Large U.S. Regional Transmission Operator (RTO)

The U.S. electric power industry has undergone a sea-change since the Federal Energy Regulatory Commission ordered open access to transmission systems, giving rise to wholesale power competition in the late 1990s. In the new environment, regional transmission operators (RTOs) balance supply offers with demand bids in the energy markets to keep the power flowing in the region of the grid that they are responsible for, at the lowest cost to utilities and to the utilities’ customers.

In 2005 one of the first such RTOs in the United States used the Lagrangian Relaxation method to optimize decision making on which power plants to turn on and how much power to transmit, and at what cost. The system uses a two-pronged approach that involves a day-ahead market and a real-time market.

On the day before power is delivered, the RTO forecasts demand for the next day, takes bids from the power generators and selects which power plants will be turned on and at what time using a “commitment algorithm.” Once the RTO has decided what plants will be used, it uses a “dispatch algorithm” to determine hourly output levels and the lowest prices. On the day of real-time energy production and delivery, the RTO solves the dispatch problem every five minutes, around the clock. The plants receive instructions on how much to alter their output every five minutes to keep the system balanced and reliable.

Both problems incorporate constraints that represent the physical limits of how much power lines and transformers can actually transmit. This introduces millions of variables and causes prices to vary by power plant and demand location. Some of these data come from instrumentation built into the power lines, which transmit information on the loads they are carrying and their capacity limits. This results in a huge amount of data that must be factored into the problem.

Piling on 300 percent more variables

Solving the commitment and dispatch problems in 2005 was a notable achievement for the RTO as well as for the energy industry, but the RTO had its sights set for even bigger challenges. In 2009, the RTO decided to integrate contingency reserves into its energy market commitment and dispatch solution. Some of the same power plants that generate energy for businesses and homes also provide reserves to respond to disruptions. Since it takes time (minutes to hours) to start up a plant, reserves are necessary to cope with rapid changes in supply and demand that can occur in a matter of seconds. If a power plant or a transmission line goes down, the RTO can increase the energy output of the power plants that provide these reserves.

Previously, a patchwork of entities managed reserves and other ancillary services in the RTO’s region. The RTO knew it could do the job more efficiently by consolidating these workloads. Calculating energy and reserves separately had less-than-optimal results because the two are interdependent. When a plant produces more power, it has less capacity for reserves.

However, optimizing both energy and reserves together creates a problem that is far more complex than optimizing them separately. In the commitment problem, adding reserves to the problem adds 300 percent more variables and constraints. A commitment problem solution can involve as many as three million continuous variables, 450,000 binary variables and four million constraints. No energy market system had ever been built to dispatch as many power plants and miles of transmission lines as the RTO had to factor into the problem: 55,000 miles of transmission lines and more than 1,500 power plants.

Plugging in Mixed Integer Programming for exact results

Performance was a major concern. In 2005, the RTO used the Lagrangian Relaxation (LR) method to mathematically optimize the millions of variables involved in the commitment problem. However, the LR method had not been able to solve such a large problem as the RTO now considered. In addition, the LR method did not deliver exact results. The operator had to use subjective judgment to estimate the range of error. This meant that the calculation for the cost of power could be higher or lower than the actual cost of the energy delivered, but no one using the LR method could predict exactly how much more or less the cost would be.

For stronger modeling capability and faster convergence rates, the RTO decided to use Mixed Integer Programming (MIP) which replaced the LR method to solve the commitment problem for energy and reserves. The advantages of MIP over LR:

• MIP is more general and doesn’t require as much customization
• MIP is more flexible and is easier to adapt to changing market rules (for example, combined energy and reserves markets in this case)
• MIP generally provides better performance (speed and reliability) due to wider applications across multiple problem types

The project team used IBM ILOG CPLEX Optimizer based on MIP, which has been widely used around the world for solving unit commitment problems and many other real-world planning and scheduling problems. IBM ILOG CPLEX Optimizer has solved a broad variety of optimization problems in different industries. It performs production planning for consumer packaged goods, scheduling for the production of semiconductors, routing for tankers and equities trade settlements for financial markets. While the LR method has to be tuned for each specific problem that it solves, advancements that are made with MIP in one industry can apply to another, so IBM ILOG CPLEX Optimizer enables everyone who uses its technology to benefit from the improvements that were made in other industries.

In addition, IBM ILOG CPLEX Optimizer provides an “optimality bound” with its solution. In other words, CPLEX doesn’t always find the optimal solution, but if it stops short of the optimal solution, the software specifies exactly how far away it is from the optimal solution. Typically users get 0.1 percent or 0.01 percent of optimality, so the cost of electricity can be expressed as plus or minus 0.1 percent or 0.01 percent of the quoted cost. This optimality bound is important for demonstrating to regulators and power generators that the RTO is making good decisions in selecting bids.

Creating $11 billion of net value

Between 2007 and 2010, the RTO region realized between $2.1 billion and $3.0 billion in net cumulative savings in which IBM ILOG CPLEX Optimizer was a major driver. The RTO also estimates that it will realize an additional $6.1 billion to $8.1 billion of net value through 2020. These savings, in which IBM ILOG CPLEX Optimizer was a major driver, help member utilities determine their investment in the grid and potentially fuel smart grid technologies and greener energy policies.

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