Optimizing the flow of power over the electricity grid could bring enormous savings. The US Federal Energy Regulatory Commission (FERC) estimates that tens of billions of dollars per year could be sliced from consumers’ utility bills if the transmission system could deliver electricity more efficiently. Achieving such savings will require refining the models that currently guide the operators of the wholesale electricity markets.
Improved models would help to optimize the flow of power over the electricity grid.
Improved models would help to optimize the flow of power over the electricity grid.
Federal regulations in the late 1990s decoupled much of the electricity generation, high-voltage power transmission, and local electricity distribution infrastructures from each other. (See the Physics Today articles by Scott Backhaus and Michael Chertkov, May 2013, page 42, and by Clark Gellings and Kurt Yeager, December 2004, page 45.) Since then, operation of more than two-thirds of the nation’s bulk power system and markets has been the function of seven independent system operators (ISOs). Those nonprofit entities operate transmission lines within their geographical regions and link electricity generation plants with the utilities that distribute the power to individual customers.
Each ISO also operates a wholesale electricity market: It takes bids from generators and purchases the required amount of power and reserve capacity at the lowest cost for the utilities it serves. The ISO accepts bids and sets prices on both a daily and an hourly basis. ISOs contract for future generation capacity up to three years in advance.
The separation of wholesale and retail power markets has complicated optimizing the flow of power, says Pascal Van Hentenryck, an engineering professor at the University of Michigan. “The loading of the bulk transmission grid is more volatile and harder to predict far in advance, because it is determined by market outcomes, through bids from generators that aren’t owned or controlled by the network operator.”
The US transmission system consists of hundreds of thousands of kilometers of high-voltage lines. In the face of disasters or during routine maintenance, the system must be able to withstand the loss of generators, wires, transformers, or other infrastructure. In response to those events, and to load fluctuations due to weather and other variables, the ISOs adjust the output of generators to maintain the balance between supply and load—sometimes as often as every few minutes. A reserve generating capacity is kept available for rapid start-up in emergencies.
A control room operator at ERCOT, the Electric Reliability Council of Texas, which controls the flow of electricity to 24 million customers in the state.
A control room operator at ERCOT, the Electric Reliability Council of Texas, which controls the flow of electricity to 24 million customers in the state.
Algorithms for optimizing power transmission have become a central feature of the wholesale markets, and their limitations have slowed progress toward greater efficiency, says a recent report from the National Academies of Sciences, Engineering, and Medicine. According to the report, Analytic Research Foundations for the Next-Generation Electric Grid, obviating the limitations will require fundamental advances in general algorithms for nonlinear, nonconvex optimization problems.
The basic equations are Ohm’s and Kirchhoff’s laws. Kirchhoff’s current equation specifies that for every node in an electrical network, the sum of the currents entering the node is equal to the sum of the currents leaving it. Ohm’s law states that the current across a conductor is proportional to the voltage difference at the two connected nodes. Electrical power, as the product of voltage and current, introduces one of the nonlinearities that makes power systems difficult to optimize in general, Van Hentenryck says.
Modifications to transformer settings, variable demand, and discrete network changes from the switching on and off of power lines and substation breakers mean the set of equations is constantly changing.
“The closer you can get to the actual physics [of the grid], the more money you can save,” says Richard O’Neill, chief economic adviser at FERC. “The power-flow equations for the alternating current model are highly nonlinear and very difficult to solve. What we do today is solve a linear approximation to that set of equations,” he says.
The problem with those approximations, says Argonne National Laboratory computational engineer Daniel Molzahn, is that when operational settings suggested by the software don’t match real-time conditions in the actual physics of the system, operators must make ad hoc adjustments to the settings the algorithms generate. “While those operators have a lot of experience and are very good at their jobs, there is no reason to believe that their adjustments are actually optimal with respect to the actual network physics,” he says.
Improved algorithms are sought mainly for flow adjustments that need to be made on a minute-by-minute or hourly basis. For subsecond time scales, automatic protection schemes in the form of breakers and fuses prevent equipment damage, Molzahn says. On the time scale of seconds, a scheme called automatic generation control uses a subset of generators that can rapidly adjust their outputs to account for imbalances between generation and load.
Backing off
During heavy load conditions, such as heat waves, the cheapest power sources may not be able to fully meet demand: The desired flow from the corresponding generators may exceed the capacity of transmission lines. Overloading lines could cause them to fail, and system operators will necessarily err on the side of caution. “If you have to stay within limits and you are doing it with a prediction that is an approximation, inevitably you save money if that predictive software tool gets more accurate,” says University of Wisconsin engineering professor Christopher DeMarco.
Adds Molzahn: “We have to back off on our transmission lines; we have to be more careful; we have to have reserves. It’s the classic engineering approach to how you handle a system when you can’t fully model it: You have a big safety margin.”
Ongoing changes to the electric power system, particularly the ever-increasing supplies of variable wind and solar generation, make linear approximations increasingly inaccurate. Transmission-system congestion may limit access to renewables, which are inherently low-cost power. “Imagine a whole bunch of wind power in the West that is really cheap to operate. But we can’t move it east because of transmission constraints. So we have to run more expensive generators to supply the power,” Molzahn says.
According to O’Neill, incremental improvements to power-flow models have already saved consumers as much as $5 billion annually in recent years. “We don’t know exactly how far off we are from the optimal solution,” he says. But he estimates that further modeling improvements could trim 5–10% from annual US wholesale electricity cost, which he puts at $250 billion to $300 billion.
DeMarco says linear algorithms were sufficient until the early 1980s, when transmission capacity began to be constrained by growing demand and increasing difficulties with siting and building new lines. Today’s transmission system is operated much closer to its capacity, and the inaccuracies of linear approximations have grown, as has the challenge of adjusting the relative phase angles of the sinusoidal voltages at each end of an alternating current transmission line. Phase angles are the key quantities determining the direction and magnitude of power flow along that line, DeMarco explains.
Unlike linear algorithms, which almost always give a solution, present nonlinear algorithms for optimizing power flow not only take far too long to be useful for operators’ short-term needs, but sometimes fail to converge and provide an answer. That situation leads to what system operators most dread, says DeMarco: Having to buy from generators within the required time frame without an answer from the software. “They’d rather take a slightly approximate but very reliable robust software solution.”
A workable nonlinear model could be available within five years, says DeMarco. “It could provide some graceful work-around in the cases where it didn’t fully converge.” The software might offer gradations of solutions, where if the most accurate case fails to provide an answer, “you step back and give up a little accuracy, but hopefully less approximation, than current linear methods,” he notes.
Test cases needed
Helping to move the research effort forward is the Department of Energy’s Advanced Research Projects Agency–Energy (ARPA–E). Its program, known as GRID DATA (Generating Realistic Information for the Development of Distribution and Transmission Algorithms), is supporting several projects to develop power-system test cases for researchers to use. Current publicly available test scenarios cover only small regions, are decades old, and don’t properly represent today’s systems, says Molzahn. He is part of an ARPA–E project led by DeMarco that is developing realistic sets of simulated data by using geographical inputs such as population density, wind speeds, and zoning information. A second ARPA–E project, led by Van Hentenryck, will use real data supplied by ISOs for the testing of new algorithms.
Improved optimal-flow algorithms, says O’Neill, will also help solve a range of challenges facing the electric industry, including maintenance of transmission lines. “Taking certain lines out of the system will degrade the performance of the system, while other lines don’t make much difference,” he says. In fact, removing a line can improve system performance and lower cost. If one line has a very low capacity—O’Neill draws an analogy to an extension cord—limiting the flow to its capacity would make other, higher-capacity lines in the circuit “practically worthless,” he says. Unplugging that cord could allow the other lines to be used more fully.
One improved model, for scheduling the start-up and shutdown of generators, is already saving PJM Interconnection, the largest ISO, $250 million annually. Because material properties require that generating plants be turned on and off gradually, O’Neill says that “it’s very important to schedule them at the appropriate time to get everything in place properly. It turns out it’s very expensive to turn one on at the wrong time.”
Improved power-flow algorithms also would help electricity distributors—the lower-voltage, utility-operated networks that deliver power to households and other end users. Those systems’ radial, or single-circuit, frameworks are more linear than the multipath, meshed transmission system. “From a theoretical standpoint,” says Van Hentenryck, “there is a real difference between radial and mesh networks.” But he notes that the advent of distributed generation—notably rooftop solar and the associated two-way power flow—could eventually lead to a meshed distribution system.
