# Rotor Current Feedback Based Direct Power Control of a Doubly Fed Induction Generator Operating with Unbalanced Grid

^{*}

## Abstract

**:**

## 1. Introduction

_{U}, THD

_{I}). In wind-based power generation units a commonly used power generator is the doubly fed induction generator (DFIG) [1,3]. It is a three-phase induction type generator with access to three-phase stator windings and three-phase rotor windings. In case of DFIG used in wind power plants the rotor is supplied by a back-to-back voltage converter and the stator is directly connected to the grid as it is presented in Figure 1. Due to this direct stator connection to the grid, DFIG is sensitive to voltage disturbances, which leads to distortions of stator and rotor currents as well as electromagnetic torque pulsation [4]. Control of generated power by the stator side is executed through the rotor circuit by a reduced power three-phase back-to-back (B2B) voltage power converter. The converter consists of two three-phase voltage converters, the one connected to the rotor is called the rotor side converter (RSC), whereas the other connected to the grid—the grid side converter (GSC). The main purpose of the former is to control the power generated by the stator, while the purpose of the latter is to maintain the DC-link voltage at the required reference level and sometimes also power conditioning. In the paper the main focus is on RSC, whereas in analysis and laboratory verification GSC is treated and controlled as a DC voltage source. The nominal power of the B2B converter for which it is usually designed varies from 1/4 up to 1/3 of the whole total nominal set-up power.

## 2. Materials and Methods

#### 2.1. DFIG Mathematical Model

_{s}, u

_{r}—instantaneous space voltage vector of stator and rotor respectively, i

_{s}, i

_{r}, i

_{m}—instantaneous space current vector of stator, rotor and magnetizing circuit respectively, ψ

_{s}, ψ

_{r}—instantaneous space flux vector of stator and rotor respectively, R

_{s}, R

_{r}—stator and rotor resistance respectively, L

_{σ}

_{s}, L

_{σr}—stator and rotor leakage inductance respectively, L

_{m}—mutual inductance, ω

_{m}—rotor mechanical speed scaled by the number of pole pairs.

_{s}, L

_{r}—stator and rotor inductance, respectively.

_{ir}—rotor flux rotational speed (slip pulsation).

_{em}—electromagnetic torque, p

_{b}—number of pole pairs, ψ

_{s}*—coupled stator flux space vector.

_{s}, q

_{s}—p and q component of instantaneous stator power, respectively.

_{em}

^{ref}have to be non-oscilating when torque oscillations can be calculated on the basis of external control algorithm requirements (22), (23), for example from grid operators.

#### 2.2. Direct Power Control Description

_{r}into (9) allows to build a relation which expresses rotor voltage as a function of stator side signals (24), all represented in the stationary orthogonal dq frame.

_{us}, the u

_{sq}component is equal to zero so it does not appear in relation to instantaneous power (28), (29), which can be simplified to the form given in Equations (30) and (31).

_{s}can be inserted into (26) and (27), which after factorization gives the rotor voltage control vector, which depends on the stator instantaneous power (32), (33), its d and q component respectively.

_{100Hz}) given in Figure 4. Principles of resonant controllers are given in [26,27].

_{sαβ}is calculated based on (5) and its components are filtered with a band pass filter (BPF), the resonant frequency of which is set to the grid frequency (50 Hz). Its passband width, in order to obtain fast performance, was set to 10 Hz and the gain factor was calculated in such a manner that the signal amplitude for grid frequency would be maintained, in the logarithmic scale equal to zero. In the same manner the stator voltage components are being filtered with BPF. Output signals of voltage BPF are used for calculation of stator space voltage vector angle θ

_{s}, which is next used in the control for frame transformation. Next, based on stator flux ψ

_{sαβ}, stator voltage u

_{sαβ}, reference torque T

_{em}

^{ref}and reference q component of instantaneous power q

_{s}

^{ref}, the reference stator current is calculated (20), (21). The obtained reference currents values allow to calculate the reference p component of instantaneous power p

_{s}

^{ref}according to (34). Next, the instantaneous power components flowing from the DFIG stator p

_{s}(17), q

_{s}(18) are calculated.

_{s}(17), q

_{s}(18) gives error signals, which are transformed with the stator instantaneous voltage vector to the stationary orthogonal frame connected with the stator. The control error signals oscillating with grid frequency are inputs of proportional-resonant controllers, the outputs of which are transformed with the rotor angle to the stationary orthogonal frame connected with the rotor. The obtained reference rotor voltage signals oscillate with the rotor electrical frequency but contain also a negative sequence component of frequency equal to double grid frequency reduced by slip frequency. Next, with the pulse width modulation (PWM) algorithm gate control signals are generated and sent to the rotor side converter (RSC), which controls the rotor circuit of DFIG.

_{PR}(s)—controller transfer function, k

_{I}—generalized integral (resonant part) gain, s—Laplace operator, 0—resonant pulsation, k

_{P}—proportional gain.

#### 2.3. Decoupling and Feedforward Implementation

#### 2.4. Rotor Current Signal Implementation in DPC of DFIG

## 3. Simulation and Experimental Results of the Proposed Control

#### 3.1. Simulation Results

_{m}= 2000 rpm, which is the worst condition for control due to the highest amplitude of induced in the rotor circuit negative sequence voltage connected with the asymmetrical grid voltage. The obtained results were elaborated using the MATLAB

^{®}software. The nominal parameters of the simulated DFIG are given in Table 1.

_{s}

^{ref}(23) and electromagnetic torque T

_{em}

^{ref}(22), based on which the reference stator current component is calculated (20), (21) and finally reference power signals used in DPC control p

_{s}—(34) indirectly and directly q

_{s}—(23).

#### 3.2. Laboratory Set-Up

^{®}software. The currents and voltages were measured directly by measurement equipment, whereas instantaneous power component p

_{s}and q

_{s}and electromagnetic torque T

_{em}were calculated in the microcontroller, for control purposes and in MATLAB

^{®}for unification of graphics in the paper. The DC-link voltage level for all tests was set to 150 V. Experimental tests were conducted in a laboratory placed in the city centre where most electrical loads are nonlinear. In consequence, small distortions connected with 5th and 7th harmonic are observed in the grid voltage.

#### 3.3. Experiment Results

_{ASM}, measured according to (19) was about 17%. In the case of transient–asymmetric voltage drop, the measured V

_{ASM}was about 22%. The value of V

_{ASM}was calculated as the ratio of signals after decomposition to positive and negative sequence components from the space vector voltage using the delayed signal cancelation method [30].

_{em}and instantaneous power components p

_{s}and q

_{s}are maintained constant. The DPC performance of DFIG connected to an unbalanced grid is presented in Figure 17. The control like in the case of asymmetrical grid allows to generate sinusoidal current and maintain constant electromagnetic torque operation despite grid voltage imbalance conditions.

_{em}is kept constant in a wide range of speed from sub-synchronous to super-synchronous. Figure 19 presents a transient of asymmetric voltage drop applied to basic DPC. The control is stable but significant oscillation occurs in rotor current, instantaneous stator power signals and electromagnetic torque. The pulsation is slowly decaying with time due to the natural damping introduced by coupling terms.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**Direct power control simulation results of DFIG in case of symmetrical grid voltage with no feedforward and decoupling mechanism implemented.

**Figure 8.**Simulation results of DPC in case of symmetrical grid voltage, at t = 3.5 s the feedforward and decoupling mechanism is enabled.

**Figure 9.**Simulation results of DPC in case of symmetrical grid voltage with the feedforward and decoupling mechanism. The stator current signal contains information about the rotor value.

**Figure 10.**Simulation results of DPC in case of asymmetrical grid voltage operation without the feedforward, decoupling mechanism and without rotor current information included in the control.

**Figure 11.**Simulation results of DPC in case of asymmetrical grid voltage with the feedforward and decoupling mechanism and with stator power calculated with consideration of rotor current.

**Figure 12.**Simulation results of simple DPC in case of asymmetrical grid voltage transients without the feedforward and decoupling mechanism and without included rotor current information in control. Constant speed operation, Q

_{s}

^{ref}= 0, T

_{em}

^{ref}= −12.7 kNm.

**Figure 13.**Simulation results of simple DPC in case of asymmetrical grid voltage transients with the feedforward and decoupling mechanism and with included rotor current information in control. Constant speed operation, Q

_{s}

^{ref}= 0, T

_{em}

^{ref}= −12.7 kNm.

**Figure 14.**Simulation results of DPC in case of asymmetrical grid voltage with the feedforward and decoupling mechanism and included rotor current information in control. Variable speed operation, change from sub-synchronous to super-synchronous speed, Q

_{s}

^{ref}= 0, T

_{em}

^{ref}= −9.5 kNm.

**Figure 16.**Experimental tests results of DPC in case of symmetrical grid voltage operation without the feedforward, decoupling mechanism and without information about the rotor current value included in the control. Q

_{s}

^{ref}= 0, T

_{em}

^{ref}= −19.5 Nm.

**Figure 17.**Experimental tests results of DPC in case of asymmetrical grid voltage operation without the feedforward, decoupling mechanism and information about the rotor current value included in the control, Q

_{s}

^{ref}= 0, T

_{em}

^{ref}= −19.5 Nm.

**Figure 18.**Experimental tests results of DPC during variable speed operation in case of asymmetrical grid voltage operation without the feedforward, decoupling mechanism and information about the rotor current value included in the control, Q

_{s}

^{ref}= 0, T

_{em}

^{ref}= −19.5 Nm.

**Figure 19.**Experimental tests results of DPC showing transient performance in case of asymmetrical grid voltage drop without the feedforward, decoupling mechanism and information about the rotor current value included in the control, Q

_{s}

^{ref}= 0, T

_{em}

^{ref}= −19.5 Nm.

**Figure 20.**Experimental tests results of DPC showing transient performance in case of asymmetrical grid voltage drop with the feedforward and decoupling mechanism included in the control, Q

_{s}

^{ref}= 0, T

_{em}

^{ref}= 0 Nm.

**Figure 21.**Experimental tests results of DPC showing transient performance in case of asymmetrical grid voltage drop with the feedforward, decoupling mechanism and information about the rotor current value included in the control, Q

_{s}

^{ref}= 0, T

_{em}

^{ref}= −19.5 Nm.

Parameter | Description | Value |
---|---|---|

P_{n} | Rated power | 2 MW |

U_{sn} | Stator nominal voltage | 690 V |

I_{sn} | Stator nominal current | 1760 A |

U_{r} | Rotor voltage (0 rpm) | 2600 V |

n_{z} | Stator/rotor turns ratio | 0.34 |

R_{s} | Stator resistance | 2.6 mΩ |

R_{r} | Rotor resistance | 2.6 mΩ |

L_{σs} | Stator leakage inductance | 0.087 mH |

L_{σr} | Rotor leakage inductance | 0.087 mH |

L_{m} | Magnetizing inductance | 2.5 mH |

p_{b} | Number of poles pairs | 2 |

Parameter | Value | |||
---|---|---|---|---|

time | 4.44–4.5 s | 4.5–4.6 s | 4.6–4.7 s | 4.6–4.7 s |

T_{em}^{ref} | 0 | 0 | 0 | 12.7 kNm |

q_{s}^{ref} | 0 | −2 MVAR | 0 |

Parameter | Description | Value |
---|---|---|

P_{n} | Rated power | 7.5 kW |

U_{sn} | Rated stator voltage (Δ/Y) | 220/380 V |

I_{sn} | Rated stator current (Δ/Y) | 27.4/15.7 A |

I_{rn} | Rated rotor current | 15 A |

U_{r} | Rated rotor voltage (0 rpm) | 182 V |

n_{z} | Stator/rotor turns ratio | 2.08 |

R_{s} | Stator resistance | 0.43 Ω |

R_{r} | Rotor resistance | 0.71 Ω |

L_{σs} | Stator leakage inductance | 10 mH |

L_{σr} | Rotor leakage inductance | 10 mH |

L_{m} | Magnetizing inductance | 120 mH |

n | Rated speed | 1445 rpm |

p_{b} | Number of poles pairs | 2 |

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**MDPI and ACS Style**

Pura, P.; Iwański, G.
Rotor Current Feedback Based Direct Power Control of a Doubly Fed Induction Generator Operating with Unbalanced Grid. *Energies* **2021**, *14*, 3289.
https://doi.org/10.3390/en14113289

**AMA Style**

Pura P, Iwański G.
Rotor Current Feedback Based Direct Power Control of a Doubly Fed Induction Generator Operating with Unbalanced Grid. *Energies*. 2021; 14(11):3289.
https://doi.org/10.3390/en14113289

**Chicago/Turabian Style**

Pura, Piotr, and Grzegorz Iwański.
2021. "Rotor Current Feedback Based Direct Power Control of a Doubly Fed Induction Generator Operating with Unbalanced Grid" *Energies* 14, no. 11: 3289.
https://doi.org/10.3390/en14113289