How flows are managed

The usual reason that a large transfer of power can be hard to handle is that there are few mechanisms to control its route through the transmission system from generator to distant load. Often that route is indirect, dictated by the impedances of the lines and places where power enters or leaves the system. In effect, a single transaction between a generator and a utility spreads throughout a large portion of the grid—a phenomenon termed loop flow.

(To be sure, current can be and is directly guided during high-voltage direct-current [HVDC] transmission. And ac current is being nudged in desired directions by devices like phase-shifting transformers and series compensation capacitors, often lumped together as flexible ac transmission (FACT) devices. However, very few of these devices are available in most large power systems, so in effect transmission flows are not controllable.)

The percentage of a transfer that flows on any component in the grid—a transformer, say—is known, in language developed for the U.S. Eastern Interconnect, as the power transfer distribution factor (PTDF). A transaction that would send power through an overloaded component, in a direction to increase the loading, may not be allowed, or if already under way, may have to be curtailed. The U.S. procedure for ordering such curtailments is known as transmission-line loading relief (TLR). Its developer was the North American Electric Reliability Council (NERC), the utilities' voluntary reliability organization in Princeton, N.J.

To reiterate, a grid component owner that detects overloading serves notice with the relevant authority—an ISO or RTO, for example—and asks for relief. The independent operator, or whoever, thereupon orders loading relief measures. For the component in question, any transaction involving a distribution factor higher than a predetermined level—set by NERC at 5 percent of the transaction—is a candidate for curtailment. If more than 5 percent of the power transferred as part of a transaction will go over a grid component subject to a TLR, the transaction may be scaled back or canceled.

Those TLR measures in turn will affect other existing and proposed transactions, requiring further near-instantaneous analysis by utilities, grid supervisors, and power marketers. The need at every level for state-of-the-art visualization tools is obvious, since any bottleneck in this complex system can quickly cause brownouts, blackouts, or nasty price spikes.

Averting price spikes, islanding

Problems with grid management are not necessarily the cause of electricity outages or price spikes—California's current electricity crisis seems to have been induced primarily by unforeseen generating shortages and misguided public policy. Here, visualization can help only indirectly, by better showing policy-makers the potential impact policy decisions can have on grid operation.

But when grid congestion is at the root of problems and floods of data are involved, visualization tools like conttouring, dynamic pie charts, animated diagrams, and two- and three-dimensional outlines have much more to offer.

Congestion played a pivotal role, for example, in the notorious U.S. midwestern price spikes of June 1998. That month, spot market prices for electricity soared three-hundredfold from US $25 to $7500 per megawatt-hour. Though there were many contributing factors, the most important were barriers to importing electricity from outside the region. Electricity was available elsewhere on the grid to the east and west, but could not be transferred because of overloads (congestion) on just two elements: a transmission line in northwest Wisconsin and a transformer in southeast Ohio.

The situation at the time of the June 1998 price spikes is diagrammed in [Fig. 1], where the small ovals represent operating areas in the Eastern Interconnect, each a potential seller. In the transaction illustrated, the buyer was a utility in northern Illinois. The contour indicates what percentage of the power transfer requested would have flowed through overloaded devices; shaded areas on the left could not sell because of the overload in northwest Wisconsin, those on the right because of the overload in southeast Ohio.

The visualization provides a picture of the complex interaction between the grid and the power market, allowing market participants to respond more quickly to changing conditions. With the market segmentation visualized on the prior page, power buyers in the affected areas could move quickly to procure long-term power capacity contracts, rather than having to buy at the astronomical spot market prices.

In the past, to form a mental picture of how line-loading relief measures might affect a market or reliability area, marketers or operators would have had to scan a long numerical list of distribution factors—no easy task once the list grows beyond a hundred or so entries. This is because in any large grid system, there are huge numbers of distribution factor sets, each depen-dent on pairs of buyers and sellers. Contouring provides a good solution, making the impact of loop flow apparent at a glance.

Another way of mapping the implications of TLRs is illustrated in [Fig. 2] the map shows the distribution factors for a hypothetical power transfer from a utility in eastern Wisconsin and the Tennessee Valley Authority. Note that the transfer affects lines as far away as Nebraska and eastern Virginia. Of the 45 000 lines modeled in the case, 171 had PTDFs above 5 percent, while for 578 the PTDFs were above 2 percent.

With the aid of such tools, a marketer can easily start considering a host of WHAT IF scenarios. How might a loading relief on a transmission line affect market participants other than those directly involved in a transaction? What if there is an outage of a major transmission line? What is the outlook for other potential buyers?

Visualizing voluminous flows

To determine how power moves through a transmission network from generators to loads, it is necessary to calculate the real and reactive power flow on each and every transmission line or transformer, along with associated bus voltages (in other words, the voltages at each node). With networks containing tens of thousands of buses and branches, such calculations yield a lot of numbers. Traditionally they were presented either in reams of tabular output showing the power flows at each bus or else as data in a static so-called one-line diagram. (One-line diagrams are so named because they represent the actual three conductors of the underlying three-phase electric system with a single equivalent line.)

The visualization challenge is to make these concepts intuitive. One simple yet effective technique to depict the flow of power in an electricity network is to use animated line flow [see figure 3, and link to PowerWorld site]. Here, the size, orientation, and speed of the arrows indicate the direction of power flow on the line, bringing the system almost literally to life.

Dynamically sized pie charts are another visualization idea that has proven useful for quickly detecting overloads in a large network. On the one-line, the percentage fill in each pie chart indicates how close each transmission line is to its thermal limit.

When thousands of lines must be considered, however, checking each and every value is not an option. Of course, tabular displays can be used to sort the values by loading percentage, but with a loss of geographical relevance. Because engineers and traders are mostly concerned with transmission lines near or above their limits, low-loaded lines can be eliminated by dynamically sizing the pie charts to become visible only when the loading is above a certain threshold.

Contouring the grid

Using pie charts to visualize these values is helpful, unless a whole host of them appear on the screen. Here, an entirely different visualization approach is useful—contouring.

For decades, power system engineers have represented bus-based values by drawing one-line diagrams embellished with digital numerical displays of the nearest bus's values. The results, being numerical, are precise and displayed next to the bus to which they refer. But for more than a handful of buses, it takes a lot of time to find a pattern. Contours are a familiar way of displaying continuous, spatially distributed data. The equal-temperature contours provided in a newspaper's weather forecast form a well-known example.

The trouble with contouring power system data is that it is not spatially continuous. Bus voltage magnitudes exist only at buses, and power only as flows on the lines, yet the spaces between buses and lines appear in contour maps as continuous gradients, not as gaps.

In practice the artificially blended spaces between nodes and lines do not matter much, as the main purpose of a contour is to show trends in data. Values are exact only at the buses or on the lines. Colors can be used to represent a weighted average of nearby data-points. This color gradation brings out the spatial relationships in the data.