Power Quality Enhancement of Remote Gas Field Generations with Smart Power Converters

: Direct power generation near gas ﬁelds offers numerous beneﬁts, including optimized economic efﬁciency and reduced environmental impact. Moreover, building on-site greenhouses emerges as a promising approach to further minimize carbon emissions and residual heat, greatly promoting resource utilization. However, such power plants generally have access to a weak grid due to their remote locations, and they also contain nonlinear local loads, such as the grow lights in the greenhouses. Consequently, the generation system is susceptible to power quality issues, manifested in overvoltage and harmonics. To address these issues, a smart back-to-back converter is employed to interconnect the gas turbine generator and the utility grid. This smart converter not only enhances power quality but also offers potential ancillary services that contribute to the dynamics of the gas generation system, such as damping low-frequency oscillation among parallel-connected generators. In this paper, three control conﬁgurations for the back-to-back converter are developed, enabling the coordinated regulation of exported active power, AC voltage, and DC-link voltage in either a grid-following or grid-forming manner. Furthermore, comparative studies are conducted to provide guidelines for selecting an appropriate control strategy that ensures stable operation under various short circuit ratios. A practical gas cogeneration system is chosen to evaluate the performance of the back-to-back converter, and real-time simulations based on RT-LAB are carried out to validate the effectiveness of the methodology.


Introduction
Fossil fuels, such as coal and oil, have served as fundamental resources for power generation, fulfilling the ever-increasing demand for energy over several decades.However, the extensive utilization of these resources has given rise to a range of problems, with the most prominent being their adverse impact on the environment, leading to air pollution and climate change [1].Meanwhile, the overexploitation of fossil fuel has also rapidly depleted reserves, causing damage to land and ecosystems [2].To address these challenges, it is imperative to proactively seek sustainable and eco-friendly solutions.One approach is to refine the extraction process of conventional fuels [3], and another involves a shift towards renewable energy sources (RESs), such as solar, wind, and hydro power [4].However, in comparison to traditional energy sources, RESs exhibit less predictability due to their intermittent nature.Consequently, conventional power plants retain their significance in contemporary power systems, serving as backup power sources to fill energy gaps during fluctuations in renewable energy production, and ensuring a consistent supply [5].Natural gas, on the other hand, as the second primary resource for electricity generation after coal [6], offers higher thermal efficiency and produces lower carbon dioxide emissions due to its minimal impurities.Nevertheless, while natural gas offers myriad benefits, certain concerns arise during its transportation process: (1) since natural gas is usually destined Energies 2023, 16, 6684 2 of 22 for sale through pipelines, the considerable cost associated with their construction and maintenance can cause an increase in electricity prices; (2) as the primary component of natural gas, methane is a potent greenhouse gas.Hence, methane leaks during compression and long-distance transportation can offset the benefits of natural gas [7].
To overcome the problems resulting from the delivery of natural gas, a realistic solution is directly applying gas to produce electricity near gas fields and constructing on-site greenhouses, forming cogeneration facilities, as shown in Figure 1.In such a system, the extracted gas is combusted to drive the turbine, which serves as the mechanical input for the generators.Furthermore, the produced electricity is primarily exported to the public grid while a portion of the power can be allocated for greenhouses functioning and local households.Additionally, byproducts from the generation, carbon dioxide (CO 2 ) and exhaust heat, respectively, can also fertilize plants and maintain the temperature of greenhouses.This innovation remarkably diminishes the environmental impacts related to gas utilization and opens the electricity market to gas producers.
while natural gas offers myriad benefits, certain concerns arise during its transportatio process: (1) since natural gas is usually destined for sale through pipelines, the conside able cost associated with their construction and maintenance can cause an increase i electricity prices; (2) as the primary component of natural gas, methane is a poten greenhouse gas.Hence, methane leaks during compression and long-distance transpo tation can offset the benefits of natural gas [7].
To overcome the problems resulting from the delivery of natural gas, a realistic so lution is directly applying gas to produce electricity near gas fields and constructing on site greenhouses, forming cogeneration facilities, as shown in Figure 1.In such a system the extracted gas is combusted to drive the turbine, which serves as the mechanical in put for the generators.Furthermore, the produced electricity is primarily exported to th public grid while a portion of the power can be allocated for greenhouses functionin and local households.Additionally, byproducts from the generation, carbon dioxid (CO2) and exhaust heat, respectively, can also fertilize plants and maintain the tempera ture of greenhouses.This innovation remarkably diminishes the environmental impac related to gas utilization and opens the electricity market to gas producers.Nevertheless, gas fields are typically far from the main load center, necessitatin the use of long-distance power lines.When transmitting generated electricity to the grid the line impedance causes a notable rise in voltage, which, in turn, leads to overvoltag issues at the gas fields and nearby communities.Simultaneously, the operation of som nonlinear appliances, such as grow lights in greenhouses and household air condition ers, introduces harmonic currents into the system, thereby deteriorating the power qua ity.These problems can potentially result in equipment damage and even power system outages, demanding urgent attention.
Being the conventional devices for enhancing power quality, the on-load tap chang er (OLTC) [8,9], voltage regulator (VR) [10], and switched capacitor banks (CBs) [11,12 are widely used to maintain the steady-state node voltages within the permissible rang while the passive filters are employed to eliminate the current harmonics [13,14].How ever, these devices lack flexibility and operate discretely [15].Thus, to achieve fast an adaptable voltage regulation and power quality improvement, the evolution of powe electronic technology has brought the thyristor-type device: static var compensatio (SVC) [16,17] and the voltage source converter (VSC)-type device: static synchronou compensator (STATCOM) [18,19] and active power filter (APF) [20,21].Further, since th control of the thyristor itself produces harmonic distortions, SVCs cannot suppress th harmonics completely [22].STATCOM and APF, on the other hand, have shown super or performance in stabilizing power quality and are broadly applied in power system where they accomplish flexible compensation for reactive power and harmonics b monitoring grid currents and voltages [23,24].
However, when dealing with the parallel generator setup in the power plant STATCOM and APF have limited contributions to the system dynamics.The presence o Nevertheless, gas fields are typically far from the main load center, necessitating the use of long-distance power lines.When transmitting generated electricity to the grid, the line impedance causes a notable rise in voltage, which, in turn, leads to overvoltage issues at the gas fields and nearby communities.Simultaneously, the operation of some nonlinear appliances, such as grow lights in greenhouses and household air conditioners, introduces harmonic currents into the system, thereby deteriorating the power quality.These problems can potentially result in equipment damage and even power system outages, demanding urgent attention.
Being the conventional devices for enhancing power quality, the on-load tap changer (OLTC) [8,9], voltage regulator (VR) [10], and switched capacitor banks (CBs) [11,12] are widely used to maintain the steady-state node voltages within the permissible range while the passive filters are employed to eliminate the current harmonics [13,14].However, these devices lack flexibility and operate discretely [15].Thus, to achieve fast and adaptable voltage regulation and power quality improvement, the evolution of power electronic technology has brought the thyristor-type device: static var compensation (SVC) [16,17] and the voltage source converter (VSC)-type device: static synchronous compensator (STAT-COM) [18,19] and active power filter (APF) [20,21].Further, since the control of the thyristor itself produces harmonic distortions, SVCs cannot suppress the harmonics completely [22].STATCOM and APF, on the other hand, have shown superior performance in stabilizing power quality and are broadly applied in power systems, where they accomplish flexible compensation for reactive power and harmonics by monitoring grid currents and voltages [23,24].
However, when dealing with the parallel generator setup in the power plants, STAT-COM and APF have limited contributions to the system dynamics.The presence of multiple generators and their interactions with the utility grid make the dynamics more intricate.
In the context of the current research, back-to-back (B2B) converters are predominantly employed within the realm of wind power generation [25][26][27][28].However, there is still a relative lack of in-depth exploration regarding their application in gas power generation systems based on the synchronous generators (SG).Hence, this study is novel to incorporate the implementation of B2B converters to connect the synchronous generator to the power grid.Superior to the traditional approaches, such as STATCOM, SVC, and APF, the B2B converter not only mitigates the power quality issues but also refines the dynamics of a multi-generator system by decaying the low-frequency oscillations (LFO).Moreover, three control approaches for the B2B converter are presented, thereby further enhancing the practicality and comprehensiveness of this research.For each control strategy, the full-order state-space model is derived.Additionally, by analyzing the stability of the converter under different grid strengths [29], this research can offer guidance for selecting a proper control.Ultimately, this paper also explores the favorable influence of the B2B converter on power quality and system dynamics in detail.
The rest of the paper is organized as follows.The background is formulated in Section 2. The hardware structure and control principles of the converter are elucidated in Section 3. The enhancement in the power quality is exhibited in Section 4. The dynamics of the multi-generator system are discussed in Section 5. Further, small-signal analysis of the three control schemes is conducted in Section 6.Finally, the obtained results are evaluated in Section 7, and conclusions are summarized in Section 8.

Background
In this section, the structure and performance of an existing cogeneration power plant located at Gull Lake, Alberta are elaborated.As in the lumped model shown in Figure 2, the main feeder includes four nodes, and the electricity is provided by a 480 V/2.5 MVA gas turbine SG at Node 4. At the output terminal of the SG, a transformer is equipped to step up the output voltage from 480 V to 25 kV, and the dashed box indicates the proposed location for installing the B2B converter.It is worth noting, however, that the measurements of power quality presented below are undertaken without the integration of the B2B converter.
Energies 2023, 16, x FOR PEER REVIEW 3 of 22 multiple generators and their interactions with the utility grid make the dynamics more intricate.In the context of the current research, back-to-back (B2B) converters are predominantly employed within the realm of wind power generation [25][26][27][28].However, there is still a relative lack of in-depth exploration regarding their application in gas power generation systems based on the synchronous generators (SG).Hence, this study is novel to incorporate the implementation of B2B converters to connect the synchronous generator to the power grid.Superior to the traditional approaches, such as STATCOM, SVC, and APF, the B2B converter not only mitigates the power quality issues but also refines the dynamics of a multi-generator system by decaying the low-frequency oscillations (LFO).Moreover, three control approaches for the B2B converter are presented, thereby further enhancing the practicality and comprehensiveness of this research.For each control strategy, the full-order state-space model is derived.Additionally, by analyzing the stability of the converter under different grid strengths [29], this research can offer guidance for selecting a proper control.Ultimately, this paper also explores the favorable influence of the B2B converter on power quality and system dynamics in detail.
The rest of the paper is organized as follows.The background is formulated in Section 2. The hardware structure and control principles of the converter are elucidated in Section 3. The enhancement in the power quality is exhibited in Section 4. The dynamics of the multi-generator system are discussed in Section 5. Further, small-signal analysis of the three control schemes is conducted in Section 6.Finally, the obtained results are evaluated in Section 7, and conclusions are summarized in Section 8.

Background
In this section, the structure and performance of an existing cogeneration power plant located at Gull Lake, Alberta are elaborated.As in the lumped model shown in Figure 2, the main feeder includes four nodes, and the electricity is provided by a 480 V/2.5 MVA gas turbine SG at Node 4. At the output terminal of the SG, a transformer is equipped to step up the output voltage from 480 V to 25 kV, and the dashed box indicates the proposed location for installing the B2B converter.It is worth noting, however, that the measurements of power quality presented below are undertaken without the integration of the B2B converter.Due to the presence of greenhouses and residential areas, nonlinear loads account for a certain portion of the total electrical demand.Unlike linear loads, the voltagecurrent relationship of nonlinear loads is not constant, introducing current distortion when connected to a power system.Using the grow light as an example, it behaves as a current-controlled voltage source, or a variable conductance [30,31].Its conductance, G, can be described as (1), where i represents the lamp current, and A, B, C, and D denote the lamp model coefficients.Due to the presence of greenhouses and residential areas, nonlinear loads account for a certain portion of the total electrical demand.Unlike linear loads, the voltagecurrent relationship of nonlinear loads is not constant, introducing current distortion when connected to a power system.Using the grow light as an example, it behaves as a currentcontrolled voltage source, or a variable conductance [30,31].Its conductance, G, can be described as (1), where i represents the lamp current, and A, B, C, and D denote the lamp model coefficients.
Table 1 shows the information regarding the load distribution and power quality measurements for the generator operating at different power ratings, 1 MVA or 2.5 MVA.As the requirements from the utility company, the upper limit for node voltages is 1.03 p.u., and the total harmonic distortions (THD) must be maintained under 5% [32,33].From Table 1, it indicates that the power quality is deemed acceptable when the generated power Energies 2023, 16, 6684 4 of 22 is 1 MVA.However, as the injected power increased, the voltage at Node 4 surpassed the limit.Furthermore, the intensified usage of HVAC (heating, ventilation, and air conditioning) systems by residents and grow lights inside greenhouses leads to a substantial rise in the nonlinear loads.Since these pieces of equipment are predominantly situated at Node 4, there is a considerable load increase at this location.Table 2 provides the measurement of power quality under this scenario, with the generator operating at 2.5 MVA, and the obtained results state that Node 4 suffers from both overvoltage and unacceptable THD.As a result, from the above tests, it can be inferred that a higher output of the generator and a greater proportion of nonlinear loads result in a more drastic deterioration in the power quality.Hence, to prevent the more severe power quality issues in systems with higher power ratings, it is essential to adopt measures that effectively handle these challenges.As depicted in Figure 2, this article focuses on the utilization of B2B converters to deliver continuous enhancement in power quality, and the following section delves into the hardware configuration of this setup and develops feasible controls.

System Configuration and Control Strategies Overview
The structure of the gas generation is shown in Figure 3.In this system, the SG is interconnected to the grid through the B2B converter, where the line impedance is R 2 and L 2 .A B2B converter comprises two VSCs connected in series through a DC link capacitor, C dc .These VSCs are differentiated by their locations, with one being referred to as the grid-side VSC and the other as the generator-side VSC.To distinguish which side of VSC the variables belong to, subscripts 'grid' and 'gen' are used.On each side of the VSC, a typical three-level DC/AC converter is applied, with an LC filter (L 1 and C f ) coupled at its output terminals.The filter inductor current is symbolized as i L1 , and u c and i L2 denote the VSCs' output voltage and current, respectively.For the SG operation, the mechanical input (P m ) is provided by the gas turbine, and the generator rotation speed (w gen ) is regulated by the frequency droop or isochronous control adopted in the speed governor (GOV).Concurrently, the automatic voltage regulator (AVR) monitors the terminal voltage of the generator and adjusts the excitation system to produce appropriate field voltage (V f ), ensuring the SG maintains a stable output voltage.In this study, the IEEE ST1A model is utilized as the excitation system to regulate the SG's field current [34].
lated by the frequency droop or isochronous control adopted in the speed governor (GOV).Concurrently, the automatic voltage regulator (AVR) monitors the terminal voltage of the generator and adjusts the excitation system to produce appropriate field voltage (Vf), ensuring the SG maintains a stable output voltage.In this study, the IEEE ST1A model is utilized as the excitation system to regulate the SG's field current [34].Moreover, the converter control is realized in dq rotation frame, and they can be divided into grid-forming (GFM) control and grid-following (GFL) control.For GFL converters, they perform as controlled current sources, and the phase-locked loop (PLL) plays a critical role in synchronizing the converter with grids [35][36][37][38].Additionally, the PLL computes the appropriate phase shift for the converter current control.The outer control loop determines the dq-axis current reference while current control is implemented in the inner loop to govern the injected current, and the voltage feedforward control is usually incorporated into the output of the current controller, enhancing the dynamic performance.
Compared to GFL, a GFM converter employes voltage-based control techniques, granting it the capability to operate not only in grid-connected condition but also in island mode.When encountering severe disturbances, such as short-circuit faults, GFM control greatly bolsters the robustness of the power system [39].Additionally, during the grid-tie operation, the converter can accomplish the power exchange via controlling the voltage magnitude and angle at output terminals.Furthermore, the virtual synchronous generator (VSG) algorithm is commonly applied in GFM converters, enabling the achievement of grid synchronization through the swing equation [40,41].Further, the output power of the converters is utilized to generate the phase and magnitude of the voltage reference through active power control (APC) and reactive power control (RPC), respectively.Then, the voltage control loop cascades with the current control, regulating the output voltage to follow the voltage reference.Finally, it is also worth noting that the inner current control loop of the GFM converter is the same as that of the GFL converter.
Tables 3 and 4 present an extensive summary of control objectives for both generator-side and grid-side VSCs, along with their associated benefits.By varying the selection of control targets on both sides, a range of diverse control strategies for the B2B converter can be derived.

Generator-Side VSC Control Objectives Advantages d-axis current reference DC link voltage
During grid faults, there is no need for additional devices, such as DC choppers or energy storage units, to sustain the DC link voltage [42][43][44][45].

Active power
When connected to certain energy sources with unpredictable operating points, such as wind turbine, the output power can be appropriately controlled [46,47].q-axis current reference Typically set to 0 Enable the generator-side VSC to operate at unity power factor.Moreover, the converter control is realized in dq rotation frame, and they can be divided into grid-forming (GFM) control and grid-following (GFL) control.For GFL converters, they perform as controlled current sources, and the phase-locked loop (PLL) plays a critical role in synchronizing the converter with grids [35][36][37][38].Additionally, the PLL computes the appropriate phase shift for the converter current control.The outer control loop determines the dq-axis current reference while current control is implemented in the inner loop to govern the injected current, and the voltage feedforward control is usually incorporated into the output of the current controller, enhancing the dynamic performance.
Compared to GFL, a GFM converter employes voltage-based control techniques, granting it the capability to operate not only in grid-connected condition but also in island mode.When encountering severe disturbances, such as short-circuit faults, GFM control greatly bolsters the robustness of the power system [39].Additionally, during the grid-tie operation, the converter can accomplish the power exchange via controlling the voltage magnitude and angle at output terminals.Furthermore, the virtual synchronous generator (VSG) algorithm is commonly applied in GFM converters, enabling the achievement of grid synchronization through the swing equation [40,41].Further, the output power of the converters is utilized to generate the phase and magnitude of the voltage reference through active power control (APC) and reactive power control (RPC), respectively.Then, the voltage control loop cascades with the current control, regulating the output voltage to follow the voltage reference.Finally, it is also worth noting that the inner current control loop of the GFM converter is the same as that of the GFL converter.
Tables 3 and 4 present an extensive summary of control objectives for both generatorside and grid-side VSCs, along with their associated benefits.By varying the selection of control targets on both sides, a range of diverse control strategies for the B2B converter can be derived.

Generator-Side VSC Control Objectives Advantages d-axis current reference DC link voltage
During grid faults, there is no need for additional devices, such as DC choppers or energy storage units, to sustain the DC link voltage [42][43][44][45].

Active power
When connected to certain energy sources with unpredictable operating points, such as wind turbine, the output power can be appropriately controlled [46,47].

q-axis current reference
Typically set to 0 Enable the generator-side VSC to operate at unity power factor.

Active power
The active power injected to the grid can be accurately regulated [50,51].
q-axis current reference

AC voltage magnitude
Grid-side VSC can regulate the output AC voltage [52,53].

Grid current
The power factor of the output power is controllable [54,55].

Grid-forming (GFM)
dq-axis current references AC voltage Empowered by GFM control, power generation systems can seamlessly transition between grid-connected and islanded modes while emulating virtual inertia to stabilize frequency [56,57].
Evidently, the application context also imposes some constraints on the design of control strategies, such as addressing the overvoltage issues in the gas generation system, where the grid-side VSC must regulate the AC voltage magnitude at the point of common coupling (PCC).Based on the above discussion, three feasible strategies are listed in Table 5. Figure 4 shows the control diagrams for both sides of VSCs, where '*' indicates the reference values; variable 'X' represents the inductor current (i L1 ), output current (i L2 ), or output voltage (u c ), and 'VC' or 'CC' stands for voltage or current control loop.Similar to Figure 3, subscripts 'grid' and 'gen' are used to identify if variables belong to either grid side or generator side, and the subscripts d and q denote the variable in respective axes.S1 shows the scheme of the GFM control, where the output active power (P grid ) and reactive power (Q grid ) of the converter are used to generate the phase angle (θ grid ) and voltage magnitude (V) of the voltage reference.Further, the orange highlighted portion expresses the swing equation used for the grid synchronization.Then, the voltage control loop (VC) employs the proportional-integral (PI) and feed-forward control to set the current reference.The inner current control loop (CC) precisely regulates the grid current based on the obtained reference, and the output of the CC is used to modulate the switching signals of the converter.Contrarily, S2-S5 belongs to GFL controls, where synchronization with the grid is achieved via the PLL.The principle of the PLL is illustrated within the gray highlighted area, where the outer loops employ the PI controllers to generate the reference of the dq-axis current.By regulating real power or DC voltage, the d-axis current reference (i L1d * ) is determined.Additionally, the q-axis current reference (i L1q * ) of the grid-side VSC is set by AC voltage control, while the generator-side VSC keeps it at zero.Then, these current references serve as the setpoints for grid current regulation within the CC.All hardware and controller parameters are given in Appendix A.

Power Quality Improvement
To demonstrate the enhancements in power quality brought about by the B2B converter, real-time simulations are conducted using the OPAL-RT platform.The setup details of this platform are provided in Figure A1.Recall Table 2 in Section 2: in the case of high-power generation and large portion of nonlinear loads, the voltage profile and THD of Node 4 exceed the permissible limits.Therefore, Figure 5 presents the voltage

Power Quality Improvement
To demonstrate the enhancements in power quality brought about by the B2B converter, real-time simulations are conducted using the OPAL-RT platform.The setup details of this platform are provided in Figure A1.Recall Table 2 in Section 2: in the case of high-power generation and large portion of nonlinear loads, the voltage profile and THD of Node 4 exceed the permissible limits.Therefore, Figure 5 presents the voltage waveforms of Node 4 in both the presence and absence of the B2B converter, providing evidence of the improvement in power quality.According to the collected results, they demonstrate that the node voltage is less distorted and maintained approximately at 1 p.u. after the B2B con- verter is connected to the system, highlighting the converter's effectiveness in enhancing power quality.Finally, Table 6 summarizes the performance of various control strategies.
Energies 2023, 16, x FOR PEER REVIEW 8 of 22 waveforms of Node 4 in both the presence and absence of the B2B converter, providing evidence of the improvement in power quality.According to the collected results, they demonstrate that the node voltage is less distorted and maintained approximately at 1 p.u. after the B2B converter is connected to the system, highlighting the converter's effectiveness in enhancing power quality.Finally, Table 6 summarizes the performance of various control strategies.By comparing outputs with the scenario where the generator is directly connected to the grid, it can be found that the B2B converter can suppress the overvoltage by regulating the reactive power and alleviate the voltage distortion by compensating for harmonics.Consequently, the existing power quality issues can be effectively resolved, and the feasibility of the proposed power electronic solution has been verified.Additionally, the B2B converter also offers prospective benefits for multi-generator systems, and more details will be explored in the upcoming section.

The Enhancement of Multi-Generator System Dynamics
Because of the power constraints of a single generator, in gas power generation, it is highly practical to employ multiple generators operating in parallel.This configuration not only enlarges the total power output [58] but also provides redundancy and backup capabilities to handle potential faults or maintenance situations, thereby improving the system reliability.However, directly connecting multiple generators to the grid worsens  By comparing outputs with the scenario where the generator is directly connected to the grid, it can be found that the B2B converter can suppress the overvoltage by regulating the reactive power and alleviate the voltage distortion by compensating for harmonics.Consequently, the existing power quality issues can be effectively resolved, and the feasibility of the proposed power electronic solution has been verified.Additionally, the B2B converter also offers prospective benefits for multi-generator systems, and more details will be explored in the upcoming section.

The Enhancement of Multi-Generator System Dynamics
Because of the power constraints of a single generator, in gas power generation, it is highly practical to employ multiple generators operating in parallel.This configuration not only enlarges the total power output [58] but also provides redundancy and backup capabilities to handle potential faults or maintenance situations, thereby improving the system reliability.However, directly connecting multiple generators to the grid worsens the system dynamics, particularly when there are changes in the output power of the generators.Because this integration setup allows the generators to share a load, any fluctuation in one generator's output, such as an increase or decrease in power, can lead to frequency variations within the grid.Based on the swing equation of generators, the power of the remaining generators will undergo low-frequency oscillations, and the risk posed by these oscillations is particularly pronounced for generators operating close to the full capacity and with large inertia since they are susceptible to triggering generator overload protection mechanisms.In extreme cases, these oscillations can escalate to the point of system instability.By employing B2B converters, generators can be decoupled from each other, effectively minimizing the LFO among them.To better explain the improvement in system dynamics brought about by the B2B converter, two dual-generator networks are established, as shown in Figure 6.The only variance between these two systems is the way SG #2 is connected to the utility grid.
Energies 2023, 16, x FOR PEER REVIEW 9 of 22 the system dynamics, particularly when there are changes in the output power of the generators.Because this integration setup allows the generators to share a load, any fluctuation in one generator's output, such as an increase or decrease in power, can lead to frequency variations within the grid.Based on the swing equation of generators, the power of the remaining generators will undergo low-frequency oscillations, and the risk posed by these oscillations is particularly pronounced for generators operating close to the full capacity and with large inertia since they are susceptible to triggering generator overload protection mechanisms.In extreme cases, these oscillations can escalate to the point of system instability.By employing B2B converters, generators can be decoupled from each other, effectively minimizing the LFO among them.To better explain the improvement in system dynamics brought about by the B2B converter, two dual-generator networks are established, as shown in Figure 6.The only variance between these two systems is the way SG #2 is connected to the utility grid.With the intention of elucidating the impact of the B2B converter on system dynamics, a quasi-stationary model in the dq rotating frame is employed.For the gridconnected converter, the quasi-stationary model is simplified from the full-order model by neglecting the dynamics of the inner current control loops.Generally, the control bandwidth of the inner loops is designed to be much higher than the outer control loops [59,60].Hence, this simplification can still capture the frequency-power dynamics of the converter.Additionally, this type of quasi-stationary model has also been implemented to investigate the stability of DC link voltage control for GFL converters [61,62] and compare the dynamics of GFM converters under stand-alone and SG-connected operations in [63].
In the modelling of generators, the dynamics of SGs' stator voltage, field windings, and excitation systems are incorporated into the conventional quasi-stationary model.This refinement improves the precision in characterizing the LFO present in SGs, and the performance of the enhanced model has been validated by comparing it with the SG's full-order model [64].
In Figure 7, the performance of both systems shown in Figure 6 is examined.The Bode plot highlights that the resonant peak experiences a significant reduction when SG #2 is integrated into the grid through the B2B converter, which suggests that the B2B converter has positive impacts on system dynamics.
Meanwhile, real-time simulations are carried out for both system configurations, and the results are shown in Figure 8.During the simulations, a step change is applied in the output power of SG #1 at 18s, while the dynamic response of SG #2 is observed.The obtained results elaborate that, in the absence of the B2B converter, modifying the output power of SG #1 leads to the power oscillation of SG #2, resulting in an instantaneous output exceeding its rated capacity by approximately 15%.With the introduction of the B2B converter, however, the output power of SG #2 can remain within the power rating, and the dynamics of a multi-generator system can be ameliorated through damp- With the intention of elucidating the impact of the B2B converter on system dynamics, a quasi-stationary model in the dq rotating frame is employed.For the grid-connected converter, the quasi-stationary model is simplified from the full-order model by neglecting the dynamics of the inner current control loops.Generally, the control bandwidth of the inner loops is designed to be much higher than the outer control loops [59,60].Hence, this simplification can still capture the frequency-power dynamics of the converter.Additionally, this type of quasi-stationary model has also been implemented to investigate the stability of DC link voltage control for GFL converters [61,62] and compare the dynamics of GFM converters under stand-alone and SG-connected operations in [63].
In the modelling of generators, the dynamics of SGs' stator voltage, field windings, and excitation systems are incorporated into the conventional quasi-stationary model.This refinement improves the precision in characterizing the LFO present in SGs, and the performance of the enhanced model has been validated by comparing it with the SG's full-order model [64].
In Figure 7, the performance of both systems shown in Figure 6 is examined.The Bode plot highlights that the resonant peak experiences a significant reduction when SG #2 is integrated into the grid through the B2B converter, which suggests that the B2B converter has positive impacts on system dynamics.
Meanwhile, real-time simulations are carried out for both system configurations, and the results are shown in Figure 8.During the simulations, a step change is applied in the output power of SG #1 at 18s, while the dynamic response of SG #2 is observed.The obtained results elaborate that, in the absence of the B2B converter, modifying the output power of SG #1 leads to the power oscillation of SG #2, resulting in an instantaneous output exceeding its rated capacity by approximately 15%.With the introduction of the B2B converter, however, the output power of SG #2 can remain within the power rating, and the dynamics of a multi-generator system can be ameliorated through damping the LFO.These findings not only validate the above theoretical analysis but also emphasize the effectiveness of the B2B converter in enhancing system dynamics.
ing the LFO.These findings not only validate the above theoretical analysis but also emphasize the effectiveness of the B2B converter in enhancing system dynamics.

Converter Control Strategy Selection Guidance
The analysis in previous sections illustrates that the B2B converter brings significant improvement in both the power quality and the dynamics of multi-generator systems.However, due to the distinct grid synchronization mechanisms between GFM and GFL converters, different control schemes encounter stability issues under varying grid strengths.Further, it is critical to consider the actual grid impedance when choosing the control strategies for the converter.To investigate the performance of grid-connected converters, the full-order state-space models for all control strategies are derived, and small-signal analysis is presented.Compared to the reduced-order model, full-order models can capture the system dynamics to the utmost [65], such as LCL circuit dynamics, PLL dynamics, outer control loops dynamics, and inner current controller dynamics.In particular, the line impedance exerts a substantial influence on the stability, apart from the converter controller parameters.Deriving the full-order models also guarantees a higher level of accuracy when analyzing the stability of converters.Moreover, consistent with the control diagrams outlined in Figure 4, all models are developed in the dq rotation frame, and variables are expressed in the per-unit form.The generator-side VSC is simplified based on its control objectives to either function as a constant voltage source or a constant current/power source.As shown in Figure 9, the power grid and ing the LFO.These findings not only validate the above theoretical analysis but also emphasize the effectiveness of the B2B converter in enhancing system dynamics.

Converter Control Strategy Selection Guidance
The analysis in previous sections illustrates that the B2B converter brings significant improvement in both the power quality and the dynamics of multi-generator systems.However, due to the distinct grid synchronization mechanisms between GFM and GFL converters, different control schemes encounter stability issues under varying grid strengths.Further, it is critical to consider the actual grid impedance when choosing the control strategies for the converter.To investigate the performance of grid-connected converters, the full-order state-space models for all control strategies are derived, and small-signal analysis is presented.Compared to the reduced-order model, full-order models can capture the system dynamics to the utmost [65], such as LCL circuit dynamics, PLL dynamics, outer control loops dynamics, and inner current controller dynamics.In particular, the line impedance exerts a substantial influence on the stability, apart from the converter controller parameters.Deriving the full-order models also guarantees a higher level of accuracy when analyzing the stability of converters.Moreover, consistent with the control diagrams outlined in Figure 4, all models are developed in the dq rotation frame, and variables are expressed in the per-unit form.The generator-side VSC is simplified based on its control objectives to either function as a constant voltage source or a constant current/power source.As shown in Figure 9, the power grid and

Converter Control Strategy Selection Guidance
The analysis in previous sections illustrates that the B2B converter brings significant improvement in both the power quality and the dynamics of multi-generator systems.However, due to the distinct grid synchronization mechanisms between GFM and GFL converters, different control schemes encounter stability issues under varying grid strengths.Further, it is critical to consider the actual grid impedance when choosing the control strategies for the converter.To investigate the performance of grid-connected converters, the full-order state-space models for all control strategies are derived, and small-signal analysis is presented.Compared to the reduced-order model, full-order models can capture the system dynamics to the utmost [65], such as LCL circuit dynamics, PLL dynamics, outer control loops dynamics, and inner current controller dynamics.In particular, the line impedance exerts a substantial influence on the stability, apart from the converter controller parameters.Deriving the full-order models also guarantees a higher level of accuracy when analyzing the stability of converters.Moreover, consistent with the control diagrams outlined in Figure 4, all models are developed in the dq rotation frame, and variables are expressed in the per-unit form.The generator-side VSC is simplified based on its control objectives to either function as a constant voltage source or a constant current/power source.As shown in Figure 9, the power grid and VSCs possess their own rotation coordinates, characterized by the angular frequencies of w grid and w VSC , respectively.To integrate the VSC into the system model while considering the dynamics entire system, it is necessary to transform the dq-axis output current of the VSC ( or iL2_q_VSC) into the grid's rotation frame (dqgrid).Further, the input variable, PCC v (VPCC_d_grid or VPCC_q_grid), should be converted into the VSC's frame.Since the grid's serves as the common reference frame and considering a phase angle difference between two rotation frames, the transformation between these two dq frames carried out by ( 2) and (3).
The state-space model for the entire system can be described as (4), where xsys usystem, respectively, represent the state vector and input vector, and Asystem and separately indicate the state matrix and input matrix.Details of matrices are provi Appendix B.


x A x B u system system system system system

= +
After developing the state-space models, the accuracy validation is conduc comparing them with the time-domain simulations.As depicted in Figure 10, change in active power reference from 0.1 to 0.11 p.u. is applied at t = 4.5 s.The clearly demonstrate that the responses of state-space models are aligned with thos simulations in the time domain thereby confirming the accuracy of the derived mo According to the parameters in state matrices, the eigenvalue trajectories are p in Figure 11 the of three controls under diverse short circuit (SCR) while maintaining all controller parameters unchanged.It can be foun when the grid-side VSC is under the GFM control (strategy #1), the conjugated values (λ1 and λ2) move toward the right-half plane with a stronger grid.Additi further increasing SCR to 9.6 causes λ1 and λ2 to reach the unstable region.In cont and λ2 of the GFL-controlled VSCs (strategies #2 and #3) shift to the right-half when the grid is weaker, and the systems eventually lose stability when the SCR r 1.37.Ultimately, the eigenvalue analysis reveals that GFM and GFL controls exhi To integrate the VSC into the system model while considering the dynamics of the entire system, it is necessary to transform the dq-axis output current of the VSC (i L2_d_VSC or i L2_q_VSC ) into the grid's rotation frame (dq grid ).Further, the input variable, PCC voltages (V PCC_d_grid or V PCC_q_grid ), should be converted into the VSC's frame.Since the grid's frame serves as the common reference frame and considering a phase angle difference of δ VSC between two rotation frames, the transformation between these two dq frames can be carried out by ( 2) and (3).
The state-space model for the entire system can be described as (4), where x system and u system , respectively, represent the state vector and input vector, and A system and B system separately indicate the state matrix and input matrix.Details of matrices are provided in Appendix B. .
x system = A system x system + B system u system (4) After developing the state-space models, the accuracy validation is conducted by comparing them with the time-domain simulations.As depicted in Figure 10, a step change in active power reference from 0.1 to 0.11 p.u. is applied at t = 4.5 s.The results clearly demonstrate that the responses of state-space models are aligned with those from simulations in the time domain thereby confirming the accuracy of the derived models.
According to the parameters in state matrices, the eigenvalue trajectories are plotted in Figure 11 to compare the stability of three controls under diverse short circuit ratios (SCR) while maintaining all controller parameters unchanged.It can be found that, when the grid-side VSC is under the GFM control (strategy #1), the conjugated eigenvalues (λ 1 and λ 2 ) move toward the right-half plane with a stronger grid.Additionally, further increasing SCR to 9.6 causes λ 1 and λ 2 to reach the unstable region.In contrast, λ 1 and λ 2 of the GFL-controlled VSCs (strategies #2 and #3) shift to the right-half plane when the grid is weaker, and the systems eventually lose stability when the SCR reaches 1.37.Ultimately, the eigenvalue analysis reveals that GFM and GFL controls exhibit opposite stability characteristics under varying grid strengths, and the GFM control is more suitable for weak grids.To verify the above eigenvalue analysis, real-time simulations are carried out, and the parameters are identical to those specified in Section 3.For each strategy, two testing points are examined.One is at the grid strength during an unstable state, while the other is at the adjusted SCR to restore the system stability.Figures 12-14 demonstrate the active power output and frequency response of three control schemes following a disturbance at different SCRs.Simulation cases 1 and 2 are conducted to validate the stability analysis of the GFM converter (strategy #1), and the corresponding SCRs are 9.64 and 2.95, respectively.Additionally, as shown in Figure 12, the output power reference is changed from 0.9 p.u. to 1 p.u. at t 1 .In case 1, the active power output and frequency experience noticeable oscillations at the frequency of approximately 6.45 Hz, which is consistent with the analysis.After decreasing the grid strength to SCR = 2.95, the oscillations are damped, and the system reaches a new steady-state operating point in case 2, indicating that the GFM converter exhibits better stability when weakening the grid strength.To verify the above eigenvalue analysis, real-time simulations are carried out, and the parameters are identical to those specified in Section 3.For each strategy, two testing points are examined.One is at the grid strength during an unstable state, while the other is at the adjusted SCR to restore the system stability.Figures 12-14 demonstrate the active power output and frequency response of three control schemes following a disturbance at different SCRs.Simulation cases 1 and 2 are conducted to validate the stability analysis of the GFM converter (strategy #1), and the corresponding SCRs are 9.64 and 2.95, respectively.Additionally, as shown in Figure 12, the output power reference is changed from 0.9 p.u. to 1 p.u. at t1.In case 1, the active power output and frequency experience noticeable oscillations at the frequency of approximately 6.45 Hz, which is consistent with the analysis.After decreasing the grid strength to SCR = 2.95, the oscillations are damped, and the system reaches a new steady-state operating point in case 2, indicating that the GFM converter exhibits better stability when weakening the grid strength.Cases 3, 4, 5, and 6 are used to verify the stability of the GFL converter (strategy #2 and strategy #3), with the SCRs being 1.37 and 2.24.As presented in Figures 13 and 14, the same disturbance is applied at t1.In cases 3 and 5, the active power and frequency undergo diverging oscillations, with a similar frequency of about 3.78 Hz.After increasing the grid strength to SCR = 2.24, the systems can converge to a new operating point in cases 4 and 6.Therefore, these simulation results illustrate that the GFL control has better stability under stiffer grids.Cases 3, 4, 5, and 6 are used to verify the stability of the GFL converter (strategy #2 and strategy #3), with the SCRs being 1.37 and 2.24.As presented in Figures 13 and 14, the same disturbance is applied at t 1 .In cases 3 and 5, the active power and frequency undergo diverging oscillations, with a similar frequency of about 3.78 Hz.After increasing the grid strength to SCR = 2.24, the systems can converge to a new operating point in cases 4 and 6.Therefore, these simulation results illustrate that the GFL control has better stability under stiffer grids.To verify the above eigenvalue analysis, real-time simulations are carried out, and the parameters are identical to those specified in Section 3.For each strategy, two testing points are examined.One is at the grid strength during an unstable state, while the other is at the adjusted SCR to restore the system stability.Figures 12-14 demonstrate the active power output and frequency response of three control schemes following a disturbance at different SCRs.Simulation cases 1 and 2 are conducted to validate the stability analysis of the GFM converter (strategy #1), and the corresponding SCRs are 9.64 and 2.95, respectively.Additionally, as shown in Figure 12, the output power reference is changed from 0.9 p.u. to 1 p.u. at t1.In case 1, the active power output and frequency experience noticeable oscillations at the frequency of approximately 6.45 Hz, which is consistent with the analysis.After decreasing the grid strength to SCR = 2.95, the oscillations are damped, and the system reaches a new steady-state operating point in case 2, indicating that the GFM converter exhibits better stability when weakening the grid strength.Cases 3, 4, 5, and 6 are used to verify the stability of the GFL converter (strategy #2 and strategy #3), with the SCRs being 1.37 and 2.24.As presented in Figures 13 and 14, the same disturbance is applied at t1.In cases 3 and 5, the active power and frequency undergo diverging oscillations, with a similar frequency of about 3.78 Hz.After increasing the grid strength to SCR = 2.24, the systems can converge to a new operating point in cases 4 and 6.Therefore, these simulation results illustrate that the GFL control has better stability under stiffer grids.These simulation results not only provide an intuitive illustration of the impact of grid strength on the stability of GFM and GFL converters but also corroborate the rootloci plots shown in Figure 11.According to the collected results, Table 7 summarizes the stability boundaries for three studied control schemes.Referring to the application context of gas generation, the geographical locations of gas fields are usually far from the grid, resulting in converters being connected to weak grids.It can be concluded that strategy #1 is the optimal choice for gas field generation, considering its distant location.

Discussion
The main barrier in the current cogeneration system is the power quality issues, including voltage profile and harmonics.Prior to integrating the B2B converter into the system, the gas turbine generator operates at unity power factor, causing the voltage at Node 4 to exceed the permissible range and contain considerable portions of distortions.Through the compensation offered by the B2B converter for harmonics and reactive power, the THD of the node voltage can be improved from 6.84% to 3.33% (lower than 5%).Meanwhile, the voltage magnitude can remain around 1 p.u., which indicates the overvoltage is effectively suppressed.Due to the responsibility of B2B converters in transmitting the generated active power to the grid and compensating for the reactive power to mitigate the overvoltage at PCC, the capacity selection of the converter becomes significant in the design of such converter-interfaced generation systems.In this research, the maximum active power output is 2.5 MW, with a corresponding reactive power compensation requirement of 0.52 MVar, resulting in a power factor of 0.97.Furthermore, the minimum allowable capacity of the VSC is 2.55 MVA.To incorporate redundancy in the design and ensure enough margin for contingencies, a rated power of 3 MVA is chosen for the converter in this study.In terms of system stability, all three controls can secure the stable operation of the converter within the range of 1.37 < SCR < 9.64.If the grid falls below this range in strength, GFM control (strategy #1) becomes the only feasible option for regulating the B2B converter.Finally, when the grid's SCR surpasses 9.64, either GFL control (strategies #2 or #3) can be utilized.

Conclusions
In this article, the power quality issues in gas cogeneration systems have been discussed.Due to a long-distance transmission line, high-power injection to the grid causes These simulation results not only provide an intuitive illustration of the impact of grid strength on the stability of GFM and GFL converters but also corroborate the root-loci plots shown in Figure 11.According to the collected results, Table 7 summarizes the stability boundaries for three studied control schemes.Referring to the application context of gas generation, the geographical locations of gas fields are usually far from the grid, resulting in converters being connected to weak grids.It can be concluded that strategy #1 is the optimal choice for gas field generation, considering its distant location.

Discussion
The main barrier in the current cogeneration system is the power quality issues, including voltage profile and harmonics.Prior to integrating the B2B converter into the system, the gas turbine generator operates at unity power factor, causing the voltage at Node 4 to exceed the permissible range and contain considerable portions of distortions.Through the compensation offered by the B2B converter for harmonics and reactive power, the THD of the node voltage can be improved from 6.84% to 3.33% (lower than 5%).Meanwhile, the voltage magnitude can remain around 1 p.u., which indicates the overvoltage is effectively suppressed.Due to the responsibility of B2B converters in transmitting the generated active power to the grid and compensating for the reactive power to mitigate the overvoltage at PCC, the capacity selection of the converter becomes significant in the design of such converter-interfaced generation systems.In this research, the maximum active power output is 2.5 MW, with a corresponding reactive power compensation requirement of 0.52 MVar, resulting in a power factor of 0.97.Furthermore, the minimum allowable capacity of the VSC is 2.55 MVA.To incorporate redundancy in the design and ensure enough margin for contingencies, a rated power of 3 MVA is chosen for the converter in this study.In terms of system stability, all three controls can secure the stable operation of the converter within the range of 1.37 < SCR < 9.64.If the grid falls below this range in strength, GFM control (strategy #1) becomes the only feasible option for regulating the B2B converter.Finally, when the grid's SCR surpasses 9.64, either GFL control (strategies #2 or #3) can be utilized.

Conclusions
In this article, the power quality issues in gas cogeneration systems have been discussed.Due to a long-distance transmission line, high-power injection to the grid causes the voltage magnitude at the remote node to reach 1.055 p.u., which exceeds the acceptable limit by 2.5%.Additionally, a substantial proportion of nonlinear loads in the system results in a notable presence of harmonic components in the node voltage, with the THD measured at 6.84%.By incorporating the B2B converter, the power quality of the above system can be significantly enhanced by compensating for the reactive power and harmonics, resulting in both voltage profile and THD falling within the permissible range.Furthermore, under the scenario of multiple generators operating in parallel, the B2B converter can optimize the dynamic response through attenuating the LFO that exists among the generators.In terms of the B2B converter control, this article presents three viable strategies that are tailored to the requirements of the gas field generation.These control options can be categorized into grid-forming and grid-following, characterizing distinct stability under different grid strengths.Therefore, when designing the converter-interface generation systems, it is essential to take the grid conditions into account.To analyze the impact of grid impedance on control stability, this paper developed the full-order state-space models for the grid-side VSCs.Through the eigenvalue analysis, the grid-forming control (strategy #1) has been evidenced to demonstrate greater stability under weak grids (SCR ≤ 1.37).On the other hand, the grid-following controls (strategies #2 and #3) have been found to be more suitable for a stiff power grid (SCR ≥ 9.64).Moreover, the stability boundaries of all controls are obtained, providing valuable insights for selecting control schemes.Finally, considering the actual grid impedance of the gas generation system, the conclusion can be drawn that strategy #1 is the optimal choice.Additionally, real-time simulations highlight the benefits of the B2B converter and validate the accuracy of the analysis.The parameters of the gas generation system are given in Table A2, and the controller parameters for the B2B converter under three control strategies are provided in Tables A3-A5.

Figure 1 .
Figure 1.System overview of proposed gas cogeneration plant.

Figure 1 .
Figure 1.System overview of proposed gas cogeneration plant.

Figure 2 .
Figure 2. Diagram of the system configuration.

Figure 2 .
Figure 2. Diagram of the system configuration.

Figure 3 .
Figure 3. Diagram of gas field generation with back-to-back converter.

Figure 3 .
Figure 3. Diagram of gas field generation with back-to-back converter.

Figure 6 .
Figure 6.Structure diagram of multi-generator system.(a) Both SGs are directly connected to the utility grid; (b) one of the SGs is connected to the utility grid through the B2B converter.

Figure 6 .
Figure 6.Structure diagram of multi-generator system.(a) Both SGs are directly connected to the utility grid; (b) one of the SGs is connected to the utility grid through the B2B converter.

Figure 7 .
Figure 7. Bode plots of systems without and with the B2B converter.

Figure 7 .
Figure 7. Bode plots of systems without and with the B2B converter.

Figure 7 .
Figure 7. Bode plots of systems without and with the B2B converter.

Figure 10 .Figure 11 .
Figure 10.Model verification.(a) Active power of the VSC in strategy #1; (b) active power VSC in strategy #2; (c) active power of the VSC in strategy #3; (d) DC link voltage in strategy

Figure 10 .
Figure 10.Model verification.(a) Active power of the VSC in strategy #1; (b) active power of the VSC in strategy #2; (c) active power of the VSC in strategy #3; (d) DC link voltage in strategy #3.

Figure 10 .
Figure 10.Model verification.(a) Active power of the VSC in strategy #1; (b) active power of t VSC in strategy #2; (c) active power of the VSC in strategy #3; (d) DC link voltage in strategy #3.

Table 1 .
Load distribution and power quality measurement.

Table 2 .
Power quality measurement under increased nonlinear loads.

Table 3 .
Overview of generator-side VSC control objectives and advantages.

Table 3 .
Overview of generator-side VSC control objectives and advantages.

Table 4 .
Overview of grid-side VSC control objectives and advantages.

Table 5 .
Control strategy overview.

Table 6 .
Power quality measurement at Node 4.
Note: unacceptable node voltages and THDs are marked in red.

Table 6 .
Power quality measurement at Node 4.
Note: unacceptable node voltages and THDs are marked in red.

Table 7 .
Stability under different grid strengths.

Table 7 .
Stability under different grid strengths.

Table A1 .
List of symbols in control diagram.P grid *, Q grid * Rated grid-side active and reactive power P grid , Q grid Measured grid-side active and reactive power V dc *, V dc Rated and measured DC link voltage V pcc *, V pcc Rated and measured voltage at point of common coupling P gen *, P gen Rated and measured generator-side active power H Rated and measured frequency θ grid , θ gen Grid-side and generator-side phase angles V*, V Rated voltage and generated voltage reference i L2d_grid , i L2q_grid Measured grid-side output current in dq u cd_grid , u cq_grid Measured grid-side output voltage in dq i L1d_grid *, i L1q_grid * Reference of grid-side inductor current in dq i L1d_gen *, i L1q_gen * Reference of generator-side inductor current in dq i L1d_grid , i L1q_grid Measured grid-side inductor current in dq i L1d_gen , i L1q_gen Measured generator-side inductor current in dq V