COMPUTATIONAL METHODS FOR POWER SYSTEMS

Posted by Winnie Melda on February 21st, 2019

Introduction

Today, system analysis is significant because of its assist in prediction and continually updating the operating status of the electric power network in the deregulated environment in which the network is forced to operate in a manner different from which it was initially designed. The power analysis includes estimation of the current power flows and bus voltages (power flow analysis and state estimation), reducing power costs (Optimal Power Flow) and determining the stability limits of the system (Numerical Integration for Transient Stability, Continuation Power Flow, and Eigenvalue Analysis). The electric power sector has adopted the use of computer technology and has become one of the first industries to embrace the potential of computer analysis after mainframes became available. Today, computer simulation is important in control and security assessment as electric power systems increasingly operate under stressed conditions. However, there is frequent failure or providing of erroneous results when commercial packages are used to simulate stressed systems. It is hence essential to understand the underlying numerical algorithms so as to interpret the outcomes of commercial packages correctly. Many complex computational simulations of the power system network have been developed so as to accomplish both operation and planning. Computational tools are essential in maintaining a reliable and secure operating environment. The different computational algorithms were developed around the requirements of power system operation. The primary algorithms that get used today in electric power system include the power flow (also known as load flow), optimal power flow (OPF) and also state estimation. These algorithms are all steady state algorithms and are developed from the same basic approach of addressing the nonlinear power balance equations. These specific algorithms do not explicitly regard the consequences of time-varying dynamics on the power system. The fields of transient and dynamic stability need a great number of algorithms that are largely different compared to the power flow based algorithms.

Power flow

The central principle of a power flow problem is that given the system loads, generation and network configuration, the system bus voltages and line flows can be determined by addressing the non-linear power flow equations. It is typically achieved by applying Kirchhoff’s law at the power system buses throughout the electric system. Power gets comprised of two elements namely active power and reactive power; therefore all the buses provide rise to two equations – one for active power and the other for reactive power. These equations of power flow are known as power flow equations.

Where is the active power and is the reactive power that will be injected at the bus i. The values of Vi and Vj are the voltage magnitudes at bus i and bus j respectively. The values of  and  are the corresponding phase angles. The constant N in the equation denotes the number of buses in the power system.

Power flow studies are crucial in planning and designing the future expansion of power systems. Power flow studies provide steady state solutions of the voltages at all the buses, for a specific load condition. Varying steady state conditions can be acquired for varying operating conditions so as to assist in planning, design, and operation of the electric system (Rao, 2010).

All power companies commonly use a power flow program that determines this power flow for planning and operation. The power flow calculations are often undertaken on the bulk power system, where the impact of the secondary underlying network is implicitly included. The determination of power flow requires that the measurements of various power system conditions. The knowledge of power flows and voltage levels under the normal operating conditions of a power system are necessary for determining fault currents if a line was to short-circuit. If all the bus voltages concerning their magnitudes and phase angles were measured with confidence, then the power flow calculations could be performed by solving the linear circuit in which voltages and branch impedances.

Optimal Power Flow (OPF)

The OPF is used in the electric power system to determine the values of the electric system state variables and parameters that reduce some cost function of the power system. The kind of cost functions are system dependent and can range significantly from application to another application and are not necessarily strictly measured in dollars. The basic formulation of the OPF is represented as reducing the cost function subject to all physical or operational constraints of the system.

The OPF problem focuses on the formulation of the power flow problem so as to determine the system voltages and generated powers within the framework of the objective function (Rao, 2010). The inputs of the power flow in this application get adjusted in a systematic manner so as to maximize or minimize a scalar function of the power flow state variables. The most common objective functions of the OPF are the maximization of generating costs and reduction of active power losses. The time frame of the OPF is on the order of minutes to an hour; hence get assumed that the optimization takes place employing only those units that are currently on-line. The decrease of active transmission losses saves both the generating costs and establishes a higher generating reserve margin. 

State Estimation in Electric Power Systems

State estimation for electric power transmission grids was formulated by Fred Schweppe in 1969 as a weighted least squares problem. A state estimator is an underlying part of all the control centers. The fundamental motivation for state estimation is that the execution of computer analysis of the electric network system is done under the conditions characterized by the current set of measurements. In a majority of physical systems, the system operating condition cannot get determined directly by an analytical solution of known equations using a provided set of known, dependable quantities.  The system operating condition is usually determined by measuring the system states at varying points throughout the system. In many electric systems, more measurements get performed so as to find the operating point uniquely. This redundancy is purposely designed into the system so as to counteract the consequences due to inaccurate or missing data caused by instrument failure. In the event of missing states in a system, there must be estimation from the others that have been measured. The process is called state estimation and is the process for the estimation of unknown states from measured quantities. State estimation provides the “best estimate” of the state of the electric system. A proper estimate will smoothen out small random errors in measurements, detest as well as identify huge measurement mistakes and also compensate for missing information (Idema & Lahaye, 2014).

Conclusion

 Power system computation methods have evolved significantly over the past few years and have attained a high level of sophistication and maturity and assist in solving electric power system problems. Some of the paramount computational techniques in the electrical system include the power flow, OPF, and state estimation.

References

Crow, M. L. (2015). Computational methods for electric power systems. Crc Press.

Idema, R., & Lahaye, D. J. (2014). Computational Methods in Power System Analysis. Atlantis Press.

Rao, K. U. (2010). Computer Techniques and Models in Power Systems. IK International Pvt Ltd.

Sherry Roberts is the author of this paper. A senior editor at MeldaResearch.Com in write my essay online if you need a similar paper you can place your order from write my essay for me services.