Andrade-Campos, A.

Coelho, Bernardete

English

Repositório Institucional da Universidade de Aveiro

INTRODUCTION On the comparison of numerical methodologies for control optimisation of variable-speed pumps B. Coelho* and A. Andrade-Campos  Department of Mechanical Engineering, TEMA/GRIDS, University of Aveiro, Aveiro, Portugal. *bcoelho@ua.pt The fast expansion of several water supply systems (WSS) due to the population growth and the immediate consumers supply without any planned strategy have led to inefficiently operated systems. In such systems, pumping stations usually represent the main operational costs (Vieira and Ramos, 2008; Van Zyl et al., 2004) revealing an important opportunity for the efficiency improvement of WSS. The operational control optimisation of these systems by a trial and error process can present difficulties due to their complexity: multiple pumps, valves and reservoirs, head losses, pressure limitations, several demand loads, etc. For this reason, innovative optimisation techniques are becoming more widely explored in this field (Coelho and Andrade-Campos, 2014).  A numerical methodology to optimise both the rotational speed and the operating time of variable-speed pumps is presented. The proposed methodology differs from other works by not considering the typical fixed 1-hour steps for the pumps operation. Instead, both set of pump speeds and operating times are used as decision variables. Additionally, a technique to reduce the number of variables according to energy price and water demand patterns is introduced.  Results of the proposed methodology using Particle Swarm Optimisation (PSO) and Differential Evolution (DE) are compared to distinct methodologies and optimisation techniques proposed by other authors. The test network introduced by Van Zyl et al. (2004) is used for comparison. In addition, a schematic representation of the real Richmond WSS model is also tested.             METHODS A computational tool for the efficient control of distinct water distribution networks is presented. This tool is based on a methodology that allies the possibility of control at the same time the pumps speed and the time of operation of both pumps and valves.  Without violating the tanks water levels constraints, the proposed methodology was able to present better results for the operation of both tested networks.  PSO demonstrated a better performance in the Van Zyl network. On the other hand, the DE  performed better in the simplified  Richmond.  A larger number of runs should be performed due to the probabilistic nature of the selected algorithms which provide distinct solutions in each run and may not always reach the global optimum.  Sensitivity analysis to the parameters of the algorithms must also be performed in order to achieve probable better results. CONCLUSIONS inspiring change The network represented in figure 3 is a simplified model of the Richmond network, which is part of the Yorkshire water supply area in the U.K. Such model is a benchmark of the Centre for Water Systems Resources of the University of Exeter (University of Exeter, 2014). The initial cost for the daily operation of the available network is £12316.79. However, the operation is not fulfilling the constraint for the tanks water levels in the end of the simulation. The network operation was adjusted and, never allowing the water levels in the end of the simulation to be inferior to the levels in the begin, the updated operational cost is £15632.72. Figure 3 – Simplified representation of the real Richmond network. The authors thank Fundação para a Ciência e a Tecnologia (FCT), Portugal, for the PhD Grant SFRH/BD/82191/2011.   Coelho, B. and Andrade-Campos, A. (2014). Efficiency achievement in water supply systems—A review. Renewable and Sustainable Energy Reviews, 30, 59-84. Hashemi, S. S., Tabesh, M. and Ataeekia, B. (2014). Ant-colony optimization of pumping schedule to minimize the energy cost using variable-speed pumps in water distribution networks. Urban Water Journal, 11(5), 335-347. López-Ibáñez, M., Prasad, T. D., & Paechter, B. (2011). Representations and evolutionary operators for the scheduling of pump operations in water distribution networks. Evolutionary computation, 19(3), 429-467. RESULTS and DISCUSSION The network represented in figure 2 was proposed by Van Zyl et al. (2004) and, since then, has been tested by several authors (some of them compared in table 1) for the control optimisation of fixed-speed pumps and, more recently, also variable-speed pumps.  The hydraulic simulation of one of the optimal operational solutions obtained by Van Zyl et al. (2004) resulted in a daily cost of £345.24, which was used as initial solution.  www.iwahq.org Figure 1 – Scheme representing the developed numerical tool.The proposed optimisation problem can be described by the minimisation of a cost function f subject to the bounds of n decision variables (xmin and xmax) and also to l equality constraints and m inequality constraints:          ?           ? ? ??? ? ???????????? ???? ???????????????????????? ?????????????????????????? ? ? ? ?? ? ?? ? ? ?? ? ??? ?? ?? ?????????   For the implementation of the proposed methodology, a numerical tool, using C++, was developed. Such tool provides an automatic connexion between the hydraulic simulator EPANET 2.0 and an optimisation module, allowing an easier implementation of distinct optimisation techniques for the energy costs minimisation of any kind of network provided by the user (see Figure 1).  Input file Network characteristics Initial data extraction Hydraulic simulation EPANET 2.0 OPTIMISATION Pumping Cost  Constraints New decision variables  Data storage   Van Zyl, J. E., Savic, D. A., and Walters, G. A. (2004). Operational optimization of water distribution systems using a hybrid genetic algorithm. Journal of Water Resources Planning and Management, 130(2), 160-170. University of Exeter (2014, May), Operation benchmarks, Centre for Water Systems Resources. Retrieved from https://emps.exeter.ac.uk/engineering/research/cws/resources/benchmarks/operation.   Authors Optimisation algorithm Method/ Decision variables Optimal cost (£/day) OF evaluations / CPU time Constraints Van Zyl et al., 2004 GA Tank level controls (pump on/off) 344.19 100 000 Tank levels and pump switches (cost penalties) Hybrid GA + Hillclimber 344.43 6 000 López-Ibáñez et al., 2011 EA Level controls 337.20 6 000 Tank levels, pump switches and pressure Time controls 315.90 6 000 Hashemi et al., 2014 ACO Pump on/off 388.04 400 000 Tank levels and pump switches Pump speed 349.43 300 000 Tank levels Coelho and Andrade-Campos PSO Pump speed and time controls 231.67 50 000 / 140 min(1)  Tank levels (cost penalties)  DE 341.40 50 000 / 300 min(1) PSO Aggregated pump speed and time controls 240.17 50 000 / 132 min(1) DE 332.93 50 000 / 295 min(1) Table 1 – Resume of the results for the optimisation of the Van Zyl network with distinct methodologies. Figure 2 – Representation of the Van Zyl et al. (2004) test network. Van Zyl water distribution network Simplified Richmond water distribution network Optimisation algorithm Decision variables Optimal cost (£/day) Percent of reduction OF evaluations / CPU time (min) (2) Constraints Fulfilled? PSO Pump speed and time controls 12541.49  12753.23 19.8 % 18.4 % 100 000 / 430 200 000 / 572 Tank levels (cost penalties)  Yes Yes DE 13070.24 12403.09 16.4 % 20.7 % 100 000 / 281 200 000 / 434 No Yes PSO Aggregated pump speed and time controls 12522.68 12514.70 19.9 % 19.9 % 100 000 / 405 200 000 / 549 Yes Yes DE 12794.68 12695.79 18.2 % 18.8 % 100 000 / 280 200 000 / 434 Yes Yes The proposed methodology for the operating costs minimisation using the PSO allowed to obtain the lowest cost results for the Van Zyl water distribution network operation (£231.67). The technique applied for the variables aggregation according to the water demand and the tariffs variation, allowed to slightly reduce the computational effort and, in the DE case, the solution was improved. Table 2 – Results for the optimisation of the simplified Richmond network using the proposed methodology.   (2)Intel® Core™ i7 processor, 3.40 GHz. For a reduced number of runs, in this more complex network, the DE provided the best result for the daily operational cost (£12403.09), which was reduced more than 20 %, maintaining the final water levels in tanks always equal or superior to the initial level. (1)Intel® Core™ i5 processor, 2.53 GHz. minx   f(x), x = (x1, x2, …, xn); subject to: hk(x)=0, k=1,…,l;    gj(x) ≤ 0, j=1,…,m;     xmin < x < xmax .   Daily pumping costs Pumps/valves speeds/settings and operating times Continuity Pressure, tank levels, limits of pump operation Objective Function: Constraints handling: 

On the comparison of numerical methodologies for control optimisation of variable-speed pumps

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On the comparison of numerical methodologies for control optimisation of variable-speed pumps

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Repositório Institucional da Universidade de Aveiro