en:cs:modelling_multi-phased_electrical_system_interconnexion

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en:cs:modelling_multi-phased_electrical_system_interconnexion [2020/08/07 14:29] – [Typescript code sketches] fraggleen:cs:modelling_multi-phased_electrical_system_interconnexion [2024/04/18 20:39] (Version actuelle) – [Quick and dirty mathematics background and rationale] fraggle
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 We suppose that all the multi-phased electrical systems are properly balanced: $ \forall n \in \{1,2\}; Iph_{n} = Iph_{n+1} $.  We suppose that all the multi-phased electrical systems are properly balanced: $ \forall n \in \{1,2\}; Iph_{n} = Iph_{n+1} $. 
  
-Let's call $ A = (p_{a}, V_{a}, I_{a}, Iph_{a}) $ and $ B = (p_{b}, V_{b}, I_{b}, Iph_{b}) $ two multi-phased electrical systems where $ p_{a},p_{b} \in \mathbb{N} $ are the number of phases, $ V_{a}, V_{b} \in \mathbb{N} $ are the voltage per phase, $ I_{b} \in \mathbb{N} $ are the total intensity and $ Iph_{a}, Iph_{b} \in \mathbb{N} $ the intensity per phase in their respective system.\\  +Let's call $ A = (p_{a}, V_{a}, I_{a}, Iph_{a}) $ and $ B = (p_{b}, V_{b}, I_{b}, Iph_{b}) $ two multi-phased electrical systems where $ p_{a},p_{b} \in \mathbb{N} $ are respectively the number of phases, $ V_{a}, V_{b} \in \mathbb{N} $ are the voltage per phase, $ I_{a}, I_{b} \in \mathbb{N} $ are the total intensity and $ Iph_{a}, Iph_{b} \in \mathbb{N} $ the intensity per phase.\\  
-We always have: $ I_{a} = p_{a} \times Iph_{a} $ and $ I_{b} = p_{b} \times Iph_{b} $. So the intensities properties can be deduced one from the other. +The intensities properties can be deduced one from the other: $ I_{a} = p_{a} \times Iph_{a} $ and $ I_{b} = p_{b} \times Iph_{b} $.
  
   * $ A $ and $ B $ are interconnected serially : $ A \triangleleft \triangleright B $.    * $ A $ and $ B $ are interconnected serially : $ A \triangleleft \triangleright B $. 
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   * $ I_{a} > I_{b} \land p_{a} < p_{b} \land p_{a}, p_{b} \in \{2,3\} \land I_{b} \ mod \ p_{a} \neq 0 \Rightarrow Iph_{A \triangleleft \triangleright B} \notin \mathbb{N} $ ;   * $ I_{a} > I_{b} \land p_{a} < p_{b} \land p_{a}, p_{b} \in \{2,3\} \land I_{b} \ mod \ p_{a} \neq 0 \Rightarrow Iph_{A \triangleleft \triangleright B} \notin \mathbb{N} $ ;
   * $ I_{a} < I_{b} \land p_{a} > p_{b} \land p_{a}, p_{b} \in \{2,3\} \land I_{a} \ mod \ p_{b} \ne 0 \Rightarrow Iph_{A \triangleleft \triangleright B} \notin \mathbb{N} $ ;   * $ I_{a} < I_{b} \land p_{a} > p_{b} \land p_{a}, p_{b} \in \{2,3\} \land I_{a} \ mod \ p_{b} \ne 0 \Rightarrow Iph_{A \triangleleft \triangleright B} \notin \mathbb{N} $ ;
-We can expose at leat two cases where $ Iph_{A \triangleleft \triangleright B} \notin \mathbb{N} $ if $ p_{a}, p_{b} \in \{2,3\} $+We can expose at least two cases where $ Iph_{A \triangleleft \triangleright B} \notin \mathbb{N} $ if $ p_{a}, p_{b} \in \{2,3\} $
  
 Let's say you only have $ Iph_{a}, Iph_{b} $ in $ A $ and $ B $. We can deduce $ I_{a}, I_{b} $ from them.\\  Let's say you only have $ Iph_{a}, Iph_{b} $ in $ A $ and $ B $. We can deduce $ I_{a}, I_{b} $ from them.\\ 
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 <code javascript> <code javascript>
-export class ElectricityUtils { +/** 
-  public static calculateAmpTotal(nbOfPhases: number, Iph: number): number {+ * Targeted to AC related values calculation. 
 + */ 
 +export class ACElectricUtils { 
 +  static amperageTotal(nbOfPhases: number, Iph: number): number {
     return nbOfPhases * Iph;     return nbOfPhases * Iph;
   }   }
  
-  public static calculatePowerPerPhase(V: number, Iph: number, cosPhi = 1): number {+  static powerPerPhase(V: number, Iph: number, cosPhi = 1): number {
     const powerPerPhase = V * Iph * cosPhi;     const powerPerPhase = V * Iph * cosPhi;
     if (cosPhi === 1) {     if (cosPhi === 1) {
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   }   }
  
-  public static calculatePowerTotal(nbOfPhases: number, V: number, Iph: number, cosPhi = 1): number { +  static powerTotal(nbOfPhases: number, V: number, Iph: number, cosPhi = 1): number { 
-    return nbOfPhases * ElectricalUtils.calculatePowerPerPhase(V, Iph, cosPhi);+    return nbOfPhases * ACElectricUtils.powerPerPhase(V, Iph, cosPhi);
   }   }
  
-  public static calculateAmpPerPhaseFromPower(nbOfPhases: number, P: number, V: number, cosPhi = 1): number { +  static amperageTotalFromPower(P: number, V: number, cosPhi = 1): number { 
-    const power = ElectricalUtils.calculateAmpTotalFromPower(P, V, cosPhi); +    const amperage = P / (V * cosPhi); 
-    const powerPerPhase = power / nbOfPhases; +    if (cosPhi === 1 && P % V === 0) { 
-    if (power % nbOfPhases === 0) { +      return amperage;
-      return powerPerPhase;+
     }     }
-    return Math.round(powerPerPhase);+    return Math.round(amperage);
   }   }
  
-  public static calculateAmpTotalFromPower(P: number, V: number, cosPhi = 1): number { +  static amperagePerPhaseFromPower(nbOfPhases: number, P: number, V: number, cosPhi = 1): number { 
-    const power = P / (V * cosPhi); +    const amperage = ACElectricUtils.amperageTotalFromPower(P, V, cosPhi); 
-    if (cosPhi === 1 && P % V === 0) { +    const amperagePerPhase = amperage / nbOfPhases; 
-      return power;+    if (amperage % nbOfPhases === 0) { 
 +      return amperagePerPhase;
     }     }
-    return Math.round(power);+    return Math.round(amperagePerPhase);
   }   }
 +}
 +
 +/**
 + * Targeted to DC related values calculation.
 + */
 +export class DCElectricUtils {
 +  static power(V: number, I: number): number {
 +    return V * I;
 +  }
 +
 +  static amperage(P: number, V: number): number {
 +    const amperage = P / V;
 +    if (P % V === 0) {
 +      return amperage;
 +    }
 +    return Math.round(amperage);
 +  }
 +}
 +</code>
 +
 +AC electrical component interface: 
 +
 +<code javascript>
 +interface ElectricACComponent {
 +  nPhases: number;
 +  Iph: number;
 +  V: number;
 +  I?: number;
 +  P?: number;
 } }
 </code> </code>
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 }; };
  
-function getCombinedElectricalObject(Car, ChargingStation) {+function getCombinedElectricObject(Car, ChargingStation): ElectricACComponent {
   return {   return {
     nPhases: Math.min(Car.nPhases, ChargingStation.nPhases),     nPhases: Math.min(Car.nPhases, ChargingStation.nPhases),
     Iph: Math.min(Car.Iph, ChargingStation.Iph),     Iph: Math.min(Car.Iph, ChargingStation.Iph),
     V: Math.min(Car.V, ChargingStation.V),     V: Math.min(Car.V, ChargingStation.V),
-    I: ElectricityUtils.calculateAmpTotal(this.nPhases, this.Iph), +    I: ACElectricUtils.amperageTotal(this.nPhases, this.Iph), 
-    P: ElectricityUtils.calculatePowerTotal(this.nPhases, this.Iph, this.V),+    P: ACElectricUtils.powerTotal(this.nPhases, this.Iph, this.V),
   };   };
 } }
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 const ChargingSchedulePeriod = { const ChargingSchedulePeriod = {
   startPeriod: 60,   startPeriod: 60,
-  limit: 15, // Sanity check: ensure the limit is below CarChargingStation.Iph +  limit: 15, // Sanity check: ensure the limit is below getCombinedElectricObject(Car, ChargingStation).Iph 
-  numberPhases: getCombinedElectricalObject(Car, ChargingStation),+  numberPhases: getCombinedElectricObject(Car, ChargingStation).nPhases,
 }; };
  
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 ====== Modelling multi-phased AC/DC electrical system ====== ====== Modelling multi-phased AC/DC electrical system ======
  
 +===== AC modelling =====
 +See first section. 
 ===== Rectifier modelling ===== ===== Rectifier modelling =====
- 
 FIXME FIXME
 +===== DC modelling ===== 
 +FIXME
 ====== Modelling multi-phased DC/AC electrical system ====== ====== Modelling multi-phased DC/AC electrical system ======
  
 +===== DC modelling =====
 +FIXME
 ===== Inverter modelling ===== ===== Inverter modelling =====
- 
 FIXME FIXME
 +===== AC modelling ===== 
 +See first section.
 ====== References ====== ====== References ======
  
 Composants symétriques : https://fr.qwe.wiki/wiki/Symmetrical_components Composants symétriques : https://fr.qwe.wiki/wiki/Symmetrical_components
  • en/cs/modelling_multi-phased_electrical_system_interconnexion.1596803373.txt.gz
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