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(b) Voltage angle of bus 3. (c) Voltage angle of bus 5. (d) Voltage angle of bus 15.
(a) Voltage angle of bus 1.
After obtaining the phase angle of Bus 2 voltage from the SRF-PLL, the three-phase instantaneous Bus 2 voltage calculated in the above subsection can be transformed from the abc reference frame into the rotating dq reference frame by means of the Park transformation.
Equation (29) represents the power balance equations for each node, where (theta_{it}) is the phase angle of bus (i) in period (t); (D_{b}) is set of loads in bus (b); (G_{b}) is set of thermal units in bus (b).
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The simulation data including amplitudes and phase angles of bus voltages, active power and reactive power outputs, are acquired to simulate PMU measurements.
Before the motor on the steering column makes each adjustment to keep the bus on course, the software checks with sensors on the steering column and on the front axle that measure the angle of the bus's wheels to make sure that the adjustment will work as intended.
(13 where V i,s and θ i,s denote voltage magnitude and angle of source bus.
Taking the angle of generator bus Node 3 as the base, the relative angles of the remaining generators have experienced the change from positive to negative 180 degrees at around 2.5 s, which indicates that the system has lost its transient stability.
(27 where ( V_{{D_{i},pcc}}^{abc} ) and ( theta_{{D_{i},pcc}}^{abc} ) are the three-phase voltage magnitude and angle of the root bus.
Line flow constraints: left| {frac{1}{{x_{{j_{ik} }} }}left( {theta_{{j_{i} }} (t) - theta_{{j_{k} }} (t)} right)} right| le left| {F_{ik}^{hbox{max} } } right| (16 where ( theta_{{j_{i} }} (t) ) is the phase angle of voltage at bus j at time t; ( x_{{j_{ik} }} ) and |F ik max | are the reactance and maximum power flow of the line between buses i and k respectively.
Reference [26] studied the influence factors of the relationship of bus voltage phase angle differences and power angle differences.
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