Electrical Energy Is The Vital Engineering Essay

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Background

Electrical energy is the vital ingredient for the day to day functioning of modern societies. It is required for providing the energy needed for transfer of information and communication

ete domain variables, the existence of a non convex feasible region, and multiple local minima, all make it difficult to find a suitable algorithm with the ability to pursue the global optimum with reasonable computational effort.

Problem statement

For the above problem of maximizing the wind penetration, there are different types of approaches

In particular, this research proposes instantaneous wind penetration problem which need to be made faster for online computations.

Objectives of the study

The aim of the research is to maximize the wind penetration to the grid with 3 fold objectives,

wind penetration.

Research contribution

existing grid by means of FACTS controllers have also been suggested for maximizing the wind penetration.

Scope and limitations

The scope and limitations of this research are the following

The normal operation of Power System presupposes that a number of constraint parameters are maintained with in predetermined bounds of which the most

Matlab environment using Particle Swarm Optimization Algorithm.

Structure of dissertation

This dissertation proposal report consists of 7 chapters as given below.

Literature Review

Introduction

Grid connected Wind Turbine Generators (WTGs) in large numbers can create unwanted conditions such as loss of synchronism, voltage collapse, load shedding, large deviations in voltage and/or frequency, leading to flicker and harmonics, high transmission and distribution losses, over loading and increased power oscillation[21] [22]. Grid has to be made prepared to receive maximum wind penetration [23],[24]. The unpredictable nature, of wind electricity generating source, can have an adverse impact on power system stability, which in turn needs to be maintained within reasonable limits to provide reliable of quality power supply to the consumers. The current research focuses on maximizing the wind penetration to the grid, which is having direct impact on end user per unit operating cost [25].

Most of the works done in the area of maximum wind penetration is based on stochastic analysis which depends on the annualized energy yield calculated through the capacity credit and capacity factor [26], [27]. A new computational algorithm for the calculation of maximum wind energy penetration in autonomous island of Greece was proposed by J K Kaldellis, et al in [28],[29], where the entire algorithm is based on a factor termed as the instantaneous upper wind energy penetration limit (λ), fixed by the network manager of Greek Public Power Corporation. The algorithm for λ seems to be not available and it so states that there is lot of wind energy rejection taking place due to under limiting of λ for maximum grid stability. Moreover, the algorithm is based on stochastic analysis cumulated for yearly average. Another method of maximum wind penetration was explained by Stavros A Papathanassiou in [30], where the maximum wind turbine output is limited by a constant CD, dynamic penetration limit factor; a grid constant and the value is assumed between 15 to 45% but stating normally 30%. CD selection algorithm also seems to be not available in the literature. J K Kaldellis also proposed a methodology for optimizing the Wind Power System [31], where the optimization is through a local energy storage power electronics buffer via Uninterrupted Power Supply (UPS) in WTG side and not by optimizing the grid parameters and none of the articles explains the methodology for maximizing the instantaneous wind penetration and is treated as a constant throughout the analysis.

Many researchers have made immense contributions for enhancing the wind penetration. However, no significant research focuses on the development of a good transparent methodology for increasing the instantaneous wind penetration in the grid by optimizing the grid control parameters especially based on advanced techniques such as Particle Swarm Optimization (PSO).

Stochastic analysis based on annualized energy yield requires the instantaneous wind energy absorption/rejection strategy of the concerned electricity authority for accurate analysis. Most of the prevailing approaches as per the literatures assume a constant value for Wind Acceptance Rejection factor set by concerned Electricity Authority. In the deregulated electricity market, authorities always under estimate the factor for maximum grid stability and the calculation of the factor is the trade secret of the electricity authority. Lots of wind energy rejections are taking place because of that; moreover the factor is quite time varying in nature depending on the dynamic nature of the grid and can no longer be treated as constant and hence, maximum penetration calculations based on annualized energy yield assuming a constant value of λ has got inherent limitations of inaccuracy.

For increasing the penetration, in wind penetration study [32] the load has to be adjusted in a tricky fashion to reach the maximum penetration strategy without affecting the grid stability. Accordingly, suitable optimization algorithm has to be used. Moreover, the problem requires detailed dynamic modeling of the wind and wind turbine generators.

In this chapter, the fundamentals of wind turbines with the modeling details, barriers and solutions for maximizing the wind penetration, Flexible AC Transmission Systems (FACTS) controllers and various heuristic optimization techniques are discussed.

Wind power generation

The wind is due to the uneven heating of the earth surface [33] by the sun and to tap the wind power, equipment termed as wind turbine generator (WTG) is used. The wind turbine generator is composed of an aerodynamic rotor, a mechanical transmission system, an electrical generator, a control system (including a soft-starter device), limited reactive power compensation and a step-up transformer. Figure 2.1 shows the basic components of a conventional wind turbine.

Anemometer

Wind

Blade

Controller

Shaft

Gear box

High Speed Shaft

Brakeade

Figure 2.1. Parts of a conventional wind turbine

WTGs can be classified into two categories [34] - Constant Speed Wind Turbine Generators (CSWTGs) and Variable Speed Wind Turbine Generators (VSWTGs) based on the ability to control speed and the type of power control method they use. CSWTGs do not have any device to control the speed and voltage where, VSWTG is equipped with some advanced electronic devices to control speed and voltage. Figure 2.2 shows the three types of wind turbine generators that are currently in use. One of the popular types of VSWTG is Double Fed Induction Generator (DFIG) which can be smoothly connected to the grid and can also provide reactive power compensation besides excellent speed control [35]. Moreover, studies have proved that DFIG based wind turbine does not provide any oscillatory instability problems [36]. Because of all the reasons stated above DFIG based wind turbine is considered in the current research.

Wind is air in motion. Air has mass but its density is low. When a mass (m) is moving with a velocity v (m/s), it is having a kinetic energy (KE) given by KE = 0.5mv2. If the density of the flowing air is ρ (kg/m3), the KE per volume of air is given by KEv=0.5ρv2 (J/m3). The air flow per second through cross sectional area (A) is (m3/s). Wind power, energy per second is given by pair = 0.5 ρAv3; which is the input wind power to the WTG. The power extracted from the wind is given by Power=Cpmax(KE)(V)=0.593*0.5ρAv3.The constant Cpmax is called the Betz coefficient whose value is 16/27 = 0.593. The conversion to the electrical power is approximately (0.7)Cpmax(KE)(V) = 0.415*.0.5*ρAv3. .

Squirrel cage induction

Generator

Direct drive synchronous generator

Capacitors

Rotor

Converter

Gear BoxDouble fed induction generator

Figure 2.2. Different types of wind turbine generating systems

Table 2.1 shows the strength and weakness of various types of wind turbines. DFIG is having lots of advantages over other two types of WTGs but the only drawback is less efficient and more expensive. The dynamic nature of the instantaneous wind penetration problem requires detailed dynamic modeling of power system components including wind and turbine generators.

Table 2.1. Comparison of various types of wind turbine generators

Type of wind turbines

Constant speed

Doubly fed direct drive

Direct drive

Strengths

Simple and robust

Less mechanical stress

Less mechanical stress

efficient

Less noisy

Less noisy

Electrically efficient

Aerodynamically efficient

Aerodynamically efficient

Standard generator

Standard generator

No gear box

Small converter suffices

Weakness

Aerodynamically less efficient

Electrically less efficient

Electrically less efficient

Gearbox included

Gear box included

Large converter

necessary

Mechanical stress

Expensive

Expensive

Noisy

Heavy and large generator

Complex generator

Wind turbine control

At low wind speeds, a wind turbine [36], [37] does not generate any power at all, because the airflow contains too little energy. Between the cut-in wind speed (in the order of 3-5 m/s) and the nominal wind speed or rated wind speed, the generated power is directly dependent on the wind speed. When the wind speed increases to levels above the nominal wind speed, the generated power cannot be increased further, because this would lead to overloading of the generator and/or, if present, the converter.

Figure 2.3. Typical wind turbine generator speed power curve

Therefore, the aerodynamic efficiency of the rotor must be reduced, in order to limit the power extracted from the wind to the nominal power of the generating system.

The first way is to design the rotor blades in such a way that their efficiency inherently decreases when the wind speed increases to values above nominal. This approach is called stall power limitation or stall control. The second possibility to reduce the aerodynamic efficiency of the rotor is to turn the blades out of the wind using hydraulic mechanisms or electric motors. This approach is called pitch control. In contrast to stall control, pitch control requires active control systems to turn the blades. A combination of the two approaches is active stall control, which is sometimes used in large constant speed turbines. In DFIG machines rotor control allows for speed control of up to 25% of synchronous.

Wind generator modeling

Wind generator modeling consists of modeling of wind farm and wind turbine. Since the research is dealing with DFIG turbine, only DFIG model has been described in this study.

Weibull distribution wind model

Wind is modeled as a Weibull distribution [38] and also as a composite model [39] which includes average, ramp, gust and turbulence components. A low pass filter is used to smooth the wind time sequence generated.

The Weibull distribution is given by the equation

Equation Chapter 2 Section 1 \* MERGEFORMAT (.)

where, is the wind speed and 'c' and 'k' are constants. Time variations (t) of the wind speed are then obtained by means of a Weibull distribution as follows

\* MERGEFORMAT (.)

where, is a generator of random numbers ([0, 1]). 'k' is a constant which governs the type of distribution.

k = 2; Rayleigh distribution

k > 3; Normal distribution

k = 1; Exponential distribution

The scale factor 'c' is chosen such that ([0, 1]). Finally, the wind speed is computed by setting the initial average speed, determined at the initialization step as the mean speed.

\* MERGEFORMAT (.)

where, is the mean value of.

Composite wind model

This composite model considers the wind as composed of four parts as given below.

average and initial wind speed

ramp component of the wind speed

gust component of the wind speed

wind speed turbulence

The resultant wind speed '' at time t is written as,

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where, all the components are time dependant except for the initial average speed

Wind ramp component

The wind ramp component is defined by amplitude Awr and starting and ending times, and , respectively.,

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Wind gust component

The wind gust component is defined by amplitude and starting and ending times, and , respectively

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Wind turbulence component

The wind turbulence component is described by a power spectral density as follows

\* MERGEFORMAT (.)

where, is the electrical frequency, the wind turbine tower height, is the roughness length and is the turbulence length scale.

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The roughness values for various ground surfaces are given in the table below.

Table 2.2. Roughness length for various ground surfaces [40]

Landscape type

Roughness length [mm]

Very smooth ice or mud

0.01

Calm open sea

0.20

Blown sea

0.50

Snow surface

3.00

Lawn grass

8.00

Rough pasture

10.00

Fallow field

30.00

Crops

50.00

Few trees

100.00

Many trees, hedges, few buildings

250.00

Forest and woodlands

500.00

Suburbs

1500.00

Centers of cities with tall buildings

3000.00

The spectral density is then converted into a time domain cosine series [41] as given below

\* MERGEFORMAT (.)

where, and are the frequency and the phase angle of the ith frequency component. and frequency step Hz and is the random phase angle introduced to avoid periodicity of the turbulence signal.

Double fed induction generator model

DFIG stator is directly connected to the grid and the rotor is connected to the grid through slip rings and power electronic converter. The steady state electrical equations are used with the assumptions that stator and rotor flux dynamics are fast in comparison with grid dynamics and converter controls basically decouples the generator from the grid [42].

\* MERGEFORMAT (.)

where,

are the three phase supply voltage and current in d - reference frame

are the three phase supply voltage and current in q - reference frame

are the three phase rotor voltage and current in d - reference frame

are the three phase rotor voltage and current in q - reference frame

is the stator reactance

is the rotor reactance

is the magnetizing reactance

is the stator resistance

is the rotor resistance

The stator voltages are functions of the grid voltage magnitude and phase as given below

\* MERGEFORMAT (.)

The generator active and reactive power depends on the stator and converter currents as follows

\* MERGEFORMAT (.)

where,

are the converter voltage and current in d - reference frame

are the converter voltage and current in q - reference frame

During converter operation, the converter powers on the grid side are given below

\* MERGEFORMAT (.)

where,

Pc is the grid side active power output of converter

Qc is the grid side reactive power output of converter

whereas, on the rotor side,

\* MERGEFORMAT (.)

where,

Pcis the rotor side active power output of converter

Qcis the rotor side reactive power output of converter

Assuming lossless converter and the active power of the converter coincides with the rotor active power; (Pc = Pr) the active and reactive power injected in to the grid by the DFIG turbine is expressed as a function of stator and rotor currents (equation 2.15). The power injected in the grid can be written as,

\* MERGEFORMAT (.)

Assuming single shaft generator and converter control can filter shaft dynamics and by neglecting tower shadow effect, the simplified expression for electrical and mechanical torque is formulated in [43]

\* MERGEFORMAT (.)

where,

Te is the electrical torque.

ωb is the system frequency rate in radian per second.

The mechanical torque (Tm) is given by,

\* MERGEFORMAT (.)

where, Pω is the mechanical power extracted from the wind and is a function of pitch angle θp, rotor speed ωm, and wind speed vω.

\* MERGEFORMAT (.)

Curve is approximated by the equation given below

\* MERGEFORMAT (.)

where , \* MERGEFORMAT (.)

Since the converter dynamics is fast compared to the electromechanical transients, the converter is modeled as an ideal current source with iqr and idr as state variables. The state variables are modeled for rotor speed control and voltage control.

\* MERGEFORMAT (.)

Where is the power speed characteristic which roughly optimizes the wind energy capture and is calculated using the current rotor speed value. It is assumed that = 0 if <0.5 pu and = 1 pu, if >1 pu.

- (xS+xm)

xmV(1+STc)

ωm

iqrmin

iqrmax

iqr

Figure 2.4. Rotor speed control scheme

idrmax

V

KV

1

(1+S)

-1

xm

idr

idrminax

Vref

Figure 2.5. Voltage control scheme

Pitch Angle Control is described by the differential equation

\* MERGEFORMAT (.)

where,

∅ is a function, which allows the variation of pitch angle when the speed exceeds a predefined set point.

Pitch angle control mainly works at super synchronous speed and is locked by an anti winding limiter which locks the pitch angle (θp = 0) at sub-synchronous speed.

Kp

(1+TpS)

Figure 2.6. Pitch angle control scheme

Power flow model

The power flow problem is evaluated as the solution of a nonlinear set of equations [44] of the form.

\* MERGEFORMAT (.)

where, are the algebraic variables such as voltage amplitudes (V) and phases (θ) at the network buses and all other algebraic variables such as generator field voltages, AVR reference voltages, etc., are the state variables, are the algebraic equations and are the differential equations. is the independent variables. Algebraic equations and differentials equations are at least twice the number of buses in the network.

Newton -Raphson method

Newton Raphson algorithms for solving the power flow problem are described in many books and papers [45]. In each iteration, the Jacobian matrix (2.21) is updated and the following linear problem given in (2.22) is solved.

\* MERGEFORMAT (.)

where,

,, and and ∆x and ∆y are the variable increments

Distributed slack bus model

The distributed slack bus model is based on a generalized power center concept and consists of distributing losses among all generators [46].The model is practically obtained by including a variable and rewriting the system active power balance equation as follows

\* MERGEFORMAT (.)

Equation (2.23) is modified by adding to the Jacobian matrix the row of the derivatives of the slack bus active power balance and a column for the derivatives of the differential and algebraic equations with respect to. The additional parameter γ is also included in order to allow tuning the weight of the participation of each generator to the losses. In single slack bus model, γ = 0 for all generators.

Wind power integration

Wind turbines are special kind of generators which are having fairly less frequency and voltage control capabilities and their supply is also intermittent in nature. The power produced from the wind farm varies all the time and leads to dynamic voltage variations. Moreover the generators are mainly asynchronous, which requires reactive power for its excitation. The main problems associated with wind farm integration are the following [47].

Voltage drop across the line impedance caused by large current surges.

Slow response of the exciter due to the synchronous generator side reactive power mismatch.

Uncoordinated capacitor switching

Apart from this voltage sags/swells may be a problem when wind farm starts and shuts downs.

Large real power surges during start up of the wind power fluctuation.

Frequency run away when the wind turbine produces more power than needed.

Connection of wind farm to a weak electrical grid would cause power surge problems.

Flicker is induced by voltage fluctuations which are caused by load flow changes in the grid or fluctuations in the output power due to wind speed variations, the wind gradient and the tower shadow effect.

Islanding may occur because of accidental or intended tripping of large circuit breaker in the grid. And if turbine is running during islanding then two separate grids are in different phases and once the connection is re-established the huge current surging into the grid and the generator.

Harmonic distortion is also an issue in the case of variable speed turbines because of the presence of power electronics devices.

With the advent of modern power electronics converters with their high switching frequencies and advanced control algorithms and filtering techniques, harmonic distortion is not a principal problem now a days where as maintaining system stability is a major issue in the large scale integration of wind power. The integration at high penetration levels requires step by step redesign of power system and operation approaches subject to the power quality and stability constraints [48]. Generally speaking, the levels of wind power integration are broadly classified into two viz small scale impacts and large scale impacts

Small scale wind power integration: - the wind power installed is relatively small in magnitude and counts to few percent eg, 2% of the total energy production. In small scale integration the frequency variation is very minute and the major issue is power quality [49].

Major Problems with Wind Farm Integration

Small Scale Impacts

Power Quality

Large Scale Impacts

Power System Dynamic Stability

Reactive Power and Voltage Control

Figure 2.7. Impacts of wind farm integration

Power quality issues related to wind turbines mainly falls into three groups; voltage, frequency and electrical noise.

Large scale wind power integration: - the wind power counts for a large part of the total energy production in the power system.eg. above 10%. There are several issues arising from the large scale integration, however, the major concern is voltage stability and dynamic power oscillations [50].

The summary of the problems associated with wind farm integration are given in the Table 2.3. Regarding the power system stability issues, it is broadly classified as given below

Angle stability

transient stability

small signal stability

Frequency stability.

Voltage stability.

Table 2.3. Problems associated with wind farm integration

Integration scale

Problems

Causes

Large scale

Small scale

Steady state voltage rise

Wind speed variation

Over current

Peaks of wind speed

Protection error action

Peaks of wind speed

Flicker emission during continuous operations

Dynamic operation of wind turbines

Flicker emission during switching operations

Switching/Start up operation of generators

Voltage drop

In rush current due to switching operation of generators

Harmonics

Power electronic convert

Power system oscillations

Inability of the power system controllers to cope with the power variations from the wind farm and loads

Voltage stability

Reactive power limitations and excessive reactive power demand from the system

In general, problems with voltage and frequency controls are the major issues in wind turbine integration. One of the major concerns with the voltage instability is that the transient voltage events created on the power grid affects the performance of wind farm and vice versa. Three main aspects of wind farm that affect the transient stability are location of wind generator, generator technology and connection of wind farm to lower voltage levels. Variable speed wind generators are able to improve transient stability margins, when being equipped with low voltage ride-through capability. The integration of wind generation into sub transmission and distribution systems has a negative impact on transient stability, because the reactive contribution is highly limited due to reactive losses in sub transmission and distribution systems.

Wind powers mainly affect oscillation of a (group of coherent) generator(s) against a strong system and to a lesser extent also inter area oscillations but no significant impact on intra area oscillations. Constant speed wind turbines increase the damping of power system oscillations, whereas, their impact on the frequency varies, depending on the type of oscillation. Variable speed wind turbines increase the frequency of power system oscillation whereas, their impact on the damping is rather limited and varies, depending on the type of oscillations. Impact of wind power on power system oscillations is affected by the loading of the lines in a quantitative sense; its impact does not change qualitatively when the line loadings are varied.

Table 2.4. Grid integration problems associated with various types of wind turbines

Local impact

Type of wind turbine

Constant speed

Doubly fed

Direct drive

Changes in node

voltages

Yes compensation only possible with additional equipment eg. capacitor bank, SVC's or STATCOMs

Yes, compensation theoretically possible but dependent on converter rating

Yes, compensation theoretically possible but dependent on converter rating

Harmonics

Hardly of interest

In theory of interest, but should not be a major problem

In theory of interest, but should not be a major problem

Flicker

Important , particularly in weak grids

Unimportant because the rotor acts as an energy buffer

Unimportant because the rotor acts as an energy buffer

Contribution to fault current

Yes

Yes, but turbine is normally quickly disconnected

No, converter not capable of carrying fault current; turbine is quickly disconnected

Power system oscillations analysis may be done by model analysis complemented by dynamic simulations [51],[52]. The models analysis uses a linear representation of the entire power system and is called as small signal analysis [53],[54]. Voltage stability issues can be addressed using suitable wind turbines in the wind farms that are connected to the best suitable buses [55]. Moreover reactive power supplementary reactive power balancing devices and fast acting regulators can address the reactive power issues in a smooth and elegant manner.

The grid integration problems of various types of wind farms are given in the Table 2.4. Double fed induction generator based wind farms are reasonably stable with regard to the grid integration issues with regard to harmonics, flicker, voltage stability, fault ride through etc., and hence, have been used in this study. Active controllers compensate for the voltage and frequency variations keeping the power quality within limits. Current research is focused on large scale integration and hence, power quality, protection schemes etc are not included in this study.

Wind penetration

Penetration is the percentage of wind power in the grid. This is usually defined as the amount of wind energy delivered during a year, compared to the total electrical demand during that year. The wind power penetration in a grid is the ratio of wind power output to the load at that instant of time, also known as instantaneous penetration [56].

The impact of wind energy in the grid has been studied in terms of the capacity credit. The capacity credit of wind power has been defined as the level of conventional generation that can be replaced with wind generation [57]. Analysis of the impacts of wind penetration in Tamil Nadu grid; the most penetrated state in India through capacity factor method is explained in reference [58].

Another method is to compute the wind power generation for time periods corresponding to high systems risk hours or approximate the system Loss of Load Probability (LOLP) curve so that high risk hours receive more weight than other hours (known as risk-based methods). Time-period-based methods attempt to capture risk indirectly, by assuming a correlation between hourly demand and LOLP [59]. Most methods to assess the capacity credit of a wind power plant are based on a related reliability measure called Loss of Load Expectation (LOLE) [60]. Another approach for maximum wind potential exploitation is stochastic analysis [61].

There are a number of barriers for efficient penetration of wind power into the grid and power system have to made prepared for a particular penetration rate by overcoming these barriers [62],[63] and experience from wind farm integration on high penetration areas is given in [64] . There are wide ranges of impacts in the grid due to high wind penetration [65].

The current research is focused on achieving the maximum instantaneous safe wind penetration to the grid by adjusting the grid parameters and is solved as an optimization problem by suitable modeling.

Barriers for high wind penetration

The main historical reason limiting the wind penetration is intermittency of wind and the sufficient storage in addition to the limited grid capacity. However the main technical barriers to high wind penetration [66] are the following

Transmission limited capacity

One of the major factor that is limiting the wind penetration in the existing grid is the lack of adequate transmission capacity. Often to solve the problem, wind farm developers are asked to invest for additional transmission infrastructure development.

Security of supply power unit scheduling

Balancing power

Wind power due to its time dependent intermittent nature does not provide any guarantee of firm power generation.

Wind power time and space variability

Often wind farm generator power having high frequency of the order of the flicker emission (from 0.1 to 20 Hz)

Wind generation technical reliability

When there is sudden perturbation of the grid, mainly in the case of voltage dips, the wind farm gets disconnected leading to islanding of some part of the network. Low Voltage Ride Through Fault (LVRTF) capability of wind turbines is one of the most requested grid code.

Operational energy congestion surplus management

In a grid where diversified generation is available, a scheme should be designed to manage the surplus generation of the system with reference to the dispatch in the most economical way.

Solutions for high wind penetration

The main technical solutions already in use for maximization of wind penetration [69] are the following.

Innovative characteristics of the wind systems

Low voltage ride through fault capability

Participation in the primary frequency control

A wind turbine, with primary frequency regulation capability reduces the impact of frequency dips. Frequency flexible power electronics system can prevent the disconnection of generators from the grid when the disturbance takes place.

Wind power control and curtailment.

Wind generation aggregation dispatch centers

Additional remote reactive power control.

Maximization of wind penetration

For maximization of wind penetration [67] the following power system requirements should be satisfied.

There should be adequate back up power plants to meet the demand during the intermittency of the wind.

There must be enough power plants with fast control during high wind situations.

The system should be robust enough to withstand a surviving fault.

There should be adequate reserve covering all possible uncertainties of supply and demand.

There should be adequate transmission capacity to the transfer the wind power to the load.

It should be able to down regulate the available wind power during low power consumption.

There should be possibility of continuous control of wind power ( pitch control, storage etc)

Flexible AC transmission system controllers

IEEE defines FACTS controllers [68] as 'alternating current transmission system incorporating power electronics based and other static controllers to enhance controllability and increase power transfer capability'. The main objectives of FACTS controllers are the following.

To provide direct control of power flow over designated transmission routes.

To increase the power transmission capability of transmission networks.

FACTS controllers increase the power system performance by delivering or absorbing real and /or reactive power and hence, provide smooth and fast response to normal and abnormal conditions of the power system. FACTS controllers are generally classified into four types according to the connection and operating criteria as given below [69]

Shunt connected controllers: Static Synchronous Compensators (STATCOM) and Static Var Compensator (SVC)

Series compensated controllers: Thyristor Controlled Series Capacitor (TCSC), Thyristor Switched Series Capacitor (TSSC), and Static Synchronous Series Compensator (SSSC).

Combined shunt and series connected controllers: Thyrsitor Controlled Phase Shifter (TCPS) or Thyristor Controlled Phase Shifting Transformer (TCPST) and Unified Power Flow Controller (UPFC)

Other Controllers : Thyristor Controlled Voltage Limiter (TCVL)

The most commonly available FACTS controllers are SVC, TCSC, and UPFC and have been incorporated in this work.

Heuristic optimization techniques

There are many optimization techniques [70] that can be applied to maximum wind penetration problems. The first group is deterministic approach such as linear programming [71], Lagrangian relaxation etc and the second group is heuristic approaches such as genetic programming and particle swarm optimization. For the current case of non linear variation of loads for the determination for maximum real time safe penetration the second group of heuristic approach suits better.

In recent years, meta heuristic [72] optimization techniques have attracted much attention of power engineers due to their ability to seek for global optimum solutions for systems with complicated constraints. These methods prove to be very efficient since they do not place restriction on the shape of the function curves and other non linearity in model representation. Although, these heuristic methods do not always guarantee to find the globally optimum solution, they will provide a reasonable solution (sub optimal near global optimum) in a reasonable computational time. Various meta heuristic optimization algorithms are explained below.

Tabu search

Tabu search is a local search optimization technique with memory. Once the potential solution is obtained, it is marked as taboo and the algorithm does not search that state again. The details about the previously visited states along with a number of states are retained in the memory. This information is updated in a list called Tabu List. The definition of a state, the area around it and the length of the Tabu list are critical parameters in the design of algorithm. Two extra parameters are often used in tabu search in addition to the Tabu parameters; Aspiration and Diversification. When all the neighboring states of the current state are also included in the Tabu list, a parameter called aspiration is used, where the Tabu obstacle is overridden by selecting a new state. Diversification is the one which adds randomness to the search else that search becomes deterministic. If the search is not converging, it is reset randomly.

Simulated annealing

Annealing is a process often used in metallurgy and the simulation of the same is termed as the Simulated Annealing [74]. It is the process by which a solid is heated up to a certain temperature until it is melted into liquid and then allowed to cool by lowering the temperature. In the melting process all particles of the solid arrange and settle randomly. In a large combinatorial optimization problem, a suitable perturbation mechanism, cost function, solution space, and cooling schedule are required to find an optimal solution. One of the distinct advantages of this method is that as the system size increases, the search capability becomes more significant. Moreover, even with the smooth cost function, it is possible that the solution escape more easily from local minima to the vicinity of an optimal solution.

Evolutionary computation

Natural evolution [75] is a hypothetical population-based optimization process. Simulating this process on a computer, results in stochastic optimization techniques that can often out-perform classical methods of optimization when applied to difficult real-world problems.

Genetic algorithm

Genetic Algorithm (GA) [76] is a heuristic computation technique which is based on the natural genetics. Up to now, many different schemes of GA have been proposed. A typical implementation of GA is shown below.

Step 1) Specify maximum number of iteration, iter_max and population size, pop_size.

Step 2) Randomly generate the old population, old_pop.

Step 3) Initialize number of generation, no_gen=1.

Step 4) Compute the fitness of each individual in old_pop.

Step 5) Copy the highest fitness of individual to the solution vector, sol_vector.

Step 6) Use tournament selection method as the below process.

Initialize number of individual, no_ind=1;

Select two parents randomly.

Perform the crossover of the parents to produce two offspring.

Mutate each offspring based on the mutation probability.

Place the offspring to the new population, new_pop.

Check if no_ind<pop_size, no_ind= no_ind+1 and go to step B; else, go to Step 7.

Step 7) Replace old_pop by new_pop.

Step 8) Check if no_gen<iter_max, no_gen=no_gen+1 and go to step 4; else, go to step 9.

Step 9) Print out the sol_vector as the final solution.

Particle swarm optimization

Particle Swarm Optimization (PSO) [77] is a popular evolutionary computation to solve nonlinear optimization problems. It is very simple and robust to find the optimal solution. It exhibits some evolutionary computation attributes like initialization with a population of random solutions and search for optimal solutions by updating. The updating equation of PSO is expressed as,

\* MERGEFORMAT (.)

\* MERGEFORMAT (.)

Figure 2.8. PSO algorithm - block diagram

In the updating, a new velocity for each particle based on its previous velocity is determined by. The particle's location at which the best fitness () and the best particle among the neighbors () have been achieved. The inertia weight controls the exploration properties of the algorithm. The learning factors, a1 and a2, are the acceleration constants which change the velocity of a particle towards Pbest and Gbest. The random numbers, rand1 and rand2, are uniformly distributed numbers in range [0, 1]. Finally, each particle's position is updated by.

For the inertia weigh approach (IWA) PSO, particles are updated according to. The linearly decreasing inertia weight from the maximum value max to the minimum value min is used to update the inertia weight as

\* MERGEFORMAT (.)

where, is number of maximum iteration.

In Nero PSO the particles are trained by using the Neural Network so that the algorithm converges fast to the global optima in less number of iterations and is very much required for online applications.

Modeling tools and test systems.

The entire algorithm has been coded in MATLAB using Power System Analysis Toolbox (PSAT) [78] developed by Dr Fedrico Milano [79]. It is a MATLAB add on for electric power system analysis and control. PSAT includes power flow, continuation power flow, optimal power flow, and small signal stability analysis and time domain simulation. The main advantage of PSAT is its flexibility for command line programming and the interfacing options to different types of solvers. PSAT core is the power flow routine, which also take care of state variable initialization. Once the power flow has been solved, further static and/or dynamic analysis can be performed. PSAT supports a variety of static and dynamic components and models.

Conclusion

Maximum wind penetration calculation for a grid is certainly a difficult task. It requires dynamic modeling of wind and power system components and a suitable optimization algorithm. Moreover grid has to be prepared for maximum wind penetration in view of the barriers and solutions discussed. FACTS controllers can also be used for increasing the wind penetration at higher cost. Conventional optimization problem could not solve maximum wind penetration problem effectively. Therefore, PSO based techniques are suggested for the same in this research work.

In the next chapter, PSO based optimization algorithm is extended to basic maximum wind penetration problem to obtain the maximum safe instantaneous wind energy penetration limit.

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