Sampled-data based discrete and fast load frequency control for power systems with wind power☆
Introduction
Load frequency control (LFC) is designed to restore the balance between load and generation in each control area for maintaining the system frequency and tie-line power between control areas [1]. Measurements of the tie-line power and the frequency are sampled and transferred to the system control centre over communication channels [2]. Plus, a discrete controller is usually implemented on embedded computers in communication channels. Such systems have continuous-time processes and discrete controllers, i.e., the LFC controller is implemented in the discrete-time domain while the power system plant is in the continuous-time domain. Moreover, there is a typical update period (sampling period) of 1–3s for the measurements of the tie-line power and the frequency in practical power system [3]. Therefore, a discrete controller design is required for the LFC as it can take the sampling characteristic into account at the design stage and assure performance in the presence of a large sampling period.
On the other hand, renewable energy sources (RESs), especially wind power [4], have been widely utilized and developed in the last two decades [5]. High penetration of RESs has introduced many new challenges on the operation of modern power system, such as stability issues, uncertainty and low inertia [6], [7]. A reduced inertia of the whole power systems leads to a faster frequency response and larger frequency deviations following a load-generation imbalance [8]. One of the effective solutions is providing faster-acting response against frequency changes. For example, in July 2016, National Grid Electricity System Operator launched and tendered a sub-second frequency response service called Enhanced Frequency Response to improve the whole frequency response structure of UK power market by accelerating the frequency response [9]. Moreover, to accomplish the high penetration of intermittent renewable generations and the increased interaction with the demand-side response, an effective future electricity market tends to employ an open communication infrastructure to support the increasingly decentralized property of control services [10]. Yet the usage of open communication channel with limited network bandwidth introduces unavoidable communication constraints into the LFC scheme [11], including packet dropout and disorder. In order to alleviate those constraints and thus to reduce the communication burden, a larger sampling period is preferred in the power system communication network to reduce the amount of transmitted information and to effectively save the communication bandwidth [12]. Therefore, to improve the performance of LFC for power system with wind power under open communication network, a discrete and fast LFC scheme will show great potential.
Many researchers have made intensive efforts on designing LFC scheme for power systems. Up to date, there are two main methods to accomplish the discrete LFC scheme for power systems. The one is that the controllers are designed in continuous-time mode, and then are discretized and implemented on embedded computers in communication channels. For example, Wang et al. proposed a robust controller in continuous-time mode for power system LFC, based on classical control methods, including the Riccati-equation approach in [13], the control approach in [14], the -Synthesis method in [15], and the pole assignment method in [16]. Similarly, a robust LFC was proposed for power disturbance and dynamical perturbation of an islanded micro-grid [17]. As an improvement, Tan et al. [18] considered the unmodeled dynamics of power systems to design a robust LFC. As for PID-type controllers, Shayeghi et al. proposed a multi-stage PID to solve the LFC of a deregulated power system [19], and Tan et al. introduced an unified PID tuning method for LFC based on the two-degree-of-freedom internal model control design method [20]. Considering the phenomena of data packet dropout and/or disordering in communication channels, Jiang et al. treated these phenomena as time-varying and random delays, and then investigated the delay-dependent stability [21], [22] and the robust PID-type controller design [23] for the LFC scheme based on Lyapunov theory. Further work can be found in [24]. Considering the penetration of wind power, LFC scheme based on doubly fed induction generator was addressed based on the linear active disturbance approach in [25]. Bevrani et al. addressed a decentralized fuzzy logic-based LFC scheme for interconnected power systems in the presence of high-penetration wind power [26]. However, the above LFC schemes designed in continuous-time mode are only valid in smaller discrete period or sampling period. With the sampling period increasing, the performance of LFC will be degraded or even unstable via discretizing continuous-time controller. Especially, there is a typical update period of 1–3s in practical power system [3].
Another method is based on discretization theory. In [27], a method of designing discrete-type load–frequency regulators of a two-area reheat-type thermal system with generation-rate constraints was presented. Thereafter, Vrdoljak et al. introduced a discrete-time LFC scheme in [28], using sliding mode control (SMC) with fast output sampling technique. As an improvement, an event-triggered SMC scheme for the LFC problem in multi-area power systems was proposed in [29], and a decentralised LFC strategy was introduced for multi-area time-delay power system with significant wind power penetration in [30]. Furthermore, Cui et al. investigated the LFC for wind power systems with modeling uncertainties and variant loads based on observer-based robust integral SMC in [31]. Zhang et al. solved the design problem of digital PID-type controller based on discrete-time LFC model for power system with time delays in [32]. A coordinated distributed model predictive control for the LFC of a power system considering inherently variable wind-power generations was presented in [33]. Yet they were designed based on the directly discretized plant model with regarding sampling period as discretized period. Note that the control signal is updated every 1–3s in hydrothermal power system [3]. When the discretized period is set to 1–3s against the time constants lying in the range 0.08–0.3s in hydrothermal power system, it cannot follow the Shannon sampling principle [2]. Fridman introduced an input delay method to analyze such continuous-discrete sampled-data system in [34], which avoids effectively the problem of discrete distortion. Based on this method, discrete sampled-data controllers were designed in a simple one-area power system in [35] and an isolated hybrid power system in [12]. To reduce communication burden and save communication bandwidth, Wen et al. designed a sampled-data based event-triggered LFC scheme with continuous-time PI or PID controllers in [36]. As an improvement, Dong et al. presented a event-triggered LFC scheme with supplementary adaptive dynamic programming in [37], and an adaptive event-triggered LFC scheme was introduced in [38]. However, the considered sampling periods are all less than 1s, which does not match practical update period of control/measurement signals.
As for the fast LFC scheme for power systems, battery energy storage systems were applied due to their fast response to load-generation imbalance in [39]. Electric vehicles as an application of controllable loads are used to fast regulate frequency deviation of power systems in the presence of intermit injection of RESs in [40]. As an improvement, considering compensation of communication latency and detection error in frequency regulation process, a hybrid modeling and control of controllable loads for LFC was proposed in [41]. Also, a virtual inertia controller provided by DFIG-wind turbines was designed to faster suppress frequency fluctuations in [42], [43]. Jia et al. presented a coordinated control strategy between electric vehicles-LFC controller and traditional power plants based LFC controller for primary frequency regulation in [44]. Note that all the above LFC schemes focus on the primary frequency regulation. Although these control strategies can fast generate effectively actions to restore the balance, a new secondary frequency controller design method needs to be proposed to conform with desired faster frequency regulation requirement in combination with above hybrid (continuous-discrete) power systems.
Motivated by above discussions, this paper proposes a discrete and fast LFC scheme for power system with wind power under open communication network. The originality and contributions of this paper can be summarized as follows:
- 1)
A discrete-mode LFC scheme is designed directly based on sampled-data control scheme. The previous studies mainly pay attention to designing continuous controller and do not consider the impact of a large sampling period. In comparison with continuous-mode controller in [19], [20], the proposed discrete LFC scheme can be directly used in power system without the performance degradation caused by discretization and the instability resulting from a larger discrete period.
- 2)
It is different from the directly discretized design method in [27], the input delay method is employed to transform sampled-data LFC system into time delay system and circumvents effectively discrete problem disobeying Shannon sampling theorem. Such method takes fully the sampling characteristic into account. The proposed LFC scheme can assure the stable operation of power systems over a large sampling period of control/measurement signals in open communication network so as to save network resources and to reduce communication burden.
- 3)
To deal with the faster frequency response and bigger frequency deviation resulting from the reduced inertia of power system, EDR is introduced to guide the design of a discrete LFC with desired faster frequency regulation requirement. The proposed fast LFC scheme focuses on the secondary frequency controller to shorten duration of the total frequency regulation, compared with using the primary frequency regulation in previous studies.
- 4)
A design procedure for LFC scheme, which integrates sampling period and EDR, is presented. By adjusting the parameters of sampling period and EDR, different requirements of LFC design can be realized, including reducing the communication network burden and faster frequency response speed.
The remainder of this paper is organized as follows. Section 2 gives the dynamic model of the discrete LFC scheme based on sampled-data control. Section 3 proposes a method of controller design of the discrete and fast LFC scheme. In Section 4, case studies based on traditional one-area LFC, traditional two-area and deregulated three-area LFC with wind power are shown to verify effectiveness of the proposed method. Conclusion is given in Section 5.
Section snippets
Dynamic model of discrete LFC scheme
This section describes a discrete model of traditional and deregulated LFC scheme with wind power. As shown in Fig. 1, the structure of control area i includes n traditional generation units, wind power, tie-line power and communication network. In the traditional LFC scheme, the generation unit represents an unit of generators, while it represents a generation company (Genco) in the deregulated LFC scheme. For simplicity, the time delay existing in signal transmission can be negligible when
Design of discrete LFC scheme
In this section, the design of the discrete LFC scheme for one-area power system is introduced. EDR is introduced as a performance index to guide the design of controller. Then, two theorems of stability and controller design are proposed based on EDR. For multi-area power system, the discrete LFC scheme for each control area can still be designed as that in a one-area system, in which only local system information is needed to design such controller.
In order to design the controller, EDR and
Case studies
In this section, effectiveness of the proposed discrete LFC scheme is demonstrated based on one-area power system, traditional two-area and deregulated three-area power system with wind power. A one-area power system is considered to illustrate the necessity of designing controllers in discrete-time mode instead of continuous-time mode. Also, a traditional two-area power system with wind power is introduced to show the influence on frequency fluctuation of the system due to the high penetration
Conclusion
A discrete load frequency control scheme has been investigated for power systems with high penetration of wind power based on sampled-data control. The proposed scheme can operate in a larger sampling period so as to reduce communication burden. Moreover, to deal with faster frequency response and larger frequency deviation resulting from reduced inertia of power system due to high penetration of wind power, exponential decay rate as a new performance index has been introduced to guide the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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