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In power engineering, the power-flow study, or load-flow study, is a numerical analysis of the flow of electric power in an interconnected system. A power-flow study usually uses simplified notations such as a one-line diagram and per-unit system, and focuses on various aspects of AC power parameters, such as voltages, voltage angles, real power and reactive power. It analyzes the power systems in normal steady-state operation.
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 complex to allow for hand solution of the power flow. Special-purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical solutions.
In addition to a power-flow study, computer programs perform related calculations such as short-circuit fault analysis, stability studies (transient and steady-state), unit commitment and economic dispatch.[1] In particular, some programs use linear programming to find the optimal power flow, the conditions which give the lowest cost per kilowatt hour delivered.
In term of its approach to uncertainties, load-flow study can be divided to deterministic load flow and uncertainty-concerned load flow. Deterministic load-flow study does not take into account the uncertainties arising from both power generations and load behaviors. To take the uncertainties into consideration, there are several approaches that has been used such as probabilistic, possibilistic, information gap decision theory, robust optimization, and interval analysis.[2]
An alternating current power-flow model is a model used in electrical engineering to analyze power grids. It provides a nonlinear system of equations which describes the energy flow through each transmission line. The problem is non-linear because the power flow into load impedances is a function of the square of the applied voltages. 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.
Usually analysis of a three-phase power system is simplified by assuming balanced loading of all three phases. Sinusoidal steady-state operation is assumed, with no transient changes in power flow or voltage due to load or generation changes, meaning all current and voltage waveforms are sinusoidal with no DC offset and have the same constant frequency. The previous assumption is the same as assuming the power system is linear time-invariant (even though the system of equations is nonlinear), driven by sinusoidal sources of same frequency, and operating in steady-state, which allows to use phasor analysis, another simplification. A further simplification is to use the per-unit system to represent all voltages, power flows, and impedances, scaling the actual target system values to some convenient base. A system one-line diagram is the basis to build a mathematical model of the generators, loads, buses, and transmission lines of the system, and their electrical impedances and ratings.
The goal of a power-flow study is to obtain complete voltages angle and magnitude information for each bus in a power system for specified load and generator real power and voltage conditions.[3] 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.
Direct current load flow gives estimations of lines power flows on AC power systems. Direct current load flow looks only at active power flows and neglects reactive power flows. This method is non-iterative and absolutely convergent but less accurate than AC Load Flow solutions. Direct current load flow is used wherever repetitive and fast load flow estimations are required.[9]
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Monique Manning is a woman who embodies Beauty and has transformed her body and spirit through yoga, dance, and most recently, birth. Unlocking ancient wisdom and flow of the feminine, Monique is overjoyed by the possibility of empowering women at all stages of life with her uniquely created Ashland class, Yoga & Bellydance Fusion. I sat down with her recently to talk about her process and why she can help other women feel amazing in their body, mind and spirit.
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