Simulations and analysis of large hydro-thermal power systems easily become computationally heavy without simplifications of the system at hand. Hydropower, in particular, presents a challenge as complex river systems add a large amount of variables and linked constraints to the analysis. A possible simplification is to use aggregated Equivalent models for different parts of the hydrosystem which give similar results, with respect to e.g. power production, as a more detailed description of the Original system. In this paper, novel linear multi-scenario Equivalent models for hourly simulations of nonlinear hydropower systems are developed and their performance investigated. The new models consider multiple scenarios for inflow, price and start resp. end content in the reservoirs as well as reserves for balancing capacity. The performance analysis is based on case studies over Swedish hydropower systems located in the electricity trading area SE1. The average relative error in power production is 9-15% and the computation time is reduced from 9 hours to between 0.4 and 36 seconds.

Simulation of sizeable hydro-thermal power systems, such as Northern Europe or larger, requires several extensive simplifications and model reductions to decrease simulation time. Such reductions for hydrosystem sare often called Equivalent models. Their purpose is to mimic a more detailed hydropower model whiled ecreasing computation time. Both aspects are vital for accurate and useable simulation results. Here, different Equivalent models for hydropower have been developed together with a new function for adaptive Equivalentinflow based on local inflows to the detailed system. The models were computed via a bilevel optimization problem factoring in the novel adaptive inflow. Based on this, the new function for adaptive inflow was calculated using regression. The Equivalents have then been evaluated in a case study of hydropower systems in Northern Sweden regarding accuracy in hourly and total power generation, revenue estimation, and relative computation time. For all Equivalents, the computation time is decreased by >96%. Further, the Equivalents demonstrate improved performances in hourly and total power production and revenue estimations. The best hourly power difference was 9.2%, and the best revenue estimation was 5.9%. Especially notable is the low total power production difference of <0.5% compared to the more detailed model.

Modeling large energy systems requires different forms of simplifications and aggregations. This is especially true for large hydropower systems. One way to simplify the modeling of hydropower as a part of large scale energy systems is to utilize so-called Equivalent models. The hydropower Equivalent model is a simplified hydropower area model with only one (or a few stations) which aims to mimic the behavior of an Original more detailed model containing all stations in a specific area. However, one drawback has been that the Equivalent model fails to match the highest production peaks of the real Original system. Methods to increase the maximum peaks in the Equivalent model have so far resulted in overall lower performance, where the production during lower peaks instead would be overestimated. Thus, in this paper, a method for computing hydrosystem area Equivalent models that not only have good average performance but also can capture the production peaks of the real hydropower system is developed. The new method allows for optimal partition and efficiency of different segments in the hydropower marginal production function.

For inclusion in large-scale power system models, various aggregations and simplifications in the modeling of relevant actors and assets are needed. This paper focuses on simplified reduced models of hydropower, or area Equivalent models. They use a simplified topology but are not a direct aggregation of the real hydropower system. Instead, the area Equivalent is constructed to mimic the simulated power production of a more detailed hydropower reference model. Here, this goal is fulfilled by formulating a bilevel problem minimizing the difference in simulated power production between the area Equivalent and its reference. Solving this can be computationally heavy. Thus, for fast solution of this bilevel problem, a single-level reduction is done which is then solved using two methods. The first method includes McCormick-envelopes to form a linear single-level problem. Second, is a modified Benders with a relaxed sub-problem to handle the non-convex single-level. These are compared to Particle Swarm Optimization. Moreover, six new upper-level objectives are investigated and compared based on a case study of the hydropower in northern Sweden. The method using McCrmick-envelopes is very fast (2-5 min) but the area Equivalent shows lower average performance. The modified Benders finds a solution in (5-31 min) with good performance.

Simulation of large hydro-thermal power systems requires several extensive simplifications and model reductions. For hydropower systems with several interconnected power stations, these reductions can be particularly challenging and are denoted Equivalent models. The purpose of the Equivalent model is to mimic a more detailed hydropower model, while decreasing computation time, to be used in larger power system models. In this paper different Equivalent models for hydropower systems have been computed with a novel approach using a Particle swarm optimization-algorithm and are evaluated with respect to accuracy in hourly and total power generation as well as computation time. For each of the Equivalent models, computation time is decreased with over 99.99 % and the difference in power production is less than 11% compared to a more detailed model.

Simplified models of hydropower systems are necessary for simulation of large power systems, long-term analysis, and future studies. One common simplification has been to aggregate all hydropower within an area based on historical data. Another option is to use mathematical so-caned hydropower Equivalents. Here, hydropower Equivalents represent an optimized model reduction of a more Detailed model depicting the complete hydropower system within a specific area. These Equivalents are computed based on a bilevel optimization problem formulation. In this paper, the impact different Equivalent model constraints have on the performance is analyzed via a novel investigation of new model formulations. Moreover, recent solution methods and a baseline aggregation of the hydropower from statistics are compared and evaluated for the first time. All bilevel Equivalents show a significantly better performance than the baseline aggregation; the accuracy in hourly power generation relative to the Detailed model is almost twice as high for all bilevel Eqmvalents.

Hydropower system Equivalents are fictive model reductions of a more detailed hydropower model of all individual hydropower stations within an area. The system Equivalent only has one or a few stations and can significantly reduce the computational effort compared to the detailed system. The aim is to at the same time maintain accuracy in power production. To achieve this a bilevel problem formulation can be utilized. In this bilevel problem, the optimal system Equivalent parameter values are calculated. However, this computation can be very time-consuming and the problem formulation is very complex. Moreover, which of the parameters are most important for overall Equivalent performance and accuracy is unknown. To get a better understanding of the system Equivalent model parameters and their connection to performance, this paper performs a sensitivity analysis and develops a method to determine the parameter importance. Based on these results methods to reduce the computational time of the bilevel problem can be devised, with an example given here. It is shown that the most important parameter is the maximum discharge limit.

Actual hydropower systems often contain complex river systems, making simulations of hydropower systems computationally extensive. With the help of an Equivalent model, which is an artificial simpler hydropower system, the computational issue can be avoided. The Equivalent model aims to imitate the actual hydropower system, hence can be used for studies of large power systems with faster computational time. In this paper, different Equivalent models of hydropower systems in different periods and trading areas in Sweden have been computed, which are then evaluated and validated by comparing the hourly relative power generation difference. The relative power difference is 4.89% - 19.36%, depending on the period and trading area. Different Equivalent model performance over time indicates that the Equivalent parameters should change over time. By dividing a year appropriately, a well performing Equivalent can be obtained, which is shown by the Equivalent with low relative power difference.

To simulate a hydropower system, one can use what s known as a Detailed model. However, due to the complexity of river systems, this is often a computationally heavy task. Equivalent models, which aim to reproduce the result of a Detailed model, are used to significantly reduce the computation time for large-scale hydropower simulations. This paper computes Equivalent models for hydropower systems in Sweden by categorizing the water inflow data using a spectral clustering method. Computing the Equivalent models is done using a variant of the particle swarm optimization algorithm. Then, the Equivalent models are evaluated based on their similarity to the Detailed model in terms of power production and objective value. The Equivalent models range from 8% - 12% error in terms of the relative power production difference and the computation time is reduced by at least 99.9%.