Magnitude And Frequency Of Generated Voltage Engineering Essay

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The wind energy is the fast growing energy in the world and is inexhaustible energy source. It has served mankind well for many centuries by propelling ships and driving wind turbines to grind grain and pump water. Small scale wind electrical power generation systems have recently attracted a lot of attention because they are cost effective, environmentally clean and safe renewable power sources compared to fossil fuels and nuclear power generation [1], [2]. Wind energy source is one of the prominent energy sources. Different types of electrical generators such as permanent magnet synchronous generators, asynchronous generators in squirrel cage and wound rotor construction [3]-[6] and reluctance generators [7] have been reported in standalone applications. In the literature for small scale wind power generation, a self excited induction generator (SEIG) is a most suitable where the external power supply is not available because of its rugged construction, low cost, mechanical simplicity, less maintenance, better transient performance and high power density (W/kg) [3], [4]. SEIGs are driven by fixed speed wind turbine; the frequency variation of the generated voltage is negligible [12]. However to produce more power, SEIGs are driven by variable speed wind turbine. In variable speed wind turbine driven SEIG, the magnitude and frequency of the generated voltage depends on the wind speed, the excitation capacitance value and the load.

To control the voltage at the generator terminals under varying wind speed and load conditions reactive power compensators are necessary [10]. In order to control the voltage and frequency at the generator terminals under varying load and speed conditions voltage source converter is proposed [11]. In the present work, Inverted sine carrier pulse width modulation based impedance source converter is proposed. The advantage of using ZSC is that there will not be a shoot through fault, when two switches of the same leg are turned on simultaneously and dead time compensation is not necessary. The proposed ZSC needs less filtering requirements than single capacitor or inductor used in traditional converters [9]. ISCPWM provides higher fundamental voltage without lower order harmonics [8].

Proposed Wind Generator System

Fig.1. shows a schematic diagram of wind turbine driven three-phase SEIG, delta connected capacitor bank, ZSC along with battery and load. In this system a delta connected capacitor bank is connected across the generator terminals such that generator develops the rated terminal voltage at no load. The additional demand of the reactive power is met by the controller. The proposed controller is having bidirectional power flow capability of active and reactive powers and it controls the voltage by controlling the reactive power while the frequency is controlled by controlling the active power. The basic principle of operation is that, when the wind speed is high the generated power is high and accordingly for frequency regulation the total generated power should be consumed otherwise difference of mechanical and electrical power is stored in the rotating components of the generator and by which the speed of the generator and in turn it increases the output frequency.

Therefore, this additional generated power is used to charge the battery to avoid the frequency variation as stated above. During deficiency of the generated power, when there is an insufficient wind power to meet the consumer demand an additional required active power is supplied by the battery to the consumer loads. In this manner, the battery energy storage system based voltage and frequency controller also provides voltage and frequency regulation and harmonic elimination. The model of the proposed system has been developed and has the following components.

II.1. Modeling of the wind turbine

The mechanical system consists of a wind turbine and gear. The gear ratio is selected such that the SEIG generates the rated voltage at rated frequency and a rated wind speed of 12m/s to extract the maximum power from the wind turbine. The aerodynamic power generated by the wind turbine can be expressed as

Where Pwind wind power

 - Specific density of air (kg/m3)

A - Area of blades (m2)

- Power coefficient of the wind turbine

V - Wind speed (m/s)

- depends on the tip speed ratio  of the wind turbine and β angle of blades.

II.2. Modeling of Self Excited Induction Generator

The electrical system consists of SEIG with excitation capacitor and load. The SEIG model is established using rotating (d, q) field reference [13]. Stator and rotor voltage equations are given by

Electromagnetic torque is expressed as a function of d and q axes stator and rotor currents


Vsd ,Vsq , Vrd and Vrq are the direct and quadrature axes stator and rotor voltages.

Rs and Rr are the stator and rotor resistances.

isd , isq ,ird and irq are the direct and quadrature axes stator and rotor currents.

sd , sq , rd and rq are the flux linkages and is the angular velocity.

Lm - Mutual inductance.

II.3. Modeling of ZSC

The ZSC consists of an impedance network along with voltage source converter which is shown in fig.1. The impedance network has split inductor L1 and L2 and capacitors C1 and C2 are connected in X shape [9].The advantage of using ZSC is that it utilizes shoot through states to boost up the battery voltage by gating on both the switches of the same leg during low wind speeds.

The ac voltage across the converter is Where M- modulation index

B- Boost factor.

The dc voltage across the battery is

Where Vln- rms line voltage.

The battery rating is chosen such that it should withstand varying wind speed and load conditions.

Control Strategy

The control strategy of the proposed controller is based on the generation of three-phase reference source currents having active and reactive components. One is in phase or active power component while other one is in quadrature or reactive power component for regulating the frequency and voltage respectively.

For generating the active power component of reference source current, the output of the frequency Proportional-Integral (PI) controller is compared with the rated generator current (IG) and the difference in these two currents is considered as amplitude of in-phase component of reference current. The multiplication of amplitude of in-phase component of reference current with in-phase unit amplitude templates (ua ,ub and uc) yields the in-phase component of reference source currents. These templates (ua ,ub and uc) are three-phase sinusoidal functions, which are obtained by dividing the AC voltages va, vb and vc by their amplitude.

The rated current of the generator is calculated as

Where Prated and Vrated are rated power and rated line voltage of the SEIG. The instantaneous line voltage at the generator terminals (va ,vb and vc) amplitude is computed as

The unity amplitude templates are having instantaneous value in phase with instantaneous voltage (va ,vb and vc) which are derived as

To generate the quadrature component of reference source current, another set of sinusoidal quadrature quantity amplitude unity template (Za ,Zb and Zc) is obtained from in-phase unit templates (ua ,ub and uc). The multiplication of these components with output of AC voltage PI controller gives the quadrature or reactive power component of reference source current.

za ,zb and zc are another set of unit templates having a phase shift of 90° leading with the corresponding unit templates ua ,ub and uc which are computed as follows

Total reference source currents are the sum of in-phase component and quadrature components of the reference source currents as

Reference source currents (i*sa, i*sb and i*sc) are compared with sensed source currents (isa, isb and isc). The current errors are computed as

These current errors are amplified and the amplified signals are compared with fixed frequency (6 KHz) inverted sine carrier wave to generate gating signals for IGBTs of ZSC.

Inverted sine carrier PWM

The control scheme uses a high frequency inverted sine carrier PWM as shown in Fig.2.

It helps to maximize the output voltage for a given modulation index. For the ISCPWM pulse pattern, the switching angles may be computed as the same way as sinusoidal pulse width modulation technique. The equations of inverted sine wave are given by (21) and (22) for its odd and even cycles respectively. The switching angles for ISCPWM scheme can be obtained from (23) and (24).

Where Ma - Modulation index

Mf - Frequency ratio

qi - Intersection between the inverted sine


Simulation Results

The proposed system has been modeled and the simulated waveforms of the load voltage, frequency, source current, load current, excitation capacitor current, ZSC current, wind speed and battery voltage is presented for different wind speed conditions. Fig.3a-3h. show the performance of the controller for the varying wind speed conditions at constant load. A 7.5KW, 415V, 50Hz asynchronous machine is used as a SEIG. At 1.8 s, the wind speed is 12 m/s and the consumer load (5kW) is applied at the generator terminals.

It is observed that, to meet the load demand during low wind speed an additional load power is supplied by the battery to regulate the frequency. At 2s the wind speed is raised from 12m/s to 13m/s, output power of the generator and current is increased. The power supplied by the battery is reduced because the load demand is met by the generator itself and the battery is charging due to the availability of excess power. At 2.5s the wind speed is reduced from 13 m/s to 11m/s, the output power of the generator and current is decreased. The generator cannot meet the load demand and the additional power is supplied by battery and is discharging. Fig. 4. Shows the total harmonic distortion of load voltage waveform. The THD obtained for the load voltage is 0.83%. The table.1 gives the lower order harmonics of the load voltage which is very low compared to conventional PWM.

Harmonic order








Fig.4. THD of load voltage


The performance of the proposed Inverted sine carrier pulse width modulated ZSC based voltage and frequency controller for standalone wind energy conversion is presented. The proposed controller is simulated in MATLAB Simulink and PSB environment. The controller has the capability to regulate the voltage and frequency under varying wind speeds. It presents a novel PWM scheme (ISCPWM) for controlling the output of an inverter to reduce the lower order harmonics. The proposed topology eliminates the risk of shoot through fault by the use of impedance components in the power converter.