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ABSTRACT At present, constant speed pumps and variable speed pumps always run in parallel in pump stations of most water supply companies in China. Research on the frequency control characteristic for the mixed-pump station based on the two-stage optimal operation is performed. Firstly, the ratio of the variable speed pump is calculated inversely according to the outlet pressure of the pump station, and then the speed range can be determined dynamically, so that the variable speed pump can play the role of energy saving as far as possible in safe and rational running status. Secondly, the two-stage optimal operation model for mixed-pump stations of multi-source is established, which is of the operating-mode adaptability, and it is solved by the intelligent genetic algorithm. Furthermore, when the operation mode of multi-source pump stations is transformed, the optimal dispatching of water distribution system in corresponding operation mode can be realized through adjusting the variable parameters in the model. At last, the utility and superiority of the optimal operation method for mixed-pump stations of multiple resources is verified by means of the application in certain urban in China.
Journal of Water and Environment Technology, Vol. 7, No. 2, 2009 - 67 - Analysis on the Optimal Dispatching of Mixed-pump Stations and the Operating-mode Adaptability Based on Safety Water Supply Dong Shen *, Lu Mou*, Ren Li** *Department of Environmental and Municipal Engineering, Qingdao Technological University, Qingdao 266033 China ** Maanshan Capital Water Co. Ltd., Maanshan 243000 China ABSTRACT At present, constant speed pumps and variable speed pumps always run in parallel in pump stations of most water supply companies in China. Research on the frequency control characteristic for the mixed-pump station based on the two-stage optimal operation is performed. Firstly, the ratio of the variable speed pump is calculated inversely according to the outlet pressure of the pump station, and then the speed range can be determined dynamically, so that the variable speed pump can play the role of energy saving as far as possible in safe and rational running status. Secondly, the two-stage optimal operation model for mixed-pump stations of multi-source is established, which is of the operating-mode adaptability, and it is solved by the intelligent genetic algorithm. Furthermore, when the operation mode of multi-source pump stations is transformed, the optimal dispatching of water distribution system in corresponding operation mode can be realized through adjusting the variable parameters in the model. At last, the utility and superiority of the optimal operation method for mixed-pump stations of multiple resources is verified by means of the application in certain urban in China. Keywords: mixed-pump stations, dynamic determination of speed range, operating-mode adaptability, safety water supply, genetic algorithm INTRODUCTION Many optimization models and mathematical algorithms have been developed to support the decision-making process of water distribution system, as shown in literature surveys by F. Fallsid (1975), 0rmsbee (1989), and more recently Sakarya (2000), among others. Genetic Algorithm has been applied to optimal operation of water distribution system by G.Mackle and D.A.Savic(1995), at the same time, many constrains were added into the optimization model to satisfy the actual demand. In China, the pump status and ratios of the variable speed pumps have been taken as decision variables for water supply control by Zhang Tuqiao and Lu Mou(2001). At present, the variable speed control is considered as the most ideal operation mode in the pump station. However, compared with the price of pump, the speed regulating device is too expensive. Therefore, in order to save the first investment, the mode that constant speed pumps and variable speed pumps run in parallel is always adopted in most of the water supply companies in China. Among them, one or more pumps run with the variable speed control mode, so as to maintain high efficient in different flow ranges, while the self-coupled antihypertensive starting mode is still adopted by other constant speed pumps. Therefore, research on the optimal operation of mixed-pump Project supported by the National Natural Science Foundation of China (NO. 50578077) and the 11th Five-Year Science and Technology Supporting Plan of China (NO. 2006BAB17B03). Address: Department of Environmental and Municipal Engineering, Qingdao Technological University, 11 Fushun Road, Qingdao, 266033, P. R. China. Email: dongshends@126.com Received November 23rd, 2008, Accepted February 13th, 2009 Journal of Water and Environment Technology, Vol. 7, No. 2, 2009 - 68 - stations is of great significance in practice. Further more, in view of the complexity and variability of the network topology and mixed-pump stations, the outlet flow and pressure of pump stations always need to be adjusted due to maintenance or unexpected pollution, thus the operating-mode adaptability of optimal dispatching model is endowed with higher requirement. ANALYSIS ON VARIABLE SPEED CONTROL OF MIXED-PUMP STATIONS Compared with the constant speed pump, the variable speed pump can run with high efficiency in different flow ranges through adjusting the speed. In this sense, the energy consumption can be reduced. The key of energy saving is to determine the best speed ratio according to the actual demand of water supply system. Because of the limitations of speed control devices and characteristic of pumps, there are different speed ranges for pumps of variable types, generally 0.75~1.0 of the rated speed, no matter what way. For two-stage optimal operation method, the best outlet flow and pressure of each pump station can be determined after the first optimization. Then the types, open number and the speed ratios of pumps will be determined in the second optimization, meanwhile, the determined outlet flow and pressure of each pump station should be satisfied as far as possible. However, according to the characteristic of the parallel operation curve, the result of the second optimization can not be accordance with the requirement of the first completely. If the outlet pressure of each pump station which has been determined during the first operation is taken as a hard constraint when the second optimization is performed, at the same time, if a lower speed ratio is adopted, the pump will unable to supply water and even suffer flow-back, just like Figure 1. n 0 n 1 = 0.75 n 0 H HS Q a b Fig.1 - Q-H Curve of the Variable Speed Pump In figure 1, a is the Q-H curve of which the pump runs with the rated speed n 0 , b is the Q-H curve of which the pump runs at the speed of n 1 , n 1 =0.75n 0 , HS is the pump head which can be determined by the outlet pressure HP of the pump station after the first optimization. As can be seen in Figure 1, there is no intersection of curve b and H=HS, this means that if the speed ratio is reduced to n 1 , the pump will unable to supply water and even suffer flow-back under the outlet pressure HP. In view of this problem, the range of each variable speed pump will be determined dynamically through reverse-calculation method in this article. Journal of Water and Environment Technology, Vol. 7, No. 2, 2009 - 69 - Fig.2 - The Speed Range Determination of Two-stage Optimal Operation 22 ii HSaQ bSQcS=+ + is the Q-H equation of the variable speed pump. If this pump is expected to supply water normally, the equation 22 0 ii aQ bS Q cS HS+ +−= should have a solution, then S i should be able to satisfy with the inequality () 2 4/(4) i SaHSbac>−⋅⋅ −⋅⋅ . As shown in Figure 2, curve c is the critical state of which the pump can supply water under the outlet pressure of the pump station determined after the first optimization. In the process of practical operation, the pump is always expected to run with high efficiency, so a proper constant K should be added to the lower limit of the speed ratio according to the pump characteristic, then d in Figure 2 is the Q-H curve of the pump at present. Therefore, the range of each variable speed pump can be expressed as () ( ) 2 4/(4),1aHS b ac K−⋅ ⋅ − ⋅ ⋅ + . As can be seen, the pump head H is higher, the speed range is smaller. In view of the variable speed characteristic, the operation mode of constant speed pumps and variable speed pumps running in parallel can satisfy the outlet flow and pressure determined after the first optimization easier compared with pure constant pumps running in parallel, for the two-stage optimal operation. OPTIMAL OPERATION MODEL OF MIXED-PUMP STATIONS WITH OPERATION-MODE ADAPTABILITY The First Optimization Model with Operation-mode Adaptability The outlet flow and pressure of each pump station on different periods are taken as decision variables during the first optimal operation. When the operation mode of certain pump station is changed, the outlet flow or pressure of the pump station needs to be adjusted. Thus, the first optimization model with operation-mode adaptability is establishes as follows: min ,, , ,, 11 11 IJ IJ ij ij ij ij ij ij ij F S QP SP C QP HP == == =⋅+ ⋅⋅⋅ ∑∑ ∑∑ Ⅰ (1) st. , 1 I ij j i QP QYC = = ∑ ； (1a) ,min 1 , ,max 2ij ij ij QP QP QP α α ⋅≤ ≤ ⋅ ； (1b) Journal of Water and Environment Technology, Vol. 7, No. 2, 2009 - 70 - ,min 3 , ,max 4ij ij ij HP HP HP α α ⋅≤ ≤ ⋅ ； (1c) ,min , ,maxcj cj cj HHH≤≤ ； (1d) ,min , ,maxkj kj kj HJ HJ HJ≤≤ ； (1e) Where i refers to the ith pump station, j refers to the jth time interval, S i,j refers to the expense of acquisition per volume unit, QP i,j is the outlet flow, I is the total number of all pump stations, SP i,j represents the electric tariff, C is the conversion factor, HP i,j is the outlet pressure for meeting the water supply system requirement, it may be derived by solving the microscopic model, QYC is the predictive value of water demand during the next interval, ,min ,max , ij ij QP QP refer to the minimum and maximum allowable outlet flow, ,min ,max , ij ij HP HP refer to the minimum and maximum allowable outlet pressure, 1234 ,,, α ααα are coefficients, H c,j refers to the pressure of the control node after the hydraulic calculation, ,min ,max , cj cj HH refer to the minimum and maximum allowable pressure of the control node, HJ k,j is the pressure of the kth monitoring point, ,min ,max , kj kj HJ HJ refer to the minimum and maximum allowable pressure of the kth monitoring point. The Second Optimization Model of Mixed-pump Stations The best outlet flow and pressure of each pump station are obtained after the first optimization, and will be considered as the dispatching commands. After that, during the second optimization, the pump parallel operation scheme and the speed ratio of speed governing pump are determined to satisfy the dispatching commands, at the same time, to minimize the total consumption of all pump stations. Therefore, the second optimization model is established as follows: min 2 ,, ,, ,, ,, ,, , 11 ,, 1 NP NP ijk ijk ijk ijk ijk ij kk ijk QS HS PS FQSPSQP η == ⎛⎞ ⋅⋅ ⎛⎞ =+ ⋅ − ⋅ ⎜⎟ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ ∑∑ Ⅰ (2) st. ,, , ,, ,,ijk ij ijk ijk HSHPZ h=++Δ ； (2a) ,, min ,, ,, maxijk ijk ijk QS QS QS≤≤ ； (2b) Where QP i,j ,HP i,j are the outlet flow and pressure respectively at ith pump station obtained by the first optimization, NP is the total number of pumps in all pump stations, QS i,j,k is the outlet flow of the kth pump whose expression can be obtained by Q-H characteristic curve of the pump, HS i,j,k is the head of kth pump, η i,j,k is the efficiency of kth pump whose expression can be obtained by the efficiency curve of the pump, ,, min ,, max , ijk ijk QS QS are the minimum and maximum outlet flow of the kth pump within the high efficiency area, Z i,j,k is the height difference between the water level of the ith impounding tank and the kth pump shaft, ,,ijk hΔ refers to the headloss of the kth pump. SOLUTION AND REALIZATION OF THE ESTABLISHED MODEL In view of the characteristic of global optimization ability and implicit parallelism, Journal of Water and Environment Technology, Vol. 7, No. 2, 2009 - 71 - genetic algorithm is widely used to solve complex nonlinear problem which can not be solved by traditional method. Genetic algorithm is combined with the hydraulic simulation software EPANET to solve the optimal operation model of mixed-pump stations with the operating-mode adaptability. The outlet flow ,ij QP of each pump station is taken as the decision variable of the first optimization. First of all, coefficiencies 1234 ,,, α ααα of the outlet flow and pressure will be determined by ANN method according to the operation status of each pump station. Then float-encoding will be performed for the outlet flow of I-1 pump stations in ( ) ,min 1 ,max 2 , ij ij QP QP α α ⋅⋅ , so the outlet flow of another pump station is ,1,1,1,,ij j j i j i j Ij QP QYC QP QP QP QP −+ =−−− − −− "" . Meanwhile, the outlet pressure of each pump station should to be constrained in ( ) ,min 3 ,max 4 , ij ij HP HP α α ⋅⋅ . When the second optimization is performed, the parallel scheme and ratios of variable speed pumps are considered as decision variables. Firstly, the pump head HS needs to be determined according to the outlet pressure HP of each pump station. Further more, the speed range () ( ) 2 4/(4),1aHS b ac K−⋅ ⋅ − ⋅ ⋅ + will be determined dynamically, then binary-encoding will be performed for running status of all pumps and ratios of all variable speed pumps. APPLICATION EXAMPLE The method noted above is applied to the optimal operation of a southern city water supply system practically. There are more than 900 nodes, 1000 pipes, three pump stations and 12 online pressure monitoring points in the network, of which the topology is shown in Figure 3. The condition of pumps in each pump station is expressed in Table 1. The predictive hourly consumption demand of June 6, 2008 is shown in Table 2. Fig.3 - Topology of the Network Journal of Water and Environment Technology, Vol. 7, No. 2, 2009 - 72 - Table 1 - General Catalogue of Pumps in Each Pump Station Pump station NO.1 NO.2 NO.3 Type 16SA -9J 16SA-9J (*) 14SA-10B (*) 12SH- 9A 24SA-10B 28SA- 10J 28SA-10J (*) 350S4 4 600S4 7E(*) Number 2 1 1 1 1 2 2 1 2 * refers to the variable speed pump Table 2 - The Predictive Demand of June 6, 2008 Time interval 0 1 2 3 4 5 6 7 Demand(m 3 /h) 6963 6544 6409 6249 6286 7301 9783 11138 Time interval 8 9 10 11 12 13 14 15 Demand(m 3 /h) 11160 11140 11044 10746 10440 9588 9134 9047 Time interval 16 17 18 19 20 21 22 23 Demand(m 3 /h) 9511 10037 10575 10742 10478 9849 9139 8003 All pump stations operate nomally from 0 to 9 time intervals, the NO.1 pump station is closed to maintain during 10 to 17 time intervals. Then after the maintenance, the NO.1 pump station is open for nomal operation from 18 to 23 time intervals. The model with the operating-mode adaptability established above is adopted to the optimal operation of the city‘s water supply system, the result is expressed in Table 3. Table 3 - The Optimal Operation Result NO.1 4# NO.2 6# NO3. 2# Time interval Operation scheme Lower limit of speed Speed ratio Pump head (m) Lower limit of speed Speed ratio Pump head (m) Lower limit of speed Speed ratio Pump head (m) 0 0001000001010 0.90 0.91 33.61 0.75 0.96 29.30 0.90 0.96 39.40 1 0001000001010 0.91 0.91 33.83 0.74 0.88 28.71 0.91 0.98 40.11 2 0001000001010 0.91 0.91 33.76 0.74 0.87 28.67 0.91 0.98 40.13 3 0001000001010 0.91 0.91 33.86 0.73 0.85 28.46 0.91 0.99 40.60 4 0001000001010 0.91 0.91 33.95 0.73 0.85 28.49 0.91 0.99 40.41 5 0001000001010 0.91 0.91 33.32 0.75 0.99 29.69 0.90 0.96 39.26 6 0001000101110 0.95 0.97 36.36 0.80 0.88 33.84 0.94 0.97 42.89 7 0001000101110 0.91 0.96 33.76 0.80 0.97 33.72 0.91 0.93 40.07 8 0001000101110 0.92 0.97 34.00 0.79 0.97 33.33 0.91 0.95 40.56 9 0001000101110 0.91 0.95 33.98 0.79 0.96 33.24 0.91 0.96 40.85 10 0000010101110 0.81 0.87 35.07 0.9 0.94 39.69 11 0000010101110 0.81 0.84 34.40 0.91 0.95 40.08 12 0000010101110 0.82 0.85 35.16 0.92 0.95 40.89 13 0000010101010 0.83 0.89 36.17 0.89 0.94 38.36 14 0000010101010 0.81 0.85 35.00 0.90 0.96 39.19 15 0000010101010 0.82 0.85 35.15 0.89 0.94 38.89 16 0000010101010 0.82 0.86 35.77 0.89 0.95 38.75 17 0000010101010 The pump station is closed to maintain. 0.82 0.88 36.01 0.90 0.98 39.18 18 0001000101110 0.93 0.96 35.07 0.80 0.95 33.87 0.92 0.95 41.47 19 0001000101110 0.93 0.95 34.89 0.80 0.98 34.18 0.92 0.95 41.28 20 0001000101110 0.93 0.95 35.08 0.80 0.92 33.61 0.93 0.96 41.79 21 0001000101010 0.92 0.92 34.10 0.81 0.92 34.83 0.9 0.97 39.78 22 0001000101010 0.92 0.92 34.41 0.80 0.92 33.93 0.91 0.96 40.03 23 0001000101010 0.93 0.93 35.34 0.78 0.82 32.17 0.92 0.98 41.09 1 refers to the pump being open, while 0 refers to the pump being closed. As can be seen in Table 3, the lower limits of varible speed ratios during most time intervals are above 0.75. Espeially for the first pump station, due to the operation mode and the characteristic of pumps, the lower limits are all above 0.9, as well as the Journal of Water and Environment Technology, Vol. 7, No. 2, 2009 - 73 - calculated speed ratios are close to the lower limits most time intervals. Therefore, for the optimal operation of mixed-pump stations, if the lower limits are not be calculated inversely and the speed range is determined as 0.75～1.0, most of pumps will unable to supply water and even suffer flow-back, at the same time, the searching range of genetic algorithm will be enlarged. After optimal calculation, the outlet flow QⅠ determined by the first optimization and QⅡ determined by the second optimization are shown in Figure 4. Obviously, the coincidence degree of the two curves in Figure 4 is well, and small differences occur at few time intervals. Through calculation, the average error of the outlet flow after the two stage optimization is 3.84%, so the water supply requirement can be satisfied. Fig.4 - The Outlet Flow for Each Pump Station of the First and Second Optimization CONCLUSION The purpose of optimal operation for water distribution system is to reduce the energy consumption as much as possible in condition of the flow and pressure demand having been satisfied. Compared with the constant speed pump, the variable speed pump can run with high efficiency in different flow range through adjusting the speed. The mechanical damage due to high speed ratio and the flow-back phenomenon due to low speed ratio of the pump can be avoided through determining the speed range rationally, which plays an important role in the realization and application of optimal operation technology for mixed-pump stations. In this article, the characteristic of the variable speed pump is researched, as well as the speed range is determined dynamically by the speed ratio reverse-calculating method, which provides effective protection for the variable speed pump running in high-efficiency area. On this basis, in view of the mode-variability and complexity of muti-resource water distribution system, the operating-mode adaptability is researched. And the two-stage optimal operation model with operating-mode adaptability for mixed-pump stations is established and solved by genetic algorithm. Therefore, when the operation modes of multi-source pump stations change, the optimal dispatching of water supply system under the corresponding mode can be realized through adjusting parameters in the model. In the end, through optimization and application practically, the practicability and superiority of optimal operation technology for mixed-pump stations which has operating-mode adaptability in condition of ratios of variable speed pumps having been determined dynamically is verified. Journal of Water and Environment Technology, Vol. 7, No. 2, 2009 - 74 - REFERENCES L. F. R. REIS, F. T. BESSLER, G. A. WALTERS, D. SAVIC, 2006. Water Supply Reservoir Operation by Combined Genetic Algorithm-Linear Programming (GA-LP) Approach. Water Resources Management., 20: 227-255. TIAN Yi-mei, G. Y. FU, CHI Hai-yan, LIU Ye, 2007. Optimal operation of water distribution networks under local pipe failures. J. Cent. South Univ. Technol., 14(3):436-441. Lu Mou, Song Shuang, 2004. Practical Optimal Control of Large-scale Water Distribution Network. HIGH TECHNOLOGY LETTERS., 10(4):79-82. Manuel Lopez-lbanez, Devi Prasad, Ben Paechter, 2008. 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G., 2003. Optimization of reservoir management and operation with hedging rules. J. Water Res. Plan. Manage. ASCE 129(2), 86–97. . 0. 97 36.36 0.80 0.88 33.84 0.94 0. 97 42.89 7 0001000101110 0.91 0.96 33 .76 0.80 0. 97 33 .72 0.91 0.93 40. 07 8 0001000101110 0.92 0. 97 34.00 0 .79 0. 97 33.33. 33.61 0 .75 0.96 29.30 0.90 0.96 39.40 1 0001000001010 0.91 0.91 33.83 0 .74 0.88 28 .71 0.91 0.98 40.11 2 0001000001010 0.91 0.91 33 .76 0 .74 0. 87 28. 67 0.91