Slack Bus And Slack Generator

Slack Bus And Slack Generator The Table below shows input data of each busbar in the system used to solve the power flow and the simulation result according to instruction described in question 1. BUS Input Data [Simulation Result] BUS 1 pu P (load) 100 MW Q (load) 0 Mvar BUS 2 P (load) 200 MW Q (load) 100 Mvar CB of Generation Open BUS 3 1 pu P (Gen) 200 MW P (load) 100 MW Q (load) 50 Mvar AVR On AGC Off Slack bus and slack generator In power flow calculation, unique numerical solution cannot be calculated without reference voltage magnitude and angle due to unequal number of unknown variables and independent equations. The slack bus is the reference bus where its voltage is considered to be fixed voltage magnitude and angle (1à ¢Ã‹â€ Ã‚  0 °), so that the various voltage angle difference among the buses can be calculated respect. In addition, the slack generator supplies as much real power and reactive power as needed for balancing the power flow considering power generation, load demand and losses in the system while keep the voltage constant as 1à ¢Ã‹â€ Ã‚  0 °. In real power system, when relatively weak system is linked to the larger system via a single bus, this bus can represent the large system with an equivalent generator keeping the voltage constant and generating any necessary power like slack bus. [1] Bus type (PQ bus or PV bus) BUS Bus type Comments BUS 2 PQ Bus Generator is disconnected to Bus 2 BUS 3 PV Bus Generator is connected to Bus 3 and the magnitude of voltage of generator keep constant by using AVR In general, each bus in the power system can be categorized into three bus types such as Slack Bus, Load (PQ) Bus, and Voltage Controlled (PV) Bus. The definition and difference between PQ Bus and PV Bus are described as follows; [2] PV Bus (Generator Bus or Voltage Controlled Bus): It is a bus at which the magnitude of the bus voltage is kept constant by the generator. Even though the bus has several generators and load, if any generators connected to the bus regulate the bus voltage with AVR, then this bus is referred to PV Bus. For PV bus, the magnitude of the bus voltage and real power supplied to the system are specified, and reactive power and angle of the bus voltage are accordingly determined. If a preset maximum and minimum reactive power limit is reached, the reactive output of the generator remains at the limited values, so the bus can be considered as PQ Bus instead of PV Bus. [2] PQ Bus (Load Bus): It is a bus at which the voltage is changed depending on total net real power and reactive power of loads and generators without voltage regulator. Therefore, in the power simulation and calculation, the real power and reactive power of the loads are specified as input data and accordingly the voltage (magnitude and angle) is calculated based on the above input. The following table specifies input and output of each bus type in the power system simulation and calculation. Bus Type P Q (Magnitude) ÃŽÂ ´ (Angle) PQ Bus Input Input Output Output PV Bus Input Output Input Output Slack Bus Output Output Input Input System Balance Total Generation Load Demand BUS Real Power (MW) Imaginary Power (Mvar) Generation Load Generation Load BUS 1 204.093 100 56.240 0 BUS 2 0 200 0 100 BUS 3 200 100 107.404 50 Total 404.093 400 163.644 150 Difference Pgen Pdemand = 4.093 Qgen Qstored in load = 13.644 Reason: Real power loss due to resistance of transmission line and imaginary power storage due to reactance of transmission line are the reasons for the difference between power generation and load demand in the system. P (Losses) Q (Storage) over the transmission line BUS Real Power (MW) Imaginary Power (Mvar) Sending Receiving Losses Sending Receiving Stored BUS 1 BUS 2 102.714 100.650 2.064 56.653 49.773 6.88 BUS 1 BUS 3 1.379 1.378 0.001 0.4141) 0.4131) 0.001 BUS 3 BUS 2 101.378 99.350 2.028 56.990 50.227 6.763 Total Plosses = 4.093 Qstored in load = 13.644 1) Imaginary power flows from Bus 3 to Bus 1. The summation of real power losses and imaginary power storage over the transmission line are exactly same with total difference between generation and load. Therefore, it is verified that the difference is shown over the transmission line. Kirchoff balance as each bus [4] Bus1 ÃŽÂ £ P1 = + Pgen1 Pload1 P12 P13 = 204.093 100 102.714 1.379 = 0 ÃŽÂ £ Q1 = + Qgen1 Qload1 Q12 Q13 = 56.24 0 56.653 + 0.413 = 0 Bus2 ÃŽÂ £ P2 = + Pgen2 Pload2 P21 P23 = 0 200 + 100.65 + 99.35 = 0 ÃŽÂ £ Q2 = + Qgen2 Qload2 Q21 Q23 = 0 100 + 49.773 + 50.227 = 0 BUS3 ÃŽÂ £ P3 = + Pgen3 Pload3 P31 P32 = 200 100 + 1.378 101.378 = 0 ÃŽÂ £ Q3 = + Qgen3 Qload3 Q31 Q32 = 107.404 50 0.414 56.99 = 0 According to the calculation above, as summation of incoming outgoing real power and imaginary power at each bus become zero, it is verified that each busbar obeys a Kirchoff balance. In addition, the total power system is completely balanced, because total generation power (real imaginary) are equal to summation of total load demand and real power loss stored imaginary power over the transmission (i.e. Pgen Pdemand = Plosses, Qgen Qstored in load = Q stored in system) as shown above. Voltage Angle and Angle Difference As a result of the Powerworld, the voltage angle and angle difference are shown in the table below. BUS Voltage Angle Voltage Angle Difference BUS1 ÃŽÂ ´1 = 0.00 ° BUS1- BUS2 ÃŽÂ ´1 ÃŽÂ ´2 = 0.00 ° (-2.5662 °) = 2.5662 ° BUS2 ÃŽÂ ´2 = -2.5662 ° BUS2- BUS3 ÃŽÂ ´2 ÃŽÂ ´3 = -2.5662 ° (-0.043 °) = -2.5232 ° BUS3 ÃŽÂ ´3 = -0.043 ° BUS3- BUS1 ÃŽÂ ´3 ÃŽÂ ´1 = -0.043 ° 0.00 ° = -0.043 ° Power System Analysis -1 The table below summarizes generation and voltage angle variation at each bus as generation at Bus 3 varies from 0 MW to 450 MW by 50MW. Simulation Results and Observation P3 = 0 MW P3 = 50 MW P3 = 100 MW P3 = 150 MW P3 = 250 MW P3 = 300 MW P3 = 350 MW P3 = 400 MW P3 = 450 MW Reactive Power Generation at Bus 3: It is found that reactive power generation Q3(gen) decrease while real power generation P3(gen) increase because Bus 3 as a PV Bus regulates the constant bus voltage magnitude by controlling excitation of the generation through the AVR. Power Generation at Bus 1: It is found that P1(gen) decreases and Q1(gen) increases simultaneously, while P3(gen) increases and Q3(gen) decrease. As the total load demand in the system keeps constant (i.e. Ptotal(load) = 400 MW, Qtotal(load) = 150Mvar), any necessary real power and reactive power for the system balance need to be supplied by generator (slack generator) at Bus 1. Therefore, power generation P1(gen) and Q1(gen) at Bus 1 change reversely compared to power generation change at Bus 3. Voltage Angle Difference: In general, real power flow is influenced by voltage angle difference between sending bus and receiving bus according to PR =. Therefore, it is observed that as real power generation P3(gen) increases real power flow from Bus 3 to Bus2 increase, accordingly voltage angle difference (ÃŽÂ ´3 ÃŽÂ ´2) between Bus 3 and Bus 2 increases. However, decrease in real power from Bus 1 to Bus 2 due to increase of P3(gen) result in decrease of voltage angle difference (ÃŽÂ ´1 ÃŽÂ ´2). In addition, Real power between Bus 1 and Bus 3 flows from Bus 1 to Bus 3 until P3(gen) reach to 200 MW and as P3(gen) increase more than 200 MW the real power flows from Bus 3 to Bus 1. So, it is also observed that voltage angle difference (ÃŽÂ ´3 ÃŽÂ ´1) is negative angle when P3(gen) is less than 200MW and the difference increase while P3(gen) increase. Power System Analysis -2 The table below summarizes the variation of power generation and voltage angle difference at each bus when the load demand at Bus 3 varies by 50MW and 25Mvar. Simulation Results and Observation P2 = 0 MW Q2 = 0 MW P2 = 50 MW Q2 = 25 MW P2 = 100 MW Q2 = 50 MW P2 = 150 MW Q2 = 75 MW P2 = 250 MW Q2 = 125 MW P2 = 300 MW Q2 = 150 MW P2 = 350 MW Q2 = 175 MW P2 = 400 MW Q2 = 200 MW P2 = 450 MW Q2 = 225 MW Power Generation at Bus 1 and Bus 3: It is observed that as the total load demand in the system increases due to increase of load demand P2(load) Q2(load) at Bus 2, any necessary real power for the system balance is supplied by generator (slack generator) at Bus 1 considering constant P3(gen), so P1(gen) increases. In addition, any necessary reactive power for the system balance is supplied from Bus 1 as well as Bus 3, so both Q1(gen) and Q3(gen) increase. Voltage Angle Difference: It is found that real power flow increase both from Bus 1 to Bus 2 and from Bus 3 to Bus 2 due to increase of load demand at Bus2. Accordingly, both voltage angle difference ÃŽÂ ´1 ÃŽÂ ´2 and ÃŽÂ ´3 ÃŽÂ ´2 increase when the power flow P12 and P32 increase. In addition, when P2(load) is less than 200 MW, P1gen is relatively low. Therefore real power between Bus 3 and Bus 1 flows from Bus 3 to Bus 1 at lower P2(load) (less than 200MW). On the other hand, while P2(load) increase more than 200 MW, the real power flow direction changes (Bus 1 to Bus 3) and the real power flow increases. Accordingly, the voltage angle difference ÃŽÂ ´1 ÃŽÂ ´3 change from negative to positive and increase. Voltage Magnitude at Bus 2: It is observed that magnitude of bus voltage at Bus2 drops due to increase of the load demand at Bus 2. Question 2 System Model Admittance Matrix In order to construct the admittance matrix of Powerworld B3 case, single phase equivalent circuit can be drawn as below; z = r + jx (r = 0, x = 0.05) z12 = z21= j0.05 pu, y12 = 1/ z12 = 1/j0.05 = -j20 pu = y12 z13 = z31= j0.05 pu, y13 = 1/ z13 = 1/j0.05 = -j20 pu = y31 z23 = z32= j0.05 pu, y23 = 1/ z23 = 1/j0.05 = -j20 pu = y32 Admittance matrix can be defined as follows; BUS = Diagonal elements Y(i,i) of the admittance matrix, called as the self-admittance [lecture slide] [6], are the summation of all admittance connected with BUS i. = y12 + y13 = -j20 j20 = -j40 pu = y21 + y23 = -j20 j20 = -j40 pu = y31 + y32 = -j20 j20 = -j40 pu Off diagonal elements Y(i,j) of the admittance matrix, called as the mutual admittance [lecture slide] [6], are negative admittance between BUS i and BUS j. = y12 = -(-j20) = j20 pu = y13 = -(-j20) = j20 pu = y21 = -(-j20) = j20 pu = y23 = -(-j20) = j20 pu = y31 = -(-j20) = j20 pu = y32 = -(-j20) = j20 pu Therefore, the final admittance matrix BUS is; BUS = = The following figure shows the BUS of the Powerworld B3 case and it is verified that the calculated admittance matrix is consistent with the result of the Powerworld. Power Flow Calculation Nodal equation with the admittance matrix can be used to calculate voltage at each bus if we know all the current (i.e. total generation power and load demand at each BUS) and finally the power flow can be calculated accordingly. , therefore, In this question, however, simulation results of the voltage at each bus from the Powerworld are used for the power flow calculation as follows; [Simulation result] Voltage at each Bus and Voltage Difference V1 = 1 à ¢Ã‹â€ Ã‚  0.00 ° pu (BUS1) V2 = 1 à ¢Ã‹â€ Ã‚  -0.48 ° pu (BUS2) V3 = 1 à ¢Ã‹â€ Ã‚  0.48 ° pu (BUS 3) Voltage difference between BUS 1 and BUS 2 V12 = V1 V2 = 1 à ¢Ã‹â€ Ã‚  0.00 ° 1 à ¢Ã‹â€ Ã‚  -0.48 ° = 3.5 x 10-5 + j 8.38 x 10-3 = 8.38 x 10-3 à ¢Ã‹â€ Ã‚  89.76 ° pu V21 = V2 V1 = V12 = 3.5 x 10-5 j 8.38 x 10-3 = 8.38 x 10-3 à ¢Ã‹â€ Ã‚  -90.24 ° pu Voltage difference between BUS 3 and BUS 2 V32 = V3 V2 = 1 à ¢Ã‹â€ Ã‚  0.48 ° 1 à ¢Ã‹â€ Ã‚  -0.48 ° = j 16.76 x 10-3 = 16.76 x 10-3 à ¢Ã‹â€ Ã‚  90 ° pu V23 = V2 V3 = V32 = j 16.76 x 10-3 = -16,76 x 10-3 à ¢Ã‹â€ Ã‚  -90 ° pu Voltage difference between BUS 3 and BUS 1 V31 = V3 V1 = 1 à ¢Ã‹â€ Ã‚  0.48 ° 1 à ¢Ã‹â€ Ã‚  0.00 ° = 3.5 x 10-5 + j 8.38 x 10-3 = 8.38 x 10-3 à ¢Ã‹â€ Ã‚  90.24 ° pu V13 = V1 V3 = V31 = 3.5 x 10-5 j 8.38 x 10-3 = 8.38 x 10-3 à ¢Ã‹â€ Ã‚  -89.76 ° pu Line Current Current flow from BUS i and BUS j can be calculated by using voltage difference and interconnected admittance of the line between buses. [ Iij = yij * (Vi Vj) ] Line current between BUS 1 and BUS 2 I12 = y12 x (V1 V2) = -j20 x 8.38 x 10-3 à ¢Ã‹â€ Ã‚  89.76 ° = 167.6 x 10-3 à ¢Ã‹â€ Ã‚  -0.24 ° pu (BUS 1 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ BUS 2) I21 = y21 x (V2 V1) = -j20 x 8.38 x 10-3 à ¢Ã‹â€ Ã‚  -90.24 ° = 167.6 x 10-3 à ¢Ã‹â€ Ã‚  -180.24 ° pu (BUS 2 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ BUS 1) Line current between BUS 3 and BUS 2 I32 = y32 x (V3 V2) = -j20 x 16.76 x 10-3 à ¢Ã‹â€ Ã‚  90 ° = 335.2 x 10-3 à ¢Ã‹â€ Ã‚  0.00 ° pu (BUS 3 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ BUS 2) I23 = y23 x (V2 V3) = -j20 x 16.76 x 10-3 à ¢Ã‹â€ Ã‚  -90 ° = 335.2 x 10-3 à ¢Ã‹â€ Ã‚  180 ° pu (BUS 2 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ BUS 3) Line current between BUS 3 and BUS 1 I31 = y31 x (V3 V1) = -j20 x 8.38 x 10-3 à ¢Ã‹â€ Ã‚  90.24 ° = 167.6 x 10-3 à ¢Ã‹â€ Ã‚  0.24 ° pu (BUS 3 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ BUS 1) I13 = y13 x (V1 V3) = -j20 x 8.38 x 10-3 à ¢Ã‹â€ Ã‚  -89.76 ° = 167.6 x 10-3 à ¢Ã‹â€ Ã‚  -179.76 ° pu (BUS 1 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ BUS 3) Apparent Power Flow Apparent flow from BUS i and BUS j can be calculated by voltage at the sending bus and line current. [ Sij = Vi * I*ij ] Apparent Power from BUS 1 to BUS 2 S12 = V1* I*12 = 1 à ¢Ã‹â€ Ã‚  0.00 ° x 167.6 x 10-3 à ¢Ã‹â€ Ã‚  0.24 ° = 167.6 x 10-3 à ¢Ã‹â€ Ã‚  0.24 ° = 0.1676 + j 7.02 x 10-4 pu Apparent Power from BUS 2 to BUS 1 S21=V2* I*21=1à ¢Ã‹â€ Ã‚  -0.48 ° x 167.6 x 10-3à ¢Ã‹â€ Ã‚  180.24 °=167.6 x 10-3à ¢Ã‹â€ Ã‚  179.76 ° = -0.1676 + j7.02 x 10-4 pu Apparent Power from BUS 3 to BUS 2 S32 = V3* I*32 = 1 à ¢Ã‹â€ Ã‚  0.48 ° x 335.2 x 10-3 à ¢Ã‹â€ Ã‚  0.00 ° = 335.2 x 10-3 à ¢Ã‹â€ Ã‚  0.48 ° = 0.3352 + j 2.81 x 10-3 pu Apparent Power from BUS 2 to BUS 3 S23=V2* I*23=1 à ¢Ã‹â€ Ã‚  -0.48 ° x 335.2 x 10-3 à ¢Ã‹â€ Ã‚  180 °= 335.2 x 10-3 à ¢Ã‹â€ Ã‚  179.76 ° = -0.3352 + j 2.81 x 10-3 pu Apparent Power from BUS 3 to BUS 1 S31 = V3* I*31 = 1à ¢Ã‹â€ Ã‚  0.48 ° x 167.6 x 10-3à ¢Ã‹â€ Ã‚  -0.24 ° = 167.6 x 10-3 à ¢Ã‹â€ Ã‚  0.24 ° = 0.1676 + j 7.02 x 10-4 pu Apparent Power from BUS 1 to BUS 3 S13=V1* I*13=1à ¢Ã‹â€ Ã‚  0.00 ° x 167.6 x 10-3à ¢Ã‹â€ Ã‚  179.76 °= 167.6 x 10-3à ¢Ã‹â€ Ã‚  179.76 ° = -0.1676 + j 7.02 x 10-4 pu Comparison with simulation results The unit of the above calculation results is pu value, so in order to compare the results with simulation results pu value of current and power flow need to be converted to actual values by using the following equation considering Sbase = 100MVA and Vline_base = 345kV. [3] Sactual = Sbase ÃÆ'- Spu = 100 MVA ÃÆ'- Spu Iactual = Ibase ÃÆ'- Ipu = ÃÆ'- Ipu = ÃÆ'- Ipu = 167.3479 A ÃÆ'- Ipu Calculation Result and Simulation Result Flow direction Value Calculation Result Simulation Result BUS 1 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ BUS 2 |S12| 0.1676 ÃÆ'- 100 = 16.76 MVA 16.67 MVA P12 16.76 MW 16.67 MW Q12 0.0702 Mvar 0.07 Mvar |I12| 0.1676 ÃÆ'- 167.3479 = 28.0475 A 27.89 A BUS 3 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ BUS 2 |S32| 0.3352 ÃÆ'- 100 = 33.52 MVA 33.33 MVA P32 33.52 MW 33.33 MW Q32 0.281 Mvar 0.28 Mvar |I32| 0.3352 ÃÆ'- 167.3479 = 56.0950 A 55.78 A BUS 3 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ BUS 1 |S31| 0.1676 ÃÆ'- 100 = 16.76 MVA 16.67 MVA P31 16.76 MW 16.67 MW Q31 0.0702 Mvar 0.07 Mvar |I31| 0.1676 ÃÆ'- 167.3479 = 28.0475 A 27.89 A BUS 2 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ BUS 1 |S21| 0.1676 ÃÆ'- 100 = 16.76 MVA 16.67 MVA P21 -16.76 MW -16.67 MW Q21 0.0702 Mvar 0.07 Mvar |I21| 0.1676 ÃÆ'- 167.3479 = 28.0475 A 27.89 A BUS 2 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ BUS 3 |S23| 0.3352 ÃÆ'- 100 = 33.52 MVA 33.33 MVA P23 -33.52 MW -33.33 MW Q23 0.281 Mvar 0.28 Mvar |I23| 0.3352 ÃÆ'- 167.3479 = 56.0950 A 55.78 A BUS 1 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ BUS 3 |S13| 0.1676 ÃÆ'- 100 = 16.76 MVA 16.67 MVA P13 -16.76 MW -16.67 MW Q13 0.0702 Mvar 0.07 Mvar |I13| 0.1676 ÃÆ'- 167.3479 = 28.0475 A 27.89 A It is found that calculation results of current flow and apparent power flows (i.e. 28.0475 A and 56.0950 A/ 33.52 MVA and 16.76MVA) are about 0.5 % higher than simulation result (i.e. 27.89 A and 55.78 A / 33.33 MVA and 16.67 MVA) which can be considered slightly different. Difference of the voltage angle at each bus between calculation (0.48 °) and simulation (0.4775 °) could be the reason for this minor difference. Question 3 Admittance Matrix and Nodal Equation Admittance between two buses y12 = y21 = -j8 pu y13 = y31 = -j4 pu y14 = y41 = -j2.5 pu y23 = y32 = -j4 pu y24 = y42 = -j5 pu y30 = -j0.8 pu (BUS3-Neutral BUS) y40 = -j0.8 pu (BUS4-Neutral BUS) Admittance Matrix Ybus (Admittance Matrix) = Diagonal elements Y(i,i) of the admittance matrix, called as the self-admittance [2] [4], are the summation of all admittance connected with BUS i. = y12 + y13 + y14 = -j8 -j4 j2.5 = -j14.5 = y21 + y23 + y24 = -j8 -j4 j5 = -j17 = y30 + y31 + y32 = -j08 -j4 j4 = -j8.8 = y40 + y41 + y42 = -j0.8 -j2.5 j5 = -j8.3 Off diagonal elements Y(i,j) of the admittance matrix, called as the mutual admittance [2] [4], are negative admittance between BUS i and BUS j. = y12 = -(-j8) = j8 pu = y13 = -(-j4) = j4 pu = y14 = -(-j2.5) = j2.5 pu = y21 = -(-j8) = j8 pu = y23 = -(-j4) = j4 pu = y24 = -(-j5) = j5 pu = y31 = -(-j4) = j4 pu = y32 = -(-j4) = j4 pu = y34 = 0 pu = y41 = -(-j2.5) = j2.5 pu = y42 = -(-j5) = j5 pu = y43 = 0 pu Therefore, admittance matrix Ybus is as follows; Ybus = = Power Flow Analysis Power flow ignoring transmission line capacitance Nodal Equation Current from the neutral bus to each bus are given and admittance matrix (Ybus) is calculated above. Therefore, final nodal equation is as follows; Ibus = Ybus * Vbus à ¢Ã¢â‚¬ ¡Ã¢â‚¬â„¢ Vbus = Y-1bus * Ibus = Ybus à ¢Ã¢â‚¬ ¡Ã¢â‚¬â„¢ = = Voltage Analysis Voltage at each bus can be derived from the equation (Vbus = Y-1bus * Ibus) and Matlab was used for calculate matrix division. (Source code is attached in Appendix-1) Vbus == V12 = 0.0034 + j 0.0031 pu V13 = -0.0277 j 0.0257 pu V14 = 0.0336 + j 0.0311 pu V21 = -0.0034 j 0.0031 pu V23 = -0.0311 j 0.0288 pu V24 = 0.0302 + j 0.0280 pu V31 = 0.0277 + j 0.0257 pu V32 = 0.0311 + j 0.0288 pu V41 = -0.0336 j 0.0311 pu V42 = -0.0302 j 0.0280 pu Current flow in the system Current flow from BUS i and BUS j can be calculated by using voltage difference and interconnected admittance of the line between buses. [Iij = yij * (Vi Vj) ] The calculation result from Matlab is as follows; I12 = 0.0249 j 0.0269 pu I13 = -0.1026 + j 0.1108 pu I14 = 0.0777 j 0.0840 pu I21 = -0.0249 + j 0.0269 pu I23 = -0.1151 + j 0.1243 pu I24 = 0.1399 j 0.1511 I31 = 0.1026 j 0.1108 pu I32 = 0.1151 j 0.1243 pu I34 = 0 pu I41 = -0.0777 + j 0.0840 pu I42 = -0.1399 + j 0.1511 pu I43 = 0 pu Power flow in the system Apparent flow from BUS i and BUS j can be calculated by voltage at the sending bus and line current. [ Sij (pu) = Vi * I*ij = Pij + jQij ] The calculation result from Matlab is as follows; S12 = 0.0311 + j 0.0175 pu S13 = -0.1283 j 0.0723 pu S14 = 0.0972 + j 0.0548 pu S21 = -0.0311 j 0.0174 pu S23 = -0.1438 j 0.0803 pu S24 = 0.1749 + j 0.0977 pu S31 = 0.1283 + j 0.0780 pu S32 = 0.1438 + j 0.0875 pu S34 = 0 pu S41 = -0.0972 j 0.0496 pu S42 = -0.1749 j 0.0892 pu S44 = 0 pu Admittance Matrix considering transmission line capacitance According to the instruction of the Question 3, power system model can be drawn by using à Ã¢â€š ¬ equivalent circuit of the lines with capacitive shunt admittance (yc) of 0.1 pu at each side as shown below. Admittance Matrix Contrary to equivalent model in Question 3-1, the current flow through the capacitor in the transmission line needs to be considered to find the admittance matrix. Therefore, considering the capacitors the current equation with Kirchhoffs current law at each bus is as follows; [2] [5] Bus 1: I1 = I12 + I13 + I14 + Ic12 + Ic13 + Ic14 I1 = y12(V1-V2) + y13(V1-V3) + y14(V1-V4) + yc12V1 + yc13V1 + yc14V1 Bus 2: I2 = I21 + I23 + I24 + Ic21 + Ic23 + Ic24 I2 = y21(V2-V1) + y23(V2-V3) + y24(V2-V4) + yc21V2 + yc23V2 + yc24V2 Bus 3: I3 = I30 + I31 + I32 + Ic31 + Ic32 I3 = y30V3 + y31(V3-V1) + y32(V3-V2) + yc31V3 + yc32V3 Bus 4: I4 = I40 + I41 + I42 + Ic41 + Ic42 I4 = y40V4 + y41(V4-V1) + y42(V4-V2) + yc41V4 + yc42V4 Equation above can be rearranged to separate and group individual products by voltage. Bus 1: I1 = (y12 + y13 + y14 + yc12 + yc13+ yc14)V1 y12V2 y13V3 y14V4 = Y11V1 + Y12V2 + Y13V3 + Y14V4 Bus 2: I2 = (y21 + y23 + y24 + yc21 + yc23+ yc24)V2- y21V1 y23V3 y24V4 = Y21V1 + Y22V2 + Y23V3 + Y24V4 Bus 3: I3 = (y30 + y31 + y32 + yc31+ yc32)V3 y31V1 y32V2 = Y31V1 + Y32V2 + Y33V3 + Y34V4 Bus 4: I4 = (y40 + y41 + y42 + yc41+ yc42)V4 y41V1 y42V2 = Y41V1 + Y42V2 + Y43V3 + Y44V4 Finally, Diagonal elements Y(i,i) and off diagonal elements Y(i,j) of the admittance matrix are calculated as follows; = y12 + y13 + y14 + yc12 + yc13+ yc14 = -j8 -j4 j2.5 + j0.1 + j0.1 +0.1j = -j14.2 pu = y21 + y23 + y24 + yc21 + yc23+ yc24 = -j8 -j4 j5 + j0.1 + j0.1 +0.1j = -j16.7 pu = y30 + y31 + y32 + yc31+ yc32 = -j08 -j4 j4 + j0.1 +0.1j = -j8.6 pu = y40 + y41 + y42 + yc41+ yc42 = -j0.8 -j2.5 j5 + j0.1 +0.1j = -j8.1 pu = y12 = -(-j8) = j8 pu = y13 = -(-j4) = j4 pu = y14 = -(-j2.5) = j2.5 pu = y21 = -(-j8) = j8 pu = y23 = -(-j4) = j4 pu = y24 = -(-j5) = j5 pu = y31 = -(-j4) = j4 pu = y32 = -(-j4) = j4 pu = y34 = 0 pu = y41 = -(-j2.5) = j2.5 pu = y42 = -(-j5) = j5 pu = y43 = 0 pu Therefore, admittance matrix Ybus is as follows; Ybus = = Annex-1: Matlab source code and Calculation results with Matlab Matlab Source Code % define self admittance and mutual admittance by using admittace between % the buses (y12=y21=-j8, y13=y31=-j4, y14=y41=-j2.5, y23=y32=-j4, % y24=y42=-j5, y34=0, y43=0, y30=-j0.8, y40=-j0.8 y12=-8i; y21=-8i; y13=-4i; y31=-4i; y14=-2.5i; y41=-2.5i; y23=-4i; y32=-4i; y24=-5i; y42=-5i; y34=0; y43=0; y30=-0.8i; y40=-0.8i; Y11=-8i-4i-2.5i; Y12=8i; Y13=4i; Y14=2.5i; Y21=8i; Y22=-8i-4i-5i; Y23=4i; Y24=5i; Y31=4i; Y32=4i; Y33=-0.8i-4i-4i; Y34=0; Y41=2.5i; Y42=5i; Y43=0; Y44=-5i-2.5i-0.8i; %Bus 3 and Bus 4 is not connected, so admittance Y34 and Y43 are equal to zero % define the 44 admittance matrix (Ybus) Ybus=[Y11 Y12 Y13 Y14; Y21 Y22 Y23 Y24; Y31 Y32 Y33 Y34; Y41 Y42 Y43 Y44]; % In order to define the nodal equation (I = Ybus*V), the given I needs to defined. i1=0; i2=0; i3=-i; i4=-0.4808-0.4808i; Ibus=[i1; i2; i3; i4]; % Each bus voltage can be calculated by using matrix division (V= YbusI) Vbus=YbusIbus; v1=Vbus(1,1); v2=Vbus(2,1); v3=Vbus(3,1); v4=Vbus(4,1); % Calculate voltage difference between buses v12=v1-v2; v13=v1-v3; v14=v1-v4; v21=v2-v1; v23=v2-v3; v24=v2-v4; v31=v3-v1; v32=v3-v2; v34=v3-v4; v41=v4-v1; v42=v4-v2; v43=v4-v3; % current flow between buses can be calculated by i12 = y12*(v1-v2) i12=y12*v12; i13=y13*v13; i14=y14*v14; i21=y21*v21; i23=y23*v23; i24=y24*v24; i31=y31*v31; i32=y32*v32; i34=y34*v34; i41=y41*v41; i42=y42*v42; i43=y43*v43; % apparent power can be calculated by s12 = v1 * conj(i12) s12=v1*conj(i12); s13=v1*conj(i13); s14=v1*conj(i14); s21=v2*conj(i21); s23=v2*conj(i23); s24=v2*conj(i24); s31=v3*conj(i31); s32=v3*conj(i32); s34=v3*conj(i34); s41=v4*conj(i41); s42=v4*conj(i42); s43=v4*conj(i43); % Real power and Reactive power can be derived by following p12=real(s12); p13=real(s13); p14=real(s14); q12=imag(s12); q13=imag(s13); q14=imag(s14); p21=real(s21); p23=real(s23); p24=real(s24); q21=imag(s21); q23=imag(s23); q24=imag(s24); p31=real(s31); p32=real(s32); p34=real(s34); q31=imag(s31); q32=real(s32); q34=imag(s34); p41=real(s41); p42=real(s42); p43=real(s43); q41=imag(s41); q42=real(s42); q43=imag(s43); % end Matlab Calculation Results

lieshod White Lies in Joseph Conrads Heart of Darkness Essay

White Lies in Heart of Darkness      Ã‚  Ã‚  Ã‚   In his novella Heart of Darkness (1899), Joseph Conrad through his principal narrator, Marlow, reflects upon the evils of the human condition as he has experienced it in Africa and Europe. Seen from the perspective of Conrad's nameless, objective persona, the evils that Marlow encountered on the expedition to the "heart of darkness," Kurtz's Inner Station on the banks of the snake-like Congo River, fall into two categories: the petty misdemeanors and trivial lies that are common- place, and the greater evils -- the grotesque acts society attributes to madmen. That the first class of malefaction is connected to the second is illustrated in the downfall of the story's secondary protagonist, the tragically deluded and hubristic Mr. Kurtz. The European idealist, believing the lies of his Company and of the economic imperialism that supports it, is unprepared for the test of character that the Congo imposes, and succumbs to the potential for the diabolical latent within e very human consciousness. Although numerous critics (including Johanna M. Smith, Peter Hyland, Herbert Klein, and Garrett Stewart) have drawn attention to how Marlow's lie to the Intended informs the whole preceding text and how that culminating scene with the Intended is connected to Marlow's initial impression of Brussels as a whited sepulchre (how appropriate in light of Belgian King Leopold II's hypocritical defense of his private company's rapacious exploitation of the ludicrously- named Congo Free State!), few have until recently focussed on how the lie affects the reader's reaction to Marlow as the protagonist and narrator of Conrad's Congo tale. Answering questions which the dead man's Intended poses him reg... ... Rosmarin, Adena. "Darkening the Reader: Reader- Response Criticism and Heart of Darkness ." Joseph Conrad, Heart of Darkness: A Case Study in Contemporary Criticism , ed. Ross C. Murfin. New York: St. Martin's Press, 1989. Pp. 148-171. Smith, Johanna M. Smith. "'Too Beautiful Altogether': Patriarchal Ideology in Heart of Darkness ." Joseph Conrad, Heart of Darkness: A Case Study in Contemporary Criticism , ed. Ross C. Murfin. New York: St. Martin's Press, 1989. Pp. 179-198. Stewart, Garrett. "Lying as Dying in Heart of Darkness ." PMLA 95 (1980): 319- 331. Trilling, Lionel. " Huckleberry Finn ." The Liberal Imagination: Essays on Literature and Society . New York: Doubleday Anchor Books, 1950. Pp. 100-113. Wright, Walter F. "Ingress to The Heart of Darkness ." Romance and Tragedy in Joseph Conrad . New York: Russell and Russell, 1966. Pp. 143-160.

My English study

Conclusion Notes References Acknowledgement [Abstract] it is acknowledged that people have always been attaching much significance to the English study on account of the globalization trend of the world to the importance of language communication. Although many people are learning English, it does not mean that every person is certain to have good command of English. I'm no exception too. This paper is concerned about my English study in three stages?in middle school, in high school and at the university.Meanwhile, this paper also gives detailed discussions about the factors: English pronunciation, Autonomous learning ability, English learning motivations and the influence of personal attitudes towards English study. Key Words] Pronunciation; Autonomous learning; Learning motivations; Personal attitudes Economical and technological advances have tremendous impact on our ways of communication. Moreover, the globalization trend of the world also indicates the importance of language com munication.Therefore, English, as a widely used foreign language, has been always meeting with great popularity. However, it is notable that not every person is doomed to have good command of English. I'm no exception too. I have gone through three stages in the process of English study, which are filled with airdrops and happiness actually. It is acknowledged that English pronunciation is essential for every English learner who expects to have a good command of English. However, it is by no means easy.Pronunciation is closely related to the study of vocabulary, listening and so on. To correctly command English phonetic symbols, a learner must not only precisely grasp the articulation of a word and Judge its meanings, but also memorize new words flexibly. The former situation was that not only many students but the teachers themselves in middle school were not truly showing solicitude for the phonetic ours. When I was in middle school, I could remember being taught the phonetics onl y once. Later on, I had to learn by myself.Therefore, it has been no easy Job for me to clearly make distinction between English and Chinese in the Phonemic and phonological pronunciation. Besides, I do not completely correct my English pronunciation until now. 1. 1. 1 Phonemic and phonological distinction between English and Chinese Wan Shining (2004) argues the Chinese belongs to the oriented phylum, whereas English is an occidental one, and that the two languages share many similarities as ell as large divergences both phonemically and phonologically; their Phonetic system are distinct from each other mainly following by three aspects: (1) absolutely.The vowels and consonants in English differentiate from the tones (shunned) and the finals (yummy) in Chinese to a large extent even if they seem to be similar with their counterparts in pronunciation. (2) The ways of distinguishing meanings. Chinese distinguishes by tones, thus labeled as â€Å"tonal language†,@while English distinguishes meaning by the intonations of a sentence. Therefore, it named s â€Å"language with intonation† (3) Phonemic structure. The phonemes, which are restricted in the latter, are able t be combined freely in the former. Take spelling rules of the consonant for example.In English, [f] and [h] can be spelled together with which is not allowed in Chinese. Besides, all the consonants in English can come at the end of a syllable, while in Chinese only [n] and [Eng] are permitted. These differences cause great difficulties for the Chinese students in their acquisition of English pronunciation. Another difficulty for them is that the two languages differ in rhythms as well. Each possesses its characteristics on applying on tone or place of stress to distinguish the word's meaning, and on the conveying a speaker tone or attitudes by means of various intonations. 1] @ Besides, there exist any other difficulties. 1. 1. 2 The transfer of mother tongue Chin Ling holds that the i nfluence of the mother tongue on the foreign language learning is mainly illustrated on the course of â€Å"transfer† between external and internal languages. External language refers too language which a person utters in his daily talks, while the internal language refers to a language which a person utilizes when thinking with his brain instead of speaking it out. Both languages serve as materials, basis as well as tools for thinking activity.A person is used applying his mother tongue or native dialect as his internal language at the beginning of learning a foreign language. Nevertheless, he may be forced to use external language that is understandable for both interlocutors in real communications. As a result, a problem arises in that external language is different from internal language. Consequently, the differences will produce the â€Å"negative transfer†. @The greater the preference is, the greater the difficulty is. [2] Totally speaking, I was tired of Englis h study in view of these difficulties during that time. 1. 2 Difficulties of inaccurate memory of English vocabulary.As we all know, vocabulary is vital for Chinese English learner, especially for the middle school students. Because only in this stage can we have a specific idea of the English. When I was in middle school, my English teacher would teach students many vocabularies every single day that we could not memory in one night. Gradually, I ran into many difficulties in English study. Recently, I read a paper with respect to the study of vocabulary learning in middle school. The author said,† The appearance of such difficulties is because the burden of English learning, the compulsory learning mode and the lacking of vocabulary learning strategies. [3]Len order to verify his assumptions, the author did experiment among the students in are divided into two classes. They are comparative class and experimental class. During the experiment, they used the old and direct voca bulary teaching mode in the former and the associative vocabulary teaching in the latter. Finally, the date shows hat after 12-week training in vocabulary learning strategy, the students of the experimental class improved their vocabulary learning ability, which is higher than that in the comparative class.The survey showed that if the students who are to meet the requirement of teacher and confine the vocabulary memory to the word lists, are proved to be less active. By comparing my English study in middle school, I thought those phenomena are also occurred on me. 2. The second acquaintance with English in high school?enthusiasm of English study Fortunately, these obstacles had not accompanied me into high school. I met excellent teachers, then grasped the method of English learning and finally set a goal for me. 2. 1 The improvement of English autonomous learning ability English teaching is not simply to teach students knowledge.The most important thing is to develop their autonom ous learning ability through teaching activities. My English teacher gave me a lot of help. Her guidance in the process of my English study aroused my great interest in English. My English teacher tried to progress from traditional teacher-centered teaching to the student-centered method. She liked to cultivate our independent learning ability. She inspired us to interact with her, proposed to audaciously ask questions and let us to do English presentations in open forms. Thanks to my dear English teacher, I regained the enthusiasm about English learning.Admittedly, it is essential for the students to have teacher's innovative guideline. The American psychologist Moscow believes that this is the best way to encourage students to express their opinion and foster their enthusiasm to learn the knowledge and build the formation of healthy personality by establishing the sincere mutual understanding teacher-student relationship. The reason for why I could become enthusiastic about Englis h study was not only owing to my teacher's help, but also the changing of my English learning method.The reason for why I could improve my English is as follows: Firstly, grasp teacher's lecture feature and the characteristics of the various disciplines. Secondly, review and prepare for new knowledge. Thirdly, interact with teacher in class. Gradually, I found that my English scored higher than the previous. Until now, I am deeply aware of the importance of independent learning. As a Chinese saying goes, â€Å"give man a sis, he will have a meal; teach him to fish, he will have the food all his life. † focuses on students' subjectivity and initiative in order to make students how to study and achieve life-long learning and development.And it is not the one side of my story. It has already been studied by others. The concept of â€Å"autonomous learning† (Holes) ($) originated in the asses. He expresses, â€Å"English as a conceptual tool which further developed its de finition. † [4] Benson and Evolve believe, â€Å"autonomous learning is not only the freedom of learning, but a good opportunity to form independent thinking ability as adult. [5] Little believes that the essence of the â€Å"autonomous learning† is a kind of ability such as â€Å"independent, critical reflection and decision-making. [6] Learners need to arouse their awareness of what to learn and how to learn. Also American futurist Alvin-Toffee once said,† The illiteracy in the future is not the one who don't know the word, but the one who do not know how to learn. † In addition to the previous factors, learning motivation is proved to be the essential factor. Motivation is the prime power of all activities. In the process of learning, many psychological factors can convert into the inner motivation, including interest, values and so on. As Www [email  protected] in his A Review of research on foreign language Learner's motivation. [email  protected] Arouse appropriate learning deeds, it can make students go into learning state and learn English initiative. † [7] I can not agree with his idea any more. When I was in high school, I still remembered that even a little achievement could take me great motivation. And this motivation accompanied me to go to university. 3. The third acquaintance with English at the university?passiveness of English After I come into university, I find that I become less positive towards English earning than ever before.And the reasons are as follows: A study of engineering students in Yemen by Taft AY-Tamil Candy Minor Squib cited previous research that found two classes of motivation for learning English: instrumental and integrative orientation. A person, who learns the language in hopes of gaining some tangible benefit, such as success in a Job or fulfilling an academic requirement, is instrumentally motivated. A person with integrative motivation learns English because he or she wishes to l earn more about the culture of the Western world or become more integrated into English-speaking society. ] And I belong to the former. I learn the English in order to regard it as a tool for my future occupation. 3. 1 Personal attitudes towards English study determined by his attitudes towards the other group in particular and by his orientation towards the learning task itself. And I totally agree with it. † [9] A positive attitude toward learning the English language is one of the leading predictors of success in gaining fluency. However, as mentioned above, I am not truly love English, but regard it as a tool of getting a Job. During this stage, my English study doe not make much progress.In the above paragraphs, I have made detailed explanation about my three stages of English study. From this paper, people can see that if one wants to get a good command of English, he must perfectly grasp these aspects: have a series of learning methods, take positive attitude toward Eng lish (namely the understanding of autonomous English learning) and pay particular attention to the pronunciation of English. Besides, the external factors are also of great importance such as the teacher's teaching methods, the environment that people are situated in and so on. As for me, my English study does not do a good Job.No matter what stage do you belong to, I believe that this paper can be beneficial to your English study. Serve to distinguish one utterance from another in a language or dialect. @Tonal language: A tonal language is a language in which pitch is used as a part of speech, changing the meaning of a word. An example of how tone can change the meaning of a word can be found in English: the word â€Å"present† can be used as a verb or a noun, with a stress on the first or second syllable changing the meaning. In tonal languages, the way in which you say a word is very important, as it radically hinges the meaning.Tonal languages are found primarily in Asia, Africa, and South America. @alienation: Intonation is a word used to refer to how a sentence sounds. How a sentence sounds if it's a question sounds different from how a sentence sounds if it's a statement @Negative transfer: Negative transfer is a situation where a person transfers old learning and knowledge to a new situation, and the old information interferes with new information acquisition and task performance. This can be inconvenient or dangerous, depending on the type of situation involved.

Analysis Of Marjane Satrapi s Book Persepolis - 1239 Words

Imagine sending your child off to an unforgiving battlefield where they lose their individual identity and assume the role of combatant. Imagine having an officer knock on your door, knowing that they bear news that will change your life forever. Imagine being enlisted from the moment you come of age, counting down the days until you are sent to war. In today’s society, ideas of violent loss and trading life for country seem like issues in an army’s world. During the Iranian revolution, loss and suffering were woven into the fabric of all Iranian lives. In Marjane Satrapi’s graphic memoir Persepolis, she argues that Marji’s developing views on death and martyrdom serve to personalize our perspective of war. From the beginning of her story, Marji is suspended in limbo between two clashing ideological worlds. Akin to many elementary aged children, she is highly impressionable by the people around her, â€Å"a child who repeats what she hears† (62). In harmonious spheres of influence regarding death and war leave her in a state of ideological confusion. She is educated in a government-controlled school rooted in nationalism and respect. Being a school age child in a government controlled school made her more susceptible to the pro-Reza Shah ideology. In her elementary years, she was taught to believe through textbook and tradition that the king was â€Å"chosen by God† and that â€Å"God himself† told her that he was the rightful ruler of Iran (19). The school system capitalized on theShow MoreRelatedEssay about Persepolis1136 Words   |  5 PagesToward the end of the novel, Marjane says about people’s fear of the Islamic Commission, â€Å"It’s only natural! When we’re afraid, we lose all sense of analysis and reflection. Our fear paralyzes us. Besides fear has always been the driving force behind all dictators’ repression.† How do Marjane and her compatriots deal with fear and th eir daily lives? To what extent do you see fear as a controlling factor in your own country’s public life? The new Islamic republic regime was beginning to spread inRead MoreMemories And The Formation Of Reality1666 Words   |  7 Pagesfilms based on memory, thus arguing that imagination does not distort memory in animation, but create a role as a form of embellishment for the film to help memory. Fredrick Bartlett is a British psychologist from Cambridge University, based on his book, Remembering (1932) that focused on how people comprehend what was being remembered. The concept of schema or schemata (plural) is to understand the key factors that affect the thinking process. (Wagoner) Other words, someone’s ability to solve problemsRead MoreMemories And The Formation Of Reality1688 Words   |  7 Pagestheme of memory, thus arguing that imagination does not distorted memory in animation, but create a role as a form of embellishment for the film to help memory. Fredrick Bartlett is a British psychologist from Cambridge University, based on his book Remembering (1932) that focused on how people made sense of what was being remembered. The concept of schema or schemata (plural) is to understand the key factors that affect the thinking process. (Wagoner) Other words, someone’s ability to solve problemsRead MoreLiterary Criticism : The Free Encyclopedia 7351 Words   |  30 Pagesnovel is sometimes used interchangeably with Bildungsroman, but its use is usually wider and less technical. The birth of the Bildungsroman is normally dated to the publication of Wilhelm Meister s Apprenticeship by Johann Wolfgang Goethe in 1795–96,[8] or, sometimes, to Christoph Martin Wieland s Geschichte des Agathon of 1767.[9] Although the Bildungsroman arose in Germany, it has had extensive influence first in Europe and later throughout the world. Thomas Carlyle translated Goethe’s novel