Modeling and Maximum Power Point Tracking Control of Wind Generating Units Equipped with Permanent Magnet Synchronous Generators in Presence of Losses
Abstract
:1. Introduction
- Defining a methodology to manage the initialization of WTG models in the presence of power system losses;
- Proposing a control scheme that allows tracking the maximum power point even in the presence of losses;
- Providing a detailed analyses on the structure of the controllers and analytical criteria to choose their parameters according to the system’s desired dynamic behavior.
2. Power System Model
2.1. Wind Turbine Model
2.2. Permanent Magnet Synchronous Generator Model
2.3. Machine Side Converter Model
2.4. Grid Side Converter Model
- RT and LT are the connection resistance and the inductance, respectively;
- ved(q) is the direct (quadrature) axis components of the voltage at the AC terminals of the GSC;
- vgd(q) is the direct (quadrature) axis components of the grid voltage and
- igd(q) is the direct (quadrature) axis components of the current flowing in the connection.
3. Initialization of Fundamental Frequency Simulations Starting from Load-Flow Calculation
3.1. Network Side Portion
3.2. Machine Side Portion
4. Application of the Proposed Initialization Procedure
- The connection between the machine and the machine side converter is characterized by resistance R = 0.05 p.u. and an inductance L = 0.05 p.u. (on the machine basis)
- The connection between the GSC and the external network has an equivalent resistance Rt = 0.005 p.u. and an equivalent inductance Lt = 0.05 p.u. (on the machine basis).
5. Fully Rated Converter Wind Generator Unit Control Scheme
5.1. Machine Side Converter Controller
5.2. Grid Side Converter Controller
6. Criteria for the Synthesis of the Wind Turbine Generator Regulators
6.1. Machine Side Converter Regulator Synthesis
- Choose a couple of parameters kPvm and kIvm;
- For any value of PWT0 belonging to the range [PWTmin, PWTmax], determine the corresponding initial working point;
- Evaluate vmd0 and vmq0 with Equations (5) and (6) having nullified the time derivatives;
- Solve Equation (42);
- Adjust the values of kPvm and kIvm s.t. for all the values of PWT0: (i) the solutions of Equation (42) have a negative real part; (ii) the solution of Equation (42) with smaller amplitude (i.e., the one that dictates the dynamic behavior of the voltage loop) is (in modulus) sufficiently smaller than the roots of Equation (30) to guarantee that the current loop is much faster than the voltage one.
6.2. Grid Side Converter Regulator Synthesis
6.3. Overall Control System Structure and Summary of the Developed Criteria
- Place the poles of the inner control loop according to Equation (30);
- Place the poles of the active power control loop zeroing the denominator of Equation (33) such that the power dynamics are sufficiently slower than the current one in order to meet Equation (31);
- Place the poles of the speed control loop zeroing the denominator of Equation (35) such that the speed dynamics are sufficiently slower than the active power one in order to meet Equation (34).
- Place the poles of the inner control loop according to Equation (30);
- Place the pole voltage control loop with the procedure described in Section 6.1.
- Place the poles of the inner control loop zeroing the denominator of Equation (47).
- Place the poles of the DC voltage control loop zeroing the denominator of Equation (49) such that the DC voltage dynamics are sufficiently slower than the current one.
- The choice of the Park reference frame such that the network voltage Vg has only a direct axis component [33] creates an algebraic link between the reactive power and the quadrature axis current; therefore, the reactive power dynamics are the same as the quadrature axis current.
7. Simulations to Validate the Controller Synthesis and the Proposed Simplified Schemes
- The poles of the machine currents loop are −27 ±45j; while the poles of the active power and of the speed loops are respectively −1.6 and −0.017 ±0.05j. With these values, the dynamics of the three loops act on different time frames, thus meeting the requirements of Equations (31) and (34).
- The poles of the grid current loops are −544 and −115, while the poles of the DC voltage one are −0.02 ±0.02j, which ensures that its dynamics are much slower than the current one.
8. Conclusions
Author Contributions
Conflicts of Interest
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Description | Value | Unit |
---|---|---|
Rated Power | 2 | MVA |
Rated voltage | 690 | V |
Stator resistance | 0.042 | p.u. |
Direct axis reactance | 1.05 | p.u. |
Quadrature axis reactance | 0.75 | p.u. |
Permanent magnet flux | 1.25 | p.u. |
Section | Variable | Initial Value with Losses | Initial Value without Losses |
---|---|---|---|
GSC | vgd0 | 1.00 p.u. | 1.00 p.u. |
igd0 | 0.80 p.u. | 0.80 p.u. | |
igq0 | 0.00 p.u. | 0.00 p.u. | |
ved0 | 1.004 p.u. | 1.00 p.u. | |
veq0 | −0.04 p.u. | −0.04 p.u. | |
MSC | vsd0 | −0.58 p.u. | −0.57 p.u. |
vsq0 | 0.76 p.u. | 0.81 p.u. | |
isq0 | 0.68 p.u. | 0.64 p.u. | |
isd0 | −0.48 p.u. | −0.47 p.u. | |
Wind | Pwind0 | 0.86 p.u. | 0.80 p.u. |
vw0 | 8.90 p.u. | 8.66 p.u. | |
ω0 | 1.14 p.u. | 1.11 p.u. |
Regulator | Symbol | Value |
---|---|---|
DC Voltage Regulator | kPDC | 10.0 |
kIDC | 2.0 s−1 | |
Active Power regulator | kpp | 4.0 |
kip | 8.0 s−1 | |
Speed regulator | kPw | 1.0 p.u. |
kIw | 0.1 s−1 |
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Bonfiglio, A.; Delfino, F.; Invernizzi, M.; Procopio, R. Modeling and Maximum Power Point Tracking Control of Wind Generating Units Equipped with Permanent Magnet Synchronous Generators in Presence of Losses. Energies 2017, 10, 102. https://doi.org/10.3390/en10010102
Bonfiglio A, Delfino F, Invernizzi M, Procopio R. Modeling and Maximum Power Point Tracking Control of Wind Generating Units Equipped with Permanent Magnet Synchronous Generators in Presence of Losses. Energies. 2017; 10(1):102. https://doi.org/10.3390/en10010102
Chicago/Turabian StyleBonfiglio, Andrea, Federico Delfino, Marco Invernizzi, and Renato Procopio. 2017. "Modeling and Maximum Power Point Tracking Control of Wind Generating Units Equipped with Permanent Magnet Synchronous Generators in Presence of Losses" Energies 10, no. 1: 102. https://doi.org/10.3390/en10010102
APA StyleBonfiglio, A., Delfino, F., Invernizzi, M., & Procopio, R. (2017). Modeling and Maximum Power Point Tracking Control of Wind Generating Units Equipped with Permanent Magnet Synchronous Generators in Presence of Losses. Energies, 10(1), 102. https://doi.org/10.3390/en10010102