TERM PAPER
ON
POWER FLOW MODEL OF SATCOM

SUBMITTED TO- SUBMITTED BY- Md. Ibrahim bhat 11010038

INTRODUCTION
In power engineering, the power flow study, also known as load-flow study, is an important tool involving numerical analysis applied to a power system. A power flow study usually uses simplified notation such as a one-line diagram and per-unit system, and focuses on various forms of AC power (i.e.: voltages, voltage angles, real power and reactive power). It analyzes the power systems in normal steady-state operation. A number of software implementations of power flow studies exist.
In addition to a power flow study, sometimes called the base case, many software implementations perform other types of analysis, such as short-circuit fault analysis, stability studies (transient & steady-state), unit commitment and economic load dispatch analysis. In particular, some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per kilowatthour delivered.
Power flow or load-flow studies are important for planning future expansion of power systems as well as in determining the best operation of existing systems. The principal information obtained from the power flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive power flowing in each line.
Commercial power systems are usually too large to allow for hand solution of the power flow. Special purpose network analyzers were built between 1929 and the early 1960s to provide laboratory models of power systems; large-scale digital computers replaced the analog methods.
MODEL
An AC power flow model is a model used in electrical engineering to analyze power grids. It provides a nonlinear system which describes the energy flow through each transmission line. Due to nonlinearity, in many cases the analysis of large network via AC power flow model is not feasible, and a linear (but less accurate) DC power flow model is used instead. Both of those models are very crude approximations to reality.
PROPAGATION PHENOMENA AND MODELING
The propagation phenomena concerning earth-space links mainly originate in the troposphere and the ionosphere. Respectively, propagation effects are separated into two categories [3]: ionosphere effects, influencing systems operating below 3GHz, and tropospheric effects, influencing systems operating above 3GHz. Since this article deals only with the frequency spectrum above 10GHz, it will focus on the tropospheric effects. The most important tropospheric phenomena affecting satellite communication systems at frequencies above
10GHz are summarized as follows

Attenuation Due to Precipitation: When propagating through rain, snow, hail, or ice droplets, radio waves suffer from power loss due to hydrometeor scattering (Fig. 1). Although hydrometeor scattering is the major limiting factor in the EHF band (>30GHz), hydrometeor absorption is the dominant phenomenon causing power loss in the lower spectral part between 10GHz and 30GHz. The combined effect of hydrometeor scattering and absorption results in a power loss proportional in dB to the square of the frequency [4]. This constitutes the main disadvantage of operating at the Ku, Ka, or V frequency bands. As far as satellite systems are concerned, the depth of rain fades also depends on the elevation and polarization angles. On the other hand, as rain attenuation depends unfavorably on the rainfall rate and the raindrop size distribution, it affects heavily tropical and subtropical regions. An indicative picture of rain fades is obtained from Fig. 2, which illustrates a typical fade incident with a peak value of 14dB. A variety of models exists for the prediction of the average rain attenuation on an annual basis: Rec. ITU-RP.618-7 [5], Leitao-Watson [6], Lin [7], Morita and Higuti [8],

and the EXCELL [9] model, all of them performing satisfactorily on a global scale. The methodology usually followed to handle propagation phenomena involves the representation of the fade depths as a function of time percentage and results in calculating the time occurrence of outages for a given attenuation level. For example, in Fig. 3 the ITU-R model predicting the annual exceedance probability of rain attenuation is implemented for the downlink frequency of the bands under consideration, and for a hypothetical satellite link operating in Athens, Greece. Gaseous Absorption: Besides hydrometeor absorption,gaseous absorption, mostly from oxygen and water vapor, contributes to the total attenuation of radiowaves, especially in the case of low elevation angles. However, the contribution of gaseous absorption to the total attenuation is small compared to the attenuation due to rain. In Fig. 4 the frequency dependence of oxygen and water vapor absorption is presented in terms of specific attenuation. One may observe that water vapor is the main contributor to gaseous attenuation in the frequency range just below 30GHz due to a maximum occurring at 22.5GHz. Moreover, other maxima that occur at 183GHz, 320GHz for water vapor and at 60GHz, 119GHz for oxygen absorption lie outside the spectral region considered in this article. The attenuation due to oxygen absorption exhibits an almost constant behavior for different climatic

conditions, whereas the attenuation due to water vapor varies with temperature and absolute humidity. A complete method for calculating gaseous attenuation is given in Annex 1 of Rec. ITU-R P.676-4 [10].
Cloud Attenuation: The liquid water content of clouds is the physical cause of cloud attenuation. Prediction models for this particular attenuation factor have been developed within the framework of ITU-R [11] and elsewhere [12]. Figure 5 depicts attenuation values due to clouds and fog exceeded for a certain range of probabilities. The ITU-R model was selected as the underlying prediction method for generating these curves, which correspond to the three frequency bands examinedin this survey. Melting Layer Attenuation: At a certain height above ground level, called the effective rain height, snow and ice precipitation are converted into rain precipitation. The region around this height is called the melting layer. During periods of light rain and for low elevation angles, the melting layer contributes significantly to the total slant path attenuation, as verified by the relevant prediction model [13].Sky Noise Increase: As attenuation increases, so does emission noise (see Rec. ITU-R P.618-7). The same factors previously mentioned, i.e. scatter/emission from precipitation hydrometeors, contribute to noise increase, which is more important than attenuation when earth stations with low noise front ends are considered. Signal Depolarization: Differential phase shift and differential attenuation caused by nonspherical scatterers (e.g., raindrops and ice crystals) cause signal depolarization. Although this phenomenon does not affect single polarized satellite systems, its effect becomes significant for systems reusing frequency by transmitting two orthogonally polarized signals for optimum RF spectrum utilization. In this case, depolarization results in cross-polar interference, i.e. part of the transmitted power in one polarization interferes with the orthogonally polarized signal [14, 15]. In Fig. 6 the relevant ITU-R method [5] has been employed to demonstrate the long-term statistics of hydrometeor induced cross-polarization in the Athens, Greece area. The cross-polarization discrimination (XPD) not exceeded for various percentages of time is shown only at the Ku and Ka bands, since validity issues arise for the proposed model at frequencies above 35GHz.
Tropospheric Scintillations: Variations in the magnitude and the profile of the refractive index of the troposphere lead to amplitude fluctuations known as scintillations. These fluctuations increase with frequency and depend upon the length of the slant path decreasing with the antenna beamwidth. Amplitude fluctuations are also accompanied by a phase fluctuation. Returning to Fig. 2, apart from the apparent single fade event, the fluctuations on the received signal are obvious. Models estimating the effects of scintillations on the received signal can be found in [5, 16] and [17].
Intersystem Interference: Interference may occur between a satellite system and terrestrial systems, or between two satellite systems whenever a frequency band is shared or adjacent orbital positions are used. During clear sky conditions, intersystem interference is mainly caused by the sidelobes of the antennas and is reflected on the clear sky carrier-to-interference ratio (C/I)nom. However, from the propagation impairments perspective, intersystem interference is aggravated by potential differential rain attenuation ,DA, whenever the desired signal undergoes a large rain attenuation, while at the same time the undesired signal from an adjacent satellite experiences a lower level of attenuation[18–22]. In this case, the carrier-to-interference ratio must be properly modified to account for the effect of rain as follows

where AC, AI (expressed in dB) are the rain attenuation values on the intended and the interfering satellite path, respectively.
To evaluate the time occurrence of such an event, i.e. the percentage of total time the C/I is not exceeded due to differential rain attenuation, the methodology described in [18] yields the results presented in Fig. 7. In this figure, operation under (C/I)nom = 25dB and an aperture angle of 2° between the two satellites are assumed. Furthermore, to generate the three curves, a fade margin equal to 15dB has been adopted.To conclude, several ITU-R Recommendations exist for the prediction of the effects of most of the propagation phenomena. The methods recommended are widely used, easy to apply, and agree satisfactorily with experimental results in various geographical regions. Still, due to the rare propagation

Measurements above 30GHz, the validity of only a few propagation models presented above has been tested.
Power flow problem formulation
The goal of a power flow study is to obtain complete voltage angle and magnitude information for each bus in a power system for specified load and generator real power and voltage conditions.[1] Once this information is known, real and reactive power flow on each branch as well as generator reactive power output can be analytically determined. Due to the nonlinear nature of this problem, numerical methods are employed to obtain a solution that is within an acceptable tolerance.
The solution to the power flow problem begins with identifying the known and unknown variables in the system. The known and unknown variables are dependent on the type of bus. A bus without any generators connected to it is called a Load Bus. With one exception, a bus with at least one generator connected to it is called a Generator Bus. The exception is one arbitrarily-selected bus that has a generator. This bus is referred to as the slack bus.
In the power flow problem, it is assumed that the real power PD and reactive power QD at each Load Bus are known. For this reason, Load Buses are also known as PQ Buses. For Generator Buses, it is assumed that the real power generated PG and the voltage magnitude |V| is known. For the Slack Bus, it is assumed that the voltage magnitude |V| and voltage phase Θ are known. Therefore, for each Load Bus, both the voltage magnitude and angle are unknown and must be solved for; for each Generator Bus, the voltage angle must be solved for; there are no variables that must be solved for the Slack Bus. In a system with N buses and R generators.
EIRP CONTROL TECHNIQUES
EIRP (effective isotropic radiated power) is the product of the transmitted power and the antenna gain, usually expressed in dBw. EIRP control consists of varying either the carrier power or the antenna gain in order to compensate for the power losses due to propagation effects. The adjustment of the carrier power can be accomplished either at the earth station (uplink power control (ULPC)) or on-board the satellite (downlink power control (DLPC)), called earth station EIRP control or satellite EIRP control, respectively. The advantages and disadvantages of both techniques will be reviewed in a later section. Moreover, the adjustment of the antenna gain carried out on-board the satellite, a technique referred to as spot beam shaping (SBS), may be viewed as another type of satellite EIRP control.
In principle, power control may be implemented in two ways:
• As an open loop power control system, in which the transmitted power is adjusted based on measurements of recently received power either from a pilot frequency or from the information signal itself.
• As a closed loop power control system, in which the transmitted power is adjusted based on reported power measurements over the channel. In closed loop power control systems the transmitter (earth station or satellite) decides whether or not to vary the output power after receiving feedback information from the receiver and not based on estimates of the attenuation only. This theoretically results in a much more comprehensive control system. In practice, however, when applied to satellite systems the closed loop system must cope with propagation delays of twice the round trip time between the earth station and the satellite for regenerative satellites, or four times the round trip time for transparent satellites. For GSO satellite systems, the propagation delay almost cancels the possibility of a closed loop system responding to channel changes, particularly since the most aggravating atmospheric phenomena (deep rain fades, scintillations) have short durations.

Uplink Power Control — ULPC [40, 41] is achieved by varyn FMT control loop flow chart.
Fade predictor FIFO-2 samples 12.5GHz
Beacon signal Filter Fade slope Frequency
Scaling of rain fade 1 second ahead rain fade prediction Standard deviation FIFO-21 samples Frequency scaling of scintillation
• Third Quarter 2004 the transmit power of an earth station in order to keep the flux density at the satellite input from falling below a certain level. Adopting the open loop principle for the rest of this section, the adjusting of the high power amplifier (HPA) of the earth station is based only on attenuation measurements, without resorting to any feedback from the receiver. In the case of transparent satellite repeaters, the adjustment of the carrier power from the transmitting earth station aims to control both the uplink and downlink power levels, by compensating not only for propagation impairments on the uplink, but also possible propagation impairments on the downlink.
A possible problem caused by ULPC is adjacent channel interference [42], when part of the energy of the satellite signal falls into adjacent channels. When the control system predicts a deep fade in the next channel state, the HPA output back-off (i.e. the margin between the operation point and the saturation point) is decreased to compensate for the uplink attenuation. The result is the partial restoration of the sidelobes of the signal spectrum and the creation of interference into adjacent channels.
Adjacent satellite interference is a type of intersystem interference due to ULPC. The rapid growth of satellite communications in the past two decades has led to congestion on the geostationary orbit, where the majority of commercial satellite systems exist. Nowadays, satellites are separated by 2–3 degrees on the geostationary orbit and, therefore, an increase of an earth station transmit power may impair the operation of adjacent satellite systems. Despite the drawbacks mentioned above, ULPC constitutes an effective countermeasure against signal fading and is preferred today by many satellite operators. Its main prerequisite is the availability of extra back-off under clear sky conditions, so that the margin necessary for ULPC under fading conditions may be provided.

Downlink Power Control — DLPC [43] is achieved by increasing the transmit power of a satellite. Unlike ULPC, it is very difficult to implement DLPC due to limitations related to the satellite size and weight, as well as to the limited ability of controlling the satellite operation. Specifically, the satellite size and weight limit the use of TWTA (traveling wave tube amplifiers), which must operate at a small output back-off. Apart from the possible adjacent channel interference, DLPC may also create intermodulation interference [42], a type of interference caused by intermodulation products generated by the nonlinear amplification of multiple carriers. The choice of the multiple access scheme is significant, with single-carrier per- transponder TDMA (Time Division Multiple Access) systems being less affected. This tolerance to interference is one of the main reasons why TDMA schemes have become preferable in recent years compared to FDMA (Frequency Division Multiple Access) schemes. Finally, DLPC also contributes to intersystem interference. A significant increase of satellite power to overcome severe signal degradations could create interference with spectrally overlapping terrestrial networks as local multipoint distribution systems and violate the regulations concerning power flux density. This drawback of DLPC is even more pronounced when the adaptive control loop allocates the extra power ineffectively due to the occurrence of false alarms or its application longer than required.

Spot Beam Shaping — When the service area of a GSO satellite is confined within a country or a certain geographical region, the coverage is provided by spot beams, so that there is no waste of satellite EIRP and the spectrum is efficiently used. A spot beam produces a higher satellite EIRP than a global one, since the antenna beamwidth reduction increases its gain.
The SBS technique consists of appropriately shaping the satellite antenna pattern so that the power received on the ground remains nearly constant, even under rainfall conditions. In a study conducted by the European Space Agency (ESA), a multi-feed antenna with a beam forming network and a Cassegrain antenna with a single feed and two shaped reflectors were evaluated as possible solutions for implementing SBS. The conclusion of this study is that the first solution is more flexible and allows higher adaptive gains. A major advantage of SBS is that real-time or instantaneous estimates of the attenuation, a requirement that constitutes the most difficult function of an FMT control loop, are not needed since compensation is carried out over the entire coverage area rather than for a single site. Short-term weather predictions termed as nowcasting and obtained through satellite imagery could be used in order to analyze the evolution of the meteorological situation and forecast the propagation conditions
[45]. Another significant advantage of SBS compared to power control is that compensation for rain attenuation is achieved by shaping the antenna pattern and not by reducing the output back-off of the amplifiers. Thus, the undesirable effects of intermodulation interference due to amplifier operation near saturation are minimized. The significant advantages of SBS indicate a wide interest in future satellite systems. Nevertheless, its use to date has been limited because the relevant technology is immature and research is in its initial stages. Specifically, the use of large active antennas on-board the satellite and the feasibility of reshaping spot beams without penalizing the global coverage are some of the imposed limitations. SBS is a subset of the wider concept of on-board processing (OBP) and its feasibility is directly connected to the advancements in this specific field.
OBP aims at enhancing the processing capabilities of satellite transponders to provide user oriented services, such as narrowcasting/multicasting, TCP/IP, and point-to-point or point to- multipoint services on demand. Thus, the additional equipment intended for OBP contains on-board modulators/demodulators, a baseband switch to accommodate end user applications, and a system controlling the direction and the coverage of spot beams.
Power flow methods * Gauss–Seidel method: This is the earliest devised method. It shows slower rates of convergence compared to other iterative methods, but it uses very little memory and does not need to solve a matrix system. * Newton–Raphson method: Most current methods are based on this. The convergence rate is typically fast, but it may sometimes fail because of the inherent problems of fractality in the basins of attraction of the underlying iterative map. * Fast-decoupled-load-flow method: A variation on Newton-Raphson that exploits the approximate decoupling of active and reactive flows in well-behaved power networks, and additionally fixes the value of the Jacobian during the iteration in order to avoid costly matrix decompositions. Also referred to as "fixed-slope, decoupled NR". * Holomorphic embedding load flow method: A recently developed method based on advanced techniques of complex analysis. It is direct and guarantees the calculation of the correct (operative) branch, out of the multiple solutions present in the power flow equations.

REFERENCES

1. ^ Grainger, J.; Stevenson, W.(1994). Power System Analysis. New York: McGraw Hill. ISBN 0-07-061293-5. 2. file:///C:/Users/Ruchi/Downloads/Powe-r_flow_study.htm 3. J.G.Proakis-Digital Communications, McGraw Hill, 4th Ed., 2001, Chapter 8 4. E. Matricciani and M. Mauri, “ITALSAT-OLYMPUS 20-GHzOrbital Diversity Experiment at Spino d’ Adda,” IEEE Trans.Antennas Propag., vol. 43, no. 1, 1995, pp. 105–07 5.