{"id":1047,"date":"2020-09-07T14:01:40","date_gmt":"2020-09-07T13:01:40","guid":{"rendered":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/?post_type=chapter&p=1047"},"modified":"2020-09-08T16:21:28","modified_gmt":"2020-09-08T15:21:28","slug":"task-5","status":"publish","type":"chapter","link":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/chapter\/task-5\/","title":{"raw":"Task 5. Synchronous generator steady state diagram","rendered":"Task 5. Synchronous generator steady state diagram"},"content":{"raw":"

Aim of the task<\/h1>\r\nThe aim of the task is to learn about the way of calculation and representation of the synchronous generator steady state. To describe of the synchronous generator state the phasor\/vector diagram will be used.\r\n

Introduction<\/h1>\r\nThe synchronous generator is a main electricity source in power system. On other hand synchronous generator is a dynamic devices whose analysis is usually stared for initial condition equals to\u00a0 steady state. Its corresponds to subtransient , transient and steady reactances of synchronous generator. The initial operation state of synchronous generator can be graphically\u00a0 described by means phasor\/vector diagram.\r\n

Phasor\/vector diagram<\/h1>\r\n

a) Two axis generator model<\/h2>\r\nModel with two equivalent circuits in d and q generator axes is typical representation of the synchronous generator. Figure 5.1 shows the phasor\/vector diagram resulting of synchronous generator. The steady state of generator is determined by the load flow solution. However, load flow equations are formulated in network complex coordinates (a<\/em> -\u00a0 real axis, b<\/em> \u2013 imaginary axis) while the current, voltage and emfs of generator are expreassed in the generator's orthogonal coordinates (d<\/em> -\u00a0\u00a0 axis, q<\/em> \u2013\u00a0 axis). The q<\/em> \u2013 \u00a0axis is shifted with respect to the network a<\/em> -\u00a0 real axis by the rotor angle d<\/em>.\r\n\r\n \r\n\r\n\r\n\r\nFig.5.1. Phasor\/vector diagram of synchronous generator : a) rotor diagram, b) circuit diagram, c) a phasor diagram in a steady state [1,2]\r\n\r\n \r\n

b) Used nomenclature<\/h2>\r\n\r\n\r\n \r\n\r\n \r\n\r\nComplex electromagnetic forces, voltages and currents can be described as follows:\r\n\r\n\r\n\r\nIn case of r<\/em> = 0 (generator armature resistance), then\r\n\r\n\r\n\r\nGenerator real and reactive power can be calculated using the following formulae\r\n\r\n\r\n\r\n\r\n

c) Determination of q-axis and emfs<\/h2>\r\nFrom diagram\r\n\r\n\r\n\r\n\r\n\r\nwhere length of segments:\r\n\r\n\r\n\r\nhence\r\n\r\n\r\n\r\n \r\n\r\n\r\n\r\n \r\n\r\nTo find the steady \u2013state of rotor angle it may use the following complex relation for the\r\nfactious emf\u00a0 \r\nThe angle of i s the angle of the generator rotor, .\r\n\r\n \r\n\r\n \r\n

Exercise<\/h1>\r\nContent and input data:<\/span>\r\nAnalysis refers to the test system presented in the task number 3 case b).\r\n\r\n\r\n

Fig.1. Schematic diagram of the test system.<\/em><\/p>\r\n \r\n\r\nTo do:<\/span>\r\n\r\nFind (calculate) and plot a phasor diagram of a a synchronous generator in a steady state.\r\nDiagram should contain the following elements (in accordance with the attached example):\r\n\r\n\r\n\r\nDiagram should also contain:\r\n\r\n\r\n\r\nMoreover:\r\n\r\n\r\n\r\nAdditional notes:\r\n1. Calculation should be carried out in per units\r\n2. The plot should contain the diagram scale\r\n\r\n \r\n\r\nSynchronous generator parameters\r\n\r\nReactances are in per unit where base values are: U<\/em>b<\/sub>= 220 kV, S<\/em>b<\/sub>=100MVA\r\n\r\n\r\n\r\n \r\n\r\n \r\n

References<\/h1>\r\n[1] Machowski J., Bialek J, Bumby J.,\u00a0 Power system dynamics: stability and control<\/em>. New York, USA: John Wiley & Sons; 2020.\r\n[2] Machowski J., Bernas S., Stany nieustalone i stabilno\u015b\u0107 systemu elektroenergetycznego<\/em>,, WNT,\u00a0 1988.\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n ","rendered":"

Aim of the task<\/h1>\n

The aim of the task is to learn about the way of calculation and representation of the synchronous generator steady state. To describe of the synchronous generator state the phasor\/vector diagram will be used.<\/p>\n

Introduction<\/h1>\n

The synchronous generator is a main electricity source in power system. On other hand synchronous generator is a dynamic devices whose analysis is usually stared for initial condition equals to\u00a0 steady state. Its corresponds to subtransient , transient and steady reactances of synchronous generator. The initial operation state of synchronous generator can be graphically\u00a0 described by means phasor\/vector diagram.<\/p>\n

Phasor\/vector diagram<\/h1>\n

a) Two axis generator model<\/h2>\n

Model with two equivalent circuits in d and q generator axes is typical representation of the synchronous generator. Figure 5.1 shows the phasor\/vector diagram resulting of synchronous generator. The steady state of generator is determined by the load flow solution. However, load flow equations are formulated in network complex coordinates (a<\/em> –\u00a0 real axis, b<\/em> \u2013 imaginary axis) while the current, voltage and emfs of generator are expreassed in the generator’s orthogonal coordinates (d<\/em> –\u00a0\u00a0 axis, q<\/em> \u2013\u00a0 axis). The q<\/em> \u2013 \u00a0axis is shifted with respect to the network a<\/em> –\u00a0 real axis by the rotor angle d<\/em>.<\/p>\n

 <\/p>\n

\"image\"<\/p>\n

Fig.5.1. Phasor\/vector diagram of synchronous generator : a) rotor diagram, b) circuit diagram, c) a phasor diagram in a steady state [1,2]<\/p>\n

 <\/p>\n

b) Used nomenclature<\/h2>\n

\"image\"<\/p>\n

 <\/p>\n

 <\/p>\n

Complex electromagnetic forces, voltages and currents can be described as follows:<\/p>\n

\"image\"<\/p>\n

In case of r<\/em> = 0 (generator armature resistance), then<\/p>\n

\"image\"<\/p>\n

Generator real and reactive power can be calculated using the following formulae<\/p>\n

\"image\"<\/p>\n

\"image\"<\/p>\n

c) Determination of q-axis and emfs<\/h2>\n

From diagram<\/p>\n

\"image\"<\/p>\n

\"image\"<\/p>\n

where length of segments:<\/p>\n

\"image\"<\/p>\n

hence<\/p>\n

\"image\"<\/p>\n

 <\/p>\n

\"image\"<\/p>\n

 <\/p>\n

To find the steady \u2013state of rotor angle \"image\" it may use the following complex relation for the
\nfactious emf\u00a0 \"image\"
\nThe angle of \"image\" i s the angle of the generator rotor, \"image\" .<\/p>\n

 <\/p>\n

 <\/p>\n

Exercise<\/h1>\n

Content and input data:<\/span>
\nAnalysis refers to the test system presented in the task number 3 case b).<\/p>\n

\"image\"<\/p>\n

Fig.1. Schematic diagram of the test system.<\/em><\/p>\n

 <\/p>\n

To do:<\/span><\/p>\n

Find (calculate) and plot a phasor diagram of a a synchronous generator in a steady state.
\nDiagram should contain the following elements (in accordance with the attached example):<\/p>\n

\"image\"<\/p>\n

Diagram should also contain:<\/p>\n

\"image\"<\/p>\n

Moreover:<\/p>\n

\"image\"<\/p>\n

Additional notes:
\n1. Calculation should be carried out in per units
\n2. The plot should contain the diagram scale<\/p>\n

 <\/p>\n

Synchronous generator parameters<\/p>\n

Reactances are in per unit where base values are: U<\/em>b<\/sub>= 220 kV, S<\/em>b<\/sub>=100MVA<\/p>\n

\"image\"<\/p>\n

 <\/p>\n

 <\/p>\n

References<\/h1>\n

[1] Machowski J., Bialek J, Bumby J.,\u00a0 Power system dynamics: stability and control<\/em>. New York, USA: John Wiley & Sons; 2020.
\n[2] Machowski J., Bernas S., Stany nieustalone i stabilno\u015b\u0107 systemu elektroenergetycznego<\/em>,, WNT,\u00a0 1988.<\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n","protected":false},"author":12,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":25,"_links":{"self":[{"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/chapters\/1047"}],"collection":[{"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":7,"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/chapters\/1047\/revisions"}],"predecessor-version":[{"id":1077,"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/chapters\/1047\/revisions\/1077"}],"part":[{"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/parts\/25"}],"metadata":[{"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/chapters\/1047\/metadata\/"}],"wp:attachment":[{"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/wp\/v2\/media?parent=1047"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/chapter-type?post=1047"},{"taxonomy":"contributor","embeddable":true,"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/wp\/v2\/contributor?post=1047"},{"taxonomy":"license","embeddable":true,"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/wp\/v2\/license?post=1047"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}