University:
Kentucky State University
Course:
PHY 212 | General Physics II
Academic year:

2021
Views:

7

Pages:

46
Author:

marthamanayay9qr11

**Electrical Machines** * Generators give our electricity from motion. * Motors give our motion from electricity. * Transformers. **Electrical Machines** Stationary Part (Rigid) Rotating Part (Flexible) Transformers Generators Motors Single-phase Tr. three-phase Tr. 1-Φ Tr. 3-Φ Tr. Synchronous M. Asynchronous M. D.C.M. Shunt Series Compound Induction Universal Asynchronous A **Rotational Motion:** θ, ω, α → τ * **Linear** v = dx/dt a = dv/dt = d²x/dt² * **Angular** ω = dθ/dt (rad/s) α = dω/dt = d²θ/dt² (rad/s²) * **Angular velocity** ω = dθ/dt → rad/sec * **rpm** rpm = revolution/min * **rpm to rad/sec** ω = 2πf (radian/sec) * **Angular acceleration** α = dω/dt → rad/sec² * **Torque** τ = F × r * **Newton's Law of Rotation** τ = Iα * **Linear** Work = ∫F.dr * **Rotational** Work = ∫τ.dθ * **Power** P = dW/dt = τ(dθ/dt) = τω * **In Rotational** P = τω = VI (electrical) 1. The im is not pure sinusoidal (is cos or sin) 2. When the peak flux reach that Saturation point When flux ↑ → im ↑ 3. im lags the voltage. Notice the following points about the core losses current: 1. It is nonlinear 2. In-phase with the voltage The total No-load current in the core is called excitation current. iex = im + io The equivalent circuit of a transformer: The losses that occur in Real transformer are: 1. Copper losses 2. Eddy current losses 3. Hysteresis losses 4. Leakage flux The model of a Real transformer: [Image of a transformer equivalent circuit] Vs = (R₁ + jX₁)I₁ + V₁ V₁ = V₂(N₁/N₂) V₂ = (R₂ + jX₂)I₂ I₂ = I₁ (N₁/N₂) Zeq = R + jX Zeq = 25 + j20 Zeq = √(25² + 20²) = 32.02 θ = tan⁻¹(20/25) = 38.66° **Refer to secondary voltage** Zeq = (R₁ + jX₁)(R₂+jX₂) / (R₁ + jX₁ + R₂+jX₂) **Refer to Vp** Zeq = (R₁ + jX₁)(R₂+jX₂) / (R₁ + jX₁ + R₂+jX₂) **Refer to Vs** Zeq = (R₁ + jX₁)(R₂+jX₂) / (R₁ + jX₁ + R₂+jX₂) **Determine the values of components in the transformer model.** *This value can be obtained with only two tests: 1- open cct test (O.C.T) 2- short cct test(S.C.T) *In the open cct test: Secondary winding is open cct & primary winding is connected to a full-rated voltage. (Refer to low voltage side) Zeq = R + jX Ye = Gc + jBm Ye = Gc - jBm = 1/Zc Rc = 1/Gc Xm = 1/Bm These two elements are in parallel. Where: |Ye| = Ioc/Voc pf = cosθ = P/Voc.Ioc θ = cos⁻¹(P/Voc.Ioc) Ye = Ioc/Voc ∠-cos⁻¹(pf) Ye = Ioc/Voc ∠-θ **O.C.T** Wattmeter → P = active power high R **S.C.T** Wattmeter → P = copper losses **Primary:** V₁ **Secondary:** V₂