Mitigation of power system forced oscillations based on unified power flow controller
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Abstract
Forced oscillations (FOs), or low-frequency oscillations (LFOs) caused by periodic, continuous, small power disturbances, threaten the security and stability of power systems. Flexible AC transmission system (FACTS) devices can effectively mitigate LFOs via stability control. We propose a novel method that mitigates FOs by shifting the resonant frequency. Based on the features of the linearized swing equation of a generator, a resonant frequency shift can be achieved by controlling the synchronous torque coefficient using a unified power flow controller (UPFC). Because of the resonance mechanism, the steady-state response of an FO can be effectively mitigated when the resonant frequency changes from the original one, which was close to the disturbance frequency. The principle is that a change in resonant frequency affects the resonance condition. Simulations are conducted in a single-machine infinite-bus (SMIB) system, and the simulation results verify that the method is straightforward to implement and can significantly mitigate FOs. The controller robustness when the resonant frequency is not accurately estimated is also analyzed in the simulations.
Keywords
Forced oscillations Flexible AC transmission systems Unified power flow controller Stability control1 Introduction
The probability of low-frequency oscillations (LFOs) is increasing with the increasing size of power grids, thereby threatening the normal operation of power systems [1, 2, 3]. As a result, the LFOs of large-area power systems have become an important issue [4]. The traditional theory of power system dynamic analysis claims that LFOs are the result of a negative damping mechanism. Under this theory, an LFO is caused by the lack of damping [5, 6, 7]. However, in recent years, an increasing number of LFO incidents have arisen that cannot be explained by the negative damping mechanism. Instead, forced oscillations (FOs) originate from periodic, continuous, small disturbances in the system [8, 9]. In these cases, a resonance mechanism is required to explain the behavior of power systems. An LFO is explained by resonances between the transmission power and the disturbances in the system [10, 11]. Relative to the LFOs of negative damping mechanisms, FOs start faster and have a larger amplitude; they also spread more broadly. As a result, FOs are more harmful to power systems than the LFOs of a negative damping mechanism [12].
Many studies on the localization and identification of FOs have been conducted. In contrast, few studies on the mitigation of FOs have been conducted. The existing methods for mitigating LFOs are typically based on the ideas of removing the disturbance sources and a power oscillation damping controller (PODC). Methods based on the first approach include removing the disturbing generators and loads, reducing the output of generators, splitting the system and modifying the control model of the prime mover [13, 14]. A PODC is also a valid method for reducing the amplitude of power oscillations and suppressing LFOs [15, 16]. Reference [17] proposed a new approach to design the parameters of the power system stabilizer (PSS) to mitigate FOs. Reference [18] provided a method to mitigate FOs using flexible AC transmission system (FACTS) devices with energy storage. This method directly reduces the disturbance sources to prevent the spread of the oscillation energy. However, damping control cannot provide ideal mitigation of FOs because the lack of damping is not the major cause of FOs. The method neglects the continuity of energy injection in the situation of a resonance mechanism; it is also limited by damping conservation theory, i.e., if we adopt a large damping ratio for one mode, then the other modes of the power system become less stable [19]. As a result, a new approach is required to mitigate FOs.
In this research, the proposed method can be realized by FACTS devices, which can mitigate power oscillations via appropriate control strategies. The unified power flow controller (UPFC) is the most comprehensive example of a FACTS device at present [20]. UPFCs have received much research attention. Reference [21] presented an approach of UPFC stability control to damp inter-area power oscillations. We adopt a UPFC because it is a serial-parallel FACTS device that can realize both voltage control and impedance control [22]. Therefore, we can carry out coordinated control between both sides to simultaneously shift the resonant frequency and guarantee large damping.
To overcome the defects of a PODC, we propose a resonant frequency controller (RFC) based on a UPFC to mitigate FOs. An RFC is added to the UPFC to control the resonant frequency. This RFC method is different from a PODC method because the effect of a PODC depends on the variation in the damping coefficient D. The proposed method can reach a mitigation independently. It can also work in conjunction with a PODC to reach a better result. A large compensation of D is required to provide adequate damping. In contrast, with the proposed method, we simply shift the synchronous torque coefficient K from its original value, which is therefore not affected by the limitation of damping conservation theory. With a resonant controller, the resonant frequency is shifted only when a FO occurs. The principle of the method is analyzed in Section 2. Section 3 presents and analyzes the proposed method of this study, providing a comprehensive model of the system. Section 4 provides a detailed design of the supplementary controller. The method effectively mitigates FOs and exhibits higher performance than a PODC. The effect of the proposed method is verified by the simulations described in Section 5. The performance of the UPFC and the robustness of the proposed method are also provided in this section.
2 Principle of the proposed method
2.1 Introduction of the system
SMIB system with a UPFC
A UPFC is installed at the midpoint of the transmission line. It can simultaneously control the local bus voltage and circuit impedance. The UPFC is implemented using two similar solid-state phase voltage source converters (VSCs) that are connected via a common DC link capacitor, as shown in Fig. 1, and each converter is coupled with a transformer [24]. The UPFC in this case is separated into a serial side and a shunt side. Both sides can be used to mitigate FOs; the corresponding models are given in the following sections.
2.2 Resonance mechanism
The first item of (4) is the steady-state response of FOs. φ is the initial phase of this component. The value of the maximum amplitude B is related to the damping coefficient D, synchronous torque coefficient K and disturbance amplitude r. The detailed expression of B is given in the following section. The frequency of the steady-state response is equal to the disturbance frequency Ω. The second and third items are the transient responses. ωd is the frequency of the transient responses. The amplitudes of transient responses B1(t) and B2(t) decrease to relatively small values several seconds after the starting point.
Curves of a synthesized FO
2.3 Influence of synchronous torque coefficient
This result shows that the resonant frequency is related to both the synchronous torque coefficient and the inertial constant of the generator.
Analogous to a mechanical system, when the disturbance frequency is close to the resonant frequency, the disturbance performs positive work on the system. The disturbance energy is continuously transformed into the system’s potential energy, thereby causing FOs. In contrast, when the resonant frequency is different from the disturbance frequency, the disturbance performs negative work, and the oscillations are damped. According to this theory, when the synchronous torque coefficient changes, the resonant frequency changes, and FOs are mitigated.
Curves of a mitigated synthesized FO
Curves of the relationship between synchronous torque coefficient and maximum power amplitude of FO
2.4 Generalization of the principle
Equation (9) shows that the amplitude of the steady-state response of the FO in a multimachine system is related to the synchronous torque coefficient of the relevant mode K i . By controlling K i , the resonant frequency of the ith-order mode can be changed, and the ith-order FO is mitigated, thereby demonstrating that the proposed method can be generalized to a multimachine system.
3 Analysis of UPFC
3.1 Integrated model of the system
This section provides a detailed analysis of the SMIB system with a UPFC shown in Fig. 1 to explain the principle of the proposed controller.
Block diagram of SMIB system with a UPFC
This diagram and the derivations below can be used to find the additional angle for the design of the supplementary controller. Details regarding the supplementary control strategy of the UPFC are discussed in the next section.
3.2 Impact of UPFC shunt side
Equivalent circuit of UPFC shunt side
In this section, we consider only the function of the shunt side; thus, the serial-side impedance XUPFC is equal to 0 in the expressions for K1-K6.
When the resonant frequency changes, FOs are mitigated according to the theory presented in Section 2.
Regarding a multimachine system, when the supplementary signal is designed to compensate for the synchronous torque of a certain ith-order mode, the FOs of this mode are mitigated, as is apparent in (9).
3.3 Impact of UPFC serial side
Equivalent circuit of UPFC serial side
Moreover, the serial side of the UPFC can compensate for the damping of the system [28] and can work in conjunction with the shunt side to improve the effectiveness of FO mitigation.
4 Design of resonant frequency controller
4.1 Structure of UPFC resonant frequency controller
In Fig. 5, the fluctuations in ∆Pm lead to FOs. The magnification of the disturbances is related to the synchronous torque coefficient K according to (7). As shown in Fig. 5, K is determined by the transfer function of the UPFC. In fact, merely the installation of the UPFC can change the original synchronous torque coefficient. However, without a supplementary controller, FOs still occur when a disturbance exists at a new resonant frequency. In this section, we propose the structure of the UPFC RFC to mitigate such FOs.
Structure of the resonant frequency controller
The RFC design of the serial side is similar to the design of the shunt side. In this study, to enable a contrast, a PODC can be used on the serial side of the UPFC [30].
4.2 Design of resonant controller
Frequency response of R(s) when ωc=2π×1.67 and KR=0.16
The main component of FOs is the steady-state response. In (2), the frequency of the steady-state response is found to be equal to the disturbance frequency Ω instead of the resonant frequency ωn. This point is important because if the resonant frequency changes from ωn0 to ωn1, then the frequency of the input signal is still Ω, which can maintain the RFC’s effectiveness. Moreover, if the disturbance frequency is equal to ωn1, then the gain of the resonant controller is close to zero because Ω is equal to ωn1. As the resonant frequency is still ωn0 under this condition, FOs can be avoided. The only problem occurs when oscillation modes of ωn0 and ωn1 exist simultaneously in the system; this situation is a low-probability event. However, the higher harmonics of the oscillation mode ωn0 have been observed to exist in real systems [32]. Therefore, when we design the RFC, we should avoid the situation in which the final ωn is equal to the frequency of any higher harmonics of the oscillation mode ωn0.
4.3 Design of phase compensation unit
Phase diagram to illustrate the proposed method
Phase diagram to illustrate the comprehensive control strategy
When a disturbance exists at the original resonant frequency, the RFC operates, and ∆TRFC is added to ∆Te1. ∆Te2 has a larger real part, i.e., the synchronous torque coefficient becomes larger. The change in ∆Te1 can shift the resonant frequency; as a result, FOs are mitigated in this situation.
In a multimachine system in which no infinite bus is considered, the relationship between the response of the rotor angle and the disturbance is no longer a 90° lag. Optimization algorithms such as the genetic algorithm (GA) and particle swarm optimization (PSO) can be used to design the parameters of the phase compensation unit [34, 35].
5 Simulation verification
5.1 Results of PODC method
In this section, we investigate the effectiveness of the proposed method in a SMIB system. A comparison between the traditional method and the new method is conducted to demonstrate the advantages of the proposed method.
Simulation results for UPFC using a PODC
First, a conventional PODC on the UPFC serial side is used to mitigate PFO. Two lead-lag components are used in this supplementary controller; thus, m = 2. The shunt-side UPFC works in a constant-voltage mode that does not compensate for the synchronous torque coefficient of this mode. The optimized parameters of the PODC are: T ω = 10.0, K = 30.0, T1 = 0.31, T2 = 0.05. The simulation results are as shown in Fig. 12, where PFO reflects the oscillation caused by the disturbance in this system and PPODC represents the mitigated power oscillation.
Performance of UPFC with PODC method
With a current is injected on the UPFC serial side, the impedance of the system changes when an oscillation arises. In addition, the UPFC current increases the damping of the oscillation mode. The injected current can reflect the influence on the active power of the system from the UPFC. FOs are mitigated when the damping is enhanced. However, the effect is not ideal because there is a limit to the amount of damping compensation that can occur.
Moreover, the disturbance source continuously injects energy into the system, making it challenging to damp FOs with a PODC because we need higher damping compensation. The reactive power in Fig. 13b is caused by the UPFC capacitor. The reactive power and the converter voltage reflect the UPFC working condition. When the controller gain is too high, they may be distorted.
5.2 Results of the proposed method
Simulation results for UPFC using a RFC
Parameters of RFC
Parameter set | K R | ξ | ω n0 | T ω | K ω | T 1 | T 2 |
---|---|---|---|---|---|---|---|
I | 0.03 | 0.01 | 10.5 | 10.0 | 9.0 | 0.04 | 0.23 |
II | 0.62 | 0.01 | 10.5 | 10.0 | 9.0 | 0.48 | 0.02 |
K is decreased when parameter set I is used. The resonant frequency changes to approximately 1.05 Hz, compared to the resonant frequency of 1.67 Hz after the installation of the UPFC. The amplitude of the oscillation is reduced to approximately 13% of the original amplitude, as shown in Fig. 14a. When using parameter set II, K is increased, and the resonant frequency is temporarily shifted to approximately 3.55 Hz. This simulation achieves a better effect, as shown in Fig. 14b, because the variation in the resonant frequency is larger.
Both simulation results demonstrate the effectiveness of the proposed method. It is better to increase K than to decrease K because a wider adjustable range exists within which K can be increased. The increase in K can also provide better static stability. Note that this result is reached without a large compensation for the damping of this mode. As a result, a transient oscillation remains at the starting stage of the oscillation. The principle of this phenomenon is analyzed in Section 2.3. Thus, we can use other methods to compensate for the damping in conjunction with the proposed method and improve the effect of mitigation.
Performance of UPFC with the proposed method
Simulation results for comprehensive method
Performance of UPFC with comprehensive method
5.3 Robustness of the proposed method
In this subsection, simulations are conducted to discuss the robustness of the controller. When designing the resonant controller, the original resonant frequency is required. The parameter is obtained after identifying the oscillation. However, identification errors should be considered in the design of the proposed controller. In common cases, the identification errors are too small to be considered [36]. However, the controller should still be designed to address certain extreme situations.
Parameters of RFC used to study robustness
Parameter set | K R | ξ | ω n0 | T ω | K ω | T 1 | T 2 |
---|---|---|---|---|---|---|---|
III | 0.62 | 0.01 | 12.3 | 10.0 | 9.0 | 0.48 | 0.02 |
IV | 0.62 | 0.01 | 16.2 | 10.0 | 9.0 | 0.48 | 0.02 |
V | 0.62 | 0.50 | 16.2 | 10.0 | 9.0 | 0.48 | 0.02 |
Simulation results characterizing robustness of controller
6 Conclusion
We proposed a novel method for mitigating FOs that involves controlling the resonant frequency using a UPFC. Because the new method is based on changing the resonance conditions, this method is a targeted and efficient approach to mitigating FOs. We designed a supplementary controller to control the resonant frequency, which is achieved via compensation of the synchronous torque coefficient. The detailed derivations theoretically show that FOs are significantly mitigated by this method without any negative effect on the normal operation of the power systems. The simulations conducted in an example SMIB system demonstrate the effectiveness of the proposed method. The results show that the proposed method can achieve an outcome superior to that of the traditional PODC. The controller also offers strong robustness even when the resonant frequency is not estimated correctly.
Many noteworthy issues regarding the mitigation of FOs remain to be studied. Firstly, online frequency identification can be adopted to meet the requirement of accuracy of the resonant controller. Secondly, considering that several oscillation modes are typically present in a real system, parallel resonant controllers can be designed to address the situation of multimode oscillations in multimachine systems. Finally, optimization algorithms should be considered to achieve a proper selection of parameters, so that the RFC can compensate for the synchronous torque coefficient of a certain mode in a multimachine system and mitigate corresponding FOs. The design of these parameters is a worthwhile topic for future study.
Notes
Acknowledgements
This work was supported by National Natural Science Foundation of China (No. 51577032) and State Grid Corporation of China (No. 5210K017000C).
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