The direct representation of the DG by means of a PV bus in the positive sequence network requires computationally tedious N-R iterations to solve load flow equations.
Therefore, the indirect modelling of DG buses is usually preferred. The general flowchart for the load flow calculation in an active distribution network, with indirect representation of DG buses, is shown in Fig. 6.3. Three levels of iteration are involved.
At the outermost level of iteration, the voltage regulators and shunt compensators are suitably adjusted so as to maintain load bus voltage magnitudes within the specified limits. The purpose of the middle loop is to convert PV buses into non-PV buses through an equivalent representation. Finally, the innermost loop of iteration takes a distribution network with no PV buses and with fixed voltage regulator/shunt compensator settings. Each iteration in the innermost loop consists of two stages.
In the first stage, the load currents are determined based upon the latest updated bus voltages, whereas, in the second stage, bus voltages are determined based upon the latest updated load currents. The convergence of a loop is indicated when the bus voltages obtained after completing a particular iteration of the respective loop do not deviate much from the corresponding result obtained from the previous iteration of the same loop. The flowchart of the N-R method also retains the same looping structure as that in Fig. 6.3. The Newton-Raphson iterations are carried out in the innermost loop only, whereas, the middle loop is required to decompose load power into sequence components. The purpose of the outermost loop is, as usual, to adjust capacitor and voltage regulator settings.
There are two ways to convert a DG bus into a non − PV bus in the middle iteration loop. In the first approach, aPVbus is converted to aPQbus by employing the methodology of current/reactive power compensation. In the other approach, the PV bus is transformed into a Vδ (or slack) bus by means of voltage compensation.
For the innermost loop also, two different methods can be employed. Those are the BFS and Gauss-Zbus techniques. Till date, only two combinations have been tried between the innermost and middle loops. The ADLF calculation in [39, 68–70] has been implemented by choosing the current/reactive power compensation technique for the middle loop and the BFS technique for the innermost loop [39, 68–70]. In another implementation that can be found in [3], Gauss-Zbus iterations have been carried out in the innermost loop after forming slack buses in the middle loop.
In the present work, the current/reactive power compensation technique is adopted
Start
Read DG, load, compensator, feeder, transformer, voltage regulator data
Network model preparation Bus voltage initialization Compensator/regulator readjustment Updating DG bus voltage phasors/reactive power
Updating shunt branch currents at P Q buses Updating P Q bus voltages
Load flow converged?
DG bus mismatch converged?
LF after compensators converged?
Stop Yes
Yes
Yes No
No
No
Figure 6.3: Flowchart for the ADLF calculation with indirect representation of DG buses.
to implement the middle loop of iteration. Before entering into the innermost loop, a DG bus can be converted into a P Q bus by updating its reactive power output through the following equation.
Q(1),(k+1)DG = max
QG,min,minn
QG,max,Q(1),(k)DG +S
Vsp(1)DG −V(1),(k)DG o
. (6.1)
Here, Q(1),(k)DG indicates the vector of DG reactive power outputs (in the positive se- quence network) calculated at the beginning of thekth iteration in the middle loop of the flowchart shown in Fig. 6.3. The DG bus positive sequence voltage magnitudes obtained at the end of the kth iteration in the middle loop is indicated by vector V(1),(k)DG . The maximum and minimum reactive power capabilities of DGs are indi- cated by QG,max and QG,min, respectively. The derivation of the sensitivity matrix S (which depends only upon network parameters) is provided in [52] and [39]. The particular matrix is essentially given by the reactive part of the positive sequence Thevenin’s equivalent impedance matrix as seen from the DG buses. Instead of sen- sitivity factors, the quadratic equation model as was proposed in [68] can also be used to update the reactive power outputs of generators. Modelling of a DG bus as an equivalent P Q bus is, however, based upon the assumption that there are only three-phase balanced feeders in the network. Therefore, a single-phase or two-phase feeder is to be equivalently represented as a three-phase feeder with no loads and no shunt charging capacitances for the phases that are originally not present. The particular equivalent representation is possible since the single-phase and two-phase feeders are usually radial in nature. Similarly, an unbalanced feeder can equivalently be represented as a balanced feeder by following the procedure prescribed in [48]
and [58].
By employing the current/reactive power compensation technique to model DG buses, the ADLF problem is, in essence, solved through a series of passive distribu- tion load flow (PDLF) calculations. Each of the respective PDLF calculations takes place in the innermost loop. It is to be noted that the DG terminal is represented as a P Q bus only within the innermost loop. After each round of PDLF calcula- tion through the innermost loop, the reactive power output of a DG is updated in the middle loop based upon the difference between the specified value and the latest solution of its terminal voltage magnitude. The middle loop keeps on adjusting the reactive power output of a DG unless its terminal voltage settles at the specified value provided the DG has adequate reactive power capacity. Therefore, when the program execution comes out of the middle loop, it is ensured that the DG bus has remained voltage-controlled unless its reactive power capacity is exhausted. How- ever, the PDLF calculation that needs to be carried out within the innermost loop is somewhat different from the normal PDLF calculation because of the involvement of DG impedances. Therefore, this chapter specifically contributes towards an effi- cient implementation of the particular loop through the deployment of Gauss-Zbus
iterations.
Figure 6.4: General two port representation of a transformer or voltage regulator.