PSIM User Manual phần 4 ppt

Chapter 2: Power Circuit Components 2-36 PSIM User Manual below: More Explanation on the Hall Effect Sensor: A hall effect position sensor consists of a set of hall switches and a set of trigger magnets. The hall switch is a semiconductor switch (e.g. MOSFET or BJT) that opens or closes when the magnetic field is higher or lower than a certain threshold value. It is based on the hall effect, which generates an emf proportional to the flux-density when the switch is car- rying a current supplied by an external source. It is common to detect the emf using a sig- nal conditioning circuit integrated with the hall switch or mounted very closely to it. This provides a TTL-compatible pulse with sharp edges and high noise immunity for connec- tion to the controller via a screened cable. For a three-phase brushless dc motor, three hall switches are spaced 120 electrical deg. apart and are mounted on the stator frame. The set of trigger magnets can be a separate set of magnets, or it can use the rotor magnets of the brushless motor. If the trigger magnets are separate, they should have the matched pole spacing (with respect to the rotor magnets), and should be mounted on the shaft in close proximity to the hall switches. If the trigger magnets use the rotor magnets of the machine, the hall switches must be mounted close enough to the rotor magnets, where they can be energized by the leakage flux at the appropriate rotor positions. Example: Start-Up of an Open-Loop Brushless DC Motor The figure below shows an open-loop brushless dc motor drive system. The motor is fed by a 3-phase voltage source inverter. The outputs of the motor hall effect position sensors are used as the gatings signals for the inverter, resulting a 6-pulse operation. The simulation waveforms show the start-up transient of the mechanical speed (in rpm), developed torque T em , and 3-phase input currents. B J τ mech = Motor Drive Module PSIM User Manual 2-37 Example: Brushless DC Motor with Speed Feedback The figure below shows a brushless dc motor drive system with speed feedback. The speed control is achieved by modulating sensor commutation pulses (Vgs for Phase A in this case) with another high-frequency pulses (Vgfb for Phase A). The high-frequency pulse is generated from a dc current feedback loop. The simulation waveforms show the reference and actual mechanical speed (in rpm), Phase A current, and signals Vgs and Vgfb. Note that Vgfb is divided by half for illustra- tion purpose. Brushless DC Motor Speed T em 3-phase currents Brushless DC Motor Speed T em Phase A current Vgs Vgfb/2 Chapter 2: Power Circuit Components 2-38 PSIM User Manual 2.6.1.5 Synchronous Machine with External Excitation The structure of a conventional synchronous machine consists of three stator windings, one field winding on either a salient or cylindrical rotor, and an optional damping winding on the rotor. Depending on the way the internal model interfaces with the external stator circuitry, there are two types of interface: one is the voltage-type interface (SYNM3), and the other is the current-type interface (SYNM3_I). The model for the voltage-type interface consists of controlled voltage sources on the stator side, and this model is suitable in situations where the machine operates as a generator and/or the stator external circuit is in series with inductive branches. On the other hand, The model for the current-type interface consists of controlled current sources on the stator side, and this model is suitable in situations where the machine operates as a motor and/or the stator external circuit is in parallel with capac- itive branches. The image and parameters of the machine are shown as follows. Image: Attributes: Parameters Description R s (stator) Stator winding resistance, in Ohm L s (stator) Stator leakage inductance, in H L dm (d-axis mag. ind.) d-axis magnetizing inductance, in H L qm (q-axis mag. ind.) q-axis magnetizing inductance, in H. Rf (field) Field winding resistance, in Ohm Lfl (field leakage ind.) Field winding leakage inductance, in H Rdr (damping cage) Rotor damping cage d-axis resistance, in Ohm Ldrl (damping cage) Rotor damping cage d-axis leakage inductance, in H SYNM3/SYNM3_I a b c Shaft Node n field-field+ Motor Drive Module PSIM User Manual 2-39 All the parameters are referred to the stator side. The equations of the synchronous machine can be expressed as follows: where and [ λ] = [L]*[I] where the inductance matrix is defined as follows: and Rqr (damping cage) Rotor damping cage q-axis resistance, in Ohm Lqrl (damping cage) Rotor damping cage q-axis leakage inductance, in H Ns/Nf (effective) Stator-field winding effective turns ratio Number of Poles P Number of Poles P Moment of Inertia Moment of inertia J of the machine, in kg*m 2 Torque Flag Output flag for internal developed torque T em Master/Slave Flag Flag for the master/slave mode (1: master; 0: slave). VRI d dt λ + ⋅ = V v a v b v c v f 00 T = I i a i b i c i f i dr i qr T = R diag R s R s R s R f R dr R qr = λ λ a λ b λ c λ f λ dr λ qr T = L L 11 L 12 L 12 T L 22 = L 11 L s L o L 2 2 θ r () cos++ L o 2 – L 2 2 θ r 2 π 3 –   cos+ L o 2 – L 2 2 θ r 2 π 3 +   cos+ L o 2 – L 2 2 θ r 2 π 3 –   cos+ L s L o L 2 2 θ r 2 π 3 +   cos++ L o 2 – L 2 2 θ r () cos+ L o 2 – L 2 2 θ r 2 π 3 +   cos+ L o 2 – L 2 2 θ r () cos+ L s L o L 2 2 θ r 2 π 3 –   cos++ = Chapter 2: Power Circuit Components 2-40 PSIM User Manual where θ r is the rotor angle. The developed torque can be expressed as: The mechanical equations are: 2.6.1.6 Permanent Magnet Synchronous Machine A 3-phase permanent magnet synchronous machine has 3-phase windings on the stator, and permanent magnet on the rotor. The difference between this machine and the brush- less dc machine is that the machine back emf is sinusoidal. The image and parameters of the machine are shown as follows. Image: L 12 L sf 2 θ r () cos L sd 2 θ r () cos L– sq 2 θ r () sin L sf 2 θ r 2 π 3 –   cos L sd 2 θ r 2 π 3 –   cos L– sq 2 θ r 2 π 3 –   sin L sf 2 θ r 2 π 3 +   cos L sd 2 θ r 2 π 3 +   cos L– sq 2 θ r 2 π 3 +   sin = L 22 L f L fdr 0 L fdr L dr 0 00L qr = T P 2 I d d θ r LI ⋅⋅ ⋅ = J d ω m dt ⋅ T em T load –= d θ r dt P 2 ω m ⋅ = PMSM3 a b c Shaft Node n Motor Drive Module PSIM User Manual 2-41 Attributes: The node assignments of the image are: Nodes a, b, and c are the stator winding terminals for Phase a, b, and c, respectively. The stator windings are Y connected, and Node n is the neutral point. The shaft node is the connecting terminal for the mechanical shaft. They are all power nodes and should be connected to the power circuit. The equations of the permanent-magnet synchronous machine can be described by the fol- lowing equations: where v a , v b, v c , and i a , i b, and i c , and λ a , λ b , λ c are the stator phase voltages, currents, and flux linkages, respectively, and R s is the stator phase resistance. The flux linkages are fur- Parameters Description R s (stator resistance) Stator winding resistance, in Ohm L d (d-axis ind.) Stator d-axis inductance, in H L q (q-axis ind.) Stator q-axis inductance, in H. The d-q coordinate is defined such that the d-axis passes through the center of the magnet, and the q-axis is in the middle between two magnets. The q-axis is leading the d-axis. Vpk / krpm Peak line-to-line back emf constant, in V/krpm (mechanical speed). The value of Vpk/krpm should be available from the machine data sheet. If this data is not available, it can be obtained through an experiment by operating the machine as a generator at 1000 rpm and measuring the peak line-to-line voltage. No. of Poles P Number of poles P Moment of Inertia Moment of inertia J of the machine, in kg*m 2 Mech. Time Constant Mechanical time constant τ mech Torque Flag Output flag for internal developed torque T em (1: output; 0: no output) Master/Slave Flag Flag for the master/slave mode (1: master; 0: slave). The flag defines the mode of operation for the machine. Refer to Section 2.5.1.1 for detailed explanation. v a v b v c R s 00 0 R s 0 00R s i a i b i c d dt λ a λ b λ c + ⋅ = Chapter 2: Power Circuit Components 2-42 PSIM User Manual ther defined as: where θ r is the rotor electrical angle, and λ pm is a coefficient which is defined as: where P is the number of poles. The stator self and mutual inductances are rotor position dependent, and are defined as: where L sl is the stator leakage inductance. The d-axis and q-axis inductances are associ- ated with the above inductances as follows: The developed torque can be expressed as: λ a λ b λ c L aa L ab L ac L aa L ab L ac L aa L ab L ac i a i b i c λ pm θ r () cos θ r 2 π 3 –   cos θ r 2 π 3 +   cos ⋅ + ⋅ = λ pm 60 V pk krpm ⁄⋅ π P 1000 3 ⋅⋅ ⋅ = L aa L sl L o L 2 2 θ r () cos ⋅ ++= L bb L sl L o L 2 2 θ r 2 π 3 +   cos ⋅ ++= L cc L sl L o L 2 2 θ r 2 π 3 –   cos ⋅ ++= L ab L ba L o – L 2 2 θ r 2 π 3 –   cos ⋅ +== L ac L ca L o – L 2 2 θ r 2 π 3 +   cos ⋅ +== L bc L cb L o – L 2 2 θ r () cos ⋅ +== L d L sl 3 2 L o 3 2 L 2 ++= L q L sl 3 2 L o 3 2 L 2 –+= T em P 2 L 2 i a i b i c 2 θ r () sin 2 θ r 2 π 3 –   sin 2 θ r 2 π 3 +   sin 2 θ r 2 π 3 –   sin 2 θ r 2 π 3 +   sin 2 θ r () sin 2 θ r 2 π 3 +   sin 2 θ r () sin 2 θ r 2 π 3 –   sin i a i b i c ⋅⋅ ⋅ – ⋅ = Motor Drive Module PSIM User Manual 2-43 The mechanical equations are: where B is a coefficient, T load is the load torque, and P is the no. of poles. The coefficient B is calculated from the moment of inertia J and the mechanical time constant τ mech as below: 2.6.1.7 Switched Reluctance Machine PSIM provides the model for 3-phase switched reluctance machine with 6 stator teeth and 4 rotor teeth. The images and parameters are shown as follows. Image: Attributes: Parameters Description Resistance Stator phase resistance R, in Ohm Inductance L min Minimum phase inductance, in H P 2 λ pm i a i b i c θ r () sin θ r 2 π 3 –   sin θ r 2 π 3 +   sin ⋅⋅⋅ = J d ω m dt ⋅ T em B ω m T load – ⋅ –= d θ r dt P 2 ω m ⋅ = B J τ mech = SRM3 a+ b+ c+ a- b- c- c 1 c 2 c 3 c 4 c 1 c 4 c 1 c 4 Phase a Phase b Phase c Shaft Node θ Chapter 2: Power Circuit Components 2-44 PSIM User Manual The master/slave flag defines the mode of operation for the machine. Please refer to Sec- tion 2.5.1.1 for detailed explanation. The node assignments are: Nodes a+, a-, b+, b-, and c+, c- are the stator winding terminals for Phase a, b, and c, respectively. The shaft node is the connecting terminal for the mechanical shaft. They are all power nodes and should be connected to the power circuit. Node c 1 , c 2 , c 3 , and c 4 are the control signals for Phase a, b, and c, respectively. The con- trol signal value is a logic value of either 1 (high) or 0 (low). Node θ is the mechanical rotor angle. They are all control nodes and should be connected to the control circuit. The equation of the switched reluctance machine for one phase is: where v is the phase voltage, i is the phase current, R is the phase resistance, and L is the phase inductance. The phase inductance L is a function of the rotor angle θ , as shown in the following figure. The rotor angle is defined such that, when the stator and the rotor teeth are completely out of alignment, θ = 0. The value of the inductance can be in either rising stage, flat-top stage, falling stage, or flat-bottom stage. If we define the constant k as: Inductance L max Maximum phase inductance, in H θ r Duration of the interval where the inductance increases, in deg. Moment of Inertia Moment of inertia J of the machine, in kg*m 2 Torque Flag Output flag for internal torque T em . When the flag is set to 1, the output of the internal torque is requested. Master/Slave Flag Flag for the master/slave mode (1: master; 0: slave) viR dL i ⋅() dt + ⋅ = θ r θ L min L max L Rising Flat-Top Fallin Flat-Bottom Motor Drive Module PSIM User Manual 2-45 we can express the inductance L as a function of the rotor angle θ : L = L min + k ∗ θ [rising stage. Control signal c 1 =1) L = L max [flat-top stage. Control signal c 2 =1) L = L max - k ∗ θ [falling stage. Control signal c 3 =1) L = L min [flat-bottom stage. Control signal c 4 =1) The selection of the operating state is done through the control signal c 1 , c 2 , c 3 , and c 4 which are applied externally. For example, when c 1 in Phase a is high (1), the rising stage is selected and Phase a inductance will be: L = L min + k ∗ θ . Note that only one and at least one control signal out of c 1 , c 2 , c 3 , and c 4 in one phase must be high (1). The developed torque of the machine per phase is: Based on the inductance expression, we have the developed torque in each stage as: T em = i 2 *k / 2 [rising stage] T em = 0 [flat-top stage] T em = - i 2 *k / 2 [falling stage] T em = 0 [flat-bottom stage] Note that saturation is not considered in this model. 2.6.2 Mechanical Loads Several mechanical load models are provided in PSIM: constant-torque, constant-power, and general-type load. Note that they are available in the Motor Drive Module. 2.6.2.1 Constant-Torque Load The image of a constant-torque load is: k L max L min – θ = T em 1 2 i 2 dL d θ ⋅⋅ = [...]... constant, in rpm PSIM User Manual 2 -47 Chapter 2: Power Circuit Components Moment of Inertia Moment of inertia of the load, in kg*m2 A constant-speed mechanical load defines the speed of a mechanical system, and the speed will remain constant, as defined by the speed constant 2.6.2 .4 General-Type Load Besides constant-torque and constant-power load, a general-type load is provided in PSIM The image of... below Image: 2 -48 PSIM User Manual Motor Drive Module GEARBOX Attributes: Parameters Gear Ratio Description The gear ratio a If the numbers of teeth of the first gear and the second gear are n1 and n2, respectively, the gear ratio a is defined as: a = n1 / n2 Let the radius, torque, and speed of these two gears be: r1, r2, T1, T2, ω1, and ω2, we have: T1 / T2 = r1 / r2 = ω2 / ω1= a 2.6 .4 Mechanical-Electrical... mechanical load (with a load torque of Tload and a moment of inertia of J2) The equation that describes the mechanical system is: PSIM User Manual 2 -49 Chapter 2: Power Circuit Components dω m ( J 1 + J 2 ) ⋅ = T em – T load dt where ωm is the shaft mechanical speed In PSIM, this equation is modelled by an equivalent circuit as shown below ωm Tem J1 speed node J2 Tload In this circuit, the two current... direction 2.6.2.2 Constant-Power Load The image of a constant-power load is: Image: MLOAD_P Attributes: Parameters Description Maximum Torque Base Speed 2 -46 Maximum torque Tmax of the load, in N*m Base speed nbase of the load, in rpm PSIM User Manual Motor Drive Module Moment of Inertia Moment of inertia of the load, in kg*m2 The torque-speed curve of a constant-power load can be illustrated below:... capacitor connected to this node represents the load moment of inertia Mechanical load model 2-50 PSIM User Manual Motor Drive Module Example: A custom machine model with a constant-torque mechanical load Similarly, one can build a custom machine model and connect it to the mechanical load available in the PSIM library The figure below shows such a circuit The custom machine model must use the capacitor... measures the torque transferred from the dotted side of the sensor to the other side alone the positive speed direction To illustrate this, the following mechanical system is taken as an example: PSIM User Manual 2-51 ... equivalent circuit One can thus connect any electrical circuits to this node With this element, users can connect the built-in motors or mechanical loads with custombuilt load or motor models Example: An induction machine with a custom mechanical load model The figure below shows an induction machine connected to a user defined mechanical load model through the mechanical-electrical interface block As explained,... the values of J1 and J2 The node-to-ground voltage (speed node voltage) represents the mechanical speed ωm This is analogous to C*dV/dt = i for a capacitor where C = J1+J2, V = ωm, and i = Tem-Tload In PSIM, the mechanical equivalent circuit for motors and mechanical loads all uses the capacitor-based circuit model The mechanical-electrical interface block provides the access to the internal mechanical... as: a = n1 / n2 Let the radius, torque, and speed of these two gears be: r1, r2, T1, T2, ω1, and ω2, we have: T1 / T2 = r1 / r2 = ω2 / ω1= a 2.6 .4 Mechanical-Electrical Interface Block This block allows users to access the internal equivalent circuit of the mechanical system for a machine Image: MECH_ELEC Mechanical Side Electrical Side Attributes: Parameters Master/Slave Flag Description Flag for the . ω m ⋅ = B J τ mech = SRM3 a+ b+ c+ a- b- c- c 1 c 2 c 3 c 4 c 1 c 4 c 1 c 4 Phase a Phase b Phase c Shaft Node θ Chapter 2: Power Circuit Components 2 -44 PSIM User Manual The master/slave flag defines the mode. Components 2 -48 PSIM User Manual A constant-speed mechanical load defines the speed of a mechanical system, and the speed will remain constant, as defined by the speed constant. 2.6.2 .4 General-Type. v a v b v c R s 00 0 R s 0 00R s i a i b i c d dt λ a λ b λ c + ⋅ = Chapter 2: Power Circuit Components 2 -42 PSIM User Manual ther defined as: where θ r is the rotor electrical angle, and λ pm is a coefficient