ROBUST OPTIMIZATION FOR HYDROELECTRIC SYSTEM OPERATION

D. Apostolopoulou and M. McCulloch (2018) Robust Optimization for Hydroelectric System Operation Under Uncertainty. IEEE TRANSACTIONS ON POWER SYSTEMS,33:3337-3348

https://ieeexplore.ieee.org/document/8295134

In Apostolopoulou et al. (2018), the authors considered the problem of robust optimization for Hydroelectric System operation under uncertainty. They proposed an optimal dispatch scheme for a cascade hydroelectric power system that maximizes the head levels of each dam and minimizes the spillage effects taking into account uncertainty in the net load variations, i.e., the difference between the load and the renewable resources, and inflows to the cascade. They founded that the operation of the cascade hydroelectric power system is robust to the variability and intermittency of renewable resources and increases system resilience to variations in climatic conditions. Thus, they demonstrate the benefits of coupling hydroelectric and photovoltaic resources. To this end, they introduce an approximate model for a cascade hydroelectric power system. They then develop correlated probabilistic forecasts for the uncertain output of renewable resources, e.g., solar generation, using historical data based on clustering and Markov chain techniques. They incorporate the generated forecast scenarios in the optimal dispatch of the cascade hydroelectric power system and define a robust variant of the developed system.

In order to compute K typical daily solar profiles, the datum from database which contains solar production profiles recorded at a quarter-hourly resolution, from the 1st of February 1994 to the 31st of January 2016, for three solar production sites located on the Tana River in Kenya, namely Masinga, Gitaru, and Kiambere sites undergone the clustering step beforehand. A Markov chain of order r with K states is identified to model the transitions between days, each state corresponding to the representative object μ( k ) of cluster C ( k ) . Comparing the conventional high order Markov chains which require O(K^r ) parameters, the parsimonious high-order Markov chain model in Ching et al. (2008) just requires O(rK²) parameters. Therefore, it is used to estimate the probability distribution of each state of the next day.  

The authors in Apostolopoulou et al. (2018) conducted an experiment to evaluate the efficacy of the proposed approach. They used hourly historical data of the power output of all the hydroelectric power output; dams head levels; and inflow data for all the hydro- electric power system from July 2015-June 2016. They assumed the cascade is working synergistically with a solar generation plant. They compared the results of the robust optimization reformulation with Monte Carlo simulations of the approximate model. In order to test how accurate the two approximations are and to justify the rationale behind this choice, they calculate the difference between the power output of each hydroelectric system as the output of the optimization problem and the actual output of each hydroelectric system calculated for a period of a whole year. It shows that the maximum error for the total power output is 3.82 MW, which is considered to be negligible. In this regard, they claim that the comparison of the robust optimization reformulation with Monte Carlo simulations of the approximate model is meaningful due to the high accuracy and low complexity of the latter.

W. Ching, M. Ng and E. Fung (2008). Higher-order Multivariate Markov Chains and

Their Applications, Linear Algebra and Its Applications, 428(2–3):492-507.

https://www.sciencedirect.com/science/article/pii/S0024379507002169