Smart Solar PV Inverters with Advanced Grid Support Functionalities. Rajiv K. Varma

regulation strategies based on active power control.

      1.1.1.2 Frequency Control

Reactive power exchange has no direct impact on the system frequency. However, several studies [5, 6] have reported that reactive power exchange indirectly influences the system frequency in systems having a large number of voltage‐dependent loads and in microgrids. In this case, change in bus voltages caused by reactive power exchange can vary the active power absorbed by the loads leading to a mismatch in the generation and loads and consequent frequency deviation. Reasonably effective strategies of frequency regulation through reactive power control can, therefore, be developed especially in power systems having substantial component of voltage‐dependent loads.

      1.1.2 Active Power Control

      1.1.2.1 Voltage Control

      1  Exchange of Active Power: The influence of active power exchange on voltage regulation is discussed in this section. A simple power system is considered with a solar PV system connected at the PCC as illustrated in Figure 1.5. The system has an equivalent source voltage E, whereas V is the voltage at PCC. The network has equivalent reactance and resistance X and R, respectively. The current I injected by the PV system is considered to be purely resistive IR, i.e., at unity power factor. Impact of this active current injection on systems with different X/R ratios is now investigated. Figure 1.6a,b depicts the phasor diagram for systems with X/R = 3, and 1/3, respectively. Active power injection is seen to increase the voltage in both cases. However, the rise in voltage is more in the network having X/R = 1/3 than in network having X/R = 3. This implies that active power injection will result in a greater voltage rise in primarily resistive networks. Similarly, active power absorption, as in energy storage systems, will be more effective in decreasing the voltage in resistive networks.

      2 Exchange of Active and Reactive Power: In this case, the solar PV system is considered to perform both active power injection and reactive power exchange. A simple explanation of the impact of active and reactive power is described here. The complex current injected by the solar PV system is denoted by I, and the complex power injected by the solar PV system is expressed by P + jQ. Assuming the open‐circuit voltage E remains constant, the change in PCC voltage due to this current injection is given by:(1.1) (1.2) since V is chosen to be the reference phasor with angle = 0.Substituting Eq. (1.2) in Eq. (1.1), the change in voltage is obtained as(1.3) (1.4) It is noted that Q can be either inductive or capacitive. Also, P can be either positive, if injected as in case of PV system, or negative if absorbed by an Energy Storage System.Figure 1.5 A simple power system with a PV solar system connected at PCC.Equation (1.4) demonstrates that the PCC voltage is influenced by both active and reactive power exchange from the DER [7]. The magnitude of voltage change is dependent on the system short circuit impedance and its X/R ratio.

      1.1.2.2 Frequency Control

      A balance between active power generation and the sum of loads and line losses results in a stable system frequency. Hence, active power exchange (injection/absorption) by IBRs and DERs with the power system directly impacts system frequency. In general, the system frequency increases with active power injection and decreases with active power absorption. The magnitude of frequency change is dependent upon the relative value of active power exchange in comparison with power generation from the remaining generators in the power system. Greater the active power exchange higher is the variation in system frequency. Consequently, the impact of DER active power exchange on microgrid system frequency is much larger than in grid connected environments. The impact of active power control on system frequency is briefly described in the next section.

Figure 1.6 Phasor diagrams for network with active power injection from the solar PV system; (a) network with X/R = 3; (b) network with X/R = 1/3.

      1.1.3 Frequency Response with Synchronous Machines

A steady‐state system frequency results when synchronous power generation matches the system load and the losses in power system supplying those loads. In case of a system disturbance, such as sudden loss of a major generation unit, the typical variation in system frequency and its subsequent restoration to the pre‐disturbance level is depicted in Figure 1.7 [8]. The frequency restoration is enabled through three sequential stages of frequency control – primary frequency control, secondary frequency control, and tertiary frequency control [8–13].

      Assume that the power system is operating at steady state at t = 0⁻ and a large generation loss occurs at t = 0⁺. The kinetic energy of all the synchronous machines (generators, condensers, motors) is autonomously extracted to supply the load (inertial response), leading to a decline in the speed of generators and consequently the system frequency. The decline in frequency continues till additional power injection from synchronous generators balance out the load. The rate at which the frequency decreases is termed “Rate of Change of Frequency (ROCOF).” The lowest level at which the frequency is eventually arrested is known as “frequency nadir.” The time period from the onset of disturbance to reaching the frequency nadir is known as “arresting period.”

      Primary frequency control (also referred as Frequency Containment Reserve [FCR]) is provided by synchronous generator turbine governors by injecting power from the generators during the arresting period and continuing thereafter. This causes the frequency to stabilize at the “settling frequency,” which is higher than the nadir but still lower than the steady‐state frequency before the disturbance. This time period until settling frequency is reached is termed “rebound period.”

      Secondary frequency control through Automatic Generation Control (AGC) is then exercised to restore system frequency to its pre‐disturbance scheduled level. The period over which this secondary frequency control is provided is known as “recovery period,” which extends over 5–10 minutes (or more).

Tertiary frequency control is provided subsequently which involves restoration of the synchronous generator and other reserves which provided primary frequency control, to their preset levels, so that they can respond to any future loss‐of‐generation events. The tertiary control involves coordinated changes in the dispatch levels (outputs) of different generators. In this control, some generators are dispatched down to restore their reserve capability while some other generators are dispatched up by a corresponding amount, while maintaining the scheduled system frequency. Deployment of tertiary frequency control is the final stage of frequency restoration in the recovery period.

Figure 1.7 Sequential frequency controls after a sudden loss of generation and their impact on system frequency.

      Source: Eto et al. [8]. Reprinted with permission from Lawrence Berkeley National Laboratory, Berkeley, CA, USA.

      The focus of this book is on the arresting period, frequency nadir, and initial parts of the