CC BY
1УДК 621.317
Ibrahimov J.A.
Lecturer, Department of Electrical Power Engineering, Azerbaijan State University of Oil and Industry (Baku, Azerbaijan)
DYNAMIC MODELING AND CONTROL STRATEGIES FOR RENEWABLE ENERGY INTEGRATION IN POWER SYSTEMS
Аннотация: the integration of renewable energy sources into power networks brings operational changes and affects system stability. Analyzing operation adjustments is vital for managing increased variable generation. This study focuses on dynamically modelling and integrating solar PV and windpower systems into a transient stability analysis toolbox. By developing high-level control functions for converter interfaces, the study ensures compliance with grid operation standards. Testing these functions on a network confirms their capability to support grid stability. Simulation results show that the proposed control functions offer features comparable to synchronous generators for renewable energy generators.
Ключевые слова: renewable energy sources, dynamic modelling, transient stability
analysis.
Introduction. Alternative energy derived from variable renewable sources, notably solar photovoltaic (PV) and wind power, is widely acknowledged for its potential in advancing future low-carbon energy systems. Recent trends underscore a significant increase in global installed capacity from such sources in recent years. However, the integration of variable renewable energy into existing power networks presents substantial operational challenges. Primarily, the dependence of these energy sources on weather conditions renders their output variable and highly unpredictable. This variability manifests as continuous fluctuations in generated power, complicating grid management.
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Moreover, the connection of variable renewable energy generators to the grid typically involves converter interfaces rather than conventional synchronous machines. Unlike synchronous machines, which contribute to system inertia and facilitate damping during disturbances, power electronic converters used in renewable energy sources lack inherent inertia provision. Consequently, replacing conventional generators with more variable counterparts results in reduced system inertia, potentially exposing the power system to abrupt disturbances [1-2].
Additionally, the predominant connection of variable renewable energy generators at the distribution level poses regulatory challenges for maintaining voltage profiles within acceptable operating limits. These operational complexities necessitate enhanced requirements in the power system analysis process. Consequently, there is a growing imperative for dynamic modelling of renewable energy sources and their associated control systems to incorporate them effectively into overall system stability analyses. This has spurred significant research and industrial efforts to address the representation of renewable energy resources as inverter-based sources in system stability studies [3].
Photovoltaic solar power system. The PV generation system in this study employs a single-stage conversion system (sFig. 1). PV components are categorized into steady-state and dynamic models due to their differing response times. Steady-state models address long-term effects, encompassing variables such as PV array power production and maximum power point tracking (MPPT), influenced by variations in solar radiation and cell temperatures. As the focus of this paper is on short-term transient behavior, long-term steady-state PV component models are excluded.
Figure 1. Single-Stage Conversion PV Interface Topology with GSC.
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In developing dynamic models, longer-term variables like solar radiation and maximum power point are assumed constant during the system dynamics study period, adhering to the time-scale separation principle based on singular perturbation theory. This simplification treats the PV array model as a constant power source, with power values determined during initialization from steady-state calculations.
DC-link model for PV System. In this paper, the DC-link serves as the intermediary between the PV array and the inverter. As a result, the input power (Pdc) to the inverter is equivalent to the output power of the PV array (Ppv), which coincides with the maximum power point (Pmpp) [4,5].
Pac Pinv Pdc Pmpp Ppv (1)
where Pac signifies the inverter's active output power, and Pinv denotes the input power to the inverter. The dynamic behavior of the DC link voltage is determined by the relationship between the input power (Pdc) and the output power (Pinv) of the DC link.
dUdc _ Pdc-Pinv (2)
dt _ CdcUdc ( )
Equation (2) defines Udc as the DC-link voltage, where Cdc represents the capacitance of the DC-link. The dynamic characteristics of the inverter's DC side are influenced by the regulation of the inverter's active current.
Wind energy generation system. Common configurations in wind power systems include fixed-speed wind turbines with squirrel cage induction generators, variable-speed wind turbines with doubly fed induction generators, and variable-speed wind turbines with direct-drive synchronous generators. Figure 2 illustrates a generic depiction of the generator system interfacing with the AC network.
IS
Rcctificr Inverter
Figure 2. A diagram depicting a wind energy generation setup comprising a wind turbine, synchronous generator (SG), and a fully rated converter system.
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Model of the synchronous generator. The synchronous generator model utilized in this study is a permanent magnet synchronous generator (PMSG). This particular choice offers the distinct advantage of obviating the necessity for a DC excitation system and slip rings, consequently leading to decreased losses and reduced maintenance requirements. The dynamic behavior of the PMSG is delineated by equations (3,4) [6].
uds = —R s ids — ws^qs +
' - D ■ I ^ddqs (3)
uqs — —R s Iqs — ws¥ds + """T-
f^ds — — Lds ids + ^pm (4)
I ^ds — — Lqs iqs
Equations (3) define the stator voltage in the rotor flux reference frame, with uds and uqs as stator terminal voltage components, and ids and iqs as stator current components along the d- and q-axis. Rs represents stator resistance, and ® s denotes the generator's electrical angular speed. Additionally, equation (4) provides expressions for the d and q stator flux linkages, y ds and yqs, where Lds and Lqs represent corresponding d and q stator leakage inductances, and ypm stands for the permanent magnet flux leakage [7-10].
Control of the converter on the generator side. The generator-side converter is represented as a fully controllable active pulse width modulated (PWM) insulated-gate bipolar transistor (IGBT) converter. However, in this study, analysis is conducted under fundamental frequency assumptions, neglecting the high-switching frequency of the IGBTs based on the time-scale separation principle. Consequently, an average model is employed for the generator-side converter.
A full torque control strategy is implemented in the converter, where the total stator current is induced in the q-axis of the stator while the d-axis current is maintained at zero to maximize torque generation, as expressed in equation (5). Fig. 3 illustrates the separation of converter control into d- and q-axis current loops.
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Te = 3 р[Фрш + (Lq — Ld )ids]iqs (5)
Ki and Kp represent the integral and proportional gains of the proportionalintegral controller in the respective control loops, with xd and Xq being the associated state variables. The signals iqr and idr from the q- and d-axis control loops regulate the PWM IGBTs of the rectifier.
Figure 3. Control strategy for the generator-side converter (a) Regulation of q-axis current with maximum power point tracking (MPPT), (b) Control of d-axis current with zero direct-axis current reference (Id, ref)
In Fig. 3, ® sCruds and ® sCj-uqs are termed as feedforward elements, compensating for the cross coupling between the d- and q-control loops resulting from the current transformation from the network reference frame to the rotating reference frame.
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Evaluation of model integration. In this section, simulation results are presented to demonstrate the dynamic response and grid support capabilities of the proposed models. Figure 4 depicts the structural layout of the network with modified generation, integrating renewable energy generators for experimental evaluation.
Gen S Om I
Figure 4. Structural layout of the network with modified generation, integrating renewable energy generators for experimental evaluation.
The original network comprises 16 generators, 68 buses, and 35 loads. In the initial test scenario, the effectiveness of control functions for grid support is assessed. This involves modifying the network by substituting two synchronous generators with photovoltaic (PV) and wind power generators. Specifically, a PV generator is linked to bus 5, while a wind power generator is connected to bus 9. The subsequent test case focuses on evaluating changes in system robustness. Here, 4 synchronous generators are replaced by renewable energy generators within the adjusted network. Given the objective of analyzing the interaction between renewable energy generators and the network, the connected generators are treated as equivalent representations of aggregated generators in a PV solar park and wind farm.
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Evaluation of grid support capabilities. Initially, the photovoltaic (PV) and wind power generators are interconnected without network support functions during fault conditions. In this setup, the renewable energy generators are configured to disconnect from the network when a fault occurs [11-13]. A three-phase short circuit fault is simulated on bus 95 at time t = 1.2 s and is resolved after 150 ms. The voltage response of selected generator buses following the fault is depicted in Figure 4. It is noteworthy to observe the voltage response on bus 5 and bus 9, connected to the PV and wind generators, respectively. At the onset of the fault, the voltage magnitudes at buses 5 and 9 are 79.6% and 91.4% of the nominal voltage, respectively. After the fault is cleared, these values change to 79.3% and 91.2%, respectively. Subsequently, the behavior of the DC side of the inverter following the fault is analyzed. For clarity, the inverter control strategy is adjusted to set the active power of the generators to zero during the fault. Figure 5 illustrates the computed power at both the DC and AC sides of the generators. The corresponding response of the DC-side voltage is depicted in Figure 6.
_ —
— BusS ■ Busti - Bus7 -BusS Bus1)
1 1.2 1.4 1.6 1.8 2
Time [s|
Figure 5. Voltage behaviour at bus during fault without grid support functionality.
As the wind generator incorporates a protective component within the DC link, the DC-side voltage is managed within the boundaries of the link capacitor by dissipating surplus power through the braking chopper. This mechanism facilitates the regulation of both the generated power and the angular rotational speed of the wind generator, as illustrated in Figures 7 and 8, respectively. This stands in contrast to a
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scenario where the braking chopper is absent in the DC link . Figure 5 displays the power dissipated in the braking chopper [14-15].
Figure 6. The behavior of AC and DC power during fault conditions with zero active power injection.
The responses depicted in Figures 7 and 8 highlight the capability of the braking chopper to enable the wind power generator to maintain optimal operating conditions following a fault, which is critical for fault ride-through (FRT) capability.
Figure 7. The DC-side voltage response during fault conditions in zero-current mode.
At the conclusion of the fault event, the DC power is regulated to the maximum power point (MPP) value, while the AC power is adjusted to restore the DC-side voltage to its nominal value, as shown in Figure 6. In a subsequent test, the
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functionality of active power reduction is assessed by simulating a load change equivalent to 10.5% of the total active power at t = 1.2 s . Figure 9 illustrates the resulting frequency response in the system, indicating a rise in system frequency to a stable value of 50.44 Hz following the reduction in electrical power.
Figure 8. Output power of the wind Figure 9. Mechanical angular velocity of turbine generator the wind turbine generator
The corresponding reduction in the active power output of the inverter-connected generators is displayed in Figure 10. As described in the implemented control function, the active power reduction is triggered when the system frequency exceeds a predefined threshold value (in this case, 50.2 Hz).
'0 2 4 6 8 10
Time [s]
Figure 11. Reduction in active power by the inverter-connected generators after a load change.
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In this scenario, both generators reduce their active power injection by 10% of the value at 50.2 Hz. For comparison, the frequency response without active power reduction is also depicted in Figure 9, showing a constant frequency value of 50.47 Hz. This underscores the role of the active power reduction function of the inverter in regulating system frequency.
Conclusions.
This paper outlines the dynamic modeling and integration of solar PV and wind power generation systems within time-domain simulations of power systems. Emphasizing the converter dynamics, the models focus on their pivotal role in the interaction between renewable generators and the power grid. A key contribution lies in developing converter functions aligned with grid standards to enhance network support capabilities in generic transient stability models. Implemented and evaluated using a transient stability analysis toolbox, simulations demonstrate that compliant renewable sources bolster grid stability. The control functions of interfacing converters endow renewable energy systems with functionalities akin to synchronous generators.
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