Dynamic Line Rating Current Calculation without Ambient...
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Dynamic Line Rating Current Calculation without Ambient
Parameters Inputs
Hengxu Ha, Gajendiran Balakrishnan, GE Grid Solutions, Stafford, UKZhiying Zhang, GE Grid Solutions, Markham, On, Canada
2019 Texas A&M Protective Relaying Conference
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Agenda
β’ Introduction
β’ Proposed Algorithms
β’ Validation and Testing Results
β’ Conclusions
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β’ The power transfer capacity of a transmission line is primarilyconstrained by stability limits and thermal limits
β’ Stability limits are reliability requirements and thermal limits,however, are mainly restrained with safety requirements in order to maintain line minimum clearance (sag limit) and to avoid conductor annealing
β’ Typically, the ampacity of long lines is primarily determined by the stability or voltage limits and the ampacity of short lines is determined by line thermal limits
Introduction
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β’ Traditionally, thermal limit is applied with a static line rating (SLR), which provides the maximum allowable current-carrying capacity based on certain environment assumptions and wonβt be altered frequently, such as summer line rating and winter lin rating
β’ However, with renewable energy penetration, a line that was originally designed to supply a relatively small load, now may carry more current because of the large reverse power, and could exceed its winter and summer line ratings
β’ Rather than applying fixed summer and winter line ratings base on the βworst-caseβ weather assumptions, a dynamically derived line rating can be adopted
Introduction
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β’ With dynamic line ratings (DLR) applied, transmission facilities can be operated up to their actual physical capacity rather than a conservative estimate of line capacity
β’ Conventional method for dynamic line rating current calculation requires ambient parameters inputs, such as ambient temperature, wind speed, wind direction and sun radiations, however, extra cost will be incurred for measuring these ambien parameters
β’ In order to avoid the extra costs for these additional measuring devices, several new techniques based only on the measuring voltage and current without ambient inputs have been proposed including
Introduction
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1. Calculate conductor temperature based on the conductivity characteristics respective to temperature. However, the coefficient of the temperature characteristic is too small to accurately calculate the temperature
2. Calculate conductor temperature based on the line sags, which significantly improved the accuracy of temperature calculation, however, no rating current can be given out
β’ This paper proposes a new method for calculating the dynamic rating current based on voltages and currents of both terminals of a line without any ambient parameter inputs
β’ The instantaneous temperature is estimated by calculating the variation of the line parameters, and then the steady state conductor temperature is calculated accordingly
Introduction
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β’ With the calculated steady state conductor temperatures and the corresponding currents, the dissipating heat curve can be obtained by curve fitting method
β’ The dynamic rating current can be calculated based on the dissipating curve at the maximum allowed conductor temperature
Introduction
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πππΆπΆπππππΆπΆππππ
= πππΊπΊ πππΆπΆ β πππ·π· πππΆπΆ , πππΊπΊ (πππΆπΆ) = πΌπΌ2π π (πππΆπΆ)Mc total heat capacity of conductorTC conductor instantaneous temperature PG(TC) heat generating power PD(TC) heat dissipating powerR(TC) conductor resistance
The Proposed Algorithm
πΌπΌππππππππ =)πππ·π·(πππΆπΆπΆπΆπππΆπΆ)π π (πππΆπΆπΆπΆπππΆπΆ
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β’ If the ambient parameters are dynamically changing, the dissipating power curve dynamically changes accordingly, and so does the rating current, as shown below
The Proposed Algorithm
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β’ Conductor heat dissipating power can be expressed as PD(TC)=pc+pr-ps, where pc is the convection heat loss, pr is radiation heat loss, and ps is solar heat gain
β’ The details for the dissipating power (PD) calculation are defined in IEEE standard 738, in which a lot of ambient parameters and inputs are required
β’ In this study, power dissipating curve is expressed in polynomial terms
πππ·π·(πππΆπΆ) = ππ0 + ππ1πππΆπΆ + ππ2πππΆπΆ2
Where a0, a1 and a2 are the coefficients to be determined
The Proposed Algorithm
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β’ At the balance point, the dissipating power equals to the generating power, we can obtain the dissipating power by calculating the generating power
πππ·π·(πππΆπΆ) = ππ0 + ππ1πππΆπΆ + ππ2πππΆπΆ2, πππΊπΊ πππΆπΆ = πΌπΌ2π π πππΆπΆ
β’ Assuming N pairs of heat generating power and temperature values are obtained, coefficients (a0, a1, a2 ) can then be solved, and rating current can be calculated accordingly
πππΊπΊ1πππΊπΊ2β―πππΊπΊπΊπΊ
=
1 πππΆπΆ1 πππΆπΆ12
1 πππΆπΆ2 πππΆπΆ22β― β― β―
1 πππΆπΆπΊπΊ πππΆπΆπΊπΊ2
ππ0ππ1ππ2
The Proposed Algorithm
πΌπΌππππππππ =)ππ0 + ππ1πππΆπΆπΆπΆπππΆπΆ + ππ2πππΆπΆπΆπΆπππΆπΆ
2
)π π (πππΆπΆπΆπΆπππΆπΆ
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β’ The difficulty is how to obtain the conductor temperature?
β’ Conventional methods include (1) direct measurement, and (2) calculation based on ambient parameter inputs
β’ However, extra cost will be incurred for both methods
The Proposed Algorithm
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β’ In our approach, the conductor temperature is calculated based on voltages and currents from both terminals of a line, but without any ambient parameter inputs
β’ Conductor temperature change will result in the line length change, which will lead to line parameters change
οΏ½ΜοΏ½πππΜπΌπΌππ
= π΄π΄(ππππ) π΅π΅(ππππ)πΆπΆ(ππππ) π·π·(ππππ)
οΏ½ΜοΏ½ππ π ΜπΌπΌπ π
The Proposed Algorithm
π΄π΄(ππππ) = π·π·(ππππ) = cosh(πΎπΎπΎπΎ);π΅π΅ ππππ = ππππ sinh πΎπΎπΎπΎ ;πΆπΆ ππππ = sinh(πΎπΎπΎπΎ)/ππππ;πΎπΎ ππππ = πΎπΎ0[1 + πΌπΌ πππΆπΆ β πππ π π π π π + π½π½ πππΆπΆ β πππ π π π π π 2]
πΎπΎ = ππ + ππππππ (πππππΆπΆ)ππππ = (ππ + ππππππ)/(πππππΆπΆ)
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οΏ½ΜοΏ½πππΜπΌπΌππ
= π΄π΄(ππππ) π΅π΅(ππππ)πΆπΆ(ππππ) π·π·(ππππ)
οΏ½ΜοΏ½ππ π ΜπΌπΌπ π
The Proposed Algorithm
Y =
οΏ½π π π π (οΏ½ΜοΏ½ππποΏ½πΌπΌπΌπΌ(οΏ½ΜοΏ½ππποΏ½π π π π ( ΜπΌπΌπποΏ½πΌπΌπΌπΌ( ΜπΌπΌππ
= F(ππππ) =
π π π π ππ1 οΏ½ΜοΏ½ππ π , ΜπΌπΌπ π ,ππππ
πΌπΌπΌπΌ ππ1 οΏ½ΜοΏ½ππ π , ΜπΌπΌπ π ,ππππ
π π π π ππ2 οΏ½ΜοΏ½ππ π , ΜπΌπΌπ π ,ππππ
πΌπΌπΌπΌ ππ2 οΏ½ΜοΏ½ππ π , ΜπΌπΌπ π ,ππππ
Newtonβs algorithm is employed for solving this non-linear equation:1) Set an initial solution, substitute it into F(TC), set k=02) Calculate the difference between Y and πΉπΉ(ππππ
(ππ))3) Substitute ππππ
(ππ) into Jacobian matrix4) Calculate the difference between kth solution and real
root value by means of least square method5) Correct the kth solution
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Calculation of Steady State Temperatureβ’ Steady state conductor temperature can be estimated with 1st
order differential equation, where ππππ is thermal time constant
β’ It can be further digitized
β’ Use at least two equations to solve TCS because of 2 unknowns. Assume one equation is at time n, another one is at time m:
The Proposed Algorithm
πππΆπΆ(ππ) = πππΆπΆππ + ππππ)πππππΆπΆ(ππ
ππππ
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Calculation of Rating Currentβ’ For simplification, linear polynomial is used for curve fitting the
heat dissipating power curve
The Proposed Algorithm
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THESCHEMEAND ALGORITHMSFORREALIZATION
The Proposed Algorithm
Ts1 = 20ms (for 50Hz system);Ts2 = 100 ms;Ts3 = 1000 ms;
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β’ How to deal with the scenarios where the measured conductor temperature points and conductor current points (or heat generating power) are on different dissipating power curve
The Proposed Algorithm
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The Proposed Algorithmβ’ The solution for overcoming the scenario where the two points are not
in the same dissipating curve is that these scenarios should be identified by checking the initial conductor temperature
β’ Before the algorithm is running, in the initialization stage, the inception conductor temperature TCS0 is set as the possible minimum value of the ambient temperature
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The Proposed AlgorithmFlow chart of calculating rating current
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Validation and Testing Resultsβ’ The data for validating the new algorithm are generated by
simulations in Matlab/Simulink
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Validation and Testing Resultsβ’ Simulation Model In details
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Validation and Testing Resultsβ’ Validation Results
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β’ This paper proposes a method for calculating the dynamic line rating current without ambient inputs
β’ The conductor temperature is calculated by the variation of the line parameters
β’ The rating current is calculated from the dissipating power curve, generated by curve fitting method, at the maximum allowed conductor temperature
Conclusions
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β’ The results of the validation show that this method is reliable and the difference between the new method and the conventional method which requires large amount of ambient inputs is less than 4%
Conclusions
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Thank You
Questions?