Academic literature on the topic 'Electrical transmission lines'

The properties of localization of the I ω electric current function in non-periodic electrical transmission lines have been intensively studied in the last decade. The electric components have been distributed in several forms: (a) aperiodic, including self-similar sequences (Fibonacci and m-tuplingtupling Thue–Morse), (b) incommensurate sequences (Aubry–André and Soukoulis–Economou), and (c) long-range correlated sequences (binary discrete and continuous). The localization properties of the transmission lines were measured using typical diagnostic tools of quantum mechanics like normalized localization length, transmission coefficient, average overlap amplitude, etc. As a result, it has been shown that the localization properties of the classic electric transmission lines are similar to the one-dimensional tight-binding quantum model, but also features some differences. Hence, it is worthwhile to continue investigating disordered transmission lines. To explore new localization behaviors, we are now studying two different problems, namely the model of interacting hanging cells (consisting of a finite number of dual or direct cells hanging in random positions in the transmission line), and the parity-time symmetry problem ( PT -symmetry), where resistances R n are distributed according to gain-loss sequence ( R 2 n = + R , R 2 n − 1 = − R ). This review presents some of the most important results on the localization behavior of the I ω electric current function, in dual, direct, and mixed classic transmission lines, when the electrical components are distributed non-periodically.

Wildfires near transmission lines are important disasters that affect power transmission. Water mist is a highly efficient method for suppressing wildfires near electrical transmission lines, where it avoids line-tripping to ensure the safety of the grid. However, few studies have investigated the electrical safety during the water mist extinguishing process, including the risk of tripping transmission lines and the shock hazard for users. In this study, we systematically studied the influence of the gap distance and the electric conductivity of the water solution on the insulation characteristics of water mist with a Dv0.99 diameter of the droplets of ca. 500 µm, including the breakdown voltage and leakage current. Furthermore, we investigated the effect of water mist on the development of a long-gap discharge, and the insulation mechanism of water mist was also considered. Finally, water mist with multi-component additives was employed for suppressing wildfires near transmission lines in China, and we demonstrated the effectiveness of this method based on the reduction of line-tripping accidents caused by wildfires near transmission lines.

This paper discusses the skin effect on lossy transmission lines in the context of undergraduate electrical engineering courses. A new definition for propagation time derived from Parseval's theorem is proposed. In lossless transmission lines the proposed definition produces the conventional results and for lossy lines it matches quite exactly with the time simulation results, as shown by an illustrative example.

On-line monitoring of high voltage transmission lines can prevent or reduce the accidents of transmission reduced by icing,wave,breeze vibrations of electric wires and the dropping of electrical insulators.An on-line monitoring system of high voltage transmission lines based on optical fiber sensing technology is setted in this paper.Fiber optic signal demodulation instrument in the transformer substation receives the signal sent by the optical fiber Bragg grating sensors fitted on transmission lines and electric power towers,and then the signal was sent to the transmission line monitoring center by the power system network.Field hang net experiments shows that the system can monitor the high voltage transmission lines accurately for a long time.

A transformation used to obtain solutions for the beam parameter equation of fiber optics is applied to the second order differential equation for nonuniform transmission lines. Methods are developed for deriving possible transmission line tapers from known solutions of the transformed equation. This study begins with a comprehensive overview of previous work done to obtain closed-form solutions for the transmission line equations. Limitations of the lumped parameter model are also discussed. As part of this thesis, a tapered transmission line is constructed, based on one of the solutions obtained from the fiber optics studies. A discussion of the design and measurement results are given in the final chapter.

Under the assumption of quasi-transverse electric and magnetic (quasi-TEM) mode of propagation, the transmission characteristics of a thin film microstrip line have been studied. Several numerical programs were employed to calculate the frequency dependent electrical parameters of the microstrip line, and to carry out the transient simulation in the thesis. Based on the simulation results, the relations of pulse distortion to the signal frequency content and the length of line have been investigated. Several transmission characteristics, such as attenuation and dispersion have been paid more attention, and their dependences on the frequency dependent electrical parameters have also been studied. Furthermore, a designing rule for the geometry of thin film microstrip lines is drawn, and a general conclusion is made concerning the effect of conductor losses on thin film microstrip line parameter and the things which should be considered in the design.

Optical fibres have been used as a key medium for telecommunication and networking for more than two decades because in principle they offer sufficient transmission capacity, reaching total rates as high as Tbits/s per fibre. Critical fibre properties such as mode field profiles, single-mode propagation conditions and dispersion characteristics can all be related to the optical fibre refractive index profiles. For this reason, it is of fundamental importance to be able to determine the optical fibre refractive index profiles. In this thesis, a novel Transmission-Line technique has been studied and extended for both the forward and inverse solutions. In the forward solution of the Transmission-Line technique, it is shown that the technique is not only capable of determining exactly the propagation constants in optical fibres with real refractive index profiles, but also evaluating accurately the complex propagation constants in single-mode fibres with arbitrary complex refractive index profiles. To illustrate the effectiveness of this technique, it is applied to the evaluation and manipulation of the gain in a typical 980 nm pumped Erbium-Doped fibre as well as to the calculation of the attenuation of optical fibres when radial loss factors are presented. Moreover, based on the Transmission-Line equivalent circuit model, the exact analytical formulas are derived for a recursive algorithm which allows direct and efficient calculation of dispersion of arbitrary refractive index profile optical fibres. The proposed algorithm computes dispersion directly from the propagation constants without the need for curve fitting and successive subsequent numerical differentiation. The algorithm results in savings for both storage memory and computation time. In the inverse solution using the Transmission-Line technique, the optical fibre refractive index profile synthesis from the given mode electric field distribution is developed and demonstrated. The application of the Transmission-Line principles in the study of optical fibre properties was developed for the first time in the early 80's. However, until now the potential of using Transmission-Line technique for the design of optical fibres based on the given electric field pattern had not been examined. From Maxwell's equations, the Transmission-Line equivalent circuits are derived for a homogeneous symmetric optical fibre. This work demonstrates how to use the Transmission-Line model to reconstruct the exact refractive index profile from the electric field data. The accuracy of the reconstructed optical fibre refractive index profile is examined numerically.

The research described in this thesis is concerned with the analysis and design of conventional wire antenna types, dipoles and loops, based on the left-handed transmission line approach. The left handed antennas have a unique feature that the wavelength of the induced current becomes shorter with decreasing frequency. The left handed transmission line concept can be extended to construct reduced-size dipole or loop antennas in the VHF frequency band. The use of higher order modes allows orthogonal polarisation to be obtained, which is thought to be a feature unique to these antennas. Efficiency is a key parameter of left handed antennas as the heavy left handed loading increases the resistive loss. A study of the efficiency of small dipole antennas loaded with a left-handed transmission line is specially described, and the comparison with conventional inductive loading dipoles. In a low order mode, the efficiency of L-loading dipole is better with low number of unit cell. If the number of cell increases, CL-loading presents comparable and even better performance. In a high mode the meandered left handed dipole gives the best efficiency due to the phase distribution, presenting orthogonal polarization as well. The optimized dipole loaded with parallel plate capacitors and spiral inductors presents the best performance in impedance and efficiency, even better than the conventional inductive loading. A planar loop antenna using a ladder network of left handed loading is also presented. Various modes can be obtained in the left handed loop antenna. The zero order mode gives rise to omnidirectional patterns in the plane of the loop, with good efficiency. By loading the loop with active components, varactors, a tunable left handed loop antenna with a switchable radiation pattern is implemented. The loop gives an omnidirectional pattern with a null to z axis while working in an n = 0 mode and can switch to a pattern with a null at phi = 45° in the plane of the loop in an n = 2 mode.

This thesis develops a new algorithm to simulate incident field coupling with high-speed interconnects. The interconnects considered in this thesis are represented by nonuniform multi-conductor transmission lines and are described through the Telegraphers Equations. The developed algorithm is based on the concept of model-order reduction via projection onto Hilbert space, where a reduced-order model representing the transmission line is constructed and employed as a stamp for representing the line. The incident field is represented by a set of terminal sources obtained from the projection operator used in constructing the reduced-order model. In addition to being developed to handle nonuniform transmission lines, the proposed algorithm offers an advantage by guaranteeing the passivity of the reduced order model. Several examples are presented to validate the validity and accuracy of the proposed algorithm.

An ultra high speed relay for the protection of long EBY transmission lines is described in this thesis. The need for ultra high speed relays is first discussed. From a brief review of protection based on "impedance" distance algorithms or methods using post fault transients, it is shown that at present, there is no truly ultra high speed relay available for the protection of long EBY transmission lines. The proposed relay operates on the incident fault transient travelling waves received at the relaying point only. After the arrival of the first incident transient at the relaying point all subsequent incident travelling waves are detected using the cross-correlation of the first reflected wave with the incident transient waves. From the amplitudes of the subsequent incident transients, two fault resistance estimates are obtained. These two fault resistance estimates are in agreement only for the subsequent incident wave which is caused by direct reflection from the fault. The fault location can then be determined from the time of arrival of this wave. Additional checks based on the ground mode delay or the line round trip wave amplitude, are incorporated to enhance further the security of the scheme. Good fault discrimination is shown to be possible over a large range of fault resistances for symmetric three phase faults to ground, phase to ground faults and phase to phase faults. Double circuit transmission lines and compensated transmission lines can also be protected. The relay has good noise tolerance and a reasonable bandwidth requirement. A real time implementation of the basic algorithm for an internal phase-a to ground fault shows that an ultra high speed relay response with good accuracy can be achieved using currently available digital hardware.

Diagnosing the type of fault and its location in a transmission lines is performed by a variety of techniques and mainly relies on monitoring currents and voltages in the transmission line. Accurate fault diagnosis plays an important role in improving the overall system reliability, has a significant effect on the quality of service provided, improves the protection system efficiency, reduces power outage time and limits the risks and the economic losses. Transmission lines extend over wide areas and are exposed to vulnerable situation, to the harsh and uncontrolled environment random events (e.g.~lightning), this can lead to loss of lines due to various faults. This fact has an attraction for researchers to focus on utilising possible methods to improve protection system and supporting fault diagnosis solutions to overcome many of the transient fault conditions. This thesis explores an alternative method of fault diagnosis and location. The approach uses chromatic methodology to extract information from current and voltage waveforms from a simulated transmission line with different fault conditions. These waveforms are processed chromatically. The process involves two steps, filtering which is performed on a cycle by cycle basis of the three symmetrical components for each waveform, and then using the chromatic transformations to represent the outputs in an information space. Various chromatic models are available but the hue, lightness and saturation (HLS) model is employed in this study and the relation between changes in the waveforms and changes in the chromatic parameters forms the foundation for building the proposed diagnosis algorithms. A fault type classifier algorithm for the asymmetrical faults has been proposed for both, double and single line transmission systems. It employs the chromatic H parameter variation with the fault type for the negative sequence component. The processed waveforms are either the voltage or the current at a single terminal of the transmission line. L chromatic parameter values of the zero sequence component are incorporated in the algorithm to add the ground fault distinguishing element and the L parameter values of the rectified negative sequence component were used to support the classification decision even with high fault resistance. Another algorithm for fault location estimation for all types of faults has been used for the double transmission line system. It employs the L chromatic parameter values of the rectified positive sequence component. The processed waveforms are the current collected from both terminals of the transmission line. Finally, the proposed algorithms have been tested by variation of possible conditions of the faults, such as changing the fault location, the fault resistance, the line configurations and parameters, etc. In addition to robustness testing with different fault scenarios. Experimental results taken from a lumped parameter laboratory system have been also used to verify the outputs of the chromatic processing. The performance of the chromatic approach and other reported methods have been compared. The error of the chromatic method compares favourably with others. As such overall performance can be described as being good, this is encouraging and future work through proposing diagnostic tools for other power system components is needed.

Accurate and efficient simulation of lossy, multi-conductor transmission lines that are terminated by nonlinear circuits is necessary to design high-performance electronic circuits and packages. In this work, theoretical and practical considerations of lossy line simulation are presented. Using delay differential equations, the class of systems with "bidirectional delay" is introduced. These systems can be partitioned such that the resulting subsystems are only linked via delayed variables. It is stated in the "decoupling theorem" that the subsystems can be solved independently for a time interval, which is not longer than the shortest time delay. Circuits that contain transmission lines are shown to form systems with bidirectional delay and, consequently, can be decoupled. Using concepts derived from waveform relaxation, the decoupling is exploited to reduce the computational effort required for transmission line simulation. Moreover, an efficient method for the approximation of lossy line characteristics by rational transfer functions is presented. The method employs nonlinear minimization techniques and yields function coefficients suitable for time-domain modeling. Furthermore, the exponential wave propagation function is represented in the time domain, and discrete-time convolution is employed to calculate the transmission line response. Also described is a filtering method which considerably improves the stability of the simulation, while the deviation in the simulation results is smaller than the local truncation error. In addition, implementation of the lossy line simulator "UAFLICS" is outlined, and practical applications demonstrate the significance of coupling and loss effects.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.
Includes bibliographical references (p. 106-109).
Millimeter wave transmission lines are integral components for many important applications like nuclear fusion and NMR spectroscopy. In low loss corrugated transmission lines propagating the HE,1 mode with a high waveguide radius to wavelength ratio (a/X), the transmission line loss is predominantly a result of mode conversion in components such as miter bends. The theory for determining losses in miter bends though is only approximate, and is based instead on the problem of the loss across a diameter-length gap between two waveguide sections. Through simulation, we verified that the existing analytic theory of this gap loss is correct; however, our simulations could not verify the assumption that the miter bend loss is half the loss in the gap. We also considered the problem of higher order modes (HOMs) mixed with an HE11 input entering the miter bend. Using a numerical technique, we found that the loss through the miter bend is dependent on both the amplitude of the HOM content as well as its phase relative to the phase of the HE11 mode. While the overall loss averaged across all phases remains the same with increasing HOM content, the power that fails to traverse the gap tends to increase, and it is this power that appears as very high order modes that will cause heating around the miter bend. For the ITER transmission line, the loss based on gap theory is 0.027 dB and, using a coherent technique, we measured a loss of 0.05 + 0.02 dB with a vector network analyzer (VNA).
(cont.) We also set out to measure the mode conversion caused by a miter bend by using a 3-axis scanner system to measure the field patterns within the ITER waveguide. Due to the presence of higher order modes output by the HE I launcher, definitive results on the mode conversion attributed to the miter bend could not be obtained. Using a phase retrieval code, we were able to calculate the mode purity of the launcher output and found it to be 98 + 0.5 %. Future work will concentrate on reducing this HOM content to enable measurements of the miter bend mode conversion.
by David S. Tax.
S.M.

This thesis describes a new accurate fault location technique for power transmission lines. The technique is based on a distributed parameter line model which inherently accounts for line conductor asymmetry and shunt capacitance. The accuracy of the new technique is not significantly affected by fault resistance, source network configuration or line length. Also, in most cases no fault type identification is required. The new fault location technique uses the current and voltage phasors at power frequency measured at the line ends. These measurements are synchronised from a knowledge of the prefault phasor data. For a single-phase network the basic idea is to equate two equations obtained for the fault point voltage; one from the sending end phasor data and the other from the receiving end phasor data. The resultant equation is solved for the distance to fault. For multiphase systems the idea is 'generalised by using the theory of natural modes which involves the evaluation of eigenvalues and eigenvectors of the lines. In this way a multiphase system is decoupled into a number of single-phase modal circuits; each circuit can be solved for fault location. For perfectly transposed lines the eigenvalues can simply be evaluated from the sequence components and a real eigenvector matrix can be defined for all the lines. For untransposed lines the new algorithm maintains its high accuracy when assuming perfect transposition to simplify the evaluation of eigenvalues and eigenvectors. Also for double-circuit applications a circuit-by-circuit fault location, without any link between the two circuits, is possible. The test results for different fault conditions presented in this thesis show the higher accuracy in fault location achieved by the new,algorithm in comparison with the algorithms used in the best commercially available fault locators.

1.1 Macroeconomic summary Economic recovery has consistently outperformed the technical staff’s expectations following a steep decline in activity in the second quarter of 2020. At the same time, total and core inflation rates have fallen and remain at low levels, suggesting that a significant element of the reactivation of Colombia’s economy has been related to recovery in potential GDP. This would support the technical staff’s diagnosis of weak aggregate demand and ample excess capacity. The most recently available data on 2020 growth suggests a contraction in economic activity of 6.8%, lower than estimates from January’s Monetary Policy Report (-7.2%). High-frequency indicators suggest that economic performance was significantly more dynamic than expected in January, despite mobility restrictions and quarantine measures. This has also come amid declines in total and core inflation, the latter of which was below January projections if controlling for certain relative price changes. This suggests that the unexpected strength of recent growth contains elements of demand, and that excess capacity, while significant, could be lower than previously estimated. Nevertheless, uncertainty over the measurement of excess capacity continues to be unusually high and marked both by variations in the way different economic sectors and spending components have been affected by the pandemic, and by uneven price behavior. The size of excess capacity, and in particular the evolution of the pandemic in forthcoming quarters, constitute substantial risks to the macroeconomic forecast presented in this report. Despite the unexpected strength of the recovery, the technical staff continues to project ample excess capacity that is expected to remain on the forecast horizon, alongside core inflation that will likely remain below the target. Domestic demand remains below 2019 levels amid unusually significant uncertainty over the size of excess capacity in the economy. High national unemployment (14.6% for February 2021) reflects a loose labor market, while observed total and core inflation continue to be below 2%. Inflationary pressures from the exchange rate are expected to continue to be low, with relatively little pass-through on inflation. This would be compatible with a negative output gap. Excess productive capacity and the expectation of core inflation below the 3% target on the forecast horizon provide a basis for an expansive monetary policy posture. The technical staff’s assessment of certain shocks and their expected effects on the economy, as well as the presence of several sources of uncertainty and related assumptions about their potential macroeconomic impacts, remain a feature of this report. The coronavirus pandemic, in particular, continues to affect the public health environment, and the reopening of Colombia’s economy remains incomplete. The technical staff’s assessment is that the COVID-19 shock has affected both aggregate demand and supply, but that the impact on demand has been deeper and more persistent. Given this persistence, the central forecast accounts for a gradual tightening of the output gap in the absence of new waves of contagion, and as vaccination campaigns progress. The central forecast continues to include an expected increase of total and core inflation rates in the second quarter of 2021, alongside the lapse of the temporary price relief measures put in place in 2020. Additional COVID-19 outbreaks (of uncertain duration and intensity) represent a significant risk factor that could affect these projections. Additionally, the forecast continues to include an upward trend in sovereign risk premiums, reflected by higher levels of public debt that in the wake of the pandemic are likely to persist on the forecast horizon, even in the context of a fiscal adjustment. At the same time, the projection accounts for the shortterm effects on private domestic demand from a fiscal adjustment along the lines of the one currently being proposed by the national government. This would be compatible with a gradual recovery of private domestic demand in 2022. The size and characteristics of the fiscal adjustment that is ultimately implemented, as well as the corresponding market response, represent another source of forecast uncertainty. Newly available information offers evidence of the potential for significant changes to the macroeconomic scenario, though without altering the general diagnosis described above. The most recent data on inflation, growth, fiscal policy, and international financial conditions suggests a more dynamic economy than previously expected. However, a third wave of the pandemic has delayed the re-opening of Colombia’s economy and brought with it a deceleration in economic activity. Detailed descriptions of these considerations and subsequent changes to the macroeconomic forecast are presented below. The expected annual decline in GDP (-0.3%) in the first quarter of 2021 appears to have been less pronounced than projected in January (-4.8%). Partial closures in January to address a second wave of COVID-19 appear to have had a less significant negative impact on the economy than previously estimated. This is reflected in figures related to mobility, energy demand, industry and retail sales, foreign trade, commercial transactions from selected banks, and the national statistics agency’s (DANE) economic tracking indicator (ISE). Output is now expected to have declined annually in the first quarter by 0.3%. Private consumption likely continued to recover, registering levels somewhat above those from the previous year, while public consumption likely increased significantly. While a recovery in investment in both housing and in other buildings and structures is expected, overall investment levels in this case likely continued to be low, and gross fixed capital formation is expected to continue to show significant annual declines. Imports likely recovered to again outpace exports, though both are expected to register significant annual declines. Economic activity that outpaced projections, an increase in oil prices and other export products, and an expected increase in public spending this year account for the upward revision to the 2021 growth forecast (from 4.6% with a range between 2% and 6% in January, to 6.0% with a range between 3% and 7% in April). As a result, the output gap is expected to be smaller and to tighten more rapidly than projected in the previous report, though it is still expected to remain in negative territory on the forecast horizon. Wide forecast intervals reflect the fact that the future evolution of the COVID-19 pandemic remains a significant source of uncertainty on these projections. The delay in the recovery of economic activity as a result of the resurgence of COVID-19 in the first quarter appears to have been less significant than projected in the January report. The central forecast scenario expects this improved performance to continue in 2021 alongside increased consumer and business confidence. Low real interest rates and an active credit supply would also support this dynamic, and the overall conditions would be expected to spur a recovery in consumption and investment. Increased growth in public spending and public works based on the national government’s spending plan (Plan Financiero del Gobierno) are other factors to consider. Additionally, an expected recovery in global demand and higher projected prices for oil and coffee would further contribute to improved external revenues and would favor investment, in particular in the oil sector. Given the above, the technical staff’s 2021 growth forecast has been revised upward from 4.6% in January (range from 2% to 6%) to 6.0% in April (range from 3% to 7%). These projections account for the potential for the third wave of COVID-19 to have a larger and more persistent effect on the economy than the previous wave, while also supposing that there will not be any additional significant waves of the pandemic and that mobility restrictions will be relaxed as a result. Economic growth in 2022 is expected to be 3%, with a range between 1% and 5%. This figure would be lower than projected in the January report (3.6% with a range between 2% and 6%), due to a higher base of comparison given the upward revision to expected GDP in 2021. This forecast also takes into account the likely effects on private demand of a fiscal adjustment of the size currently being proposed by the national government, and which would come into effect in 2022. Excess in productive capacity is now expected to be lower than estimated in January but continues to be significant and affected by high levels of uncertainty, as reflected in the wide forecast intervals. The possibility of new waves of the virus (of uncertain intensity and duration) represents a significant downward risk to projected GDP growth, and is signaled by the lower limits of the ranges provided in this report. Inflation (1.51%) and inflation excluding food and regulated items (0.94%) declined in March compared to December, continuing below the 3% target. The decline in inflation in this period was below projections, explained in large part by unanticipated increases in the costs of certain foods (3.92%) and regulated items (1.52%). An increase in international food and shipping prices, increased foreign demand for beef, and specific upward pressures on perishable food supplies appear to explain a lower-than-expected deceleration in the consumer price index (CPI) for foods. An unexpected increase in regulated items prices came amid unanticipated increases in international fuel prices, on some utilities rates, and for regulated education prices. The decline in annual inflation excluding food and regulated items between December and March was in line with projections from January, though this included downward pressure from a significant reduction in telecommunications rates due to the imminent entry of a new operator. When controlling for the effects of this relative price change, inflation excluding food and regulated items exceeds levels forecast in the previous report. Within this indicator of core inflation, the CPI for goods (1.05%) accelerated due to a reversion of the effects of the VAT-free day in November, which was largely accounted for in February, and possibly by the transmission of a recent depreciation of the peso on domestic prices for certain items (electric and household appliances). For their part, services prices decelerated and showed the lowest rate of annual growth (0.89%) among the large consumer baskets in the CPI. Within the services basket, the annual change in rental prices continued to decline, while those services that continue to experience the most significant restrictions on returning to normal operations (tourism, cinemas, nightlife, etc.) continued to register significant price declines. As previously mentioned, telephone rates also fell significantly due to increased competition in the market. Total inflation is expected to continue to be affected by ample excesses in productive capacity for the remainder of 2021 and 2022, though less so than projected in January. As a result, convergence to the inflation target is now expected to be somewhat faster than estimated in the previous report, assuming the absence of significant additional outbreaks of COVID-19. The technical staff’s year-end inflation projections for 2021 and 2022 have increased, suggesting figures around 3% due largely to variation in food and regulated items prices. The projection for inflation excluding food and regulated items also increased, but remains below 3%. Price relief measures on indirect taxes implemented in 2020 are expected to lapse in the second quarter of 2021, generating a one-off effect on prices and temporarily affecting inflation excluding food and regulated items. However, indexation to low levels of past inflation, weak demand, and ample excess productive capacity are expected to keep core inflation below the target, near 2.3% at the end of 2021 (previously 2.1%). The reversion in 2021 of the effects of some price relief measures on utility rates from 2020 should lead to an increase in the CPI for regulated items in the second half of this year. Annual price changes are now expected to be higher than estimated in the January report due to an increased expected path for fuel prices and unanticipated increases in regulated education prices. The projection for the CPI for foods has increased compared to the previous report, taking into account certain factors that were not anticipated in January (a less favorable agricultural cycle, increased pressure from international prices, and transport costs). Given the above, year-end annual inflation for 2021 and 2022 is now expected to be 3% and 2.8%, respectively, which would be above projections from January (2.3% and 2,7%). For its part, expected inflation based on analyst surveys suggests year-end inflation in 2021 and 2022 of 2.8% and 3.1%, respectively. There remains significant uncertainty surrounding the inflation forecasts included in this report due to several factors: 1) the evolution of the pandemic; 2) the difficulty in evaluating the size and persistence of excess productive capacity; 3) the timing and manner in which price relief measures will lapse; and 4) the future behavior of food prices. Projected 2021 growth in foreign demand (4.4% to 5.2%) and the supposed average oil price (USD 53 to USD 61 per Brent benchmark barrel) were both revised upward. An increase in long-term international interest rates has been reflected in a depreciation of the peso and could result in relatively tighter external financial conditions for emerging market economies, including Colombia. Average growth among Colombia’s trade partners was greater than expected in the fourth quarter of 2020. This, together with a sizable fiscal stimulus approved in the United States and the onset of a massive global vaccination campaign, largely explains the projected increase in foreign demand growth in 2021. The resilience of the goods market in the face of global crisis and an expected normalization in international trade are additional factors. These considerations and the expected continuation of a gradual reduction of mobility restrictions abroad suggest that Colombia’s trade partners could grow on average by 5.2% in 2021 and around 3.4% in 2022. The improved prospects for global economic growth have led to an increase in current and expected oil prices. Production interruptions due to a heavy winter, reduced inventories, and increased supply restrictions instituted by producing countries have also contributed to the increase. Meanwhile, market forecasts and recent Federal Reserve pronouncements suggest that the benchmark interest rate in the U.S. will remain stable for the next two years. Nevertheless, a significant increase in public spending in the country has fostered expectations for greater growth and inflation, as well as increased uncertainty over the moment in which a normalization of monetary policy might begin. This has been reflected in an increase in long-term interest rates. In this context, emerging market economies in the region, including Colombia, have registered increases in sovereign risk premiums and long-term domestic interest rates, and a depreciation of local currencies against the dollar. Recent outbreaks of COVID-19 in several of these economies; limits on vaccine supply and the slow pace of immunization campaigns in some countries; a significant increase in public debt; and tensions between the United States and China, among other factors, all add to a high level of uncertainty surrounding interest rate spreads, external financing conditions, and the future performance of risk premiums. The impact that this environment could have on the exchange rate and on domestic financing conditions represent risks to the macroeconomic and monetary policy forecasts. Domestic financial conditions continue to favor recovery in economic activity. The transmission of reductions to the policy interest rate on credit rates has been significant. The banking portfolio continues to recover amid circumstances that have affected both the supply and demand for loans, and in which some credit risks have materialized. Preferential and ordinary commercial interest rates have fallen to a similar degree as the benchmark interest rate. As is generally the case, this transmission has come at a slower pace for consumer credit rates, and has been further delayed in the case of mortgage rates. Commercial credit levels stabilized above pre-pandemic levels in March, following an increase resulting from significant liquidity requirements for businesses in the second quarter of 2020. The consumer credit portfolio continued to recover and has now surpassed February 2020 levels, though overall growth in the portfolio remains low. At the same time, portfolio projections and default indicators have increased, and credit establishment earnings have come down. Despite this, credit disbursements continue to recover and solvency indicators remain well above regulatory minimums. 1.2 Monetary policy decision In its meetings in March and April the BDBR left the benchmark interest rate unchanged at 1.75%.