This was seen as necessary due to the wide spectrum of influences and interrelationships of the parameters that make up a bulk water supply system. A model developed by Chang & van Zyl (2012) attempted to address this inefficiency by optimizing a bulk water supply system, with the primary objectives of cost and reliability. In addition, the costing system was based only on capital cost and did not consider the life cycle cost involved in implementing a bulk water supply system.
The reliability further decreased towards complete bulk water system failure under continuous Stage 3B/4 load shedding conditions. The findings and developments made contribute to the advancement of the optimal-reliability-based model and the approach of optimal-reliability-based design of bulk water infrastructure, including pumping systems. 89 Figure 4.1.3: Pareto-optimal solution front for feasible solution region 96 Figure 4.2.1: Pareto-optimal solution front - Chang and base models 101 Figure 4.2.2: Error frequency vs.
146 Figure 4.3.15: Relative component size as a percentage of design criterion solution 147 Figure 4.3.16: Comparison of sensitivity analysis parameters 149 Figure 4.3.17: Comparison between sensitivity analysis parameters (without pipe length).
List of Tables
Acknowledgements
Plagiarism Declaration
Introduction
- Background and motivation for research
- Limitations and scope of investigation
- Objectives
- Plan of development
The simplicity of the model allowed reasonable assumptions to be made regarding the hydraulics, components and topology of the system. The intended result is an optimization model applicable to a wider spectrum of real bulk water supply applications that can be compared to the model developed by Chang & van Zyl (2012) and the CSIR (2000)/Red Book Guidelines. Give details about the operative mechanics of the original model so that a full understanding of its functions, mechanisms and nuances can be obtained.
Develop a comparative model that adheres to the original, gravity-fed approach, while allowing for a wider range of possible solutions by incorporating the hydraulic solver. Compare the results of the comparative model with the original, uniform pipe model to validate the accuracy of the extended model and determine if any improvement has been made. Draw conclusions about the results obtained and the implication for promoting the applicability of the model.
The methodology is presented in a detailed form that describes the fundamentals and processes involved in the development of the original and extended optimization models.
Literature Review
- Design of bulk water supply and storage systems
- Objectives of bulk water supply infrastructure
- Defining and quantifying reliability
- Costing and cost models
- Stochastic analysis
- Stochastic analysis within science and engineering
- Stochastic analysis in bulk water infrastructure
- Simulation and sampling techniques
- Application of the stochastic analysis process
- Integration of stochastic unit models
- Optimisation
- Objectives of optimisation
- Genetic optimisation
The primary purpose of a bulk water supply system is to supply potable water to members of the service population. This simulated world is observed for an extended period of time to draw conclusions about the reliability of the imposed system, as proposed by Van Zyl et al. The success and reliability of a bulk water distribution system does not rely solely on the size of the service tank.
The reliability of the plumbing systems to be investigated is defined as described in 2.2.1 as the inverse of the failure frequency. This definition is extended to the reliability of power transmission to the pumping station. These values were used to fit a lognormal cumulative distribution function for all NERC regions combined.
Since the genetic algorithm used in the model suggested by Chang & van Zyl (2012) is a non-dominated classification genetic algorithm (NSGA), the scope of the review will be limited as such.
Methodology
- Application of the Monte Carlo and optimisation methods
- Computational Platform
- Revised optimisation model base code
- Algorithm description
- Mechanics of the Chang model
- Macroscopic model topology
- Basic hydraulic calculation
- Supply ratio filtering
- NSGA II model parameters
- Demands pre-run
- NSGA-II optimisation process
- Generation of initial population
- Evaluation of cost and reliability
- Non-dominated sorting and crowding distance
- The evolutionary process
- Development of the base model
- Integration of EPANET
- Application of demands-only pre-run
- Expanded base model topology
- Decision variables and initialisation of population
- Evaluation of cost and reliability
- Verification of model and sensitivity analysis
- Methodology summary
Where: length (SR) = length of the vector in which each delivery ratio is stored, length (RC) = length of the vector in which each tank volume is stored. The end result of the demand-only preliminary run is a curve fitting of the demand error frequency for each supply ratio. The algorithm for this process is shown in Figure 3.5.8: Pipe diameter (Table 3.5.1) and pipe configuration (Table 3.5.2) are discrete, while tank capacity is chosen from a continuous range.
The overall reliability of the chromosome is evaluated through the event-driven component of the stochastic algorithm. The model jumps to the beginning of the week in which the event will occur and starts the stochastic analysis. In the NSGA-II algorithm, this information is the value of each of the decision variables in the chromosome vector.
The solution system is composed of randomly generated values for each of the decision variables according to 3.5.7. Dimensioning the pump system according to pump power enables easier optimization of the system's energy costs. This is used to adjust the present net capital cost of a system component by factoring in the effect of the chosen discount rate.
The operation and maintenance of the pipeline are seen as relatively small total costs. The operating and maintenance costs of the pipeline (𝐶𝑜𝑚𝑃𝑖𝑝𝑒) were determined using the financial factors mentioned above and equation 3.20. The cost of each of the chambers is based on the individual connecting pipe size and number of connections.
The operation and maintenance cost of the pump system (𝐶𝑜𝑚𝑃𝑢𝑚𝑝𝑁𝑃𝑉) was determined using the financial factors listed above and Equation 3.20. The reservoir operation and maintenance cost (𝐶𝑜𝑚𝑅𝑒𝑠𝑁𝑃𝑉) was determined using the financial factors listed above and Equation 3.20. The four system cost components are combined and assigned to the chromosome being evaluated.
The event-run algorithm was added with the pump failure unit model and the updated hydraulic solver application.
Results
- Verification of base model
- Adaptation of base model for comparison
- Incorporation of demands-only pre-run data
- Verification model simulation results
- Comments and observations
- Summary
- Base model
- Base model simulation results
- Comments and observations
- Summary
- Sensitivity analysis
- Sensitivity to pump failure frequency
- Sensitivity to pump failure duration
- Sensitivity to power failure mechanism
- Sensitivity to pipe failure rate
- Sensitivity to pipe failure duration
- Sensitivity to fire event frequency
- Sensitivity to fire event duration
- Sensitivity to static head
- Sensitivity to focusing by parameter restriction
- Summary
Most of the solutions are not feasible for implementation because the failure frequency is too high. The reliability of the pump system has a significant effect on the failure frequency as shown in the figure above. The probability of supply failure is lower in the Chang model, as the supply system is not affected by power grid failure.
The baseline model exhibits a larger tube diameter than the Chang model over most of the failure frequency range. The size of the range of system parameters affects how quickly the model converges to the Pareto-optimal front. Pump and tube costs account for most of the cost of chromosomes with a high frequency of defects.
The optimization model forces an increase in pipe size to achieve the failure frequencies on the lower end of the failure frequency scale. The sharp rise seen in the lowest failure frequency range (far left) is due to the reservoir capacity reaching the 48 hour seasonal peak demand storage level. In this section, the cost sensitivity of the converged generations (above 15th generation), solution fronts, will be tested against variation in system parameters, such as pipe length, static pump head, pump failure frequency, among others, and application to real-world environmental conditions (load).
The sensitivity of the cost of a bulk water supply system to supply failure rate is an important consideration when designing a bulk supply system. The result of this inefficiency is the ambiguity of the effect of pipe failure to. This is suggested because of the dominance of the pump failure duration influence on the model (discussed in 4.3.6) and the consequent increase in supply ratio and reservoir capacity.
This is probably due to lower frictional losses as the pipe length remains the same. The percentage of deviation from the design criterion solution for each of the system component sizes is shown in Figure 4.3.15. This key point is illustrated again in Figure 4.3.18, where the delivery ratio and reservoir capacity of the design criteria are presented for each of the sensitivity values tested.
This is consistent with the previous observation of the criticality and sensitivity of supply ratio around the desired design criterion failure frequency level.
Conclusions
- Method summary
- Primary findings
- Verification of the model
- Base model
- Comparison to the Chang model and CSIR (2000) guidelines
- Sensitivity analysis
- Contributions to research
- Recommendations for future research
- Development of the current model
- Research into the optimisation approach
The baseline system to be simulated was outlined and the results of the optimization presented. The relevant results from the various applications of the developed model are presented in the following sections. The comparison between the results of the base model against the model developed by Chang.
The results obtained gave relatively few solutions in the acceptable range due to the crowding distance function of the NSGA-II optimization model. This sparsely populated region of solutions surrounding the desired design criterion can be overcome by focusing the model on producing more reliable solutions by limiting the values of the decision variables (system components). Limiting the minimum feasible delivery ratio of Chang's model to 1.34 shifted the balance of the optimal solution of the design criterion toward the lower capacity tank so that.
This was determined to be due to the system's evolutionary response to pump failures, resulting in a system that can withstand long-term failures. This observation, as well as the model's relative insensitivity to variation of the stochastic model parameters, attests to the optimization model's ability to minimize both cost and failure rate over a broad spectrum of conditions. All of these factors contribute to model advancement and the optimal reliability-based design of bulk water supply systems, including pumped flow.
While substantial progress has been made in the optimization model by including pumping systems and life cycle costs, there is still significant opportunity to improve both the developed model and the approach to bulk water supply system optimization. One of the more technical ways is to increase the computational efficiency of the encryption itself. This would allow shorter run times and increase the feasibility of using the model on less powerful computers.
This model can be extended to include the effects of mechanical failure of the pump mechanism; however this is not seen to be as critical as a power outage. The overall structure of the model can be developed to incorporate planned system improvements.
Reading, Massachusetts: Addison-Wesley Publishing Co. 2002. Dimensioning of bulk water supply systems with a probabilistic method. Introduction to Summer 1997 Monte Carlo Simulation Envision-It. http://phsics.gac.edu/~huber/envision/instruct.MonteCar.html. North American Electric Reliability Corporation, 2014. http://www.nerc.com/pa/RAPA/ra/Reliability%20Assessments%20DL/2014LTRA_ER.
Network analysis vir water supply reliability determination. ed.), Proceedings of the American Society of Civil Engineers National Conferences on Hidraulic Engineering. United States Department of Energy, 2014, Electric Disturbance Events (OE-417) https://www.oe.netl.doe.gov/OE417_annual_summary.aspx.
