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je suis revenu sur ma question "exprimer la puissance d'un réseau électrique en fonction de sa fréquence"
Petite question technique sur l'équilibrage de réseau je cherche une formule pour exprimer la puissance d'un réseau électrique en fonction de sa fréquence
https://www.energystream-wavestone.c...electrique-12/
Donc lorsqu’un utilisateur enclenche un appareil électrique, la puissance consommée supplémentaire est prélevée sur l’énergie cinétique de rotation des rotors des générateurs.
Et donc qu'équilibrer un réseau électrique instantanément, c'est largement réguler sa fréquence, d'où pas mal des questions liées aux ENRi
Je ne veux pas entrer dans les questions de déphasage etc.. simplement trouver la relation physique entre puissance et fréquence pour les petites variations de celle-ci
Voici ce que répond Gemini https://gemini.google.com
Mais je ne retrouve pas cette formule en clair dans des sources fiables
Est-ce que je suis en train de me faire abuser par une IA qui raconte n'importe quoi ? Apparemment c'est du flan cette formule... à moins que ce ne soit vrai approximativement quand on est dans les toutes petites variations
Genre des faibles valeurs du cosinus phi qui est indiqué par ChatGPT
je viens d'essayer avec Deepseek, qui me donne son raisonnement
quelle est la formule pour exprimer la puissance d'un réseau électrique en fonction de sa fréquence
Okay, the user is asking for the formula to express the power of an electrical network in terms of its frequency. Let me start by recalling my knowledge about electrical power systems.
First, I know that in AC systems, power is typically calculated using formulas involving voltage, current, and power factor. The basic formula for active power is P = V × I × cosφ, where V is voltage, I is current, and cosφ is the power factor. But the question specifically relates power to frequency.
Hmm, how does frequency come into play here? I remember that frequency is related to the rotational speed of generators. The grid frequency, like 50 Hz or 60 Hz, is maintained by the balance between generated power and consumed power. If demand increases, generators slow down slightly, causing frequency to drop, and vice versa. So maybe the relationship is more about system stability rather than a direct formula.
Wait, there's also the concept of the swing equation in generators, which relates the rate of change of frequency to the power imbalance. The equation is something like ΔP = 2H/ω₀ × dΔf/dt + DΔf, where H is the inertia constant, ω₀ is the nominal angular frequency, and D is the damping coefficient. This might be relevant for dynamic analysis of power systems when frequency changes.
But the user might be looking for a simpler relationship. Let me think again. In some contexts, like in induction motors, the speed of the motor is related to the supply frequency. The power consumed by the motor would depend on the load torque and speed, which is linked to frequency. The formula for motor speed is N = 120f/P, where P is the number of poles. But this relates mechanical power to frequency, not the network's electrical power directly.
Alternatively, in terms of reactive power, inductors and capacitors have impedance that depends on frequency. The reactive power Q = V²/(X_L - X_C), where X_L = 2πfL and X_C = 1/(2πfC). So reactive power does depend on frequency, but active power is more about real energy consumption. However, the question is about the power of the network, which could refer to active power, reactive power, or apparent power. Need to clarify that.
But maybe the user is referring to the overall power generation in a grid and how it's related to maintaining frequency. The key idea here is that the system frequency is a measure of the balance between generation and load. If generation matches load, frequency stays constant. If there's a mismatch, frequency changes. The primary control (governors) adjusts power output based on frequency deviations. The formula here would involve the droop characteristic: ΔP = (f_nominal - f_actual)/R, where R is the droop coefficient. So power adjustment is proportional to frequency deviation.
Alternatively, the power-frequency relationship can be modeled using the concept of load-frequency control (LFC). The transfer function between power and frequency involves the inertia of the system, damping, and governor response. But these are control system models rather than a direct formula for power in terms of frequency.
Wait, perhaps the user is thinking of the power delivered in a transmission line considering skin effect, which increases with frequency, leading to higher losses. But that's about power loss, not the network's power itself.
Alternatively, in three-phase systems, power formulas involve frequency when considering rotating machines, but the standard P = √3 V I cosφ doesn't include frequency explicitly.
So, putting this together, there isn't a direct formula where power is expressed as a simple function of frequency. Instead, frequency is an indicator of the power balance in the network. The relationship is more about control systems and dynamics. The primary formulas would be the swing equation for generators and the droop control for power adjustment.
I should explain that the power of the network isn't directly given by a formula involving frequency, but frequency stability is maintained by balancing generation and load. The key equations involve the rate of change of frequency with respect to power imbalance. For example, the swing equation: ΔP = 2H * (dΔf/dt)/f0 + DΔf, where ΔP is the power imbalance, H is the inertia constant, f0 is the nominal frequency, and D is the damping coefficient.
Additionally, the steady-state frequency deviation can be related to the power imbalance through the system's droop characteristics, where Δf = -ΔP * R / (1 + R/D), with R being the droop. But these are more about how power adjustments affect frequency, rather than expressing power as a function of frequency.
Therefore, the answer should clarify that while there's no direct formula, frequency is related to power balance through control mechanisms and dynamic equations. The key formulas involve power imbalance causing frequency changes, such as the swing equation and droop control equations.
la réponse ensuite
La puissance d'un réseau électrique n'est pas directement exprimée par une formule simple en fonction de sa fréquence. En revanche, la frégence du réseau (50 Hz ou 60 Hz) est un indicateur de l'équilibre entre puissance générée et puissance consommée. Voici les concepts clés :
sur un autre essai, en deux prompt et dont "quelle est la formule permettant d'exprimer cette relation"
Okay, the user previously asked about the relationship between grid frequency and energy. Now they're asking for the formula that expresses this relationship. Let me recall the key points from the previous answer.
I mentioned that frequency is tied to the balance between production and consumption. The main formula there was the energy stored in rotating generators as kinetic energy, E = 1/2 I ω², where ω is angular frequency related to the grid frequency. But maybe the user wants the formula that shows how frequency changes when there's a power imbalance.
Hmm, right. The swing equation is the fundamental formula here. It relates the rate of change of frequency to the power imbalance. The swing equation is dΔf/dt = (P_m - P_e)/(2H S), where H is the inertia constant, S is the rated power, and P_m and P_e are mechanical and electrical power.
Wait, but to make it understandable, I should present it step by step. Start with the kinetic energy stored in generators, then link that to the power imbalance causing a change in rotational speed (frequency). The formula Δf ≈ (ΔP × t)/(2H S) might be more intuitive for a simplified explanation.
Also, the user might not be familiar with all the variables. Need to define each term clearly. Explain that when there's a power difference (ΔP), over time (t), it causes a frequency deviation (Δf), and the system's inertia (H) determines how sensitive the frequency is to that imbalance.
Make sure to connect it back to the earlier points about inertia and energy balance. Maybe provide an example, like how a 100 MW imbalance affects frequency over 10 seconds with a certain H value.
Check if there are other relevant formulas, like the relationship between angular velocity and frequency (ω = 2πf). But the main formula they need is the one showing how power imbalance leads to frequency change. Also, clarify that this is a simplified model; real systems have more complex controls.
Need to confirm that the swing equation is indeed the right approach here. Yes, in power systems, the swing equation is used to model rotor dynamics and frequency changes. So present that equation, explain each term, and maybe give a simplified version for clarity. Also, mention that frequency deviation is proportional to the integral of the power imbalance over time, divided by the system's inertia.
Make sure the formulas are correctly formatted and explained in simple terms. Avoid too much jargon, but still be accurate. The user probably wants to see the mathematical relationship that underpins the concepts discussed earlier. So wrap it up by summarizing how the formula ties back to maintaining grid stability through balancing power and inertia.
et au final
La relation entre la variation de fréquence (ΔfΔ f) dans un réseau électrique et le déséquilibre de puissance (ΔPΔ P) peut être modélisée par une formule simplifiée issue de la dynamique des systèmes électriques. Voici la formule clé et son explication :
tout cela me parait très raisonnable, quoique je me gratte encore un peu la tête mais la conservation d'énergie c'est la bonne manière d'attaquer le problème
chatGPT 4o lui s'égare toujours dans la puissance réactive
https://chatgpt.com/share/6798c6b4-e...0-81e52a89402a
// ne comprenant pas bien le droop
Dernière modification par znog ; 28/01/2025 à 13h26.
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24/01/2025, 14h46
