Overhead line thermal ratings are normally calculated by conservative weather conditions and a maximum allowable conductor temperature that will ensure adequate electrical clearance and avoid annealing the conductor. In contrast to power transformers or underground cable, both the maximum allowable conductor temperature and the worst-case weather conditions used in calculating line ratings are selected by the utility rather than by the manufacturer or standards groups. Under these circumstances, the thermal line rating of an overhead line is, more than any other type of power equipment, determined by the engineering judgment of the individual engineer. The exercise of this judgment leads to a range of calculated ratings that can exceed 2:1 for the same conductor in similar environments.

While the power transfer capabilities of long EHV lines are rarely determined by thermal ratings. Shorter HV lines in the range of 69 to 230 kV are often limited by thermal considerations rather than by voltage drop or stability. The thermal capacity of HV lines may limit system transfer levels either during, or in anticipation of, first or second contingency loads. As a result of such system reliability concerns, HV lines have rarely operated at loads in excess of 30% of their thermal capacity, except for in emergencies. At normal, steady-state loads, the usual peak temperature of the conductor increased only a few degrees above the ambient air temperature. For emergencies, the conductor seldom reaches temperatures at which annealing or clearance infringements might occur.

In recent years, a number of factors have converged to increase both pre- and post-contingency loading of HV lines and to intensify utility interest in increasing the thermal ratings. This interest arises as a consequence of the opposition to the construction of new HV lines, the fact that system load growth has slowed making circuit load growth unpredictable and the use of new FACTs devices that can increase normal line loads, which allow post-contingency loads to approach thermal limits without exceeding them. In addition, utilities are increasingly reluctant to spend money on reconductored lines. As a result, utilities search for inexpensive, incremental methods that will increase the thermal capacity of their HV lines. In this respect, several different incremental uprating methods can be combined to increase thermal ratings while reducing the risk of over-loading. Among the incremental methods available for this purpose, the most widely used are: -Assume less conservative weather conditions for conductor environment. -Use a higher maximum allowable conductor temperature. -Use real-time, rather than fixed, weather conditions.

Calculation of Ratings Thermal ratings for overhead lines are typically calculated on the basis of heat balance methods such as that found in IEEE 738-1993. Given a maximum allowable conductor temperature, the corresponding maximum allowable current, which is the thermal rating, is determined for "worst-case" weather conditions. Maximum allowable conductor temperatures typically range from 50 deg C to 150 deg C and typical "worst-case" weather conditions specify a wind speed of 2 ft/sec (0.6 m/sec) perpendicular to the conductor with full solar heating and an ambient air temperature of 30 deg C.

Table 1 illustrates both the advantage of assuming a higher wind speed and the consequence of doing so. Use of a higher wind speed for thermal rating calculations increases the rating even when the maximum conductor temperature remains constant at 100o C. For example, an increase in wind speed from 2 to 3 ft/sec produces an increase in rating from 990 to 1080 A. Since the conductor temperature is the same for both conditions of wind, no line modifications are required. The major advantage of this method is that it is inexpensive. The major disadvantage is illustrated in the right-hand column of the table, which shows the temperature attained by the conductor for zero-wind, still air conditions, when the line load is at the load equal to the calculated rating. Historically, the joint probability of maximum line loading and worst-case weather conditions has always been considered to be a rare event. Recent studies indicate that, in certain areas, the probability of still air may be in excess of 10%. Combined with the previously noted increase in normal and emergency line loading, the temperature indicated in the last column of Table 1 may be a real concern and the use of a less conservative wind speed may impact line reliability.

Maximum Conductor Temperatures The second uprating method involves physical modification of the line structures to increase ground clearance in certain spans. The method allows the use of higher maximum allowable conductor temperatures and yields a corresponding increase in the calculated thermal rating.

As shown in Table 2, using conventional sag estimates, column 2, starting with a maximum allowable temperature of 75o C, the rating of 730 A can be increased to 990 A by modifying the existing line to accommodate an increased sag of only 1 ft and further increased to 1170 A by similarly accommodating an increase in sag of 2.2 ft. This level of increased sag can be allowed either by increasing the everyday tension of the conductor or by selectively raising attachment points. Unfortunately, there is some uncertainty as to the actual increase in sag with temperature for older ACSR as is shown by the differing sag estimates in columns 2 and 3. The uncertainty of sag at high temperatures can be resolved by monitoring sag or tension under high current conditions. As shown in the next section, high temperature sag behavior can be verified as part of the process of dynamic thermal line rating. Without such field measurements, modifications to the line may not adequately ensure proper minimum ground and underbuild clearances.

Dynamic Thermal Ratings The thermal rating of an overhead line may be increased by the use of actual rather than worst-case weather and line loading conditions. This method involves the need for monitoring devices and communications links between the remote monitoring devices and a central computing location (SCADA). Such dynamic rating of overhead lines typically requires, at a minimum, real-time measurement of circuit current and environmental parameters. The EPRI DYNAMP project showed that given the weather conditions immediately adjacent to the line and with the line current known, the conductor temperature could be calculated accurately.

In addition to these real-time parameters, it may also be advisable to monitor either the line temperature or its tension directly, at least during the field calibration phase of setting up dynamic thermal line rating methods. This calibration is usually undertaken to prove that the dynamic algorithms are accurate. Figure 1 shows a typical real-time rating communications arrangement used for the original EPRI Dynamic Thermal Circuit Rating field test at Georgia Power in 1994. The real-time monitoring of line sag, tension and/or temperature is used to "improve" the engineer's knowledge of actual high-temperature behavior and to detect differences in calculated and measured quantities related to these parameters. These data will serve to increase the accuracy of the dynamic line ratings. In Fig. 1, the PC is in the substation and does all of the rating calculations, reporting results to the EMS computer by telephone modem. The field data could also be relayed directly to the EMS computer with rating calculations done there.

The field calibration tests necessary to verify dynamic rating methods are also useful and necessary to two other methods of incremental uprating. The recorded data provide a solid basis for the probability of still air events and their coincidence with high loads and, if tension or sag is monitored, the data provide a clear estimate of high-temperature sag upon which to base line modifications. In addition, the dynamic rating system allows the use of less conservative weather conditions while reducing the risk of clearance failure by warning the operator of low rating conditions.

How the Methods Fit Together The mutual advantages of field data collection and dynamic thermal ratings in combination with the other incremental uprating methods is illustrated in Fig. 2. The right-most bell-shaped curve represents the probability distribution of the calculated line thermal ratings based upon actual wind speed and direction, air temperature and solar heating. Note that the ratings of the line actually vary over a range of more than 2:1. The very lowest ratings correspond to still air, maximum air temperatures and full sun. A typical static thermal rating of 800 A, based on the typical worst case weather conditions, is shown in the left tail of the rating distribution as is a second static rating of 900 A due to assumption of less conservative weather conditions.

The left-most distributions are line loadings (which vary as a result of varying customer load levels and system configuration changes) appropriate to each of the static ratings. Note that the line loads approach but do not exceed the static ratings and that the increased line loading distribution increases the frequency of times the load exceeds the actual line rating.

The advantage of using the actual line rating distribution through installing a real-time monitoring system is that the ratings are normally higher than the static rating. Also, the operator is warned when the ratings are less than the load and is able to avoid clearance infringements by reducing line load temporarily. The disadvantage of dynamic thermal ratings is the difficulty system operators have in utilizing variable ratings in light of their need to make contract commitments and allow maintenance outages.

The joint use of these uprating methods is being investigated by PTI in two ongoing research projects (EPRI RP3986-01 and RP3957-01). Simultaneous application of these line rating methods offers greater increases in rating with less risk than any single method.

The use of less conservative weather conditions is assumed to yield an increase in the conventional static rating from 800 to nearly 900 A. The operator and system planners would use this new rating to replace the old, more conservative rating on the operator's display and in evaluating system reliability and in planning equipment replacements. The operator would normally not be aware of the dynamic thermal rating system, which was continually re-calculating the line rating using actual weather and load conditions provided by real-time monitors. However, when the dynamic line rating is less than the load current, the operator would see a warning and either a projected time to overload in hours or minutes or a dynamic rating. By intervening at this point to reduce the line's electrical load, the operator avoids the potential clearance infringement and improves the reliability of the line. By reviewing historical records of real-time line tension or sag during times of high electrical loading, the line design engineer obtains a much clearer idea of the actual sag behavior at high loadings and can plan physical changes in the line to increase the rating with reduced risk of error.

Conclusion Because of uncertainty over load growth on particular circuits and increasing interest in finding economical methods of increasing capacity, a number of low cost incremental methods have been used to increase the thermal capacity of older overhead lines. This article shows that by combining dynamic thermal rating and monitoring methods with these other methods, the utility gains higher line ratings while reducing risk of clearance infractions or annealing under high electrical loading conditions.

Dale Douglass received the Ph.D. in electrical engineering from Carnegie-Mellon in 1967. He worked for Bell Labs until 1973 when he joined Kaiser Aluminum & Chemical Corp., where he concentrated on overhead line products. He joined PTI in 1978 as a senior engineer involved in experimental and analytical research of electrical and mechanical characteristics of overhead line conductors. He was elected a fellow of IEEE and is vice chairman of the IEEE/PES subcommittee for towers, poles and conductors. He is presently senior consultant in overhead transmission for PTI.