Advanced SVC models for newton-raphson load flow and ... - ITCJ

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XC fi' Fig. I. SVC stmctiirc. 60 - - E J 40 - Reactive region - 6 20 - U " c - 4 o- n r + -20 - - 0 c3 .f -40 - w LT Fig. 2. -60 1 , , , , , , , , - - Capacitive region 90 100 110 120 130 40 150 160 170 180 Firing angle (degrees) SVC equivalent reactancc as function of firing angle. their main operating Characteristic at the expense of generating harmonic currents and filters are employed with this kind of devices. SVC's normally include a combination of mechanically controlled and thyristor controlled shunt capacitors andreactors [U, [Z]. The most popular configuration for continuously controlled SVC's is the combination of either fix capacitor and thyristor controlled reactor or thyristor switched capacitor and thyristor controlled reactor [3], [41. As far as steady-stale analysis is concerned, both configurations can be modeled along similar lines. The SVC structure shown in Fig. I is used to derive a SVC model that considers the TCR firing angle (Y as state variablc. This is a new and more advanced SVC representation than those currently available in open literature. The variable TCR equivalent reactance, X.ce,, at fundamental frequency, is given by [31, wherc IY is the thyristor's firing angle. The SVC effective reactance X,, is determined by the parallel combination of X
AMBRIZPkREZ ctnl.: ADVANCE0 SVC MOUE1.S FOR NEWTON-RAPHSON LOAD FLOW AND NEWTON OPTIMAL POWER FLOW STUDIES 131 v4 Capacitive ratine - Ir Inductive rating I I IMlN 0 IM4X System reactive characteristics b Is - 112r 110- 108- &? 106- ' 104 - I 102- - e g 100 - Generator model /' --- Susceptonce model // /' , Fig. 4. Comparison between actual and idcalized SVC voltage c~irrcnt characteristic. changing the SVC representation to a fixed reactive susceptance. This combined model yields accurate results. However, both representations require a different number of nodes. The generator uses two or three nodes [4] whereas the fixed susceptance uses only one node [I]. In Newton-Raphson load flow implementations this may require Jacobian reordering and redimensioning during the iterative solution. Also, extensive checking becomes necessary in order to verify whether or not the SVC can return to operation inside limits. It must be remarked that for operation outside limits, it is important to model the SVC as a susceptance and not as a generator set at its violated limit, QvioliLtcc~. Ignoring this point will lead to inaccurate results. The reason is that the amount of reactive power drawn by the SVC is given by the product of the fixed susceptance, nfiXed, and the nodal voltage magnitude, V, , Since V, is a function of network operating conditions, the amount of reactive power drawn by the fixed susceptance model may differ from the reactive power drawn by the generator model, i.e. Qviolalcd f - Rfixcd vb2. (4) This point is exemplified in Fig. 5 where the reactive power output of the generator was set at 100 MVAR. This value is constant as it is voltage independent. The result given by the constant susceptance model varies with nodal voltage magnitude. A voltage range of 0.95-1 .OS was considered. A susceptance value of 1 pa. on a 100 MVA base was used. The SVC model presented above, based on the generator and fixed susceptance representations, is better handled as a susceptance model only. It takes the form of a variable susceptance when the SVC is operating within reactive limits and it takes the form of a fixed susceptance otherwise. Moreover, a new and more advanced SVC representation then becomes possible, wherc the thyristor firing angle mechanism is represented explicitly as a function of network operating conditions. In contrast to all SVC models proposed heretofore, this model assesses ranges of firing angle operation leading to intrinsic, internal SVC resonances. Both representations, the total susceptance and the firing angle models, are presented below. Fig. 5.1. - Variable shunt susceptance. IV. NEW SVC LOAD FLOW MODELS In practice the SVC can be seen as an adjustable reactance with either firing angle limits or reactance limits. The circuit shown in Fig. 5.1 is used to derive the SVC's nonlinear power equations and the linearized equations required by Newton's method. In general, the transfer admittance equation for the variableshunt compensator is, and the reactive power equation is, / = jov, (4) Q, = -v;u. (3 Linearized, positive sequence SVC models for Newton-Raphson load flows are presentcd in this section whereas SVC models optimal power flows are presented in Scction V. A. SVC Total Suscnptance Model (H = BSVC;) The linearized equation ofthe SVCis given by (6), wherc the total susceptance BSVC is taken to be the state variable,
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Advanced SVC models for newton-raphson load flow and ... - ITCJ

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