Improved Memory Event-Triggered Load Frequency Control in Multi-Area Power System With Renewable Energy

To mitigate the data transmission burden, an new memory event-trigger scheme is developed for the load frequency control (LFC) of multi-area networked power systems with the integration of various new energy sources. <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> stability criteria under less conservative conditions are established by utilizing an improved Lyapunov stability theory and a second-order Bessel-Legendre (B-L) inequality for the LFC power system using the presented memory event-trigger scheme. Simulation on a two-area LFC system and IEEE-39 bus station test system are performed to validate the proposed method.

general, there are two main types of event-trigger schemes: continuous event-trigger scheme and discrete event-trigger scheme.Besides, there are some improved event-trigger schemes [8], [9].Hence, research into the LFC power system is required, particularly in introducing an improved eventtrigger scheme.
Many researchers have paid attention to the improved eventtrigger scheme in power systems.At first, the traditional event-trigger scheme is applied in power system [10], [11].Liu et al. utilizies the event-triggered LFC for multi-area power systems [12].The event-trigger scheme for power systems with communication delays is investigated to reduce the amount of data transmission in [13].In an event-trigger scheme, the trigger performance is related to the threshold parameter.However, for the traditional event-trigger scheme, the trigger threshold needs to be preset, limiting the performance of the scheme.Then, an adaptive scheme with adaptive eventtrigger communication scheme is studied in power system.The adaptive event-triggering H ∞ LFC for power systems is investigated in [14].Moreover, adaptive event-triggered sliding mode control is utilized in multi-area power systems [15].However, when the system is at a peak or trough, the burden of data sampling is very heavy in order to shorten the control time and achieve synchronization, and this is expected to be alleviated by advanced techniques.
With the deepening of research on event-trigger schemes, the memory event-trigger scheme is applied in power system.A memory event-trigger H ∞ LFC of a multi-area power system with transmission time delay is proposed in [16].Mu et al. apply the memory event-trigger power system with a fuzzy model [17].The memory-based event-triggering H ∞ LFC for power systems under deception attacks is built in [18].For the memory event-triggered scheme, the trigger criteria are determined by several recently released signals and current trigger data; thus, the event-trigger scheme can obtain better trigger performance.However, the amount of data storage and computation in memory event-trigger scheme is increased, owing to some released data packets being saved in storage areas.Therefore, improving the memory event-trigger scheme is the motivation for this brief.
Motivated by the challenges influx of various network information into power systems, a novel memory eventtriggered LFC is presented in this brief.The main contributions of this brief can be summarized as follows: Considering the higher percentage of renewable energy resources within the power system, a multi-area LFC power system with both wind power and energy storage is studied.To reduce the burden of 1549-7747 c 2023 IEEE.Personal use is permitted, but republication/redistribution requires IEEE permission.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.mass information transmission, a novel memory event-trigger scheme is developed.An improved Lyapunov function and second-order Bessel-Legendre (B-L) inequality are used to build the stability criteria with less conservation.

TABLE I NOTATIONS
The remaining sections of this brief are structured as follows: Section II builds the model of novel memory eventtriggered LFC power system with wind energy and energy storage units.In Section III, the stability of the designed multiarea LFC power system based on linear matrix inequality (LMI) is discussed.Section IV presents the simulation results and comparative analysis.Finally, Section V concludes this brief.

II. PROBLEM STATEMENT A. Load Frequency Control System Modelling
Considering the small fluctuations of load, the dynamic model of the multi-area power system LFC can be expressed as the following equation (1).Then the investigated multi-area LFC flow is described in Fig. 1.The parameters of the i-th control area are represented in Table I. where The area control error (ACE) signal can be written as

B. Novel Memory Event-Trigger Scheme for LFC Power System
To relieve the information transmission burden of multi-area power system, a improved event-trigger scheme is employed in this brief.Compared with traditional event-trigger schemes, the improved memory event-trigger scheme can store a recent triggering threshold, which is used to adjust the event-trigger condition.For traditional event-trigger schemes, signal packets can be delivered if the designed trigger threshold can be satisfied.The traditional event-trigger criterion is designed as where is an unknown positive matrix; λ denotes the triggering threshold which needs to be preset.
Unlike the traditional event-trigger scheme, the proposed memory event-trigger scheme utilizes not only the changes between the current sampling moment data and the last released information but also the previous trigger threshold.Therefore, the designed novel memory event-trigger scheme can be described as where ≤ c , a + b = 1, and 0 ≤ c ≤ 1 is a unknown positive matrix.Define: where The controller input can be described as: Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply. where Therefore, the designed novel memory event-trigger condition can be described as Then, the studied LFC power system model can be revised as: Remark 1: For the designed trigger scheme, the current sampling moment data, along with the last released information and the previous trigger threshold, are utilized to determine whether the current sampling moment data can be transmitted.Compared with traditional event-trigger schemes, the designed scheme can better release redundant information with the adaptively trigger threshold.In addition, compared with memory event-trigger scheme, the proposed scheme does not require calculating the previous triggering condition; it only stores the previous trigger threshold, reducing the computational burden.Therefore, the applied novel memory event-trigger scheme possesses excellent performance.

III. STABILITY ANALYSIS OF MEMORY
EVENT-TRIGGERED LFC Applying the proposed novel memory event-trigger scheme, the stability and stabilization criteria of the multi-area LFC model will be derived.Then, an improved Lyapunov function and integral inequality with an auxiliary function are employed to build the stability criteria in the following.
Proof: Build the following Lyapunov function: Calculating the derivative of V(t) along the trajectory of (1) with ω(t) = 0 yields: Set the augmented vector as follows: Then, the following inequality can be derived as where Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
Therefore, if φ2 > 0 can be satisfied, the following inequality can be yielded: Thus, by utilizing the [20, Lemma 1] the condition (8) can be derived.With a condition that ω(k) = 0, if ( 8) and ( 9) are satisfied, there exists a sufficiently small scalar c ∈ (0, 1], such that V(k) < −c ξ 1 (t) 2 < 0 can be procured.As a result, the system (1) with ω(k) = 0 is asymptotically stable.Remark 2: The improved Lyapunov function with the triple integral term in V(t) is applied in this section.Then, the maximum time delay τ M and τ are considered in this theorem.In addition, a second-order B-L inequality is applied in Ṽ1 (t) which can provide tighter upper bounds than those acquired by [20].
Following that, H ∞ stability criterion of the multi-area LFC model (1) will be developed.
Theorem 2: For given constant λ m , τ M , τ , if there exist positive definite matrices P, Q 1 , Q 2 , R 1 , R 2 , S 1 , S 2 , , appropriate dimensions T 11 , T 12 , T 13 , T 21 , T 22 , T 23 ,T 31 , T 32 , T 33 , and the following LMIs hold, the multi-area LFC model ( 1) is asymptotically stable with an H ∞ norm bound γ . where For prescribed attenuation level γ > 0, taking the disturbance ω(t) into account, the cost function J is considered as Setting the augmented vector as Remark 3: The sufficient stability condition of the multiarea LFC model ( 1) is provided in Theorem 1 and Theorem 2. To design the controller gain, recalling (12) and employing [20, Lemma 1], the following inequality can be obtained: ). Pre-multiplying and post-multiplying both sides of ( 14) with diag{I, . . .9 , I, P, P, P}, and utilizing the fact that Z < 0, Y T = Y, then Y T ZY ≤ −2Y − Z −1 can be obtained, and 2 < 0 can be further converted.Therefore, the theorem is proved and the controller gain is K = PK.

IV. CASE STUDY AND DISCUSSION
A two-area interconnected power system and IEEE-39 bus station test system are applied in this section to validate the proposed novel memory event-trigger scheme.
Case A: Two-area LFC power system with improved memory event-trigger scheme Consider a two-area LFC power system with wind farms and energy storage units as shown in [20].The detailed parameters are in [20].To analyze the designed memory event-trigger scheme performance for two-area LFC power system, the improved memory event-trigger scheme with c = 0.2 and c = 0.6 are explored in this case, respectively.
To evaluate the designed improved memory event-trigger scheme performance, release time instants and intervals with c = 0.2 and c = 0.6 are depicted in Fig. 2(a), (b).It can be observed that less information is transmitted in the second situation with c = 0.2, compared with the first situation with c = 0.6.The proposed improved memory event-trigger scheme can eliminate unnecessary information exchange and relieve the transmission burden for LFC power system.
To scrutinize the LFC scheme performance under developed novel memory event-trigger scheme, frequency deviation changes and ACE changes are manifest in Fig. 2(c), (d).When external disturbances occur, the designed power frequency deviation changes and ACE changes can go back to the preset value immediately.Therefore, the designed LFC with novel memory event-trigger scheme can adjust frequency to near-stable conditions effectively, and the designed memory event-trigger scheme can reduce the redundance of signal data transmission.
Case B: The modified IEEE-39 bus test power system with improved memory event-trigger scheme To verify the performance of the proposed improved memory event-trigger scheme in power system, an IEEE-39 bus model is built using MATLAB/Simulink, as shown in Fig. 3.The system is divided into three control areas, with Gen3, Gen7 and Gen9 as the selected generator in Area 1, Area 2 and Area 3, respectively.Moreover, the traditional event-trigger scheme, adaptive event-trigger scheme and the improved memory event-trigger scheme is utilized in Area 1, Area 2 and Area 3, respectively.
At t = 20s, t = 50s and t = 80s, perturbation is added to Bus 8, Bus 16 and Bus 3, respectively.At this time, the response, trigger interval and trigger time in three areas are shown in Fig. 4.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.As can be seen from Fig. 4, the frequency deviation in three areas converges to a steady state within a short period of time.At the moment of the perturbation, the system performance needs a large amount of data for improvement, the event-trigger scheme transmits a large amount of data at this time.However, the least amount of data is transmitted in Area 3 under designed improved memory event-trigger scheme.Therefore, the proposed improved memory eventtrigger scheme in this brief has a better performance in reducing the amount of redundant information transmission.
V. CONCLUSION An new memory event-trigger scheme is developed for the load frequency control of power systems with renewable energy resources.An improved Lyapunov function and a second-order B-L inequality are applied to obtain the stability criteria with less conservation.The simulation of two-area LFC power system and IEEE-39 bus test system are conducted to validate the proposed novel memory event-trigger scheme.In comparison with the traditional event-trigger scheme, the presented event-trigger scheme can significantly reduce redundant data transmission and there is no need to calculate the previous triggering condition.

Fig. 1 .
Fig. 1.Transfer function model of multi-area power system.