Thermal Line Rating Research Articles

Dynamic thermal rating of power lines – Model and measurements in rainy conditions

The transfer capabilities of overhead power lines are often limited by the critical power line temperature that depends on the magnitude of the transferred current and the ambient conditions, i.e. ambient temperature, wind, precipitation, etc. To utilize existing power lines more effectively and more safely concerning the critical power line temperatures and to enforce safety measures during potentially dangerous events, dynamic assessment of the thermal rating is required. In this paper, a Dynamic Thermal Rating model that covers the most important weather phenomena, with special emphasis on rain, is presented. The model considers a dynamic heat generation due to the Joule losses within the conductor and heat exchange with the surrounding in terms of convection, radiation, evaporation, rain impinging and solar heating. The model is validated by comparison of the skin and core temperature of the power line with measurements under realistic environmental conditions.

New DTR Estimation Method Without Measured Solar and Wind Data

Dynamic thermal rating (DTR) of overhead transmission lines can provide a significant increase in transmission capacity compared to the static thermal rating. However, the DTR are usually estimated by the traditional thermal model of overhead conductor that is highly dependent on the solar, wind speed and wind direction data. Consequently, the estimated DTR would be unreliable and the safety of transmission lines would be reduced when the solar and wind sensors are out of function. To address this issue, this study proposed a novel thermal model of overhead conductor based on the thermal-electric analogy theory and Markov chain. Using this thermal model, the random variation of conductor temperature can be simulated with any specific current level and ambient temperature, even if the solar and wind sensors are out of function or uninstalled. On this basis, an estimation method was proposed to determine the DTR in the form of probability. The laboratory experiments prove that the proposed method can estimate the DTR reliably without measured solar and wind data.

A Method for Accurate Transmission Line Impedance Parameter Estimation

Real-time estimation of power transmission line impedance parameters has become possible with the availability of synchronized phasor (synchrophasor) measurements of voltage and current. If sufficiently accurate, the estimated parameter values are a powerful tool for improving the performance of a range of power system monitoring, protection, and control applications, including fault location and dynamic thermal line rating. The accuracy of the parameter estimates can be reduced by unknown errors in the synchrophasors that are introduced in the measurement process. In this paper, a method is proposed with the aim of obtaining accurate estimates of potentially variable impedance parameters, in the presence of systematic errors in voltage and current measurements. The method is based on optimization to identify correction constants for the phasors. A case study of a simulated transmission line is presented to demonstrate the effectiveness of the new method, which is better in comparison with a previously proposed method. The results, as well as limits, and the potential extensions of the new method are discussed.

Robust Corrective Control Measures in Power Systems With Dynamic Line Rating

The increasing injections of energy from renewable energy sources far away from load centers have resulted in a more congested transmission grid. As the construction of new lines is costly, other options should be exploited as well. One possible solution is dynamic thermal line rating (DLR), which, instead of static thermal line rating, adapts the transmission capacity based on the expected weather conditions. This results, on average, in higher transmission capacities. First pilot projects have proven its efficiency. This paper analyzes the potential of DLR and demonstrates how DLR can be integrated in a dispatch optimization while managing possible errors in the forecasts of the line ratings with two different approaches. Both approaches result in robust optimization problems and guarantee that there is a suitable remedial action for all realizations of forecast errors given by uncertainty sets. The first approach relies on corrective control actions that are calculated centrally, once the actual line rating is known. The second approach relies on affine policies, which directly relate the current line rating to corrective control measures. This approach can be deployed in a decentralized manner. In case studies, the two approaches are applied and the reduction of overall operational costs is investigated exemplarily as a function of the forecast accuracy.

Security Constrained Unit Commitment With Dynamic Thermal Line Rating

The integration of the dynamic line rating (DLR) of overhead transmission lines (OTLs) in power systems security constrained unit commitment (SCUC) potentially enhances the overall system security as well as its technical/economic performances. This paper proposes a scalable and computationally efficient approach aimed at integrating the DLR in SCUC problem. The paper analyzes the case of the SCUC with AC load flow constraints. The AC-optimal power flow (AC-OPF) is linearized and incorporated into the problem. The proposed multi-period formulation takes into account a realistic model to represent the different terms appearing in the Heat-Balance Equation (HBE) of the OTL conductors. In order to include the HBE in the OPF, a relaxation is proposed for the heat gain associated to resistive losses while the inclusion of linear approximations are investigated for both convection and radiation heat losses. A decomposition process relying on the Benders decomposition is used in order to breakdown the problem and incorporate a set of contingencies representing both generators and line outages. The effects of different linearization, as well as time step discretization of HBE, are investigated. The scalability of the proposed method is verified using IEEE 118-bus test system.

Loadability formulation and calculation for interconnected distribution systems considering N-1 security

Abstract Traditional distribution loadability applies to radial systems; this paper proposes a new concept of loadability considering N-1 security principle for interconnected distribution systems, in which feeders are connected with normally-open tie-switches. Firstly, this paper presents a nonlinear model to formulate the N-1 loadability, in which network topology, thermal rating of lines and substation transformers, voltage limits and losses are considered. Secondly, Generalized Reduced Gradient (GRG) method is then used to solve the nonlinear programming problem. Meanwhile, a backward/forward sweep algorithm is also employed to solve the load flow calculation in the model. Finally, both an IEEE RBTS case and a real system are given to illustrate the proposed model and calculation method; and the accuracy is verified by the traditional N-1 contingency simulation.

Key Considerations for the Selection of Dynamic Thermal Line Rating Systems

Recent reviews have shown that many methods can be used for estimating the dynamic thermal capacity of overhead transmission lines. A number of approaches are described and key features of each system are organized. Data from field trials provide a unique basis for assessing the variation in ten different parameters. Characteristics of distributed measurement systems are underscored and contrasted against point measurements systems.

Thermo-Mechanical Model of Multi-Span Overhead Transmission Lines Equipped with High-Temperature Low-Sag Conductors

Increasing the thermal rating of existing overhead transmission lines is a valid alternative to the construction of new links. Dynamic thermal rating (DTR) of power lines is particularly interesting for Transmission System Operators, because the thermal time constant of conductors is relatively high (more than 10 minutes); in case of temporary grid congestions, DTR allows exploiting the dynamic performances of conductors, i.e. currents much higher than the steady-state limits, instead of redispatching generating plants. DTR is strictly connected with the possibility of calculating the actual sag of the most critical spans of a transmission line, the power flow and the weather conditions being known. However, the conventional calculation tools do not take into account the non-linear nature of novel high-temperature low-sag (HTLS) conductors and usually adopt a simplified model (the so-called ruling-span technique) to analyze multi-span transmission lines. In the present paper a non-linear mechanical model for bimetallic conductors is proposed, to be used for studying HTLS conductors. Such model is than combined with the equation of change of state, written in a form that can be applied to multi-span lines. The novel resulting model allows the traction/compression status of the external section of the conductor to be correctly calculated span by span, thus estimating the sag of each span. The traditional ruling span technique is also applied for comparison purposes and the relevant results are discussed.

Risk constrained short-term scheduling with dynamic line ratings for increased penetration of wind power

Limited transmission capacity may lead to network congestion which results in wind curtailment during periods of high availability of wind. Conventional congestion management techniques usually involve generation management which may not always benefit large wind farms. This paper investigates the problem in detail and presents an improved methodology to quantify the latent scheduling capacity of a power system taking into account stochastic variation in line-thermal rating, intermittency of wind, and mitigating the risk of network congestion associated with high penetration of wind. The mathematical model converts conventional thermal constraints to dynamic constraints by using a discretized stochastic penalty function with quadratic approximation of constraint relaxation risk. The uniqueness of the approach is that it can limit the generation to be curtailed or re-dispatch by dynamically enhancing the network latent capacity as per the need. The approach is aimed at strategic planning of power systems in the context of power systems with short to medium length lines with a priori known unit commitment decisions and uses stochastic optimization with a two stage recourse action. Results suggest that a considerable level of wind penetration is possible with dynamic line ratings, without adversely affecting the risk of network congestion.

High Temperature Low Sag Upgrades and Payback for the Economic Operation Improvement of Power Transmission Systems

—The increase of transmission line thermal ratings by reconductoring with high temperature low sag conductors is a comparatively new technology introduced for transmission expansion. A special design permits high temperature low sag conductors to operate at higher temperatures, therefore allowing passage of higher current and, thus, increasing the thermal rating of the transmission line. The comparatively high cost of high temperature low sag conductors may be an obstacle to its large-scale implementation. This article evaluates the expenditures for transmission line reconductoring using high temperature low sag, the consequent benefits obtained from the potential decrease in operating cost for thermally limited power transmission systems. Estimates of the “payback period” are used to evaluate the cost effectiveness of reconductoring with high temperature low sag. The evaluation is performed using a 225 bus equivalent of the 2012 summer peak Arizona portion of the Western Electricity Coordinating Council. The method is offered for transmission expansion analysis in which an economic benefit is calculated to assist in the transmission expansion decision.

An Application of Dynamic Thermal Line Rating Control System to Up-Rate the Ampacity of Overhead Transmission Lines

A method is proposed to utilize the dynamic-line rating system on old transmission lines to up-rate ampacity without replacing old conductors or increasing line voltage. A DLR system applicable to double-circuit transmission lines is designed based on maximum-allowable conductor temperature, conductor temperature at the limit-dip (sag) margin, and transformer maximum load. The improved performance of the system is reported.

Flexible load shedding strategy considering real‐time dynamic thermal line rating

In recent years, real-time dynamic thermal line rating (RT-DTLR) technology has been developed and implemented in operations to improve transmission line capacity, so that congestion costs and/or risk of load shedding can be reduced. Power systems obviously benefit from this technology but also bear the risks because of thermal overload of transmission lines. To involve RT-DTLR technology into conventional power system load shedding strategies, this study explains the concept of flexibility in power system analysis, expresses transmission line capacity constraints into flexible forms and proposes a flexible load shedding strategy considering RT-DTLR. The two sub-objective functions, representing load shedding quantity and system risk increment, are normalised and expressed as the confidence levels from system security consideration and load loss consideration, respectively. The proposed method takes advantage of both the advanced hardware and software technologies in smart grids and the simulation results showed that it can trade off the benefits and risks brought about by RT-DTLR in load shedding.

Application and Evaluation of Short-term Emergency Ratings for Double-circuit Transmission Lines

Emergency ratings have been introduced for operating transmission lines safely and supplying current capacity efficiently, as well as controlling load flow when line faults occur. In this article, short-term emergency ratings are calculated by using a thermal equilibrium equation for bared conductors in double-circuit transmission lines. Overhead transmission lines installed in double circuit have been extensively utilized worldwide to enhance power transmission. Such lines show various advantages in increasing transmission capacity and decreasing power loss as well as being operated flexibly during a contingency. Even when a fault occurs in one circuit, the healthy circuit can supply power continuously during an emergency without outage. The utilization of such double-circuit transmission lines during normal and/or emergency operations is described. Maximum normal operating current based on fault duration, maximum allowable temperature of conductor, and thermal line ratings is evaluated. Several performances of dip/clearance affecting short-term emergency rating are also presented.

Probabilistic ampacity forecasting for overhead lines using weather forecast ensembles

Dynamic thermal rating of overhead lines is a promising approach to increase transmission capacity by calculating weather-dependent thermal ratings (ampacities) of overhead lines in real time instead of using constant ratings. However, knowledge about ampacity is not only needed in real time but also on a day-ahead basis within network operational planning in order to assess network security. As life of humans may be endangered by inadmissible sag of overhead lines when current limits are violated there are high safety requirements concerning thermal ratings. Therefore, ampacity forecasts have to be complemented by a description of forecast uncertainty. So far, there is no method to forecast ampacities on a day-ahead basis considering uncertainty. As a comprehensive description of uncertainty is given by probability densities, this paper presents a novel method to calculate probability density functions of future ampacities based on probabilistic weather forecasts. The method’s functionality is proved by application to exemplary data.

Effect of time resolution of meteorological inputs on dynamic thermal rating calculations

Dynamic thermal rating (DTR) of power transmission lines can provide a significant increase in transmission capacity compared to the more traditional static rating. This gained capacity can be used to increase the normal and emergency operational flexibility of power transmission systems. Ampacity values can be determined either directly or indirectly from sag or ambient weather conditions. The most important inputs to weather-based DTR systems are meteorological data. The data can be obtained in the form of instantaneous or averaged values, and with various sampling/update intervals. This study examines the effect of the character of the meteorological inputs on the performance of DTR calculations. The analysis is based on real high-resolution wind and temperature measurements. Owing to the random character of the updates with instantaneous weather data, the averaged inputs provide more accurate estimates of ampacity and temperature. Update intervals of 10 minutes are sufficient, while longer intervals cause significant calculation errors. This could lead to a substantial risk of conductor thermal overload. The presented results can be used for effective data management in DTR systems. They can help to avoid substantial errors in ampacity calculations, thus minimising the risk of transmission system outages and premature ageing of transmission conductors.

Probabilistic Index for Increasing Hourly Transmission Line Ratings

The steady state thermal rating of overhead transmission lines is limited by the conductor`s maximum design temperature, which is related to the maximum sag and the loss of tensile strength of the conductors. Traditionally, this overhead transmission lines rating is computed using a deterministic approach, with reference to severe weather conditions. Thus, the application of this method leads to conservative results resulting in under-utilization of conductors. In this paper, a new method based on an hourly probabilistic index is proposed to predict the line thermal rating for each hour of the day; this index is evaluated using the conductor current limit probability density function (pdf). The method uses Bayesian time series models for the weather parameters (ambient temperature, wind speed and wind direction) and calculates the conductor current limit pdf using a Monte Carlo simulation. The probabilistic index is applied by considering measured weather data of both hot and cold seasons; the corresponding lines ratings are reported and analyzed.

The Evaluation of Stochastic Available Transfer Capability

Due to uncertainty in bus loading, the evaluation of the available transfer capability (ATC) between two points in a network also becomes uncertain. The ATC is a measure of ‘available capacity’ in a power transmission system beyond already committed uses, i.e., beyond base case loading. A stochastic power flow algorithm can be used to help quantify and evaluate the uncertainty of the ATC. The limitations considered in the stochastic ATC algorithm are: circuit stability limits, transmission line thermal rating limits, and bus voltage magnitude limits. Transmission circuit outages, while important and also of a stochastic nature, are not considered. The analytical calculation of stochastic ATC is described and tested using the WECC 179 bus system. The analytical calculation is compared to a computationally intensive Monte Carlo calculation. The value of stochastic modeling of ATC relates to a realistic evaluation of power exchange.

On selecting transmission lines for dynamic thermal line rating system implementation

The author presents a systematic approach to: (1) selecting the candidate lines on which an implementation of a dynamic thermal line rating (DTLR) system will have the biggest return; and (2) determining the economic value of this undertaking. To develop this approach, information about contingently overloaded lines, which have the biggest impact on the penalty for off-cost generation, and about individual fuel cost, savings from implementing a DTLR system on each one of these lines is needed. To get this information, the approach is divided into two steps. Step one is for screening of contingently overloaded lines and ranking the severity of the overloading conditions of these lines. Step two is to determine the fuel cost savings from the uprating of these lines. Details of these steps are given. Analytical tools used in the two steps are the same as those used online in the control center.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Weather-dependent versus static thermal line ratings (power overhead lines)

Some of the practical limitations on the use of weather-dependent thermal rating methods for overhead transmission lines are explored. A distinction is made between weather-dependent thermal ratings for a single span and for an entire line. Based on hourly historical weather data for Rochester, NY, USA, it is demonstrated that while the probability distribution of the weather-dependent thermal rating of each span in a line is similar, the probability distribution of line ratings is dependent upon the orientation of the spans in the line. The maximum weather-dependent line ratings are found when all spans are parallel. Minimum weather-dependent line ratings are found for lines whose span orientations vary. Historical weather data are studied in order to estimate minimum predicted thermal ratings for 1 and 4 hours into the future. It is found that such minimum predicted thermal ratings are not greatly in excess of traditional static thermal line ratings. >

Dynamic Thermal Line Rating - Summary and Status of the State-of-the-Art Technology Prepared by a Task Force of the Working Group on Calculation of Bare Overhead Conductor Temperatures, IEEE Towers, Poles and Conductors Subcommittee

Dynamic Thermal Line Rating - Summary and Status of the State-of-the-Art Technology Prepared by a Task Force of the Working Group on Calculation of Bare Overhead Conductor Temperatures, IEEE Towers, Poles and Conductors Subcommittee