# Systematic Coordination for the Central Interconnected System in Chile

A systematic coordination of a hydrothermal system requires determining an optimal policy which minimizes thermal costs along the simulation period. The resolution of this problem is complex and requires a mathematical tool to solve it. PLEXOS® offers a methodology which can determine an operational policy in medium-term and then use these results in a detailed short-term problem including hydro unit commitment. Results of medium-term simulation using PLEXOS® have been compared to public results from Chilean regulator to set nodal prices and simulate the system’s operation in medium term in the Chilean interconnected System.

Similarities in the results provide validated proof against official current procedures from the regulator. A graphical comparison has been included to summarize these results.

The challenge

The systematic coordination of a system composed of hydroelectric and thermal plants require determining an operative strategy, which for each stage of the planning horizon produces a scheduling plan of generation. This strategy should minimize the expected operational cost along the period, which is mainly composed of fuel costs plus penalties for failure in load supply.

The problem became complex to solve because:

• Natural inflows to dams are stochastic processes in nature.

• The availability of water stored in dams is limited.

• The system may have hydro cascade models.

• There may be some specific water usage policies and constraint (e.g. Irrigation settlements).

Water is cost-free, but its opportunity cost is fundamental to find this optimal strategy, this issue creates a link between a decision in a given time, so we don’t want to drain the storages too low to incur in generation shortfall (or excessive thermal usage). On the other hand, we want to avoid spillage.

The solution

PLEXOS® can find a releasing policy that minimizes expected thermal cost for all possible outcomes of the stochastic inflow sequences using 2-stage stochastic optimization formulation. With PLEXOS®, we can make the releasing policies for large storages a first stage variable, which means that we’ll try to find an optimal trajectory for them. This is a recourse problem which initially could be solved using linear programming although it may require integers for integrality conditions.

From the stochastic solution, we know how sensitive the objective function is to changes in the final optimal volumes (shadow prices), then we can say that in each stage (e.g. Monthly) the objective function is:

Min: φ=Thermal Costs(t)- π*EndVol(t)

Subject to:

• Hydro-thermal unit commitment

Since Stochastic optimization computed fixed targets now the problem is decomposable and we may know a proxy for opportunity costs if we deviate from targets.

We have the following information from Stochastic Optimization solution:

Price decomposition is now tight and the operational problem is fully decomposable and flexible. Now that we have a strong water value approximation we can solve the short-term hydro unit commitment in detail.

Case study: Chilean System

The regulator of Chilean electric system called National Energy Commission (CNE) set every 6 months a nodal price calculation of the main nodes for the next 4 years, these calculations are performed using an in-house dynamic programming methodology. Public info was downloaded from CNE web page and a PLEXOS® database was built.

The comparison focuses on the main Chilean interconnected system called Central Interconnected System (SIC).

The inputs for this calculation are described in the following points:

• Load forecasting for next 10 years

• Actual and planned transmission system for next 10 years (up to 58 nodes and 65 lines).

• Actual and planned generation plants for the next 10 years (up to 259 generators at the end of horizon).

• Price indexation of fossil combustibles.

• Maintenance of all generators along the horizon of simulation.

• Forced out rate of thermal units.

• 4 cascading hydro networks. (11 dams in total)

• Irrigation settlements of two main cascading hydro networks.

• 52 historical inflow samples. Future inflows are built concatenating historical consecutive years to create each inflow possibility up to the end of the horizon, meaning that one scenario is composed by a sequence of annual consecutive in_ows equally probable.

The results are summarized in the following graph taking an average of 52 samples in “Quillota 220 kV” node, which is located north of Santiago (Main center load of SIC).

In conclusion, we can see similar results along the horizon and a slightly difference in summer periods, which could be explained by undocumented irrigation settlement developed inside the code of the referenced simulation and the snow melting approach which was not incorporated in this PLEXOS simulation.