 Original research
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Ageofinformationaware PI controller for load frequency control
Protection and Control of Modern Power Systems volumeÂ 8, ArticleÂ number:Â 39 (2023)
Abstract
Open communication system in modern power systems brings concern about information staleness which may cause power system frequency instability. The information staleness is often characterized by communication delay. However, communication delay is a packetcentered metric and cannot reflect the requirement of information freshness for load frequency control (LFC). This paper introduces the age of information (AoI), which is more comprehensive and informative than the conventional communication delay modeling method. An LFC controller and communication are integrated into the design for LFC performance improvement. An AoIaware LFC model is formulated first, and considering each allowable update period of the smart sensor, different AoIaware PI controllers are then designed according to the exponential decay rate. The right AoIaware controller and update period are selected according to the degree of frequency fluctuation of the power system. Case studies are carried out on onearea and twoarea power systems. The results show the superior performance of the AoIaware controllers in comparison to the delaydependent controllers.
1 Introduction
Load frequency control (LFC) is one of the fundamental applications of the cyberphysical power system [1, 2]. LFC aims to maintain frequency and power interchanges with neighborhood areas at scheduled values by regulating generation units [3, 4]. LFC works in a sampleddata form due to the discrete information update process and continuous physical plant operation process. The information update process involves smart sensors, communication system, and control center. The information is updated by smart sensors and is transmitted through the communication system to the control center. The information update process inevitably increases information staleness, especially in the open communication system widely used in LFC [5]. However, severe information staleness may threaten the frequency stability of a power system [4, 6, 7].
Communication delay is often applied to the LFC study to characterize the information staleness [8]. To deal with the delayconstrained LFC problem, the previous studies on the stabilization of power system frequency are mainly from two perspectives: the modeling of communication delay and the design of the controller [9]. For example, delaydependent stability for a traditional LFC scheme with constant and timevarying delays is investigated in [10], while a delaydependent robust controller is studied in [11]. In addition, there are different LFC algorithms, such as robust decentralized PIbased LFC [12,13,14], decentralized slidingmodel LFC [15], active disturbance rejection control [16], modelbased control [17] and model predictive control [8]. However, most of these advanced methods suggest complex state feedback or highorder dynamic controllers. As shown in [18], power systems still prefer conventional PI controllers. However, the communication delay is not the optimal metric to describe the information staleness [19]. Communication delay is an informationpacketcentered metric. It overlooks the control factors of the update process such as the update period, the routing selection, and the retransmission mechanism [20]. Therefore, it cannot provide the controllability of the communication system. Therefore, the above delaydependent controllers may be conservative and cannot provide good solutions for the LFC performance based on the delay model [18].
This paper introduces the age of information (AoI) to the LFC study to characterize the information staleness, and to capture the randomness of state updates [19, 21]. AoI is the length of time that elapsed from the generation of the most recently delivered packet [22], and contains richer connotations than communication delay, including the effects of the control factors of the information update process. In this study, an AoIaware method is made to couple the LFC controller and communication as an integrated entity, which is called as AoIaware controller.
This paper consider the control factors of the information update process and the information update period, to show the design process. With the right update period, the control center can receive fresher information and make better decisions to regulate the output of generation units. Thus, the LFC performance is improved. Compared with the communication delay, AoI is more accurate to describe the information staleness. The proposed AoIaware controller shows superiority to stabilize the power system theoretically.
The design of the AoIaware PI controller contains three steps. The AoIaware LFC model of the power system is formulated first. Different AoIaware PItype controllers are then designed for different update periods according to the exponential decay rate (EDR). The values of EDR are adjusted by the performance evaluation conditions of parameter Hâˆžâ€‰performance. Finally, a right AoIaware PItype controller and update period are selected according to the degree of frequency fluctuation of the power system because the optional update period is relatively limited in practical power systems [4, 23].
The Main contributions of this paper are:

1.
Formulate an AoIaware LFC model, and AoI is used instead of communication delay to describe the information update process in the LFC.

2.
Design an AoIaware PI controller to improve LFC performance. The LFC controller and the communication are integrated as a single design entity.
Reference [24] introduces the AoI in the communication area to describe the information staleness of LFC and optimizes the controller parameters from the perspective of the information update process. The main differences in novelty, analysis, and case study parts between [24] and this paper can be summarized as follows.

For novelty, the role of AoI in [24] is to alleviate the effect of limited communication bandwidth, whereas in this paper it is used to stress the information staleness issues for LFC. The difference between AoI and communication delay is elaborated, while [24] designs an LQR controller for the LFC system, this paper designs a PI controller. Compared with the complicated LQR controller, the PI controller is much simpler and easier to implement in practice.

For the analysis of LFC models, reference [24] employs the eventtriggered communication mechanism while this paper uses the timetriggered communication mechanism. Different communication mechanisms involve different analyses and models. Besides, this paper considers operating points and practical nonlinear constraints, including the GRC and GDB constraints. However, these nonlinear constraints are simplified in [24], which makes its model limited.

For the case study, this paper considers the scenarios under the nonlinear GRC and GDB constraints and different operating points while [24] does not study such conditions.
The remainder of this paper is organized as follows. SectionÂ 2 includes the structure of the communication system and the AoI model, while Sect.Â 3 proposes the AoIaware LFC model and introduces the design process of the AoIaware PI controller. SectionÂ 4 presents the results of onearea and twoarea AoIaware LFC performances, and compares the abilities of delaydependent PI controllers and AoIaware PI controllers. Finally, Sect.Â 5 concludes this paper.
2 Problem formulation
This section describes the communication process for LFC, gives the comparison between communication delay and AoI, and presents the metric descriptions.
2.1 Communication process for LFC
LFC aims to maintain the frequency stability and the tielie power exchange in a scheduled value. FigureÂ 1 illustrates the equivalent model of the ith area LFC system. It includes the communication system and the physical power system. The communication system samples the area control error (ACE) message and generates the control command u(t_{k}) to govern the output of generation unit Î”P_{mi}. The ACE of the ith area, denoted as ACE_{i}, is the combination of the frequency deviation Î”f_{i} and net exchange power deviation Î”P_{tiei}, i.e.:
where ÃŸ_{i} is the frequency deviation factor.
The sensors, such as remote terminal units (RTUs), sample the area control error signal ACE_{i} at t_{k}. The sensor updating information interval is called update period Î». Then, the sampled packets y(t_{k}) are queuing in front of the communication channel for transmission. Subsequently, y(t_{k}) is transmitted through the communication channel and is received by the controller. The controller receiving information rate is called service rate Âµ. Information staleness will rise in the communication process [7, 25].
In this paper, the communication process is abstracted as an M/M/1 queue system which means the update rate Î»^{âˆ’1} obeys the Poisson distribution random process, and the service rate Âµ obeys the exponential distribution random process. Additionally, the communication process follows a firstcomefirstserve (FCFS) principle.
2.2 AoI and communication delay
AoI is first proposed in [10, 26] to measure information freshness at the destination node such as the control center. Note that each information packet includes the time stamp information that indicates the update time and received time of the packet. Define the update time of the information packet as t_{k}, the AoI g_{k}(t) at the controller can be defined as [10, 27]:
Figure 2 shows the model of AoI g_{k}(t) at the controller. Information packet k is updated at time t_{k} and received at the time. AoI g_{k}(t), as a function of time t, is jagged. Whenever the controller receives more fresh information, the AoI drops to the next informationâ€™s communication delay. Otherwise, it grows linearly.
Average AoI is the area under the jagged function in Fig.Â 2 by the observation interval T. Over the interval (0, T), the average AoI E[g_{k}(t)] is:
Considering the FCFS M/M/1 communication system, its average AoI g_{ave} is expressed as:
It is clear from (4) that the average AoI g_{ave} is related to the updating period Î» and service rate Âµ. To guarantee that the sensors can update their status stably, the region of the update period is 0â€‰<â€‰Î»_{min}â€‰â‰¤â€‰Î»â€‰â‰¤â€‰Î»_{max}. The service rate is associated with the communication infrastructure and is a constant [19]. The average AoI g_{ave}(Î») can be minimized with respect to the update period Î».
Let the service rate Âµâ€‰=â€‰1 message/second, the update period Î»â€‰=â€‰1.83Â s, and g_{ave} (1.88) is minimal, the minimized average AoI is obtained by choosing an update period Î» that makes the communication channel to be only slightly busier than idle.
Note that Î»^{âˆ’1}Â â†’Â Âµ can achieve maximum throughput and Î»Â â†’Â 0 can minimize the communication delay. The maximum throughput may cause a large communication delay and the minimization of communication delay will make the control center lack sufficient information for decisionmaking. Thus, these two methods cannot make information updated freshly.
The period time \(t_{k}^{\prime }  t_{k}\) is called the communication delay d_{k} of information packet k, which includes the queuing time and service time of information packet k [28], as:
TableÂ 1 shows the difference between AoI and communication delay in these aspects [29]. Firstly, AoI describes the whole communication process, whereas the conventional communication delay model is usually defined for each information packet. Secondly, AoI employs the communication queue model to model the communication process while the conventional communication delay model is characterized by random sequences. The AoI model is more accurate because the sensor can update the information according to its will. Thirdly, AoI model takes into account the effects of control factors, such as the frequency of information transmission, so that it shows the controllability of the communication system.
2.3 Metric descriptions
The LFC performance metric W, namely, average frequency fluctuation, is introduced first to describe the average frequency fluctuation. Then the EDR m and Hâˆžâ€‰gain Î³ are respectively proposed to describe the frequency convergence with load disturbance Î”P_{d} = 0 and disturbance rejection capability of the power system with load disturbance Î”P_{d} â‰ 0. W and EDR m are frequency performance metrics, and their difference is that the LFC performance metric W describes not only the frequency convergence but also the amplitude of frequency fluctuation. Generally, the AoIaware PI controller is designed according to the EDR m and Hâˆžâ€‰gain Î³. The right AoIaware controller is then selected by the LFC performance metric W.
The LFC design objective is to improve LFC performance. The LFC performance metric W is defined as:
where T is the observed time, Î”f_{i} is the frequency deviation of the ith area. Small W means that power system frequency can converge to stable value quickly and smoothly. The average frequency fluctuation W can be minimized by the integration design of the update period and LFC controller.
The EDR is introduced as a performance metric to describe the controllerâ€™s robustness and frequency response dynamic performance. It can vary in the interval [0, âˆž). When EDR m â†’ 0, the robustness becomes the strongest, and the dynamic frequency response performance becomes the worst. When EDR m â†’ âˆž, the robustness becomes the weakest, but the frequency response dynamic performance is considered to be the best.
Hâˆžâ€‰gain Î³ describes the disturbance suppression capability of a power system, and the small Hâˆžâ€‰gain Î³ means strong disturbance suppression ability.
The design of the AoIaware PI controller contains three steps. The AoI guides first choose the update period of the communication system. A right update period decides a small AoI, which means the PI controller can receive fresher information and then change the units to stabilize the frequency more quickly. The EDR is then introduced to guide the design of an AoIaware PI controller. The values of EDR are adjusted by the given robust performance evaluation conditions of Hâˆžâ€‰performance. Finally, the right AoIaware PI controller is selected by the LFC performance metric W.
3 Design of AoIaware PI controller
This section formulates the AoIaware LFC model and proposes the AoIaware PI controller.
3.1 AoIaware LFC model
Considering the multiarea power system depicted in Fig.Â 1, the generation units are equivalent to the model of the governor and turbine. In this paper, the model of a nonreheating steam turbine generator unit with a governor is considered, and its transfer function is 1/[(1â€‰+â€‰sT_{gi})(1â€‰+â€‰sT_{chi})], where T_{gi} and T_{chi} represent the governor time constant and steam turbine time constant, respectively.
The frequency dynamics can be linearized for smallsignal stability analysis:
where
Define that x(t) = [x_{1}(t) x_{2}(t) â€¦ x_{n}(t)]^{T}, y(t) = [y_{1}(t) y_{2}(t) â€¦ y_{n}(t)]^{T}, u(t) = [u_{1}(t) u_{2}(t) â€¦ u_{n}(t)]^{T}, and Î”P_{d}(t) = [Î”P_{d1}(t) Î”P_{d2}(t) â€¦ Î”P_{dn}(t)]^{T}, where x_{i}(t), y_{i}(t), u_{i}(t), Î”P_{di} (t) represent the state vector, the output of the sensor, the output of the control center, load deviation of the ith area, respectively. Define the system matrix A = [A_{ij}]_{nÃ—n}, the control matrix Bâ€‰ = â€‰diag[B_{1}B_{2} â€¦B_{n}], the output matrix Câ€‰=â€‰diag[C_{1}C_{2} â€¦C_{n}], the disturbance matrix Fâ€‰=â€‰diag[F_{1}F_{2} â€¦ F_{n}]. Î”P_{mi} and Î”P_{vi} represent the generator mechanical power output deviation and control valve position deviation of the ith area LFC power systems, respectively. In addition, T_{ij} is the synchronization factor of the contact line between area i and area j, where T_{ij} = T_{ji}.
The ACE_{i} acts as the input of the PI controller. The information staleness of the ACE messages herein is characterized by AoI g_{ki}(t), where g_{ki}(t) represents the AoI of the kthACE_{i} at the controller at the time t in the ith area LFC. Based on (7b), the output of the LFC controller can be expressed as:
where K_{i} = [K_{pi}K_{Ii}].
The multiarea closedloop AoIaware LFC system can be expressed as:
Defining A_{di} = [0â€¦B_{i}K_{i}C_{i}â€¦0] and assuming each area has the same AoI with g_{k1}(t)â€‰=â€‰g_{k2}(t) = â€¦= g_{kn}(t)â€‰=â€‰g_{k}(t), there is:
The discretetime representation of multiarea AoIaware LFC model can be expressed as:
3.2 Design of an AoIaware PItype controller
In this part, the AoIaware PI controller can be designed and the right AoIaware PI controller can be chosen to improve the LFC performance.
EDR is introduced first to guide the design of the AoIaware PI controller shown in Theorem 1. This step guarantees that the LFC system (11) is exponentially stable and has EDR m. Next, the Hâˆžâ€‰gain Î³ metric is introduced to evaluate the EDR of the designed controller with nonzero load disturbance shown in Condition 1. The values of EDR can be adjusted by Hâˆžâ€‰performance, which describes the disturbance rejection capability of the power system while ensuring the frequency convergence rate. Meanwhile, Algorithms 1 and 2 are respectively proposed to introduce the process of AoIaware PI controller design.
Theorem 1
[9]: Consider AoIaware LFC system (11) with zero load disturbance Î”P_{d} = 0. When given average AoI g_{ave}(Î»), EDR m and turning parameters l_{1} and l_{2}, existing symmetric positive definite matrices P_{1}, P_{3} and symmetric matrices P_{2}, Z, and any appropriately dimensioned matrices X_{1}, X_{2}, S, Y, and R_{2} satisfy the following inequalities:
where Î¶ is the dimension of the matrix A in (11). Then any AoI smaller than g_{ave}(Î») can keep the AoIaware LFC system stable with EDR m. The control gain of the AoIaware PI controller can thus be obtained by:
To evaluate the EDR of the designed controller, Hâˆžâ€‰performance analysis is introduced in Condition 1.
Condition 1
Here Î³ is introduced to present Hâˆžâ€‰performance. Considering an AoIaware LFC system (11) with Î”P_{d} â‰ 0, when given Hâˆžâ€‰gain Î³, existing symmetric positive definite matrices P_{1}, P_{3} and symmetric matrices P_{2}, Z, and any appropriately dimensioned matrices X_{1}, X_{2}, R_{2}, and L satisfy the following inequalities.
Then any AoI smaller than g_{ave}(Î») can keep the AoIaware LFC system stable with load disturbance Î”P_{d} and Hâˆžâ€‰gain Î³. c_{1}^{T}C_{i}^{T}C_{i}c_{1} should be added into Ï†_{1} and the other matrix notations are the same as Theorem 1. The proof of Condition 1 is given in [30].
The algorithm of design of the AoIaware PI controller is discussed. For a given allowable average AoI g_{ave}(Î»_{i}), the following Algorithm 1 is developed to determine the AoIaware PI controller gains K_{pi}, K_{Ii} with desired EDR, including Hâˆžâ€‰gain Î³.
Next, Algorithm 2 is proposed to optimize the LFC performance W. W can be minimized by following two steps. The optional update period is relatively limited in practical power systems. The first step is to design the different AoIaware PI controller gains for each allowed update period according to EDR, while the second step is to find the appropriate AoIaware PI controller and the update period based on the degree of frequency fluctuation of power system W. The specific process to optimize LFC performance is shown in Algorithm 2.
4 Case study
In this section, the correctness of the AoIaware LFC model is proved and case studies are carried out on onearea and twoarea power systems. The performances of the system with different update periods are evaluated. Additionally, the abilities of the proposed AoIaware PI controller and delaydependent PI controller to stabilize the system are compared.
4.1 Prove the correctness of the AoIaware LFC model
Considering the onearea power system in TableÂ 2, the update period is Î»â€‰=â€‰2.2Â s, the AoIaware PI controller gains are K_{p} = 0.6952, K_{I} = 0.3752, and the load disturbance is Î”P_{d} = 0.02 pu. FigureÂ 3 compares the frequency deviation Î”f from the Simulink results and simulation results based on the proposed AoIaware LFC model. As can be seen from Fig.Â 3 that the frequency deviation curves are almost the same, which proves the correctness of the AoIaware LFC model.
4.2 Onearea AoIaware LFC
Considering a onearea AoIaware LFC system, the systemâ€™s parameters are reported in TableÂ 2. It assumes that Î±_{1}â€‰=â€‰1, the constant load disturbance Î”P_{d}=0.02 pu, and the observation interval Tâ€‰=â€‰17Â s. Let the tuning parameters l_{1}â€‰=â€‰0, l_{2}â€‰=â€‰2.03, and Hâˆžâ€‰gain Î³â€‰=â€‰20, the AoIaware PI controller gain parameters K_{p} and K_{I} with different update periods are listed in TableÂ 3.
FigureÂ 4 demonstrates the performance of the onearea system with different update periods. As the update period grows from 1.4 to 2.2Â s, the system performance index W decreases rapidly. While the update period increases from 2.2 to 4.6Â s, the worse system frequency performance is obtained. Thus, Î»â€‰=â€‰2.2Â s is the right point for optimal onearea power system performance. FigureÂ 4 reveals that LFC performance and update period are related. Therefore, the right update period can be found directly for optimal performance. It also reveals that both too long and too short update periods significantly deteriorate the onearea power system performance.
Additionally, it can be seen from Fig.Â 4 that the average AoI is a convex function with the update period, while both long and short update periods lead to larger average AoI. A long update period means the control center may not receive fresh information frequently, whereas a short update period leads to information queuing in the communication channel. FigureÂ 4 shows that the average AoI can reflect timely information updates.
FigureÂ 5 compares the frequency deviations of the onearea power system with update periods Î»â€‰=â€‰1.4Â s, 2.2Â s, and 4.6Â s. It is observed from Fig.Â 5 that the fluctuation and convergence time of Î”f with Î»â€‰=â€‰2.2Â s are smaller and shorter than the Î”f with Î»â€‰=â€‰1.4 and 4.6Â s. Thus, Fig.Â 5 verifies that system performance can be degraded by inappropriate update periods. For example, when Î»â€‰=â€‰1.4Â s, information packets are queued heavily in the communication channel, which increases the communication delay and AoI. In contrast, when Î»â€‰=â€‰4.6Â s, the control center cannot receive enough information for decisions, which leads to poor system performance. The above results are consistent with Fig.Â 4, which also proves the correctness of Algorithm 1 and Algorithm 2.
It is clear from Fig.Â 6 that the frequency deviation Î”f with the proposed AoIaware controller, excels the smaller settling time and overshoots compared to the delaydependent controller in [9]. The superiority of the proposed controller over the delaydependent one may attribute to AoI. Long and short update periods lead to a larger average AoI. The AoIaware controller can improve LFC performance by choosing the optimal update period better than the delaydependent controller. Therefore, the AoIaware controller has better performance than the delaydependent one.
Considering the scenario with random load disturbances depicted in Fig.Â 7a, it is clear from Fig.Â 7b that the frequency deviation Î”f with the right update period of 2.2Â s, excels the smallest settling time and overshoots than the others.
FigureÂ 8 illustrates the frequency responses of the onearea system by the proposed AoIaware controller and delaydependent controller. It can be seen that frequency convergence during random load disturbances is quicker by the proposed AoIaware controller than the delaydependent controller.
Consider the onearea AoIaware LFC system in TableÂ 2 with GRC and GDB constraints. GRC is the constraint on the rate of change in the generating power due to physical limitations [31], while GDB is the total magnitude of a sustained speed change within which there is no change in the valve position of the turbine [32]. The nonlinear model of the GRC and GDB shown in Fig.Â 9 replaces the linear nonreheating steam turbine generator model in Fig.Â 1. The GRC of the reheat units is set as 3% of the rated power per minute [33] and the GDB is 0.036Â Hz [34]. Defining the update period Î»â€‰=â€‰3.0s, the AoIaware PI controller gains K_{p} = 0.500 and K_{I} = 0.336, the delaydependent controller gains [9] K_{p} = 0.601, K_{I} = 0.367 and the load disturbance Î”P_{d} = 0.02 pu, Fig.Â 10 shows the frequency responses of the onearea system with GRC and GDB by the proposed AoIaware controller and the delaydependent controller. It is clear from Fig.Â 10 that frequency deviations are relatively small with the proposed AoIaware controller. It demonstrates that, when the onearea system considers the GRC and GDB, the frequency with the proposed AoIaware controller converges faster than the delaydependent controller.
The onearea AoIaware LFC system in TableÂ 2 with generator temporary faults is considered, and four identical generators are selected with rated capacity of 100 MVA, i.e., S_{N1}=S_{N2} = S_{N3} = S_{N4} = 100 MVA, and reference power value of 2000 MVA. Assume the load capacity is 100 MVA and the four generators distribute the power generation equally. Under normal operating conditions, each generator produces 25 MVA power output. In this case, it assumes that the first, second, and third generators have temporary faults at 3â€“8Â s, 12â€“18Â s, and 11â€“15Â s, respectively. The update period is Î»â€‰=â€‰2.2Â s, the AoIaware PI controller gains are K_{p} = 0.695, K_{I} = 0.375, the delaydependent controller gains are K_{p} = 0.698, K_{I} = 0.243, and the load disturbance Î”P_{d} = 0.02 pu.
FigureÂ 11a shows that the frequency deviation Î”f with the proposed AoIaware controller excels the smaller settling time and overshoots compared to the delaydependent controller with generator temporary faults. FigureÂ 11b, c respectively illustrate the generator mechanical power output deviation under generator temporary faults with the AoIaware controller and delaydependent controller. It is clear that the generator mechanical power output deviations with the AoIaware controller are relatively small.
4.3 Twoarea AoIaware LFC
Considering a twoarea AoIaware LFC system, the systemâ€™s parameters are reported in TableÂ 4. It assumes that Î±_{1}â€‰=â€‰Î±_{2}â€‰=â€‰1, the constant load disturbance Î”P_{d} = 0.02 pu, the observation interval Tâ€‰=â€‰27Â s, and l_{1}â€‰=â€‰0, l_{2}â€‰=â€‰2.03, Î³â€‰=â€‰20. Different AoIaware PI controller gain parameters K_{p1}, K_{I1,} and K_{p2}, K_{I2} are calculated by following Algorithm 2 as shown in TablesÂ 5 and 6, respectively. K_{p1}, K_{I1,} and K_{p2}, K_{I2} represent the AoIaware controller gains for area 1 and area 2, respectively. the AoIaware LFC system performance W is then calculated by Algorithm 1 as shown in Fig.Â 12.
FigureÂ 12 shows the performance index W with different update periods. It shows that system performance is improved as the update period grows from 1.4 to 2.2Â s. When the update period increases from 2.2 to 4.6Â s, the system frequency performance degrades. Therefore, the update period 2.2Â s is the right choice for the system. A long or short update period makes the system performance index W worse. The results are similar to those in Fig.Â 4.
To show the superiority of the right update period on improving the system performance, Fig.Â 13 compares the performances with different update periods and same load disturbance in the twoarea system. It can be seen from Fig.Â 13a that when area 1 has the right update period of 2.2Â s, the frequency converges faster with less fluctuation. For area 2, similar results can be seen from Fig.Â 13b. The above results are consistent with Fig.Â 12, proving the correctness of Algorithm 1 and Algorithm 2.
FigureÂ 14 illustrates the superiority of the AoIaware controller to stabilize the twoarea power system with load disturbance. It can be seen from Fig.Â 14a that the AoIaware PI controller stabilizes the frequency of area 1 in 15Â s. However, the delaydependent controller stabilizes the system in around 25Â s. A similar conclusion can be seen for area 2 from Fig.Â 14b. Î»â€‰=â€‰2.2Â s is the right update period for the twoarea system. The AoIaware controller can improve LFC performance through choosing the right update period but the delaydependent controller is unable to. Therefore, the AoIaware controller has better performance than the delaydependent one.
Considering the scenario with random load disturbances of area 1 and area 2, the results are depicted in Fig.Â 15a, b, respectively. Additionally, it can be seen from Fig.Â 15c that the AoIaware PI controller in area 1 with the optimal update period of 2.2Â s results in faster convergence and less fluctuation in the frequency. FigureÂ 15c shows that with the random load disturbance, the performance of the area 1 system can be improved by using the right update period. A similar conclusion for area 2 can be seen from Fig.Â 15d.
FigureÂ 16 shows the abilities of the proposed AoIaware controller and delaydependent controller to stabilize the twoarea power system. It has random load disturbances shown in Fig.Â 15a. It can be seen from Fig.Â 16a that frequency convergence is quicker by using the proposed AoIaware controller for area (1) Additionally, Fig.Â 16b demonstrates that AoIaware LFC response is faster in area (2) Above all, the AoIaware controller shows superiority in stabilizing the power system than the delaydependent controller.
The twoarea AoIaware LFC system in TableÂ 4 with GRC and GDB constraints is now considered. Set the GRC of the reheat units as 3% of the rated power per minute [33] and the GDB as 0.036Â Hz [34]. Define the update period Î»_{1}â€‰=â€‰Î»_{2}â€‰=â€‰3.0Â s, the area 1 AoIaware PI controller gains K_{p1} = 0.496, K_{I1} = 0.209, the delaydependent controller gains K_{p1} = 0.542, K_{I1} = 0.251, the area 2 AoIaware PI controller gains K_{p2} = 0.492, K_{I2} = 0.217, the delaydependent controller gains K_{p2} = 0.540, K_{I2} = 0.253 and the load disturbance Î”P_{d} = 0.02 pu. FigureÂ 17 shows the superiority of the proposed AoIaware controller compared with the delaydependent controller in stabilizing the twoarea power system with GRC and GDB. It can be seen from Fig.Â 17a that frequency convergence is quicker by using the proposed AoIaware controller for area 1, while Fig.Â 17b demonstrates that LFC with an AoIaware controller response is also faster in area 2.
The twoarea AoIaware LFC system in TableÂ 4 with generator temporary faults is considered. Each area elects four identical generators with a rated capacity of 100 MVA, and the reference power value of this twoarea system is 2000 MVA. Assume the load capacity is 100 MVA and the four generators in each area distribute the power generation equally. In area 1, the first, second, and third generators have temporary faults at 10â€“15Â s, 7â€“16Â s, and 9â€“13Â s, respectively. Additionally, with the update period Î»â€‰=â€‰2.2Â s, the AoIaware PI controller gains K_{p1} = 0.610, K_{I1} = 0.242, the delaydependent controller gains K_{p1} = 0.502, K_{I1} = 0.136, and the load disturbance Î”P_{d} = 0.02 pu, Fig.Â 18a shows area 1 frequency deviations with the proposed AoIaware controller and the delaydependent controller under generator temporary faults. FigureÂ 18b, c respectively illustrate area 1 generator mechanical power output deviations under generator temporary faults with the AoIaware controller and the delaydependent controller. As seen, Fig.Â 18 clearly illustrates the superiority of the AoIaware controller in stabilizing the area 1 system with generator temporary faults.
In area 2, the first and third generators have temporary faults at 5â€“16Â s and 17â€“23Â s, respectively. The update period is Î»â€‰=â€‰2.2Â s, the AoIaware PI controller gains are K_{p2} = 0.773, K_{I2}=0.245, the delaydependent controller gains are K_{p2} = 0.440, K_{I2} = 0.181, and the load disturbance is Î”P_{d} = 0.02 pu. FigureÂ 19 illustrates the superiority of the proposed AoIaware controller compared with the delaydependent controller in stabilizing the area 2 system. The area 2 generator mechanical power output deviations under generator temporary faults with an AoIaware controller and a delaydependent controller are respectively shown in Fig.Â 19b, c. It can be seen from Fig.Â 19a that frequency convergence is quicker by using the proposed AoIaware controller for area 2.
5 Conclusion
This paper designs an AoIaware PItype controller to optimize LFC performance. AoI is first applied to characterize information staleness, and in comparison with communication delay, AoI contains control factors of the update process and provides the communication system model controllability. Compared with the delaydependent controller, the AoIaware controller greatly improves the LFC system performance. Different AoIaware PItype controllers are then designed for different update periods according to EDR based on the AoIaware LFC model. A right AoIaware PItype controller and update period are selected according to the degree of frequency fluctuation of the power system. The case studies show the effectiveness of the proposed AoIaware PItype controller. When the LFC system has the right AoIaware PItype controller and update period, high performance can be achieved. It also illustrates the superiority of the proposed AoIaware controller over the delaydependent controller in stabilizing the LFC system. In the future, redesigning a controller based on the AoIaware LFC model with the GRC and the GDB may be considered by chaosbased firefly algorithm or firefly algorithm.
Availability of data and materials
Data and materials are obtained simulation program. This simulation program is MATLAB.
References
Shayeghi, H., Shayanfar, H. A., & Jalili, A. (2009). Load frequency control strategies: A stateoftheart survey for the researcher. Energy Conversion and Management, 50(2), 344â€“353.
Pandey, S. K., Mohanty, S. R., & Kishor, N. (2013). A literature survey on loadâ€“frequency control for conventional and distribution generation power systems. Renewable and Sustainable Energy Reviews, 25(1), 318â€“334.
Kundur, P., Balu, N. J., & Lauby, M. G. (1994). Power system stability and control. New York: McGraw Hill Press.
Bevrani, H. (2019). Frequency response characteristics and dynamic performance. In Robust power system frequency control (pp. 49â€“59). Springer Press. https://doi.org/10.1007/9783319072784_3
Singh, V. P., Kishor, N., & Samuel, P. (2016). Load frequency control with communication topology changes in smart grid. IEEE Transactions on Industrial Informatics, 12(5), 1943â€“1952.
Bhowmik, S., Tomsovic, K., & Bose, A. (2004). Communication models for third party load frequency control. IEEE Transactions on Power Systems, 19(1), 543â€“548.
Yu, X., & Tomsovic, K. (2004). Application of linear matrix inequalities for load frequency control with communication delays. IEEE Transactions on Power Systems, 19(3), 1508â€“1515.
Ojaghi, P., & Rahmani, M. (2017). LMIbased robust predictive load frequency control for power systems with communication delays. IEEE Transactions on Power Systems, 32(5), 4091â€“4100.
Shangguan, X. C. (2021). Robust load frequency control for power system considering transmission delay and sampling period. IEEE Transactions on Industrial Informatics, 17(8), 5292â€“5303.
Jiang, L., Yao, W., Wu, Q., Wen, J., & Cheng, S. (2012). Delaydependent stability for load frequency control with constant and timevarying delays. IEEE Transactions on Power Systems, 27(2), 932â€“941.
Zhang, C. K., Jiang, L., Wu, Q., He, Y., & Wu, M. (2013). Delaydependent robust load frequency control for time delay power systems. IEEE Transactions on Power Systems, 28(3), 2192â€“2201
Wang, X., Chen, C., He, J., Zhu, S., & Guan, X. (2021). AoIaware control and communication codesign for industrial IoT systems. IEEE Internet of Things Journal, 8(10), 8464â€“8473. https://doi.org/10.1109/JIOT.2020.3046742
Yang, F., He, J., & Wang, D. (2018). New stability criteria of delayed load frequency control systems via infiniteseriesbased inequality. IEEE Transactions on Industrial Informatics, 14(1), 231â€“240.
Jin, L., Zhang, C. K., He, Y. (2019). Delaydependent stability analysis of multiarea load frequency control with enhanced accuracy and computation efficiency. IEEE Transactions on Power Systems, 34(5), 3687â€“3696.
Yang, T., Zhang, Y., Li, W., & Zomaya, A. Y. (2020). Decentralized networked load frequency control in interconnected power systems based on stochastic jump system theory. IEEE Trans. Smart Grid, 11(5), 4427â€“4439.
Liu, F., Li, Y., & Cao, Y. (2016) A twolayer active disturbance rejection controller design for load frequency control of interconnected power system. IEEE Transactions on Power Systems, 31(4), 3320â€“3321.
Liu, S., & Liu, P. X. (2018). Distributed modelbased control and scheduling for load frequency regulation of smart grids over limited bandwidth networks. IEEE Transactions on Industrial Informatics, 14(5), 1814â€“1823.
Singh, V. P., Kishor, N., & Samuel, P. (2017). Improved load frequency control of power system using LMI based PID approach. Journal of the Franklin Institute, 354(15), 6805â€“6830.
Kaul, S., Yates, R., & Gruteser, M. (2012). Realtime status: How often should one update? In Proceedings of the 2012 proceedings IEEE INFOCOM (pp.Â 2731â€“2735). https://doi.org/10.1109/INFCOM.2012.6195689
Talak, R., Karaman, S., & Modiano, E. (2017). Minimizing ageofinformation in multihop wireless networks. In Proceedings of the 2017 55th annual Allerton conference on communication, control, and computing (Allerton) (pp.Â 486â€“493). https://doi.org/10.1109/ALLERTON.2017.8262777
Kaul, S., Gruteser, M., Rai, V., & Kenney, J. (2011). Minimizing age of information in vehicular networks. In 2011 8th annual IEEE communications society conference on sensor, mesh and adhoc communications and networks (pp.Â 350â€“358). https://doi.org/10.1109/SAHCN.2011.5984917
Liao, K., & Xu, Y. (2018). A robust load frequency control scheme for power systems based on secondorder sliding mode and extended disturbance observer. IEEE Transactions on Industrial Informatics, 14(7), 3076â€“3086.
ShangGuan, X. C., He, Y., & Zhang, C. K. (2020). Sampleddata based discrete and fast load frequency control for power systems with wind power. Applied Energy, 259, 114202.
Lin, C., et al. (2023). Eventtriggered load frequency control based on ageofinformation. IEEE Transactions on Power Systems, 38(3), 2348â€“2361.
Hauser, C. H., Bakken, D. E., & Bose, A. (2005). A failure to communicate nextgeneration communication requirements, technologies, and architecture for the electric power grid. IEEE Power & Energy Magazine, 3(2), 47â€“55.
Yates, R. D. (2015). Lazy is timely: Status updates by an energy harvesting source. In 2015 IEEE international symposium on information theory (ISIT) (pp.Â 3008â€“3012). https://doi.org/10.1109/SAHCN.2011.5984917
Zhang, C. K., Jiang, L., Wu, Q., He, Y., & Wu, M. (2013). Further results on delaydependent stability of multiarea load frequency control. IEEE Transactions on Power Systems, 28(4), 4465â€“4474.
Inoue, Y., Masuyama, H., Takine, T., & Tanaka, T. (2017). The stationary distribution of the age of information in FCFS singleserver queues. In 2017 IEEE international symposium on information theory (ISIT) (pp.Â 571â€“575). https://doi.org/10.1109/ISIT.2017.8006592
Jiao, D., Lin, C., Xie, K., Hu, B., Shao, C., & Gao, S. (2022). Stability analysis of load frequency control based on ageofinformation. In 2022 IEEE 5th international electrical and energy conference (CIEEC) (pp.Â 2103â€“2108). https://doi.org/10.1109/CIEEC54735.2022.9846373
Peng, C., Zhang, J., & Yan, H. (2018). Adaptive eventtriggering Hâˆž load frequency control for networkbased power systems. IEEE Transactions on Industrial Electronics, 65(2), 1685â€“1694.
Bevrani, H., & Hiyama, T. (2011). Intelligent automatic generation control. Boca Raton: CRC Press. https://doi.org/10.1201/b10869
Zare, K., Hagh, M. T., & Morsali, J. (2015). Effective oscillation damping of an interconnected multisource power system with automatic generation control and TCSC. International Journal of Electrical Power & Energy Systems, 65, 220â€“230.
GolpÃ®ra, H. (2011). Application of GA optimization for automatic generation control design in an interconnected power system. Energy Conversion and Management, 52(5), 2247â€“2255.
IEEE Recommended Practice for Functional Performance Characteristics of Control Systems for Steam TurbineGenerator Units. In IEEE Std 122â€“1985 (Vol.Â 54, pp.1â€“26) (1985. https://doi.org/10.1109/IEEESTD.1992.101082
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This research was partially funded by grants from the National Natural Science Foundation of China under grant 52107072, China Postdoctoral Science Foundation under grant 2022T150768 and 2021M693711.
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Conceptualization: DJ, XZJ and CRL. Methodology: DJ and CRL. Validation: DJ and CRL. Formal analysis: DJ, CRL, and CZS. Writingâ€”original draft: DJ. Writingâ€”review and editing: DJ, CRL, and CZS. Supervision: KGX and BH. All the authors read and approved the final manuscript.
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Jiao, D., Shao, C., Hu, B. et al. Ageofinformationaware PI controller for load frequency control. Prot Control Mod Power Syst 8, 39 (2023). https://doi.org/10.1186/s4160102300311z
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DOI: https://doi.org/10.1186/s4160102300311z