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Research on Emotional Interaction Problems and Countermeasures of Intelligent Products based on Consumer Behaviours Analysis

Intelligent products should not only pay attention to their mechanical function, but also give users emotional and spiritual pleasure, have higher personification degree and improve the use experience. Intelligent products should interact with users naturally, perceive the different moods, environments and mood changes of users, find the core needs of users through intelligent technology, and provide suggestions and solutions quickly and accurately. By using the methods of literature research, investigation and comparative analysis, this paper discusses the emotional interaction design scheme of intelligent products based on consumer behavior. Through a questionnaire survey, focus group forum and analysis of collected data, the paper summarizes the influence of emotional interaction mode of intelligent products and the expression mode and voice tone of an intelligent voice assistant on user experience, purchase standard and product personification degree, and the satisfaction and hope improvement of consumers when using intelligent products. In addition, the personalized design of product shape, color and scene mode should be carried out according to the different user groups, so as to produce an intelligent product with higher user comfort and dependence, promote the development of intelligent products and improve user experience.

INTRODUCTION
With the rapid development of the Internet and intelligent technology, the process of information technology is accelerating. More products are developing in the direction of intelligence. People's dependence on machines is gradually increasing. For example, the washing machine which can automatically and intelligently identify the color and quantity of clothing fabrics to determine the amount of water and washing liquid; the sweeping robot which can avoid obstacles intelligently, and combine dry and wet cleaning; Smart bracelet, a wearable intelligent product, can monitor our heartbeat, blood pressure and other data at any time, and then give real-time exercise suggestions; intelligent products related to children's learning can make personalized learning plans according to the user's performance fluctuation and learning situation. All of them bring great benefits to people's life. At the same time, the vigorous development of e-commerce platforms and high-tech companies has also brought huge economic benefits. The change of lifestyle and shopping style is quietly changing our society, followed by the transformation and development opportunities of all walks of life. The gradual optimization of intelligent products has reduced the employment and development costs of many enterprises and companies, but also increased many new jobs to solve social employment problems. Only by combining science and technology with people's feelings, can we have a better development market, be accepted by more consumers, and bring huge economic benefits and social development. The ultimate goal of science and technology is to enable everyone to enjoy the welfare of science and technology development and facilitate people's life.
With the rapid development of all kinds of science and technology products, it is very important to update the products that meet the needs of customers. Users are no longer satisfied with the cold machine and its various simple functions, but gradually pay more attention to the use experience and emotional and spiritual pleasure. Even the appearance of the product, the voice of the voice system, and different scenarios in different environments all affect the user's ratings to varying degrees. In 1997, Picard of MIT put forward the concept of affective computing. By giving machines the ability to recognize, understand and express human emotions, computers have higher intelligence. The relationship between people and intelligent products is not only a relationship of asking for and executing orders, but also a role that intelligent products can communicate with like friends. When users use it, it not only completes a task, but also shares happiness with people after that. It requires designers to design an intelligent product based on user, scene and emotional mode. By combing the relevant literature，Liao Qinglin found that the higher the degree of emotional interaction, the higher the degree of personification of product perception. Under the same conditions, the degree of personification of intelligent voice assistant of female image is higher than that of intelligent voice assistant of male image. The degree of personification of product perception and user satisfaction is in line with the linear regression model, that is, to a certain extent, with the increase of personification, the degree of user satisfaction will increase. It should be increased. Users hope that the smart home assistant can initiate dialogue actively, and record user habits and basic information appropriately, so as to realize multiple rounds of dialogue and continuous interaction [1]. Norman once said, "We know a lot of information products, especially those closely related to our daily life. The design goal of the products is not only to make products more reasonable, more efficient, more multifunctional and more operational tools, but also to become a more comfortable and interesting emotional design, which has gradually become an important factor for users to buy the product." [2] Lin Wenqian used a convolution neural network to collect a variety of human physiological parameters through wearable devices, and tried to send different control commands to the manipulator according to the change of emotion [3].
Most scholars mainly study the application of emotional interaction design in intelligent products or emotional computing, but there is still a lack of research on emotional interaction of intelligent products based on consumer behaviour analysis. This paper will use the literature research method, survey method and comparative analysis method to find out the shortcomings of current intelligent products and the future development and improvement aspects. Through the feedback analysis of users after use, we found some problems, such as the response of intelligent products when calling is too indifferent; the intelligent bracelet cannot give encouragement when running for new mileage; the appearance design of children's intelligent wearable products is too common or the emergency call positioning function is not perfect and so on. We will sort out and count these problems, sort out some of the most popular imperfect functions, analyse the status quo and find solutions. Finally, design intelligent products with higher user experience and satisfaction under the support of artificial intelligence technology.

METHODOLOGY
The ultimate goal of emotional interaction is to make the computer automatically adjust on the premise of understanding human emotional state, so that users can have a more perfect experience when using products and rely on intelligent products. In order to achieve this goal, we analyzed a lot of user feedback and some sales data, and carried out comparative analysis and in-depth research, using three methods: literature research method, survey method and comparative analysis method.

Literature research method
Literature review, also known as research review, refers to the paper formed by analysing, summarizing, sorting out and commenting on the existing research results and problems of an academic problem (or research field) in a certain period of time on the basis of comprehensively mastering and analysing the relevant literature of an academic problem (or research field). Literature review generally needs to objectively describe and comment on the current research situation, so as to predict the development and research trend or seek new research breakthrough. The writing steps of literature review can be generally divided into literature collection, literature reading and classification, literature processing, comparison and review, forecasting trends or proposing problems to be further studied [4]. Through reading journals and papers, this paper understands that there are still insufficient researches on emotional interaction of intelligent products at present; through the interpretation of intelligent product industry report, this paper deeply explores the development status and prospects of intelligent products; through reading relevant books, this paper understands the concept and characteristics of emotional interaction

Survey method
Investigation and research method refers to the research method of obtaining relevant materials directly through investigation and understanding of the objective situation, and analysing these materials. In this paper, through the analysis of user reviews of intelligent products, we will find out the functions that users most want to update, and design diversified and personalized product function adjustments that can Advances in Economics, Business and Management Research,volume 190 attract customers, so as to maximize the economic benefits.

Comparative analysis
Comparative analysis method is an analysis method that compares two or more things or objects to find out the similarities and differences between them [5]. This paper will compare the user feedback and product sales changes before and after the same product upgrade, judge whether the economic benefits brought by the function upgrade meet the expectations, and make further product upgrade plan and user satisfaction survey.

Survey and Analysis on emotional interaction of intelligent products (based on survey) (questionnaire)
Ghost s et al. from Samsung company found that for mobile phone voice assistants, calm, professional and rational characters are more favoured by users, and the personality and emotion of virtual assistants should not be displayed too much [6]. Niculescu et al. conducted a group of experiments on Hotel inquiry robots to study the influence of tone, humour and compassion of social robots on user experience [7]. Lee et al. believe that for smart home products, emotion and companionship are the key influencing factors of user satisfaction [8]. Therefore, based on the study and thinking of the above conclusions, we conducted a questionnaire survey and data collection and analysis of group focus Forum on the emotional interaction of intelligent products.

The role of intelligent products
Through the data analysis of the questionnaire survey, we found that respondents are more willing to treat intelligent products as family and friends in life, so product design should pay more attention to emotional accompaniment, communication and other functions, so that users can trust and rely on intelligent products. Fig.1 The role of intelligent products

The basis of judging product role
Respondents' judgment on the role of smart appliances in your life mainly comes from the expression and voice tone of smart products. It shows that intelligent products need to be constantly updated and strengthened in terms of personification to bring users the best experience. So that users can give smart appliances the most needed role in their mind, and truly meet the needs of users. At the same time, it makes a variety of modes of voice intonation and response time setting function, so that users can set their own according to their personal preferences, and have a more comfortable experience, so as to meet everyone's personalized needs as much as possible and occupy more intelligent product market.

Pay more attention when buying products
Respondents pay more attention to the powerful functions of intelligent products when they buy intelligent products. For example, when they buy a sweeping robot, they first pay attention to its cleaning ability, automatic obstacle avoidance function and whether it is suitable for families with children and the elderly, and then they will pay attention to its intelligence and other functions. Therefore, the product should first have perfect functions, and then upgrade the intelligent and emotional interaction.

Response time
We asked the testers to enter the room one by one, and tested the response time of five kinds of calling intelligent assistants: 600ms, 800ms, 1000ms, 1200ms and 1400ms. The responses show that people are more inclined to receive the response in 800ms ~ 1000ms. If the response time is less than 800ms, they will feel interrupted. Moreover, if they respond too eagerly, they will feel monitored all the time. If the response time is longer than 1000ms, the user will think that the product is too slow to respond to the user's questions or requests in time, which will increase the user's impatience and dissatisfaction, and some test subjects will feel that they are not valued.

3.2.2.Speed of speech
We also tested the user's preference for the speech speed of the voice assistant, which is divided into slow speed (7S), medium speed (5S) and fast speed (3S). The data collected show that the test takers prefer medium speed, not only can they hear the content clearly, but also feel comfortable and natural; too fast will have a sense of urgency, cannot hear the content clearly; too slow will not have enough patience to listen to the complete sentence.

Pronunciation and intonation
Finally, the test compares the male's high, middle and low bass with the female's high, middle and low bass. We use the computer to simulate different tones and command them to read the same sentence: "I am very glad to serve you. May I help you?" The results show that the subjects prefer mezzo, which can bring them a sense of pleasure and steadiness, and think that the advice or scheme provided is more reliable. For those who have difficult situations to deal with, they will think that such a voice can ease their anxiety and tension, and generate a sense of dependence that they want to solve problems by asking this intelligent assistant next time.

Problems in emotional interaction of intelligent products
At present, most of the intelligent products in the market are not perfect in the function of perceiving users' emotion changes through tone or language, and need to be further upgraded and strengthened. What's more, some intelligent products have slow voice response, mechanized response, no natural humour in the conversation between people, and poor user experience. Besides, the function of interaction with customers should be upgraded, and the user's voice chat interaction experience is poor. Last but not least, personalization functions such as tone, response time and humour adjustment need to be improved.

Relevant suggestions
Combined with the statistical results of the questionnaire and the test data analysis of the focus group forum, it is concluded that the product should first have powerful functions, and then improve and upgrade the intelligence and emotional interaction. When users use the intelligent products, they will take them as family or friends. When designing the products, they should pay attention to emotional company and communication from the perspective of similar identity, and strive to bring the same company and existence to the users' family and friends. For intelligent products with voice communication, the response time should be controlled between 800ms and 1000ms. The reply content of the intelligent assistant should first respond to the core requirements and questions put forward by users, and pay attention to that the reply should focus on the target requirements, and tell users clearly and directly what to do and how to do. The use of language is simple and natural, not too complicated or mechanized, with the tone close to daily life and sentence structure, and even according to the user's tone to judge their mood and add some jokes to adjust the atmosphere. The voice tone of voice assistant is the most popular among female middle school voice, which can bring users a pleasant and reliable feeling of using and produce a sense of dependence.

Personal pronouns
Professor Clifford NASS and Dr. Scott brave of Stanford University, in their 2005 Book wired for speech, studied whether the voice system should use the personal pronoun "I". The results showed that the design of a recorded voice system using the personal pronoun "I" to reply users would make users feel more relaxed and more like human voice for the speech system using synthetic tone, due to the limitation of sound quality, it is necessary to use "I" with caution [9]. So in the voice system design of intelligent products, the choice and frequency of personal pronouns should be determined according to the main customer groups and product functions, so as to bring the best customer experience.

Appearance colour
For most people, seeing blue makes people feel calm and peaceful; seeing yellow makes people alert and pay attention; seeing green makes people comfortable and relaxed; seeing red makes people warm and excited [10]. Therefore, in product design, we should design different colours according to customers' personal preferences and product design concept.

Scene application
Different scenarios for users to use intelligent products will also bring different use experience. Products should design different scenarios to cooperate with users, so that they can experience a variety of best use feelings in different scenarios. For example, provide a variety of menus and cooking methods in the kitchen, enter the home mode; provide relevant websites or help in work and study, enter the business mode; provide travel routes and accommodation food help when traveling, enter the leisure mode, etc.

Emotional interaction
According to Marx Scheler, "emotion is all human senses, organism, psychology and spirit "It's my feeling." [11] Liu identified the anxiety level of players from the reactions of the autonomic nervous system (ANS), and used it to adapt to the difficulties encountered in table tennis competition; they used similar methods to identify the entertainment of children playing with robots, and let robots change their behaviour to maximize the entertainment [12]. Therefore, the promotion of emotional interaction of intelligent products can greatly improve the user experience and obtain a larger consumer market.

Easy to operate
Any intelligent product should be easy to operate and easy for users to learn to use. For example, the apple watch interface design is simple and convenient, in line with the user's habits; various functional designs make it easy for people to learn, reducing the difficulty of the user's operation. At the same time, the download of app is also very convenient for the learning and use of the elderly and children.

Personalized design
In the view of psychology, personalized, unique or contrary to people's cognitive common sense things are more likely to arouse people's interest and attention. For example, the popular Huawei mobile phone has a simple appearance design, a large screen, few buttons, a unique camera shape and dazzling and colourful appearance colour, which attract consumers' attention and stimulate their purchase desire and behaviour. Therefore, intelligent products should also pay attention to the personalized design of products, such as the tone and volume of voice assistant, response time, product appearance colour, scenario and operation interface.

Summary
Nowadays, the development of intelligent products is very rapid, and various businesses have made a lot of innovations in product design and function. Most of the hard functions of products have been perfect, so the design of emotional interaction must occupy an important position in the future intelligent product design. Therefore, it is very important to optimize the interaction of intelligent products, not only in its own function, appearance design, content improvement, but also in the personification communication with users to make innovation and upgrading.

Summary
In recent years, the emotional interaction of products is a hot topic. With the emergence of various powerful intelligent products on the market, most products mainly focus on the development of their own functions. In order to attract customers' attention and improve user satisfaction, it is necessary to focus on the emotional interaction design of products. Our research found that in addition to the function of the product itself, users prefer to regard intelligent products as friends who can communicate and accompany in their Advances in Economics, Business and Management Research,volume 190 lives. This requires more attention to emotional interaction design and intelligence in the design concept and scheme of the product, so as to ensure that the product can accompany and communicate with users to the maximum extent, and make users rely on it. In addition, we should also improve the details in the use of personal pronouns of voice assistant, the diversification of product scene mode, whether it is easy to operate and personalized design, so that users can improve the satisfaction of product use and appearance from all angles.

Limitations
However, there are still limitations in this survey: First, the sample size of the survey is limited; second, most of the respondents are college students, and their ages are generally between 20 and 30 years old; Third, the respondents generally accepted the intelligent products with high learning ability. In the future experiments, we should increase the sample size, age group, occupation category, to make the personnel structure of the research object more comprehensive and scientific, so as to get more comprehensive and convincing experimental data and analysis results.


Optimal Control Strategy of Turbine Governor Parameters Based on Improved Beetle Antennae Search Algorithm

: Aiming at the occurrence of long-term and ultra-low frequency oscillations in the hydropower network system, this paper derives the generalized turbine transfer function speed control system model including the flow factor T pq based on the generalized turbine model, and analyzes the influence of T pq and PID parameters on the ultra-low frequency damping of the hydraulic turbine governing system. In order to better suppress the ultra-low frequency oscillation caused by improper PID parameter settings, a comprehensive optimization objective function reflecting damping and turbine speed deviation index (ITAE) in ultra-low frequency band is established. Based on the fast and efficient optimization strategy of Beetle Antennae Search, an improved beetle antennae particle swarm optimization is constructed. In single-machine and multi-machine systems, the improved algorithm is compared with different optimization algorithms. The simulation results show that the improved algorithm can overcome the slow convergence speed and easily fall into local optimization problem, effectively improve the damping level of hydraulic turbine governing system in ultra-low frequency, and is more effective and superior than other optimization algorithms. It provides a new way of thinking and technical means to suppress the ultra-low frequency oscillation by optimizing the parameters of the speed control system. algorithm;

INTRODUCTION
In recent years, the ultra-low frequency oscillation phenomenon with an oscillation frequency lower than 0.1 has repeatedly appeared in the power grid dominated by hydropower units, and its oscillation frequency is significantly lower than the low-frequency oscillation range [1][2]. For example, on March 8, 2016, an ultra-low frequency oscillation with an oscillation frequency of about 0.05 Hz and a frequency fluctuation range of 49.9 -50.1 Hz occurred in the asynchronous interconnection test of the Yunnan power grid. After exiting the primary frequency modulation performance of some power plants, the oscillation subsided [3][4][5]. After the Chongqing-Hubei back-to-back flexible DC project is put into operation, there is also a risk of ultra-low frequency oscillation when the Sichuan-Chongqing power grid is asynchronously interconnected with the main grid. The ultra-low frequency oscillation restricts the stable operation of the power grid after asynchronous interconnection to a certain extent. Therefore, great attention must be paid to this kind of ultralow frequency oscillation phenomenon.
Aiming at the problem of ultra-low frequency oscillation, different scholars put forward different solutions and analysis methods. Based on the phenomenon of ultra-low frequency oscillation in Colombia power grid, the influence of turbine model and controller on oscillation is studied by time-domain simulation method in reference [6], and a method to suppress ultra-low frequency oscillation by adding thermal power units is proposed. In reference [7], the stability of the system is analyzed through the linear and nonlinear models of hydraulic turbines, and the mechanism of ultra-low frequency oscillation is studied by using the limit cycle in the nonlinear model. In reference [8], a method for on-line evaluation of generator damping characteristics based on energy flow is proposed and applied to online analysis and emergency control of ultra-low frequency oscillation. Finally, it is verified in a four machine two area model. In order to improve the primary frequency regulation performance of the unit, most of the research work mainly realizes the suppression of ultra-low frequency oscillation behavior by optimizing the speed control parameters of the speed regulation system. The optimization and adjustment methods can be generally divided into two categories: one is to redesign the turbine governor by combining the fuzzy theory, collaborative control, neural network and other advanced control algorithms [9][10][11][12] to replace the classic PID Governor. The other is based on particle swarm optimization, bacterial colony optimization and other intelligent optimization strategies [13][14][15][16][17][18], which optimizes the parameters of the classic PID governor to adapt to different operating conditions of the prime mover. This kind of method makes full use of the good robustness of the classical PID control strategy and is widely used in Engineering practice. In the analysis and optimization of ultra-low frequency oscillation model of hydraulic turbine, the ideal turbine model based on the linearization of stable operation point or the linear and nonlinear model proposed by IEEE working group are mostly used in the analysis and optimization of ultra-low frequency oscillation model of hydraulic turbine, and different control strategies are adopted in different controlled objects, and the suppression effect of ultra-low frequency oscillation of hydraulic turbine unit is also different. In dealing with the problem of ultra-low frequency oscillation, the system needs to be able to respond to different disturbances quickly and efficiently, so that the system can quickly recover to the original stable state.
In order to better simulate the dynamic behavior of hydraulic turbine, the generalized turbine model is derived based on the generalized equation of hydraulic turbine. Combined with the model, the damping characteristics of the turbine governing system in the ultra-low frequency region are analyzed, and the comprehensive optimization objective function is established considering the damping performance index of ultra-low frequency oscillation and the ITAE index of turbine speed deviation. Then, the PID parameters in the single load model are optimized by improved beetle antennae particle swarm optimization algorithm, and the optimal PID parameter solution is obtained by using the built comprehensive optimization objective function. Finally, the BPA software is used to simulate and analyze the 4 -machine -2 -zone system, which verifies the influence of the optimized PID parameters on the ultra-low-frequency oscillation of the power system.

ANALYSIS OF DAMPING PERFORMANCE INDEXES OF ULTRA-LOW FREQUENCY OSCILLATION
The damping characteristics of hydropower units in ultra-low frequency band are mainly affected by water hammer effect of prime mover system and control parameters of governor. The open-loop system composed of governor and prime mover is shown in Fig. 1. In Fig. 1, Δω is the speed deviation; G gov (s) is the governor transfer function; Δy is the turbine guide vane opening deviation; G ht (s) is the turbine transfer function, and ΔP m is the mechanical power deviation of the generator.
From Fig. 1, the open-loop transfer function G K of the governor and turbine system is: The governor adopts a proportional-integral-derivative (PID) governor, and its transfer function can be expressed as: In Eq. (2), B p is the adjustment coefficient; K p is the proportional adjustment coefficient; K I is the integral adjustment coefficient; K D is the differential adjustment coefficient; T G is the guide vane servomotor response time constant.
When deriving the hydraulic turbine model, starting from the generalized hydraulic turbine equation, calculate the dynamic moment of the water flow acting on the turbine runner blades under instantaneous conditions, and then use the moment of momentum theorem to obtain the generalized hydraulic turbine equation: In Eq. (3), P m is the output power of the turbine, q is the flow of the turbine, h is the working head of the turbine, dW is the volume of any fluid element in a certain flow layer in the runner area; ρ is the water flow density; v u is the water flow The circumferential component of the absolute velocity of the element; r is the radius of the flow element relative to the center of the turbine shaft; Ω is the fluid volume of the entire turbine runner.
According to the flow velocity triangle in Francis turbine runner, the circumferential component v u of absolute velocity of fluid element satisfies: In Eq. (4), F is the cross-sectional area of the runner, and β is the installation angle of the intermediate flow surface wing grid.
Considering that the dynamic angular velocity ω and the flow rate q are only related to the time t, but not to the coordinate position, the Eq. (4) is substituted into the integral term on the right side of the Eq. (3) to get: From the volume of the fluid micro-element: In Eq. (6), rdθ, dr, and dz respectively represent the length, width, and height of the fluid element.
For Francis turbine, substituting Eq. (6) into Eq. (5): In Eq. (7), D is the nominal diameter of the turbine; ; D1, D2 is the inlet and outlet diameter of the turbine runner; b1, b2 is the width of the water cross section at the inlet and outlet of the runner; ᵠ1, ᵠ2 is the crowding coefficient of the inlet and outlet blades of the middle flow surface to the flow; β1, β2 is the placement angle of the blade inlet and outlet. Define the speed factor T pω and flow factor T pq respectively: The Eq. (7) can be expressed as: When the ultra-low frequency oscillation of the hydrogenerator set occurs, the speed variety is very small, and the influence on the output power of the turbine can be ignored. The turbine power output can be expressed as: It can be seen from Eq. (12) that the output power of the turbine is related to the generator flow and head, and also to the instantaneous dynamic variation of the generator flow dq/dt. The flow factor T pq can be used to measure the influence of the instantaneous dynamic change dq/dt on the turbine output power. If the rigid water hammer model is adopted in the diversion system, the transfer function between the turbine generator flow and head can be expressed as: In Eq. (13): T w = (LV 0 )/(gH 0 ) is the inertia time constant of water flow. and V 0 is the initial velocity; H 0 is the initial head; L is the length of the diversion pipe.
The relationship between generator flow and guide vane opening and water head can be expressed as: In Eq. (14): y is the opening of guide vane. Substituting Eq. (12) and Eq. (14) into Eq. (13), the transfer function of the generalized turbine model can be obtained after the Laplace change is: When the system input signal −Δω, substituting Eq. (2) and Eq. (15) into Eq. (1), the mechanical deviation ΔP m produced by the prime mover can be obtained as: Substituting s = jω d into Eq. (16), then decomposition in the Δδ-Δω coordinate plane, the Eq. (16) can be expressed as: In Eq. (17), the specific expressions of K 1 to K 7 are shown in Appendix A. Define: Then D md represents the damping torque coefficient provided by the turbine governing system, and K ms represents the synchronous torque coefficient provided by the turbine governing system. When D md > 0, the speed control system provides positive damping to the system; when D md < 0, the speed control system provides negative damping to the system, and when the sum of the damping component caused by electromagnetic power deviation and the damping of the generator itself is not enough to offset the negative damping generated by the turbine speed regulation system, the whole hydropower unit will be in weak damping or negative damping state, which will induce system overload Low frequency oscillation.
From Eq. (18), it can be seen that the damping level of the turbine governor system in the ultra-low frequency band is closely related to the PID parameters of the governor. Substituting ω = 2πf into Eq. (18) and setting the frequency change range from 0.01 to 0.1, the characteristics of the damping coefficient D md with the PID parameters of the governor and the system frequency in the ultra-low frequency range can be obtained as shown in Fig.  2 to Fig. 4. As shown, the model parameters are:  It can be seen from Fig. 2 that in the ultra-low frequency range, appropriately increasing the K P value can improve the damping level of the hydraulic turbine governing system; from Fig. 3, it can be seen that the oscillation frequency is about 0.05 Hz as the demarcation point for the influence of K i on the damping of the turbine governing system, when the frequency is 0 ～ 0.05 Hz, increasing K i is beneficial to improve the damping level of the turbine governing system, but when the frequency is higher than 0.05 Hz, the effect is just the opposite; Fig. 4 shows that it is known that the influence of K d on the damping level of hydraulic turbine governing system has no obvious difference when the frequency is 0 ～ 0.05 Hz. When the frequency is greater than 0.05 Hz, appropriately increasing K d can effectively improve the damping level of hydraulic turbine governing system.

PARAMETER OPTIMIZATION CONTROL STRATEGY 3.1 Comprehensive Objective Function
In order to not only satisfy that the generator speed can be stabilized in the shortest time after the turbine is disturbed, but also to improve the damping level of the system in the ultra-low frequency band so that the system has stronger anti-interference ability under different disturbance conditions the damping level of the governor in the ultra-low frequency band is used as the ultra-low frequency oscillation damping performance index, combined with the ITAE index of the speed deviation of the turbine to establish a comprehensive optimization objective function.

Damping Level Measurement Index
In this paper, the damping level of the hydraulic turbine governor in the ultra-low frequency band is taken as the ultra-low frequency oscillation damping performance index, and its function J Dmd is defined as: In Eq. (20), n = (f max − f min )/Δf, f max and f min are the maximum and minimum of the oscillation frequency, respectively, Δf = 0.01 Hz is the step length of the frequency point, and for the i-th frequency point, f i = f min + (i − 1)Δf, change D md (f i ) as follows: In Eq. (21), D md (f i ) is the damping torque coefficient of the turbine speed control system when the oscillation frequency is f i .

ITAE Index of Speed Deviation
Take the ITAE criterion of the rotational speed deviation of the hydro-turbine generator set as one of the objective functions of the optimization algorithm, that is, the absolute value of the hydro-generator output speed error multiplied by the time integral as the fitness function of the algorithm, the expression is: In Eq. (22): t is the time; t s is the integral upper limit time; Δω(t) is the speed deviation of the turbine unit.

Comprehensive Objective Function
Taking into account the Ultra-low frequency oscillation damping performance index and ITAE index of the speed deviation of hydraulic turbine, according to Eq. (20) and Eq. (22), the comprehensive objective function J of the optimization algorithm in this paper can be expressed as: In Eq. (23): K 1 and K 2 are the damping level index and speed deviation of hydraulic turbine governor respectively, and the weight coefficient of ITAE index is obtained. When calculating the comprehensive objective, each target component should be normalized. When K 1 > K 2 , it means that the proportion of damping torque in the objective function is larger; when K 1 < K 2 , the proportion of speed deviation in the objective function is larger. In this paper, the proportion of the two is balanced, taking K 1 = K 2 = 0.5.

Optimization Algorithm of Governor Parameters 3.2.1 Standard Particle Swarm Optimization Algorithm
In order to solve the optimal PID control parameters, the optimization space of the standard Particle Swarm Optimization (PSO) is set in the three-dimensional search space. A population composed of n particles X = (X 1 , X 2 , X 3 , ..., X n ), where the i-th particle is represented as a 3- corresponding to the values of K p , K i , K d . According to the fitness function, the fitness value corresponding to each particle is calculated, and the individual extreme value Pbest and the group extreme value Gbest are updated. During each iteration, the particles update their speed and position by tracking Pbest and Gbest. The update formula can be expressed as: In Eq. (24): w is the weight of inertia; d = 1, 2, 3; i = 1, 2, ..., n; t is the current iteration number; V id (t) and X id (t) represent the t-th iteration ,the position and velocity of the i-th particle in the d-dimensional space; c 1 and c 2 are nonnegative constants, called learning factors; r 1 and r 2 are random numbers distributed between (0, 1).

Improved Particle Swarm Optimization Based on Beetle Antennae Search
It can be seen from Eq. (24) that the position update of traditional PSO is not only related to the current speed, but also related to the historical performance of particles and mutual communication, which makes it have a good group character, so that it can be used in fine search. Performance is better. However, in some cases, the convergence speed is slow or it is easy to form premature convergence due to the early search speed being too fast, and eventually fall into the local optimal value. The Beetle Antennae Search (BAS) is different from most optimization algorithms in that there is only one individual "beetle" in the search process, so that the optimization process is fast and the amount of calculation is low, and it does not need to know the specific form of the function, and does not require gradient information, can achieve efficient optimization. Based on the advantages of the BAS, this paper proposes an improved PSO based on the BAS, which is called BASPSO. The algorithm integrates the judgment of the BAS and the PSO to update the position of the particles, so that it can better jump out of the local optimum, and can find the global best point faster and more accurately, so as to realize the comprehensive improvement of global search ability and search speed. Among them, the formula Y id used by the BAS to determine the particle's next direction can be expressed as: In Eq. (25), step represents the step length of beetle; dir represents the direction of beetle randomly generated; sign is a symbolic function; fleft and fright respectively represent the intensity of "food" odor perceived by the left and right antennae of beetle, and its expression for: In Eq. (26), x l and x r respectively represent the coordinates of the left and right antennae of beetle, which can be expressed as: In Eq. (27), x represents the position of the centroid of beetle, and d 0 represents the distance between the two antennaes of beetle.
In order to improve the calculation performance of the algorithm, an adaptive step size strategy is adopted for the step size step of the BAS, which protects particles with fitness values better than the average fitness value, and gives larger step sizes to the poorer particles. So that it can quickly jump out of the poor search range, its formula is expressed as: In Eq. (28): J i is the fitness value of the i-th particle; J min is the minimum fitness value of the current particle swarm; J v is the average fitness value of the current particle swarm.
From Eq. (24) and Eq. (25), we can get the speed and position update formula of BASPSO: In Eq. (29),   0, 1 g  is the weighting coefficient. When g > 0.5, it means that the proportion of PSO judgment in the particle position update is larger; g < 0.5, means the proportion of the BAS judgment in the particle position update is larger. In this paper, in order to highlight the advantages of the BAS and make it account for a larger proportion, g = 0.4.

Optimization Algorithm Flow
The process steps of the BASPSO are shown in Fig. 5.

CASE SIMULATION 4.1 Single-Machine System
Single unit single load system is a common system used to study stability. The analysis model of ultra-low frequency oscillation of hydro generator governing system is given in Fig. 6. Based on this model, the influence of different PID parameters optimization control strategies on ultra-low frequency oscillation of hydropower units is analyzed. The model and parameter selection of the turbine and its governor are the same as the above analysis. The generator and external system are usually simplified as a first-order system, and the transfer function can be expressed as: In Eq. (30): T a is the unit inertia time constant, e n = D + K L , D is the generator damping coefficient; K L is the load frequency adjustment effect coefficient. Generally take T a = 8, e n = 1.3.
A frequency perturbation is applied at the initial moment of the system, and the PID parameters of the governor are optimized by the BASPSO. The relevant parameters are set as follows: Particle swarm size n = 100, the maximum number of iterations is 50, c 1 = c 2 = 2.0, step min = 0.1, step max = 1, w = 0.7, g = 0.4, d 0 = 1. The optimized PID parameters are K p = 2.36, K i = 0.31, K d = 2.49. Fig. 7 shows the change of the damping torque coefficient D md of the turbine governor system before and after optimization. 8 Figure 7 Variation curve of damping coefficient before and after optimization It can be seen from Fig. 7 that the damping torque coefficient D md before optimization is less than 0 in the ultra-low frequency range from 0.04 to 0.1 Hz, and the optimized damping torque coefficient D md is greater than zero in the ultra-low frequency range, indicating the BASPSO has a larger damping torque coefficient in the ultra-low frequency range of 0.04 ～ 0.1 Hz, which is beneficial to the stability of the system. In order to compare the advantages of the improved algorithm in this paper, a disturbance signal of the same frequency is applied at the initial moment of the system, using the PSO, the BAS and the BASPSO optimizes the PID parameters in the singlemachine single-load system in Fig. 6, so as to obtain the fitness value change curve under different algorithms (as shown in Fig. 8), and the generator speed deviation change curve in the first 50s (such as Fig. 9) and optimized parameter values and corresponding performance indicators (shown in Tab. 1).

Figure 8 Convergence curve of fitness value of different algorithms under frequency disturbance
It can be seen from Fig. 8 that the improved optimization algorithm is obviously better than the PSO and the BAS when considering the fitness value and iteration speed, which shows that the improved algorithm has stronger optimization ability. Analysis of Fig. 9 and Tab. 1 shows that compared to the other two algorithms, the improved algorithm has better improvements in overshoot (represented by the maximum value under frequency disturbance) and adjustment time. Under disturbances, the maximum deviation of the improved algorithm is 0.38, and the adjustment time is 12 s, which is reduced compared to the BAS and PSO algorithms. It also shows that the improved algorithm is effective in setting the governor parameters of hydroturbine generators.

Multi-Machine System Simulation
Using this method to build a 4-machine 2-area system in BPA for simulation testing, the model diagram is shown in Fig. 10. Since the ultra-low frequency oscillation phenomenon mostly occurs in hydropower-dominant units, in order to more easily analyze the mechanism of the ultra-low frequency oscillation phenomenon in the hydropower unit, the generators in the four-machine system are all hydraulic generator units, and all generators The M card considering the damping winding is adopted, the excitation regulation system uses the new excitation system bus FV card, and the PSS uses the Three Gorges PSS model SI card. The hydraulic turbine model is shown in Eq. (15). The governor model is a PID governor, and its model is shown in Eq. (2). The initial parameters of the governor and the turbine are shown in Tab. 2. Among them, G1 and G2 are optimized by the beetle algorithm, G3 and G4 are optimized by the particle swarm algorithm, and the remaining parameters remain unchanged. Then use the BASPSO to optimize the PID parameters of the governors of each unit. Since the parameters of the four turbines are the same, the PID parameters of each unit are optimized using BASPSO in 3.1 to optimize the PID parameters of a single turbine speed control system. The governor PID parameters of a turbine: K p = 2.36, K i = 0.316, K d = 2.49. At t = 3 s, apply a frequency disturbance to the system to induce the ultra-low frequency oscillation of the system. It can be seen from Fig. 11 that the system oscillation frequency is about 0.14 Hz before optimization, 0.1 Hz after G1 and G2 optimization, and 0.08 Hz when all units are optimized. It can be seen that the ultra-low frequency oscillation of the system is effectively suppressed after the BASPSO, which shows the effectiveness of this method. Moreover, the optimization of all units has shorter regulation time, less oscillation times and smaller frequency deviation than only optimizing G1 and G2 units.

CONCLUSION
In order to better solve the problem of ultra-low frequency oscillation in hydropower-dominant power systems, this paper studies the ultra-low frequency oscillation mechanism and suppression methods of hydropower units, and draws the following conclusions: (1) Based on the generalized hydraulic turbine model, increasing the values of K p and K d can improve the damping level of the turbine governing system. When the oscillation frequency of K i is 0 ～ 0.05 Hz, the larger the value, the better the damping level of the turbine governing system. When 0.05 ～ 0.1 Hz, its effect is just opposite.
(2) Compared with the PSO and BAS, the BASPSO has the characteristics of small overshoot and good stability after tuning the PID parameters, which can effectively improve the dynamic performance of the hydraulic turbine adjustment system during the transition process. At the same time, the algorithm has fast convergence speed and high accuracy, which effectively overcomes the shortcomings of standard particle swarm algorithm, such as easy maturity, and improves the accuracy of the algorithm.
(3) The PID governor parameters obtained by the improved optimization algorithm are not only verified in a singlemachine system, but also applicable in a four-machine twozone system.