Mathematical model helps plan operation of reservoirs and water distribution systems

Computational platform sets rules for rationing water supply during periods of drought.

By Elton Alisson  |  Agência FAPESP – Researchers at the University of São Paulo’s Engineering School (POLI-USP) and the University of Campinas’s School of Civil Engineering, Architecture & Urban Design (FEC-UNICAMP) have developed novel mathematical and computational models to optimize the management and operation of complex water and electricity supply systems such as those existing in Brazil.

Development of the models began in the early 2000s and was enhanced by means of the Thematic Project entitled “Hydro Risk: Risk Management Technologies Applied to Water and Electricity Supply Systems”, which was funded by FAPESP.

“The idea is that the mathematical and computational models we develop can help managers of water and electricity distribution and supply systems make decisions that have a significant social and economic impact, such as the imposition of rationing,” said Paulo Sérgio Franco Barbosa, a professor at FEC-UNICAMP and principal investigator for the project, in an interview with Agência FAPESP.

According to Barbosa, many of the technologies used in Brazil’s water and electricity systems to manage supply and demand, as well as the risk of water and power shortages due to extreme climate events such as severe drought, were developed in the 1970s, when Brazilian cities were smaller and water and hydroelectric systems were less complex.

As a result, he said, these management systems have flaws such as not taking into account the connections between different basins and not computing the probability of more extreme climate events than in the past when planning the operation of reservoirs and water supply systems.

“For example, the Cantareira reservoirs’ water storage requirement was underestimated because no one foresaw a worse drought than the one that occurred in 1953, the driest year in the system’s history before 2014,” Barbosa said.

To upgrade the risk management systems in use today, the researchers developed new mathematical and computational models that simulate the operation of water and power supply systems in an integrated manner and under different demand and supply scenarios.

“The models we’ve developed use statistical and computational techniques to perform better simulations and provide better protection for a water or electricity supply system against climate risks,” he explained.

Sisagua

One of the models, developed by the researchers in collaboration with colleagues at the University of California Los Angeles (UCLA) in the US, is a water supply system optimization and simulation platform called Sisagua.

The computational platform integrates and represents all supply sources in a water distribution system, including reservoirs, canals, pipelines, treatment plants and pumping stations, for a large city such as São Paulo.

“Sisagua can be used for integrated planning of operations, analysis of supply capacity, and assessment of alternatives for expansion or contraction of supply in a water distribution system,” Barbosa said.

One of the platform’s unique features, he added, is the ability to set rules for rationing in a large-scale reservoir and water supply system during periods of drought such as the one experienced by São Paulo in 2014, thereby minimizing the harm caused by water shortages to people and the economy.

When the volume of water stored in any reservoir falls below normal and comes close to the minimum operating level, the model indicates a first stage of rationing in which the water supply is reduced by 10%, for example.

If the water shortage lasts longer, the model suggests ways of minimizing the intensity of rationing by distributing supply cuts more evenly in time and across other reservoirs in the system.

“Sisagua has the built-in computational intelligence to show where and when to cut water supply so as to minimize damage to the system, to the public, and to the economy of a city,” Barbosa said.

Cantareira water storage subsystem

The researchers used Sisagua to simulate the operation and management of the water distribution system in metropolitan São Paulo. The system supplies some 18 million people and is considered one of the largest in the world, with an average flow rate of 67 cubic meters per second (m³/s).

Cantareira, the largest of its eight subsystems, supplies water to 5.3 million people with an average flow rate of 33 m³/s.

To estimate Cantareira’s supply capacity under a scenario in which a water shortage is concurrent with rising demand for water, the researchers used Sisagua to simulate such a situation over a ten-year period. They fed the platform with water inflow data from the 1950-1960 period, which were furnished by the São Paulo State Basic Sanitation Company (SABESP).

“The period was chosen as a baseline for projections using Sisagua because it was a time of severe drought, when inflows were significantly below average for four consecutive years, between 1952 and 1956,” Barbosa explained.

Based on the water inflow data for this period, the model simulated scenarios with demand for water from the Cantareira subsystem ranging from 30 m³/s to 40 m³/s.

The output from the model included the finding that Cantareira is capable of meeting demand for up to 34 m³/s during a water shortage such as the one that occurred in the 1950-1960 period without a significant risk of interrupting supply. Demand in excess of that amount exponentially increases the shortage and hence the risk of rationing.

For Cantareira to be able to meet demand amounting to 38 m³/s during a water shortage, the model showed that rationing of the water in the reservoir would have to start 40 months (3 years and 4 months) before the water storage level reached the critical point, below normal volume and close to the minimum operating limit.

This would enable 85%-90% of demand to be met during a drought while simultaneously restoring the ideal volume and avoiding the more severe rationing that would be necessary if full supply were allowed. 

“The sooner rationing begins, the better the losses are spread over time,” Barbosa said. “It’s easier for consumers to prepare for 15% rationing over a two-year period, for example, than a 40% cut in two months.”

Integrated systems

In another study, the researchers used Sisagua to assess the capacity of the Cantareira, Guarapiranga, Alto Tietê and Alto Cotia subsystems to meet current levels of demand in a situation of water shortage. They fed the platform with water inflow data from the four subsystems from the 1950-1960 period.

The results of the analyses performed by the mathematical model showed that the Alto Cotia subsystem reached a critically low level, requiring rationing several times during the ten-year simulation, whereas the Alto Tietê subsystem remained above-target storage with frequent spills. 

Based on these findings, the researchers proposed new interconnections to enable water transfers among the four subsystems. Part of the demand for water from the Alto Cotia subsystem could be met by the Guarapiranga and Cantareira subsystems, whereas the latter two subsystems could also receive water from the Alto Tietê subsystem, according to the projections computed by Sisagua.

“Water transfers among the subsystems would increase flexibility and result in better distribution, efficiency, and reliability for the entire water distribution system in metropolitan São Paulo,” Barbosa said.

The projections produced by Sisagua also indicated the need for investment in new water sources for supply to metropolitan São Paulo, he went on. The main basins that supply São Paulo suffer from problems such as urban concentration.

Almost 50% of the population of São Paulo State is concentrated around the Alto Tietê basin, which occupies only 2.7% of the area of the state. This population density is five times that of Japan, South Korea or the Netherlands.

The Piracicaba, Paraíba do Sul, Sorocaba and Santos Coastal subsystems, which account for 20% of the state’s area, are home to 73% of its population. This density is higher than that of Japan, the Netherlands or the United Kingdom.

“New sources of water supply for metropolitan São Paulo must inevitably be found,” Barbosa said. “An example is the Juquiá system farther inland. It has plenty of high-quality water. However, engineering a connection would be costly because of the distance, and it has therefore been postponed. Now it can’t be put off any longer.”

In addition to São Paulo, Sisagua has also been used to model water distribution systems for Los Angeles in the US and for Taiwan.

The article entitled “Planning and operation of large-scale water distribution systems with preemptive priorities” (doi: 10.1061/(ASCE)0733-9496(2008)134:3(247)) by Barros et al. can be read by subscribers to the Journal of Water Resources Planning and Management at ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9496%282008%29134%3A3%28247%29.