Benmeziane Meriem, Zebirate Soraya, Chaker AbelkaderLaboratory SCAMRE, ENPO, Oran, Algeria

REAL TIME CONTROL OF DOUBLY FED INDUCTION

GENERATOR

This paper presents a real time simulation method of wind power generationsystem with doubly fed induction generator (DFIG) using our OPAL-RT digitalreal time simulator which is based on RT-LAB platform with the models build inSimulink.

With the ever increasing energy demand and the depleting natural resources of fossilfuels, renewable energy technologies, specifically wind power plants, have becomeone of the most popular sources of energy over the last decades. Variable speedoperation of wind turbine is usually used to provide energy with best efficiency.

Those based on doubly fed induction generators are widely used especially in highpower fields thanks to different advantages it presents namely: reducing the size ofthe converter, operating in a large game of speed, and the possibility of controllingindependently the generated active and reactive powers

A doubly-fed induction generator is a standard wound rotor induction machine.

-The stator is directly connected to the grid and the rotor is fed from a back-to-back AC/DC/AC converter set as shows .

-The rotor side converter (RSC) controls the wind turbine output power and the voltage measured at the grid side.

-The grid side converter (GSC) regulates the DC bus voltage and interchange reactive power with the grid, allowing the production or consumption of reactive power .

Block diagram of the simplified model of the GADA

The DFIG Modeling

𝑉𝑑𝑠 = 𝑅𝑠𝐼𝑑𝑠 +𝑑𝜑𝑑𝑠

𝑑𝑡− 𝜔𝑠𝜑𝑞𝑠

𝑉𝑞𝑠 = 𝑅𝑠𝐼𝑞𝑠 +𝑑𝜑𝑞𝑠

𝑑𝑡− 𝜔𝑠𝜑𝑑𝑠

𝑉𝑑𝑟 = 𝑅𝑟𝐼𝑑𝑟 +𝑑𝜑𝑑𝑟

𝑑𝑡− 𝜔𝑟𝜑𝑞𝑟

𝑉𝑞𝑟 = 𝑅𝑟𝐼𝑞𝑟 +𝑑𝜑𝑞𝑟

𝑑𝑡− 𝜔𝑟𝜑𝑞𝑟

The classical electrical equations of the DFIG in the Park frame are written asfollows

The stator flux can be expressed as:

𝜑𝑑𝑠 = 𝐿𝑠𝐼𝑑𝑠 + 𝐿𝑚𝐼𝑑𝑟𝜑𝑞𝑠 = 𝐿𝑠𝐼𝑞𝑠 + 𝐿𝑚𝐼𝑞𝑟

The rotor flux can be expressed as:

𝜑𝑑𝑟 = 𝐿𝑠𝐼𝑑𝑟 + 𝐿𝑚𝐼𝑑𝑠𝜑𝑑𝑟 = 𝐿𝑠𝐼𝑞𝑟 + 𝐿𝑚𝐼𝑞𝑟

The electromagnetic torque is expressed as:

𝑇𝑒𝑚 = −3

2𝑝 ×

𝐿𝑚

𝐿𝑟× (𝜑𝑠𝑑 × 𝐼𝑟𝑞 − 𝜑𝑠𝑞 × 𝐼𝑟𝑞)

Active and reactive power control

Direct Control

We present the regulation independent of the powers active and reactive by the machine. Itwas highlighted the link enters, on the one hand the active power and the Vqr on the otherhand the reactive power and the Vdr.

Vector oriented control stator flux

To easily control the production of electricity from wind, we will achieve an independent control of activeand reactive power by the stator flux orientation. The idea is to align along the axis of the rotating framestator flux. We therefore:

φqs =dφqs

dt=0 and consequently φds = φs.

This choice is not random but is justified by the fact that the machine is often coupled with a powerfulnetwork voltage and constant frequency, which leads to a finding stator flux of the machine. Neglectingthe resistance of the stator windings, often accepted hypothesis for high power machines: The systems ofequations can be simplified as follows:

𝑽𝒅𝒔 = 𝑹𝒔𝑰𝒅𝒔 +𝒅 𝝋𝒅𝒔

𝒅𝒕≈ 𝟎

𝑽𝒒𝒔 = 𝑹𝒔𝑰𝒒𝒔 + 𝜽𝒔 𝝋𝒅𝒔 ≈ 𝜽𝒔 𝝋𝒔

𝑽𝒅𝒓 = 𝑹𝒓𝑰𝒅𝒓 + 𝝈𝑳𝒓𝒅 𝒊𝒅𝒓𝒅𝒕

− 𝒆𝒒

𝑽𝒒𝒓 = 𝑹𝒓𝑰𝒒𝒓 + 𝝈𝑳𝒓𝒅 𝒊𝒒𝒓

𝒅𝒕+ 𝒆𝒅 + 𝒆𝜱

𝝋𝒔 = 𝑳𝒔𝑰𝒅𝒔 +𝑴𝑰𝒅𝒓𝟎 = 𝑳𝒔𝑰𝒒𝒔 +𝑴𝑰𝒒𝒓

𝝋𝒅𝒓 = 𝝈𝑳𝒓𝑰𝒅𝒓 +𝑴

𝑳𝒔𝝋𝒅𝒔

𝝋𝒒𝒓 = 𝝈𝑳𝒓𝑰𝒒𝒓

𝑪𝒆𝒎 = −𝐩 𝝋𝒔

𝑴

𝑳𝒔𝒊𝒒𝒓

The stator active and reactive power in the orthogonal coordinate system can be written:

𝐏𝐬 = 𝐕𝐝𝐬𝐈𝐝𝐬 + 𝐕𝐪𝐬𝐈𝐪𝐬𝐐𝐬 = 𝐕𝐪𝐬𝐈𝐝𝐬 − 𝐕𝐝𝐬𝐈𝐪𝐬

Under the assumption of a stator flux oriented, this system of equations can be simplified as:

𝐏𝐬 = 𝐕𝐪𝐬𝐈𝐪𝐬𝐐𝐬 = 𝐕𝐪𝐬𝐈𝐝𝐬

From the expressions of the stator flux, we can write:

𝑖𝑑𝑠 =

𝜑𝑠

𝐿𝑠−

𝑀

𝐿𝑠𝑖𝑑𝑟

𝑖𝑞𝑠 = −𝑀

𝐿𝑠𝑖𝑞𝑟

𝑃𝑠 = −𝑣𝑠𝑀

𝐿𝑠𝑖𝑞𝑟

𝑣𝑠𝜑𝑠 𝑣𝑠𝑀

Implementation of the regulation

If one looks at the relation which binds the rotor currents to the stator powers, one seesappearing the term (MV_s)/L_s . In our study, we considered that the wind-engine wasconnected to a grid of strong power and stable, therefore this term is constant. We will thus notplace of regulator between the rotor currents and the powers.

We will neglect the terms of coupling between the two axes of control because of low value of theslip. We then obtain a vectorial control with only one regulator by axis.

PI-D decoupled controller

The controller PI is simple to elaborate. Figure 3 shows the block diagram of the systemimplemented with this controller. The terms kp and ki represent respectively the proportionaland integral gains.

For the synthesis of this PI controller the pole compensation method is used. The time response of the controlled system will be fixed at τ=10ms. This value is sufficient for our application and a lower value might involve transients with important overshoots. The calculated terms are:

𝐾𝑃 =1

𝜏

𝐿𝑠 𝐿𝑟−𝐿𝑚2

𝐿𝑠

𝐿𝑚𝑉𝑠

𝐾𝑖 =1

𝜏

𝐿𝑠𝑅𝑟

𝐿𝑚𝑉𝑠

𝐼𝑟𝑑/𝑞

𝑟𝑒𝑓

𝐼𝑟(𝑑/𝑞)

𝑉𝑟(𝑑/𝑞)

𝐾𝑝 +𝐾𝑖

𝑝

𝐿𝑚𝑉𝑠

𝐿𝑠𝑅𝑟 + 𝑝𝐿𝑠(𝐿𝑟 −𝐿𝑚

2

𝐿𝑠)-

+

Real-Time simulation

Details of master and slave block diagrams respectively as implemented in RT-Lab environment.

0 2 4 6 8 10 12 14 16 18 20-2

0

2

4

6

8

10

12x 10

5

Time (s)

Active

Pow

er

(w)

Ps

Pref

0 0.5 1 1.5 2 2.5 3 3.5-2

0

2

4

6

8

10

12x 10

5

Time (s)

Re

active

Pow

er (

va

r)

Qmes

Qref

Conclusion

In this work, we have presented a real-time simulation of DFIG using RT-Lab platform and Matlab/Simulink environment for educational purpose.Also this paper is an important contribution to rapid prototyping of highPerformance induction machine controllers since real time simulations arerequired by hardware in the loop applications.

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