A method for constructing equilateral triangle effect coordinate system for three-phase electric physical quantity space mapping and analysis

Abstract

The application discloses a method for constructing an equilateral triangle effect coordinate system for three-phase electric physical quantity space mapping and analysis, and belongs to the technical field of three-phase power system data analysis, which comprises five steps: step 1, constructing an equilateral triangle effect field with a 120-degree effect axis in a plane, taking the centroid as a double balance point of electric potential and space, and realizing voltage and current double-mode normalization relying on rated extreme value capacity; step 2, establishing a dynamic overflow mapping rule to solve the problem of physical quantity overrun and truncation distortion and completely retain fault distortion information; step 3, synchronously collecting three-phase instantaneous voltage and current at a high frequency, and generating continuous dynamic effect trajectories through coordinate transformation; step 4, extracting trajectory exclusive geometric characteristic parameters; and step 5, combining geometric boundary and physical quantity numerical double early warning to match a four-level control model to output a graded early warning graph. The application reduces multi-dimensional electrical parameters to geometric criteria, covers normal to extreme full scenes, and improves real-time sensing and active defense capabilities of a three-phase system.

Description

Technical Field

[0001] This invention relates to the field of data processing and status monitoring technology for three-phase AC power systems (such as three-phase power generation, three-phase power transmission and distribution, three-phase motor control, and three-phase power quality analysis), and particularly to a method for spatial mapping of three-phase electrical quantities, power quality assessment, and trajectory rendering based on equilateral triangle geometric topology and dynamic overflow mechanism. Background Technology

[0002] Currently, the mainstream analytical approach for three-phase AC systems employs time series dimensionality reduction methods in Cartesian coordinates. Typical examples include Fourier transform, symmetric component method, and orthogonal transformation schemes such as α-β-0 orthogonal coordinate system and Clarke / Park transform. This type of technique belongs to the typical reductionist analytical approach of "orthogonal decoupling + time evolution," which decomposes the complete three-phase coupled system into multiple independent one-dimensional time series, fundamentally severing the inherent physical essence of three-phase power systems—the three-dimensional coupling and spatial antagonistic balance.

[0003] In routine online power quality monitoring scenarios, the shortcomings of traditional solutions are further amplified: maintenance personnel need to interpret massive amounts of data and complex algebraic equations, making it impossible to intuitively and comprehensively grasp the overall balance of the three-phase system; at the same time, traditional geometric drawing solutions set the vertices of the graph as insurmountable hard boundaries, and when the grid voltage and current exceed the limits, the trajectory is directly truncated, the geometric data is distorted, and ultimately a series of problems such as the failure of power quality assessment results and the lag in fault warnings are caused.

[0004] Existing electrical analysis systems are largely based on time-function relationships, using time as the core analytical benchmark. Essentially, they are a historical product of time reductionism and have significant limitations. The inventors, in constructing the effects science system, pointed out its philosophical essence: the underlying nature of electromagnetic interaction is a three-dimensional spatial antagonistic equilibrium relationship. Relying on the complete and rigorous quantitative analysis methods and supporting philosophical system of effects science, spatial analysis approaches can be translated into a complete set of algorithms that can be deployed in engineering.

[0005] While various three-phase spatial geometric representations exist in the power electronics industry, such as Space Vector Modulation (SVM), Clarke / Park orthogonal transformation, and the α-β-0 stationary coordinate system, they are generally regarded merely as mathematical computational techniques and temporary variables in control algorithms. They are not given an independent coordinate system with intrinsic physical meaning. The core shortcomings are threefold: ① The lack of a unified and self-consistent underlying scientific and philosophical logic and physical mapping rules makes it impossible to clearly define the correspondence between the three core quantitative elements (quantity, potential, and product) and geometric elements; ② The inability to establish a one-to-one quantitative mapping relationship with engineering indicators such as power quality assessment, fault diagnosis, and system stability determination; ③ The overall analytical framework still relies on the time-frequency analysis framework, failing to completely break free from the inherent limitations of time reductionism. Simply relying on geometric drawing and numerical calculations without a complete and self-consistent methodology means that geometric figures can only serve as visual aids and cannot become a physical coordinate system with full computational capabilities. This solution shares some similarities with traditional three-phase geometric analysis tools such as SVM, Clarke / Park, and α-β-0 in terms of surface graphics, but the underlying analysis logic is completely different. This invention uses the spatial characteristics analysis of electricity as the fundamental analysis method, which is somewhat similar in form but completely different in essence.

[0006] In addition to the aforementioned common traditional vector scheme, two existing patents also employ triangular geometry for three-phase analysis, with the specific schemes as follows: Publication No. CN109149983B discloses a fast three-phase space vector modulation method based on a three-dimensional coordinate system. This method constructs a modulation triangle, selects the modulation vector closest to the origin, and calculates the corresponding three-phase switching state. Then, it scales the reference voltage vector, simplifying the multi-level vector space into a two-level vector space. Finally, it compares the processed vector with the converter's triangular carrier wave to generate a switching drive signal. The entire design of this patent serves only pulse modulation for power electronic converters; the geometric triangle is merely a temporary intermediate tool to simplify switching operations.

[0007] Announcement No. CN116879642A discloses a method for judging three-phase electrical imbalance based on the Fermat point and circumcenter of a triangle. The steps are as follows: 1. Construct a three-phase voltage phasor triangle; 2. Obtain the coordinates of the circumcenter W of the three-phase voltage phasor triangle; 3. Obtain the coordinates of the Fermat point F of the three-phase voltage phasor triangle; 4. Determine the three-phase imbalance caused by the difference in amplitude and phase of the three-phase voltage by using the distances of the Fermat point and circumcenter from the origin O. Simple qualitative judgment of imbalance is completed by relying on only two sets of static geometric points.

[0008] Compared to CN109149983B, this patent focuses on converter switching vector modulation and simplifies pulse generation calculations. This invention aims to cover power quality monitoring, distortion reduction, and fault classification in all scenarios of power generation, transmission and distribution, and motors. It features a unique dynamic overflow mechanism that preserves the complete over-limit trajectory and establishes a multi-dimensional spatial quantitative index and a four-level automatic early warning closed loop. This patent is completely different from CN109149983B in terms of application scenarios, basic methods, and underlying geometric architecture.

[0009] Compared to CN116879642A, this patent relies solely on static triangular points for a simple qualitative judgment of three-phase imbalance, lacking dynamic time-series trajectory generation, multi-dimensional distortion reduction, and adaptability to variable frequency unsteady-state operating conditions. This invention extracts three types of spatial features based on a time-series continuous dynamic rheological trajectory, and achieves accurate quantification across all operating conditions using a complete geometric system of centroid, effect axis, and inscribed and circumscribed circles, coupled with numerical and graphical collaborative hierarchical control. This patent has a fundamental difference in underlying principles, technical completeness, applicable scope, and quantification accuracy.

[0010] All existing technologies, including the two patents mentioned above, orthogonal transformation, and SVM vector modulation, while utilizing triangular geometry to achieve simple vector operations or imbalance judgments, suffer from multiple inherent and insurmountable defects: At the logical analysis level: the orthogonal decoupling approach is generally used to sever the underlying physical relationship of the three-phase natural spatial coupling and spatial antagonistic balance. The geometric figure is only a temporary calculation carrier and does not have an independent and complete physical coordinate system definition. There is no dedicated centroid balance point, 120° equally divided effect axis, and a complete set of normalized reference geometric system for voltage and current. Over-limit data processing: All solutions set the graph vertices as rigid boundaries. When voltage and current exceed the limits, the trajectory is directly truncated, and the complete information of fault amplitude and distortion is lost, making it impossible to continuously quantify the severity of the fault. At the level of quantitative indicators: it can only complete the judgment of a single static imbalance or the simplified calculation of switching modulation. It has not built a complete set of dynamic geometric quantitative indicators with multiple dimensions such as eccentricity, centroid offset, and trajectory area change rate, and cannot adapt to various non-steady-state dynamic working conditions such as frequency conversion and transient impact. At the early warning and control level: numerical calculation and graphical display are completely separated, there is no dual criterion of geometric boundary + feature value, and there is no four-level hierarchical early warning, automatic control and manual graphical review collaborative closed-loop mechanism; Steady-state / non-steady-state adaptation: Both rely on integral calculations within a fixed time window, which can lead to severe spectral leakage and phase errors under variable frequency speed regulation and transient disturbance conditions, making it impossible to achieve high-precision and accurate perception and graded fault prevention under all operating conditions. Summary of the Invention

[0011] The purpose of this invention is to provide a method for constructing an equilateral triangle effect coordinate system for spatial mapping and analysis of three-phase electrical physical quantities, in order to solve a series of background technical pain points such as the traditional orthogonal transformation and triangle discrimination schemes that break the integrity of three-phase spatial coupling, the forced truncation of over-limit trajectories causing data distortion, the inability of the early warning system to take into account both automated numerical driving and global graphical intuitive criteria, and the large calculation error of unsteady-state conditions.

[0012] To achieve the above objectives, this invention adopts the following complete technical solution, comprising five core steps and corresponding detailed implementation rules: A method for constructing an equilateral triangular effect coordinate system for spatial mapping and analysis of three-phase electrical physical quantities, comprising the following steps: S1: Constructing an equilateral triangle effect field and three-phase effect axes: Construct an equilateral triangle ABC as the effect field boundary of the three-phase AC system; define the centroid O as the origin of the coordinate system, which simultaneously represents the three-phase potential equilibrium point and the spatial absolute equilibrium point; draw three rays from the origin to the three vertices as effect axes, with the included angle between each pair of the three effect axes strictly 120°, perfectly matching the natural spatial distribution of the three-phase windings and the three-phase power supply; the vertices of the triangle can be independently configured as the corresponding phase voltage rated peak value or phase current rated value, and the two sets of physical quantities of voltage and current are mapped to the trajectory using a normalized reference that does not interfere with each other and can be switched independently. Furthermore, under ideal symmetrical three-phase operating conditions, the three-phase dynamic rheological trajectory is a standard circumcircle with centroid O as the center and the distance from centroid to vertex as the radius; an inscribed circle is synchronously generated within the effective field, with centroid as the center and the perpendicular distance from centroid to each side of the triangle as the radius. Geometrically, the radius of the inscribed circle is half the radius of the circumcircle, and the area of ​​the inscribed circle is one-quarter of the area of ​​the circumcircle, serving as the criterion for determining the minimum effective work basis of the system.

[0013] S2: Establish a dynamic overflow mapping mechanism for the three-phase effect axis: When the actual instantaneous physical quantity of any phase exceeds the rated extreme capacity of that phase, the dynamic effect trajectory point extends outward along the corresponding effect axis to the vertex; when the physical quantity is less than or equal to the rated extreme value, the trajectory projection falls between the origin and the vertex; when the physical quantity is greater than the rated extreme value, the projection extends outward beyond the vertex, and the distance of the trajectory beyond the vertex is strictly linearly proportional to the physical over-limit amplitude; no coordinate clamping or truncation is performed throughout the process, and all original coordinate values ​​under the over-limit state are completely preserved, realizing continuous mapping of the full amplitude.

[0014] S3: Three-phase dynamic effect trajectory point mapping and image acquisition: The instantaneous physical quantities of the three phases A, B, and C are synchronously acquired using a synchronous clock from the same source; the sampled values ​​of each phase are normalized by dividing the corresponding phase's rated extreme capacity (single-phase rated peak voltage or current), and the normalized values ​​are used as the projection length of the corresponding effect axis; the two-dimensional plane coordinates are solved through three-way projection vector synthesis operation, and the same set of coordinate transformation formulas are used regardless of whether the limits are exceeded; the coordinate points are continuously stored in time sequence, and the points are connected and rendered one by one to generate a continuous closed three-phase dynamic rheological trajectory image, supporting independent rendering of voltage and current dual trajectories.

[0015] S4: Numerical Extraction of Three-Phase Spatial Geometric Features: Based on the coordinates of all trajectory points in a single cycle, three core quantitative features are extracted uniformly: First, centroid offset, taking the average value of points in a single cycle as the actual centroid of the trajectory, calculating the vector magnitude between the actual centroid and the origin, and subtracting the static centroid offset stored in the equipment calibration to obtain the relative centroid offset. The offset vector directly points to the effect axis corresponding to heavy load and fault. Second, eccentricity, performing ellipse fitting on the single-cycle trajectory, using the ratio of the focal length to the major axis length of the ellipse as the eccentricity value, characterizing the degree of three-phase impedance and voltage asymmetry. Third, trajectory area change rate, using polar coordinates to solve the sector area derivative of the radius vector with spatial angle. This indicator only depends on pure planar geometric topology and is completely decoupled from the system frequency. Its periodic fluctuation amplitude corresponds to harmonic distortion and mechanical vibration intensity. These three features together serve as standard input parameters for system state perception and upper-level quantitative calculation.

[0016] S5: Hierarchical Early Warning Based on Numerical Driving and Graphical Collaboration: Extracted geometric features such as eccentricity and relative centroid offset are compared with preset multi-level threshold intervals, dividing the system into four layers of processing logic: The first interval outputs a normal archiving signal with no control action; the second interval outputs reactive power compensation and online intelligent phase commutation fine-tuning instructions; the third interval outputs a single-phase load limit alarm and generates a maintenance work order; the fourth interval outputs emergency load shedding and fault isolation protection instructions; when multiple features exceed limits simultaneously, the action with the highest priority is executed. Simultaneously, the real-time dynamic trajectory is rendered to the display terminal, with the trajectory line color changing according to the early warning level. Overflow and centroid offset positions are visually labeled, achieving dual-track collaboration between automatic numerical processing and manual graphical verification.

[0017] Compared with the prior art, the present invention has the following five significant advantages: Rooted in the fundamental nature of three-phase electrical space, reconstructing an independent physical and geometric analysis foundation: Abandoning the traditional reductionist analytical framework of "orthogonal decoupling + time evolution", this paper constructs an independent coordinate system for equilateral triangle effects with exclusive physical mapping rules, relying on the 120° equally divided effect axis, double-defined centroid, and a complete set of geometric systems of circumscribed / inscribed circles. This system transforms abstract three-phase algebraic parameters into intuitive geometric forms, distinguishing it from traditional SVM, Clarke transform, and triangle imbalance discrimination schemes that are only used as temporary calculation tools. This system establishes a unified and self-consistent spatial analysis carrier.

[0018] The pioneering dynamic overflow continuous mapping mechanism completely solves the industry pain point of data truncation and distortion beyond the limit: Breaking away from the rigid boundary limitations of traditional vector graphics vertices, the trajectory extends linearly along the effect axis after voltage and current exceed the limits, completely preserving the coordinate information corresponding to the fault exceedance amplitude, without losing the quantitative basis of fault severity. At the same time, it is equipped with the minimum work basis judgment logic of the inscribed circle, which can identify invalid operating conditions such as undervoltage, stalled rotor, and loss of excitation, avoiding measurement and evaluation distortion caused by invalid integration.

[0019] 3. Numerical-driven automated control combined with graphical visualization forms a closed-loop hierarchical early warning system covering all scenarios: Using pure spatial geometric feature values ​​as the sole trigger source for early warning and control, it can output layered handling instructions in milliseconds without human intervention, covering four levels of full-condition handling: normal recording, fine-tuning and optimization, load limiting, and emergency fault isolation. It simultaneously renders time-series change trajectories, allowing maintenance personnel to intuitively locate distortion types and fault phases through graphics. It combines automatic proactive defense by machines with global review and diagnosis by humans, solving the problem of complete disconnect between numerical values ​​and graphics in traditional solutions.

[0020] A standardized, universal geometric framework provides a unified underlying data foundation for the entire family of patents related to effects and spatial electricity. This patent generates standardized dynamic trajectories and basic geometric features, which can serve as a unified input carrier for algorithms 1, 2, 3, and 4, providing a standardized coordinate mapping basis.

[0021] Achieving strict decoupling between spatial geometry and time frequency, adapting to fully dynamic, unsteady, and complex operating conditions: The core geometric parameters of this invention are all calculated based on pure two-dimensional planar geometry, which is decoupled from time and frequency variables, so that the geometric coordinates will not be distorted under variable frequency and transient operating conditions. Attached Figure Description

[0022] The present invention will now be described in further detail with reference to the accompanying drawings and specific implementation methods.

[0023] Figure 1 This is a schematic diagram of the process for generating three-phase dynamic effect trajectory points, extracting features, and numerically driven early warning in an embodiment of the present invention.

[0024] Figure 2This is a schematic diagram of the three-phase dynamic rheological trajectory and overflow mechanism based on the equilateral triangle effect coordinate system in an embodiment of the present invention. Detailed Implementation

[0025] Prerequisites In recent years, the inventor has established the scientific philosophy system of effects science. The theoretical origins can be found on the official website of effects science, which elucidates some of the underlying principles of the operation of the objective world. This patent is derived from the underlying principles of spatial antagonistic balance of electromagnetic phenomena in effects science. In this series of patents, only patents 1 and 2, which involve the most fundamental principles, inevitably involve some basic effects science terminology. Subsequent patents 3-6 have made every effort to avoid this.

[0026] The applicants for this series of patent applications are identical to the copyright holders of the Effects Theory, and there are no obstacles to referencing the copyrighted content (no infringement). This application does not protect the copyright of Effects Theory (which is protected by copyright laws in China and the United States), but only the coordinate system geometric implementation method that can be implemented in engineering.

[0027] 1.2 Positioning and Synergy of This Patent Among a Series of Patents This invention is based on spatial analysis of electricity and relies on the core principles of electromagnetic phenomena in effectology, such as spatial antagonistic balance or imbalance. For brevity, this series of patents is referred to as the Effectology Spatial Electricity Patent Family. This patent, referred to as Patent 1, is the unified geometric foundation and underlying data carrier of the entire series of patents. It features three original designs: dynamic overflow mapping, 120° equally divided effect axis, and dual definition of centroidal balance point. These designs provide unified and distortion-free pre-geometric data for Patent 2's hierarchical quantization mapping rules, Patent 3's low-computing-power topological feature extraction, Patent 4's synchronous sampling hardware, Patent 5's analysis, diagnosis, and traceability, and Patent 6's hierarchical closed-loop control. The entire set of patents is divided into a principle family (Patents 1, 2, and 3) and an implementation family (Patents 4, 5, and 6). The terminology, geometric variable symbols (including subscripts), and quantization rules within the family are highly correlated and inseparable.

[0028] To clearly illustrate the positioning and synergistic relationship of this patent within the entire series of inventions, the following is now... The list is as follows:

[0029] 1.1 Terminology and Engineering Definition of Effects Effects science: The study of the elements, processes, and results related to the occurrence of effects is called effects science. The book contains approximately 350,000 words. Effects science can explain all effects from the underlying principles and can apply this underlying epistemology and methodology to transform the world.

[0030] Dynamic effects and static effects: The process and result of matter undergoing rheological changes in a field are called dynamic effects, i.e., events; static effects refer to the potential of matter to undergo rheological changes in a field. The main indicators for quantifying the potential of matter or the actual performance of matter rheological changes in dynamic effects are the following three categories: quantity, potential and product.

[0031] Quantity: Indicators that quantify the breadth of things (such as electrical power, area).

[0032] Productivity: The process quantity that is constructed together with potential. The essence of productivity is also quantity, but it plays the role of accumulation and release in the process of constructing quantity, and is therefore given the role of productivity.

[0033] Potential: An indicator for quantifying the nature of things. According to its mathematical essence, potential can be divided into difference potential, rate potential, and functional potential. Difference potential is the potential established by the difference between two quantities; it mostly belongs to the indicator of the ability to drive actions (such as voltage). Rate potential refers to the potential obtained by comparing two quantities; it is usually used to quantify the state properties of things (such as electric current). Electric potential belongs to the point difference potential in effects science, but its meaning is much narrower than the "potential" in effects science; single-point electric potential rarely participates directly in calculations. Potential difference (voltage) belongs to the quantity difference potential in effects science and participates extensively in calculations.

[0034] Effect field: The environmental conditions under which dynamic effects occur, also known as the field, which includes time and space and is considered the field of existence in the field of effects science.

[0035] Equilateral triangular effect field: a two-dimensional normalized geometric projection plane of a three-phase AC system. The centroid O is the absolute equilibrium point in space, and the effect axes are 120° apart.

[0036] 1.3 Geometric elements of the coordinate system, and the representation and interpretation of cross-patent collaborative symbols. To ensure the consistency of symbols and logical rigor in data flow and feature extraction of this patent and related patents filed on the same day (Patents 2 to 6), the core geometric elements and derived variables of this coordinate system are defined with the following unified symbols: Ideal standard circumcircle radius (R) _ideal ): This refers to the distance from the vertex of the equilateral triangle effect axis to the centroid O, mapped from the single-phase rated extreme capacity of the system. It serves as the normalized reference denominator in subsequent geometric characteristic calculations (such as centroid offset rate). Minimum effective work base area of ​​the inscribed circle (S) _in Let r be the area of ​​the inscribed circle centered at centroid O and with a radius equal to the perpendicular distance from centroid to the side of the triangle. Geometrically, it is always equal to one-quarter of the area of ​​the circumscribed circle. In this scheme, this area serves as the quantitative cutoff physical threshold for determining undervoltage, stall, and demagnetization conditions of the system. Invalid integration is automatically stopped when the trajectory envelope area is less than the area of ​​the inscribed circle. This unified geometric threshold can also be reused in the hierarchical quantization calculation process of the accompanying patent 2. The radius of the inscribed circle is denoted by r. _in express; Static centroid (O) _static ) and relative centroid offset vector (δ _rel In actual engineering data acquisition, the geometric center of the trajectory will inevitably shift due to the influence of background harmonics in the power grid and sensor installation errors. The centroid of the trajectory under the equipment's health calibration state is denoted as the static centroid O. _static Subtract O from the centroid of the real-time dynamic trajectory. _static The offset vector after that is denoted as the relative centroid offset vector δ. _rel Its modulus length is denoted as ; Area change rate: Calculated using polar coordinates, this is the derivative of the sector area dS / dθ, which varies with the spatial angle as the trajectory radius changes. It is a purely spatial geometric characteristic, and the calculation process does not introduce time and frequency parameters, thus it is unaffected by frequency conversion or transient operating conditions. The periodic fluctuation amplitude of this indicator can simultaneously reflect two types of fault characteristics: electrical harmonic distortion and motor rotor mechanical vibration. It is the most fundamental principle and core innovation of this patent family, enabling it to break away from traditional time-domain analysis, and it is also the fundamental source of derivation for all spatial topology analysis indicators in this patent family.

[0037] Eccentricity: After fitting a single-cycle closed dynamic trajectory to a standard ellipse, the ratio of the focal length to the major axis length of the ellipse is used as the eccentricity ε, which is used to quantify the degree of three-phase voltage and impedance asymmetry and the reactive power deficit of the system. Under ideal three-phase symmetrical conditions, the eccentricity value is 0. The more severe the trajectory distortion, the closer the eccentricity value is to 1.

[0038] 1.4. Mechanism for Acquisition and Generation of Trajectory Images In this invention, the generation of the "trajectory image" does not rely on external camera capture, but is based on real-time mathematical mapping of underlying physical quantities (including but not limited to voltage, current, power, etc.). The specific process is as follows: A high-precision analog-to-digital converter synchronously samples the three-phase voltage or current at high frequencies (e.g., sampling rate greater than or equal to 10kHz) to obtain instantaneous physical quantity values; the microprocessor normalizes the three-phase values ​​according to a preset coordinate transformation matrix and maps them to two-dimensional coordinates (x, y) within an equilateral triangular effect field; these coordinate points are continuously plotted and rendered according to a time sequence, thus generating a dynamic rheological trajectory image.

[0039] This coordinate system supports two operating conditions: independent analysis of a single physical quantity and synchronous analysis of voltage-current composite. When it is necessary to synchronously generate voltage and current dual dynamic rheological trajectories (corresponding to the composite spatial trajectory feature extraction scenario of patent 3), voltage and current are normalized and mapped using their own rated extreme values. The two sets of trajectories are rendered and calculated independently in the same coordinate system, and the two sets of normalized scales do not interfere with each other, thus avoiding geometric scale distortion problems.

[0040] 1.5 Early Warning Triggering Mechanism Based on Numerical Driving and Graphical Collaboration The alarm or graded early warning system of this invention adopts a dual-track mechanism of "bottom-level numerical-driven automatic alarm and top-level graphical visualization assistance." The system's bottom layer directly collects the values ​​of three-phase physical quantities and calculates geometric characteristic values ​​such as eccentricity and centroid offset in real time. The trigger source for early warning and control is whether these geometric characteristic values ​​exceed preset thresholds. Once a value exceeds the limit, the system does not need to wait for manual graphical analysis; it directly outputs relevant control signals or executes relevant actions based on the numerical comparison results. Simultaneously, the system renders the trajectory image on the screen or converts the core features into text, numbers, or status codes and outputs them to a simple monitoring device. Operators can then verify and diagnose the problem by observing the graphic pattern or reading the status indications. This mechanism ensures both the real-time nature of automated control and leverages the intuitive advantages of graphical and status indications.

[0041] Based on the above definitions and mechanisms, the present invention will be described in detail below through specific embodiments, in conjunction with the actual engineering standards of China's power grid.

[0042] Implementation Examples The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0043] 2.1 Example 1: Generation of three-phase dynamic effect trajectory, potential equilibrium point and over-limit overflow mechanism Regarding the dual normalized benchmark (U _max with I _max Engineering Setting Explanation: The equilateral triangular effect coordinate system constructed in this invention incorporates two completely independent and non-interfering normalized references for voltage and current. In actual engineering applications, the setting logic of these two references follows different physical rules, and the geometric warning mechanism of this patent possesses complete adaptive capability to this. 2.1.1 Voltage Normalization Reference (U _max Adaptive settings: Because the actual long-term operating voltage of the power grid is often higher than the nominal value (for example, the actual phase voltage of the domestic power grid often fluctuates in the range of 230V~237V), in actual deployment, U _max The voltage should be flexibly set according to the actual long-term operating peak voltage of the equipment access point (e.g., set to 332V or higher), rather than rigidly limited to the nominal peak voltage of 311V.

[0044] 2.1.2 Current Normalization Reference (I) _max Independent settings for: The current reference is entirely determined by the rated current on the nameplate of the monitored equipment, transformer, or line. It is an inherent property of the equipment and is not affected by the long-term high voltage of the power grid.

[0045] All subsequent normalized mappings in this invention (u'=u / U) _max or i'=i / I _max The dynamic overflow judgment, four-level early warning threshold (such as centroid offset rate SLCOR), and inscribed circle base truncation mechanism all rely purely on geometric relative ratios and topological morphology, and have nothing to do with the numerical magnitude of absolute physical quantities. As long as U is correctly configured according to the on-site working conditions... _max Or I _max The geometric diagnostic logic of this coordinate system can be perfectly applied.

[0046] The following explanation uses a nominal line voltage of 380V (effective phase voltage 220V, peak value approximately 311V) at the user end of a low-voltage distribution network in China as an example: A triangular effect field is constructed. In this embodiment, the voltage analysis condition is used as an example, with the vertex configured as the rated extreme value of a single-phase voltage of 311V. If switching to the current analysis condition, the vertex can be replaced with the rated single-phase current of the equipment. The voltage and current are generated into dynamic rheological trajectories using independent normalized scales. The electrical significance of the centroid O (origin): The centroid O is not only the absolute equilibrium point in space, but also the equilibrium point of the three-phase potential (zero potential point). In an ideal state, the zero potential point of the three-phase potential is located at the centroid O, and its dynamic rheological trajectory is an circumcircle with the centroid O as the center and the distance from the centroid to the vertex as the radius. Engineering verification of the over-limit overflow mechanism: According to the national standard GB / T12325, the upper limit of the allowable deviation of the 220V single-phase power supply voltage is +7% (peak value approximately 333V). When a light load shedding occurs, the voltage may instantly surge to 245V (peak value approximately 346V). At this point, a dynamic overflow mapping mechanism is triggered, and the projection of state point P crosses vertex A, extending outward along the OA effect axis. The extension distance is strictly proportional to the amplitude exceeding 311V (35V). This mechanism ensures the continuity of spatial coordinates under severe overvoltage conditions.

[0047] 2.2 Example 2: Derivation of Coordinate Transformation in the Calculation Process of Mapping Three-Phase Instantaneous Physical Quantities to the Effects Coordinate System 2.2.1 Derivation of Orthogonal Projection: This coordinate transformation is derived based on the orthogonal projection of vectors with the OA, OB, and OC axes at 120° to each other: 2.2.1.1: A-axis is along the positive y-axis (see...) Figure 2 B and C are respectively clamped to axis A. Angle 120°; Three-phase normalization, vector superposition along the y-axis: Vector A is fully preserved, and the projections of B and C in the y-direction are respectively... Therefore, y=u _a '- (u _b '+u _c '); 2.2.1.2: B and C have opposite values ​​on the horizontal x-axis, and the sine coefficient of the 120° included angle is... Therefore, x = (u _c '-u _b '); This formula removes the scaling factor of the traditional Clarke transform, and the vertex is directly used as the unit nominal boundary. The cross-limit can be determined when the radius vector r > 1, which is compatible with the dynamic overflow mechanism of this invention.

[0048] 2.2.2 Data Acquisition: Real-time acquisition of instantaneous voltage u of three phases A, B, and C _a u _b u _c The rated extreme capacity is set to U. _max (311V).

[0049] 2.2.3 Calculate the normalized value: u _a '=u _a / U _max u _b '=u _b / U _max u _c '=u _c / U _max , where u _a '、u _b '、u _c 'These are the normalized projection lengths of the three-phase instantaneous physical quantities onto the effect axes OA, OB, and OC, respectively.

[0050] 2.2.4 Coordinate Transformation: Mapping to a two-dimensional coordinate system with centroid O as the origin, new coordinates (x, y) are generated for state point P. The following effector coordinate transformation formula is used: x = ×(u _c '-u _b '), y=u _a -0.5×(u _b '+u _c ').

[0051] 2.2.5 Overflow Trigger: Calculate distance r= If r > 1, the overflow mechanism is triggered, the out-of-limit coordinates (x, y) are retained and marked with an "overflow flag".

[0052] 2.2.6 Numerical Calculation Example: Suppose that phase A is overvoltage at a certain moment, u _a =346V (out of limit), u _b =-150V, u _c =-190V. U _max =311V.

[0053] Step 1, Normalization: u _a =346 / 311≈1.1125, u _b =-150 / 311≈-0.4823, u _c =-190 / 311≈-0.6109.

[0054] Step 2, calculate x: Substituting into the formula, we get u _c '-u _b =-0.6109-(-0.4823)=-0.1286, x= ×(-0.1286)≈0.8660×(-0.1286)≈-0.1114.

[0055] Step 3, calculate y u _b '+u _c =-0.4823+(-0.6109)=-1.0932, y=1.1125- ×(-1.0932)=1.1125+0.5466=1.6591.

[0056] Step 4, calculate the radius vector r r= ≈1.663>1 Conclusion: The overflow mechanism is triggered, and the new coordinates of state point P are (-0.1114, 1.6591), with a radius vector of ≈1.663. The overflow along the OA effect axis is significant, which accurately quantifies the physical fact of the A-phase overvoltage.

[0057] 2.3 Example 3: Innovative Criteria for System Spatial Topological Distortion (Including Electrical and Pure Mechanical Features Converted to Electrical Features) Based on Geometric Features Spatial potential balance: characterized by the eccentricity ε. A circular trajectory (ε=0) indicates that the system is in perfect symmetry and balance; a flattened ellipse indicates reactive power deficit or impedance asymmetry.

[0058] Spatial load centroid offset rate: characterized by the centroid offset δ. The centroid deviates from the origin O, with its vector direction directly pointing to the heavily loaded or faulty phase; its magnitude is equivalent to the unbalance. In practical engineering, the static centroid O caused by the power grid background and installation errors must be deducted. _static The relative centroid offset vector δ is obtained. _rel Its modulus length is denoted as For the sake of brevity, the basic geometric derivation in this patent refers to it as the centroid offset δ.

[0059] High-frequency petal distortion rate: "Petal-shaped periodic protrusions" appear at the trajectory edges, and the number of petals corresponds to the ratio of the perturbation frequency to the fundamental frequency. The petal distortion rate η characterizes the "amplitude / fluctuation characteristics of the periodic protrusions at the trajectory edges." This characteristic has electromechanical isomorphism: at the electrical level, it is used to characterize power quality distortions such as specific subharmonic pollution; at the mechanical level, it is used to characterize high-frequency mechanical vibrations (including pure mechanical vibration signal mapping and electromechanical coupling modulation) caused by bearing wear, rotor eccentricity, or mechanical loosening.

[0060] 2.4 Example 4: System Limits and Basis Early Warning Based on Equilateral Triangular Geometric Boundaries Total capacity and phase-to-phase limits: The total area of ​​the equilateral triangle represents the maximum apparent power boundary; the three small triangles (such as triangle OAB) cut by the centroid and the two vertices represent the extreme capacity of the two-phase line voltage.

[0061] Reverse safety margin: The perpendicular distance from the centroid to each side represents the reverse safety margin. If the projection of the state point breaks through the three sides of the equilateral triangle (i.e., it crosses the boundary from the side rather than from the vertex), it indicates a severe reverse potential or zero-sequence imbalance, triggering emergency isolation.

[0062] Inscribed circle basis warning: The inscribed circle with centroid O as its center and the perpendicular distance from the centroid to the edge as its radius represents the minimum effective work boundary. Geometrically, the area of ​​the inscribed circle is equal to one-quarter of the area of ​​the circumscribed circle, and the radius of the inscribed circle is equal to one-half the radius of the circumscribed circle (i.e., r). _in =R _ideal / 2). In a physical sense, the quantization of the inscribed circle area represents the "minimum effective work basis" for the system to maintain three-phase symmetrical spatial coupling. When the system is in a state of severe undervoltage, phase loss, or stall, the trajectory is severely contracted, and the spatial geometric product (area) swept by a single cycle will be less than the area of ​​the inscribed circle. In the underlying algorithm engineering implementation, in order to balance physical rigor with the extremely low computing power requirements of edge devices, the system adopts the judgment logic of radius and area equivalence: the main control unit calculates the Euclidean distance from the trajectory point to the centroid O in real time (i.e., the instantaneous radius r). _actual ), or calculate the area of ​​the single-cycle trajectory envelope (S _actual When r is satisfied _actual ≤r _in (i.e. r)_actual ≤R _ideal / 2), or equivalently satisfying S _actual ≤S _in When the system determines that the spatial integration is insufficient to maintain the counterbalance, it loses its effective work basis. At this point, the system can automatically trigger a "quantization truncation" mechanism to forcibly stop the accumulation of invalid integrals at the time layer and immediately output "underload / demagnetization / stalled" alarms and emergency lockout commands. Radius determination and area determination are geometrically equivalent; edge devices with limited computing power prioritize single radial distance calculations to reduce computational load.

[0063] 2.5 Example 5: Multiphase extension application of the effector coordinate system (3n-sided effector coordinate system) This invention is described in detail using a three-phase AC system (equilateral triangular effect coordinate system) as a preferred embodiment. However, based on the underlying logic of "spatial antagonistic balance" in effect theory, this method can theoretically be seamlessly extended to any multiphase AC system (such as six-phase, nine-phase, twelve-phase, etc., i.e., a 3n-phase system, where n is a positive integer). For a 3n-phase system, it is only necessary to extend the effect field boundary from an "equilateral triangle" to a "regular 3n-gon", and extend the three effect axes that differ by 120° to 3n effect axes that differ by (360 / 3n)°. Its centroid O still represents the potential equilibrium point and the spatial absolute equilibrium point of the multiphase system, and the dynamic overflow mapping mechanism, geometric feature extraction, and quantization hierarchy construction logic remain isomorphic. This embodiment uses a three-phase equilateral triangle as the preferred implementation. The specific coordinate transformation matrix and overflow boundary calculation logic of the polygon extension can be directly derived by those skilled in the art based on the isomorphism principle of this patent without departing from the protection scope of this invention. Generally, the larger n is in a 3n-sided polygon, the higher the complexity of geometric conversion and feature solving operations. Therefore, this multiphase extension scheme is mainly suitable for high-reliability, high-value special power equipment, such as submarine propulsion motors.

Claims

1. A method for constructing an equilateral triangular effect coordinate system for spatial mapping and analysis of three-phase electrical physical quantities, characterized in that, Includes the following steps: S1: Constructing an equilateral triangular effect field and three-phase effect axes: An equilateral triangle ABC is constructed in the plane as the effect field boundary of the three-phase AC system; the centroid O is defined as the origin, representing the potential equilibrium point and the spatial absolute equilibrium point of the three-phase system; rays pointing from the origin to the three vertices are defined as three effect axes, and the vertices can be independently configured as the rated extreme values ​​of the voltage or current of that phase. The voltage and current are mapped using two sets of switchable, non-interfering normalized references; an inscribed circle is synchronously generated within the effect field, with an inscribed circle radius r. _in R is the radius of the ideal circumcircle _ideal 1 / 2, the area of ​​the inscribed circle S _in The circumcircle is 1 / 4 of the circumcircle, serving as the benchmark for determining the minimum effective work done in the system. During engineering implementation, the inscribed circle of this standard can be used as the basis for determining the actual minimum work done, with a larger or slightly smaller circle adjusted according to the equipment scenario. S2: Establish a dynamic overflow mapping mechanism for the three-phase effect axis: When the actual instantaneous physical quantity of a certain phase exceeds the rated extreme capacity, the state point is allowed to extend outward along the vertex direction on the corresponding effect axis, and an overflow mapping mechanism beyond the vertex is established to prevent over-limit distortion and feature truncation in subsequent calculations. S3: Three-phase dynamic effect trajectory point mapping and image acquisition: Real-time synchronous acquisition of instantaneous physical quantity values ​​of three phases A, B, and C, which are mapped to dynamic effect trajectory points within the equilateral triangle effect field through coordinate transformation, and continuously recorded and rendered to generate three-phase dynamic rheological trajectory images; S4: Numerical extraction of three-phase spatial geometric features: Complete standard trajectory is collected in advance under the no-load, fault-free steady-state operating condition of the equipment, and the static centroid O is calculated and permanently stored. _static Calculate the eccentricity of the trajectory, the original centroid offset, and the trajectory area change rate, and combine this with the pre-stored static centroid O. _static After deducting the fixed system offset, the relative centroid offset is obtained. The three types of features are used together as input data for subsequent feature perception or quantization calculation modules. S5: Trajectory Visualization and Rendering: Renders the dynamic rheological trajectory generated by coordinate transformation to the display interface in real time, adds annotations to the trajectory overflow and centroid offset areas, and intuitively displays the geometric distortion morphology of three-phase space. Only completes the geometric graphic output and does not output control commands.

2. The method according to claim 1, characterized in that, In step S1, the three vertices of the equilateral triangle are 120° apart in space, precisely corresponding to the physical spatial positions of the A, B, and C three-phase windings or the three-phase power supply in the three-phase AC system. Under ideal and standard three-phase power generation conditions, the zero potential point of the three-phase potential is located at the centroid O, and its dynamic rheological trajectory is an circumcircle with the centroid as the center and the distance from the centroid to the vertex as the radius.

3. The method according to claim 1, characterized in that, In step S2, the specific rules of the dynamic overflow mapping mechanism are as follows: when the instantaneous physical quantity of a certain phase is less than or equal to the rated extreme capacity, the projection of the dynamic effect trajectory point on the phase effect axis is located between the origin and the vertex; when the instantaneous physical quantity of a certain phase is greater than the rated extreme capacity, the projection of the dynamic effect trajectory point on the phase effect axis crosses the vertex, and the distance it exceeds the vertex is proportional to the magnitude of the physical quantity exceeding the rated extreme capacity. The two sets of normalized references for voltage and current independently perform overflow mapping, and the two mapping processes do not interfere with each other.

4. The method according to claim 1, characterized in that, In step S3, the specific process of the trajectory point mapping is as follows: the collected three-phase instantaneous physical quantity values ​​are normalized and used as the projection lengths of the dynamic effect trajectory points on the corresponding three effect axes. The two-dimensional coordinates of the dynamic effect trajectory points are uniquely determined by the intersection of the projections.

5. According to the method of claim 1, during the implementation of steps S4 and S5, the system state mapping rule corresponding to the three types of geometric features after static centroid deduction is as follows: the eccentricity ε is the ratio of the focal length to the major axis of the trajectory ellipse fitting; the relative centroid offset |δ _rel | represents the offset distance of the trajectory center point relative to the standard origin, and the offset vector points to the trajectory distortion direction; the petal distortion rate η is used to describe the degree of periodic convex distortion at the trajectory edge.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1 to 5.

Images