number of pumps. Express it into a formula using the symbols in the diagram. (1) Constraint equation (a) Equilibrium equation (i) Irrigation canal flow delay equation (ii) Pumping well balance equation (iii) Reservoir equilibrium equation (b) Facility capacity upper and lower limit formula (i) Water intake limit (ii) Pumping volume limitation However, C={0, P ₁ , P ₂ , ......, P
_j ,……,P _N } (iii) Water storage limit (c) Objective function Given by a penalty table (described later). Here, the penalty is to introduce a negative factor due to pump switching as a negative cost, and to minimize the cost. However, i is the symbol representing the time period, ₁ X _i is the water intake amount at the water intake, ₁ Y _i is the water intake amount at the pumping well, ₂ X _i is the pumping amount, ₁ b _i is the reservoir water storage amount, and ₁ L _i is the pumping well water amount. ₂ L _i is the downstream load of the reservoir, K ₁ is the flow delay proportional distribution coefficient of the irrigation canal, δ is the subscript indicating the time period of the flow delay, P _j is the pumped water amount per unit time when pump j is operated , C is the set of P _j , P is the pumped water amount selected from the set C,
_{1 i} is the upper limit of water intake at the water intake, and ₁ is the reservoir capacity. Based on the above formula, we invented a method for determining the number of vehicles using the cumulative load curve. First, find the operable range of the pump. If we move i in equation (3) from i=1 to T and add both sides, we get However, ₁ b ₀ is the initial water storage volume of the pond, and T is an arbitrary time period. Setting i in equation (6) as i=T and substituting the above equation into this equation, we get The above formula shows that the initial water storage volume plus the cumulative pumping volume of the pump must always be within the range of the cumulative load and the cumulative load plus the reservoir capacity. This is illustrated in Figure 4. In the figure, the cumulative curve (curve _{3 )} of _{the pumped} water ₂ Must be. The difference between curve 3 and curve 1 at a given time represents the amount of water stored at that time. Curve 3 means that if it falls below curve 1, it will not be able to cover the load, and if it exceeds curve 2, the reservoir will overflow. In Figure 4, the slope of curve 3 is determined by the number of pumps in operation, so even within the range surrounded by curves 1 and 2, if there is a sudden load, the load cannot be covered even if all pumps are operated. It may disappear. Therefore, it is necessary to find a feasible region excluding the region into which curve 3 cannot fit. below,
This will be explained. In Figure 3, from the upper limit of water intake _{1 i} for each time period at the water intake, the upper limit value for each time period of the water intake flow rate ₁ y _i at the pumping well is calculated by taking into account the flow delay of the irrigation canal.
By subtracting the load ₁ L _i in each time period downstream of the pumping well from this, the amount of water Q _i that the pump can pump in each time period is determined. From the above, Q _i is P≦Q _i (10). The value of the feasible region upper limit curve for time period i is i-
The value obtained by adding the pumpable water amount for the i time period to the upper limit of the feasible area for one time period is compared with the value of curve 2 for the i time period, and the smaller value is taken. However, time 0
The upper limit of the feasible region is the initial water storage amount. Therefore, the upper limit of the feasible area for any i time period is However, UB _i is the value of the feasible area upper limit curve for the i time period, and UT _i is the value of the curve 2 for the i time period. The value of the lower limit curve of the feasible area for time period i is i+
The maximum value of the three values is the value obtained by subtracting the pumpable water amount for the i+1 time period from the lower limit value for the 1 hour period, the value of curve 1 for the i time period, and the initial water amount of the reservoir. However, the value of the lower bound curve of the feasible area in the final time period is
This is the value of curve 1 in the final time period. Therefore, the lower limit of the feasible region for any i time period is LB _T = LT _T LB _i = max {LB _i+1 −Q _i+1 , LT _i , ₁ b _p }...(12) However, LB _i is , the value of the lower limit curve of the feasible region for the i time period, LT _i is the value of the curve 1 for the i time period, and T represents the final time period. In the manner described above, the executable region (the part not shaded) in FIG. 4 can be determined. The number of operating units may be determined so that the number of times the cumulative water pumping amount curve (curve 3) changes is minimized within this region. PDP, which introduces a penalty to the DP method as a method for determining the number of pumps within the feasible region
invented the law. Divide the feasible region shown in Fig. 4 into a grid by unit time Δx and unit cumulative flow rate Δy, and calculate the width of the line connecting any point in the previous stage and any point in the next stage among these grid points. A possible line is called a path. The problem of minimizing the number of devices switching is to determine the path that minimizes the number of switchings from the starting point (i=1) to the ending point (i=T) among these paths. In this case, the path itself does not have an evaluation point, but a predetermined evaluation point is given depending on the transition state of two adjacent paths. The PDP method is used to evaluate this transition state. The PDP method will be explained using FIG. N ₀ in FIG. 5 is the initial number of units that reach the point (x ₀ , y ₀ ). x ₀
It is assumed that one-unit operation is specified in advance for the path from stage to stage _x1 . The evaluation score of each node under these initial conditions is g(x ₀ , y ₀ )=0 g(x ₁ , y ₁ )=g(x ₀ ,y ₀ )+P(N ₀ , 1)
...(13) g (x ₂ , y ₁ ) = g (x ₁ , y ₁ ) + P (1, 0)
...(14) g (x ₂ , y ₂ ) = g (x ₁ , y ₁ ) + P (1, 1)
...(15) g (x ₂ , y ₃ ) = g (x ₁ , y ₁ ) + P (1, 2)
...(16) is given by. Here, g(x, y) is the point (x,
y) evaluation point, P(i, j) is the penalty for changing from pump i operation to j pump operation,
N ₀ is the number of pumps operating in the last hour of the previous day.

[Table] Here, using the penalty table shown in Table 1,
Give an evaluation score for P(i,j). In general, the amount of water pumped per pump (called pump characteristics) increases due to friction loss as the number of pumps in operation increases.
Since the amount of water pumped per unit decreases, it exhibits nonlinear characteristics. This situation is shown in FIG. 6a. Keeping this nonlinear characteristic as it is, the feasible region in Figure 4 can be changed to unit time Δ
Divide into a grid shape by x and pumped water amount Δy per number of units,
If you try to apply the PDP method, the number of grid points will increase like a mouse over time, resulting in an increase in memory. Therefore, from a practical point of view, a linear method is used as shown in FIG. 6b. The details of the linearization method are shown in Japanese Patent Application No. 49-9374 filed earlier by the present applicant, so the explanation will be omitted here. A _b in the figure is the value of the interlattice distance (mesh). Since the pump characteristics are linearized by the mesh amount A _b , the grid point for each time is a value obtained by adding a multiple of the mesh amount based on the initial water storage amount, and is within the feasible region for each time. It is a point. This point is called the mesh point. Here, when the pump characteristics are linearized into mesh points, unused points (dummy points) occur among the mesh points, so these points are not evaluated (see FIG. 6b). The evaluation of each mesh point is performed according to the following procedure. (1) Calculate mesh points for each time period. (2) For each mesh point, determine whether there is a path reaching from the mesh point in the previous time period, and determine mesh points other than the dummy points. This is called a node. This means that the pump characteristic P _j (=
0, P ₁ , P ₂ , . . . , P _{j ,} . (3) If there is a path to reach, calculate the evaluation point (cumulative penalty) for that node, and calculate the starting point (previous node) and ending point (next node) of the path.
The node number, the number of vehicles in operation at that time, and the evaluation score are stored. However, if there are paths reaching from multiple nodes, the evaluation score for each path is calculated, and the one with the highest evaluation score is determined as the optimal path to that node. (4) If no path is reached, the mesh point is a dummy point, so move to the next mesh point. (5) Calculate steps (2) to (4) from the initial time period to the final time period. The above procedure will be explained using FIG. 7. In the illustrated example, there are paths from nodes in the i-1 time period to and among the mesh points in the i time period, and these two points become nodes in the i time period. to node A
and B, but the evaluation points of the nodes according to each path are as follows, using the penalties shown in Table 2 in order to minimize the frequency of switching the number of nodes.

[Table] Evaluation by path from A f()=f(A)+P(1,1)=10+0=10
...(17) Evaluation by path from B f()=f(B)+P(1,0)=8+1=9
...(18) Therefore, the path to is B→, and the evaluation point is 9. If the same calculation is performed for , the pass will be B → and the evaluation score will be 8. The PDP method has been described above for minimizing the frequency of pump switching, but the purpose can be changed by changing this penalty table. Second
The table was a penalty table for minimizing switching frequency, but this table gives penalties in proportion to the switching width of the number of pumps. Table 3 shows the penalty table for maximizing reservoir water storage capacity.

[Table] This table gives penalties in proportion to the small number of pumps after switching to increase the amount of water pumped into the pond in order to store water in the reservoir. Table 4 is a penalty table for minimizing operating costs and minimizing switching frequency.

[Table] In order to minimize pump operating costs, the table gives penalties in proportion to the number of pumps in operation after switching. However, if this continues, the number of pumps will try to reduce to 0 as much as possible, and will hunt between 0 and 1 along the lower limit of the feasible region.
The penalty table for minimizing switching frequency in Table 2 has been added. When changing the number of pumps in operation, the pumps are switched so that the pump usage performance evaluation (cumulative operating time of each pump, switching frequency) is equalized. The usage history of the pump is E(i)=K ₁・T(i)+k ₂・N(i)…(19) However, E(i): Pump usage performance evaluation value T(i): Pump i’s usage history Cumulative operating time N(i): Switching frequency of pump i k ₁ , k ₂ : Evaluated by coefficient, and when increasing the number of pumps in operation, start the one with the smallest E(i) among the pumps that are not in operation, When reducing the number of pumps in operation, it is possible to equalize the usage history of the pumps by stopping the pump in operation with the maximum E(i). FIG. 8 shows one embodiment of the present invention. The amount of pumped water for each number of pumps is input manually from the outside into the pump characteristic input device 1 (see Fig. 6a). Based on this input information, this pump characteristic is approximated to a linearized characteristic by the pump characteristic linearizer 2 (see Japanese Patent Application No. 49-9374 for details) (see Fig. 6b).
Next, the forecasting device 3 predicts the load on the outlet side of the reservoir for a period of time (for example, 24 hours in advance) for which an operation plan is desired. Based on this prediction result, the feasible region of the pump as shown in FIG. 4 is determined using the feasible region calculating device 4. At this time, the initial water storage amount of the reservoir and the initial number of operating pumps are input using the initial condition input device 5. In order to determine the number of pumps within the feasible range determined by the device 4, the node evaluation device 6 performs node evaluation for each time period. This device provides evaluation points for all nodes in an arbitrary number of stages in order to search for an optimal route from i=1 to T stage (final stage). At this time, since a penalty table corresponding to each objective is created by the penalty table creation device 7, the objective function for evaluation is performed while referring to this table. Note that the purpose is manually given from the outside. Among the evaluation points of all the nodes of the arbitrary number of stages calculated by the device 6, the optimum route to this stage is determined by the optimum number of operating units determining device 8. This determination method is
According to the method shown in FIG. The device 8 also determines whether all stages have been completed. If it has not been completed, the process returns to device 6 and performs node evaluation again. On the other hand, once all the stages have been completed, the optimal route (how many pumps to operate each time) from i=1 to T stage (final stage) is determined, and the information is sent to the pump usage equalization device 9. is output to the display device 10. The equalization device 9 issues operating instructions to each pump 11 so that the cumulative operating time and switching frequency of each pump are equalized.
This operating status is stored in the operating record storage device 12 and provides input information to the pump usage equalization device 9 at the next stage. As explained above, conventional pump number control is
Feedback control based on pond water level has been the mainstream, but with the present invention, it is possible to determine how to optimally switch the number of pumps for operation within the operational range determined by the cumulative load curve and the water storage capacity of the reservoir. It has become possible to perform predictive control based on an operation plan that determines the optimal driving route. Predictive control based on demand forecasts has made it possible to operate the entire water system smoothly. In addition to the PDP method, there are other methods to determine the optimal number of units for each stage.
BBM method (Brach and Bound Method), Heuristic
Laws may be considered as an alternative. Although these two methods cannot necessarily guarantee optimum results, they are considered to be sufficient from a practical standpoint. The BBM method is called the branch and bound method, for example, Operations Research Vol. 18 No. 24 1970 1
Month, February (Operations Research vol 18,
No.24, 1970; 1, 2)
This is described in a paper by LGMitten. When applying this method to the optimal operation control of pumps, the region that includes the optimal number of pump operation solutions is branched out, and the route search evaluation value in each subregion is used as a guide to find the route that is considered more advantageous. Search for partial areas that can be used, and finally search for the entire route. The Heuristic method is also called a heuristic search method, and it uses human intuition to find an approximate optimal solution, without relying on a mathematically systematized, rigorous theory.

[Brief explanation of the drawing]

Figure 1 is a diagram showing how the number of units is controlled depending on the water level of the reservoir. Second
The figure shows the number of units controlled by program control. Figure 3 is a representative model diagram of a water system. FIG. 4 is a diagram showing a region in which pump operation is possible. Figure 5 is an example of determining the number of units using the PDP method. Figure 6 shows the number of pumps in operation and linearization.
FIG. 7 is an example diagram of node evaluation. FIG. 8 is a diagram of a pump number control device.

Claims (1)

[Scope of Claims] 1. A step of predicting the load on the outlet side of the fluid storage means for a predetermined period, and an upper limit curve obtained by adding the capacity of the storage means to a cumulative load curve obtained by accumulating the predicted loads. 1. A method for controlling a plurality of pumps based on an operation plan, comprising the step of determining an optimal route that optimizes the number of pumps set in between. 2. The operation candidate area is the area surrounded by the cumulative load curve and the upper limit curve, excluding the unoperable portion determined from the initial storage amount of the storage means, the initial number of pumps in operation, and the processable amount of each pump. 1. A method for controlling a plurality of pumps based on an operation plan as set forth in item 1, characterized in that the area is a controlled area. 3. Control of a plurality of pumps based on the operation plan as set forth in item 1 or 2, wherein the step of determining the optimal route includes a calculation that applies a predetermined penalty in response to a change in the operating route due to pump switching. Method. 4. A method for controlling a plurality of pumps based on an operation plan according to any one of items 1 to 3, wherein the calculation is based on a dynamic programming method. 5. Based on the operation plan set forth in any one of paragraphs 1 to 4, wherein the switching is performed by an operation command issued so that the operating time and switching frequency of each pump for the determined route are averaged. How to control multiple pumps.