NEWAVE  Long and Medium Term Operation Planning Model for Interconnected Hydrothermal Systems
Introduction
The main objective of the operation planning in a hydrothermal system is to compute a socalled operation policy, that estimates the water values in the reservoirs and allows to determine monthly generation targets for each plant of the system which meets the energy demand and at the same time minimizes the expected operation costs throughout the planned period, also considering a risk aversion criterion. This cost is composed by the variable fuel cost of thermoelectric plants and the cost assigned to power supply deficits, represented by an energy deficit penalization function.
The decision regarding when to use the stored energy, represented by the water stored in reservoirs, is intrinsically linked to the uncertainty of future inflows, and must be the result of a probabilistic analysis of inflow behavior. Moreover, the most adequate operational decision for each moment depends on the system's conditions. Thus, it is necessary to take operational decisions as a function of the possible states of the system. In systems with large participation of hydroelectric power plants, two types of information compose the system's state: reservoir storage levels and the future hydrological trend of the system, which may be represented by the inflows to the reservoirs during the previous months, using the stochastic model PAR(p).
The existence of interconnections among subsystems (system areas) allows reducing operating costs through energy interchanges, and increasing supply reliability through the sharing of reserves. In hydrothermal systems, it is necessary to determine the value of the hydropower generation, given by the value of thermal generation that could be replaced now or in the future.
This value is not measured separately for each plant, since it depends on the joint operation of the system. In order to obtain maximum operational gains in an interconnected hydrothermal system, it is necessary to operate the system in an integrated manner, jointly optimizing the operation of all plants –thermal, hydropower, biomass, wind and solar power, and the energy interchanges decisions with the aim of minimizing total operation costs. In Brazil and many other countries, the solution to this problem is obtained in stages. These stages use models with different degrees of detail to represent the system, covering study periods with different time horizons  NEWAVE model for the long and medium term, DECOMP model (ShortTerm Operation Planning Model for Interconnected Hydrothermal Systems) for the short term, and DESSEM model (ShortTerm Hydrothermal Dispatch Model) for daily operation scheduling.
The NEWAVE model was developed by Cepel for application in long and mediumterm operation and expansion planning of interconnected hydrothermal systems, also considering intermittent renewables such as wind and solar power. As the operating strategy should be calculated for all combinations of storage levels and hydrological trends, in large systems such as Brazil, the problem of optimal system operation, depending on the study horizon, becomes rapidly intractable from the computational point of view if high quality results are desired. Thus, in the NEWAVE model, the hydropower plants can be represented in an aggregated form through energy equivalent reservoirs (EERs), in an individualized way or in a hybrid way  in the first years of the study period hydropower plants are individually considered and in the other years they are represented by EERs, providing the benefits of an individualized representation in the horizon closer to the decision making, without too much computational time.
The calculation of the operation policy employs the stochastic optimization technique called Stochastic Dual Dynamic Programming (SDDP), considering the uncertainties in the future inflows, represented explicitly through scenarios of inflows generated synthetically by using a periodic autoregressive model and a selective sampling process – the GEVAZP model.
In the long / medium term operation planning studies of the Brazilian interconnected system, where the typical horizon considered is five years discretized in monthly periods, with 20 hydrological scenarios in each period, the complete tree representing the uncertainties has about 10^{78} scenarios, which makes the resolution of the problem computationally unfeasible. Thus, the SDDP strategy, instead of going through all the subproblems of the scenario tree during the forward simulation, solves only a subset of scenarios (subtree), which are chosen from the original distribution of the random variable. The Benders cuts that represent the costtogo function are constructed iteratively during each backward recursion for all subtree nodes traversed in the last forward simulation, and in the next forward simulation, new values for the state variables related to the storage levels in the hydropower plants are obtained. The operation policy, represented by the expectedcosttogo function at each stage of the study horizon, is calculated accurately, and considers the same constraints used in the simulation of the system operation. It also considers the representation of anticipated dispatch restrictions for LNG plants.
In order to ensure theoretical convergence and increase the number of scenarios of the sampled subtree for the forward simulation without compromising the computational time to solve the problem, and thus to enable an improvement of the future cost function, the NEWAVE model allows the use of scenario resampling techniques during the calculation of the optimal operating policy.
Two risk aversion mechanisms were developed and embedded in the model with the aim of providing greater supply reliability: (i) CVaR (Conditioned Value at Risk), where a component related to the cost of the most expensive hydrological scenarios is added to the objective function; (ii) SAR (Risk Averse Surface), which represents an extension, for the multivariate case, of the minimum energy storage constraints in EERs.
Based on the obtained operational policy, the NEWAVE model simulates the system operation over the planning period, for distinct hydrological scenarios – either from the historical record or generated by the GEVAZP model, calculating performance indices, such as average operational costs, deficit risks and expected values of unsupplied energy. The model also provides a cost togofunction that acts as a boundary condition for the optimization of the system in shorter time horizons, where a more detailed time discretization is used.
To increase computational performance in large scale systems, two approaches have been developed. The first was the release of the executable version of the NEWAVE model in a high performance environment  it was the first program of the Cepel´s Chain of Energy Models to use parallel processing techniques. The second is an iterative process to solve each linear programming subproblem, where the cuts already constructed in past iterations of the SDDP algorithm are inserted progressively, as they are needed. Thus, a reduction in the computational time is obtained for the resolution of the LP problems and, consequently, of the convergence process as a whole, but maintaining the same precision in the results.
In addition to being employed in the definition of corporate strategies of companies and agents, the NEWAVE model is used in the following official activities of the Brazilian Electrical Sector: Tenyear generation expansion plan (PDE); Monthly Operation Program (PMO) and Energy Operation Plan (PEN); Calculation of spot prices in wholesale energy market (PLD); Calculation of the maximum volume of energy that a power plant is allowed to trade in longterm contracts; and computation of figures of merit for the public energy purchasing auctions.
