The objective of this research is to introduce a novel framework to quantify the risk of the reservoir system outside the design envelope, taking into account the risks related to flood-protection and hydro-energy generation under unfavourable reservoir element conditions (system element failures) and hazardous situations within the environment (flood event). To analyze water system behavior in adverse conditions, a system analysis approach is used, which is founded upon the system dynamics model with a causal loop. The capability of the system in performing the intended functionality can be quantified using the traditional static measures like reliability, resilience and vulnerability, or dynamic resilience. In this paper, a novel method for the assessment of a multi-parameter dynamic resilience is introduced. The multi-parameter dynamic resilience envelops the hydropower and flood-protection resilience, as two opposing demands in the reservoir operation regime. A case study of a Pirot reservoir, in the Republic of Serbia, is used. To estimate the multi -parameter dynamic resilience of the Pirot reservoir system, a hydrological model, and a system dynamic simulation model with an inner control loop, is developed. The inner control loop provides the relation between the hydropower generation and flood-protection. The hydrological model is calibrated and generated climate inputs are used to simulate the long-term flow sequences. The most severe flood event period is extracted to be used as the input for the system dynamics simulations. The system performance for five different scenarios with various multi failure events (e.g., generator failure, segment gate failure on the spillway, leakage from reservoir and water supply tunnel failure due to earthquake) are presented using the novel concept of the explicit modeling of the component failures through element functionality indicators. Based on the outputs from the system dynamics model, system performance is determined and, later, hydropower and flood protection resilience. Then, multi-parameter dynamic resilience of the Pirot reservoir system is estimated and compared with the traditional static measures (reliability). Discrepancy between the drop between multi-parameter resilience (from 0.851 to 0.935) and reliability (from 0.993 to 1) shows that static measure underestimates the risk to the water system. Thus, the results from this research show that multi-parameter dynamic resilience, as an indicator, can provide additional insight compared to the traditional static measures, leading to identification of the vulnerable elements of a complex reservoir system. Additionally, it is shown that the proposed explicit modeling of system components failure can be used to reflect the drop of the overall system functionality.

To optimize the design of a water distribution network (WDN), a large number of possible solutions need to be examined; hence computation efficiency is an important issue. To accelerate the computation, one can use more powerful computers, parallel computing systems with adapted hydraulic solvers, hybrid algorithms, more efficient hydraulic methods or any combination of these techniques. This paper explores the possibility to speed up optimization using variations of the ΔQ method to solve the network hydraulics. First, the ΔQ method was used inside the evaluation function where each tested alternative was hydraulically solved and ranked. Then, the convergence criterion was relived in order to reduce the computation time. Although the accuracy of the obtained hydraulic results was reduced, these were feasible and interesting solutions. Another modification was tested, where the ΔQ method was used just once to solve the hydraulics of the initial network, and the unknown flow corrections were added to the list of other unknown variables subject to optimization. Two case networks were used for testing and were compared to the results obtained using EPANET2. The obtained results have shown that the use of the ΔQ method in hydraulic computations can significantly accelerate the optimization of WDN.

The paper presents a functionality investigation of the key dam elements based on finite element analysis. A detailed analysis of filtration processes, dam strength, and the surrounding rock mass was conducted. Dam elements whose potential damage could jeopardize the normal functioning of the embankment dam have been identified. A particular emphasis was placed on the analysis of dam elements that have been identified as weak points. A numerical analysis of the impact of individual grout curtain zone failure on leakage under the dam body, a strength analysis of the overflow section, as well as the analysis of the slope stability that can compromise the functioning of the spillway have been performed. To analyze the partial stability of individual structural elements, a new measure of local stability was introduced as the remaining load-bearing capacity. As a case study, the Zavoj dam, which is a part of the Pirot reservoir system in the Republic of Serbia, was used. Investigation revealed that local damage to the grout curtain will not significantly increase leakage under the dam body, the overflow section is one of the most robust elements of the dam, but the slope above the spillway can compromise the functioning of the overflow and thus the safety of the entire dam. Based on the analysis of the results of the remaining load-bearing capacity, the dependence of the spillway capacity on earthquake intensity has been defined. The established relationship represents a surrogate model for further assessment of dynamic resilience of the complex multipurpose reservoir system, within the scope of the advanced reservoir system management.

Different methods have been developed in the past to formulate and solve steady-state hydraulics of a water distribution system (WDS). The most widely used method nowadays is probably the global gradient algorithm (GGA). The loop-flow method (also known as the $\mathrm{\Delta }Q$ method) represents a viable alternative to GGA, especially when combined with suitably preprocessed network data. The main advantage of the $\mathrm{\Delta }Q$ method over the GGA is in the smaller number of unknowns to solve for, which is coming from the fact that real WDSs typically have far less loops than nodes. A new loop-flow-type method, relying on the novel triangulation based loops identification algorithm (TRIBAL) that was implemented in the corresponding new hydraulic solver ($\mathrm{\Delta }Q$ ), is presented in this paper (TRIBAL-$\mathrm{\Delta }Q$ ). The new method aims to exploit this advantage, while overcoming key drawbacks of existing $\mathrm{\Delta }Q$ methods. The performance of the TRIBAL-$\mathrm{\Delta }Q$ -based solver is compared with the GGA-based solver on four large real networks of different complexity and topology. The results obtained demonstrate that, despite requiring an increased number of iterations to converge, the TRIBAL-$\mathrm{\Delta }Q$ method–based solver is substantially computationally faster, has slightly better numerical stability, and is equally accurate in making predictions when compared with the GGA-based hydraulic solver.

Dam and reservoir systems (DRSs) are crucial aspects of the infrastructure necessary for reliable water resource management. Nowadays, DRSs are being increasingly affected by numerous natural and anthropogenic impacts (aging and outdated infrastructure, climate change, natural hazards, global crises, etc.). Hence, additional pressure on DRS management is being applied as DRSs must be operated in adverse operating conditions, outside of their design envelopes. Since there is no practical way to redesign DRSs to meet all possible adverse conditions, efficient simulation tools are necessary for various “what-if” analyses. A system dynamics (SD) approach can be used, as it has shown the capacity to comprehend the intrinsic system complexity. In this paper, an 11-step framework for the dynamic modelling of reduced functionality in a DRS and the emulation of the system operation in adverse conditions is proposed. The framework covers the system model design, input scenario generation, system simulation, and performance evaluation steps. A focus is placed on the steps related to system decomposition, the identification of failure-indicative parameters, the definition and implementation of failure functions in the subsystem dynamic models, and dynamic failure modelling. Through these steps, a novel procedure is proposed for the dynamic modelling of the DRS subsystems’ failures (reduced functionality), common in the operation of DRSs under adverse conditions. For each subsystem prone to failure, failure-indicative parameters are identified. Failure functions employing generic functionality indicators, with values spanning from 0 to 1, are suggested to modify the values of the failure-indicative parameters in simulations and emulate the component failure impacts on DRS operation. Possibilities for modelling failure modes for different subsystems, varying in nature, duration, and magnitude are discussed. Potential physical damage to the system components, increases in measurement uncertainty, and the lack of the spare parts during periods of global crisis are applied as disturbances to the Pirot DRS case study to illustrate the possibilities of the suggested framework’s application for DRS failure modelling. It was concluded that the proposed framework allowed for the detection of severe impacts on system performance, emphasizing the need for DRS dynamic failure modelling in system analysis.