Reflections on the Topic of Volt/Var Control by Smart Inverters of DERs

Reflections on the Topic of Volt/Var Control by Smart Inverters of DERs

Nokhum Markushevich

The Key Requirements for Rule 21 [1] introduced an example curve for Volt/var control by smart inverters (Figure 16 in [1]). The curve is presented here in Figure 1. Actually, it is a piecewise droop control function with a -2% droop value. However, the y-axis presents the available kvars. The available kvars depend on the  Watts of the DER and on the Volts at the inverter terminals. Hence, the value at the 100% mark on the y-axis will depend on the operating conditions of the DER (see Figure 2).  

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Figure 1. Example Volt/var control curve [1]. V1-V4 and Q1-Q4 are the settings of the curve.

Figure 2. Volt/var curves based on available kvars under different Watts and Volts of the DER

As seen in Figure 2, the inverter will inject different amounts of kvars for the same voltage deviation from the target settings for different Watts and Volts of the DER. Hence, the intensity of the volt/var control is different for different available kvars. This also means that the droop (on the scale of the rated kVAs) is different for different operating conditions of the DER: the smaller the available kvars, the greater the droop (absolute value), as seen in Figure 3.

Figure 3. Droop factor under different operating conditions of DER.

The curves presented in Figure 2 can be described by the following equations:

Q(DER)h, i =(V2–Vi, h) / |droop|h+ Q(DER)init≤ Qmax(DER) h, i   for V1< Vi, h< V2        (1)

Q(DER)h, I  =Qmax(DER) h, i   for Vi, h <V1                                                            (2)

Q(DER) = Q(DER)init    for V2 <Vi <V3                                                                                    (3)

Q(DER)h, i =(V3 –Vi) / |droop|h+ Q(DER)init≥ Qmin(DER) h, i   for V3 <Vi<        (4)

Q(DER)h, I  =Qmin(DER) h, i   for Vi, h >V4                                                          (5)

Where

Vi- grid voltage at iteration i

Q(DER)init–DER’s vars when the voltage is within the dead zone

h – hour of the day

In the example curve  Q(DER)init = 0.

If the same intensity (and the same droop) of control is desired, the volt/var curve should be based on a given percentage of the rated kVA. Then, the inverters will inject the same amount of kvars for the same deviation of voltage. However, the injection will be limited by different available kvars for different operating conditions (see Figure 4). Such a curve is more aggressive than the one represented in Figure 3 and may need an adjustment of the base percentage of the rated kVA.

Figure 4. Volt/var curve based on rated DER’s kVA with kvar limits for different Watts and Volts of the DER

The injection of kvars by smart inverters based on such Volt/var control curves is an iterative process. The inverter of the DER injects kvars in order to arrive at a particular voltage in accordance with the curve. However, the grid response to this injection is based on its voltage sensitivity to the kvars. Hence, the final grid voltage after the injection may be different from the target of the volt/var control function. Then the inverter will inject another amount of kvar in accordance with the new grid voltage, and so on. When the grid’s inherent voltage sensitivity factor is greater than the droop factor, the process may diverge. The process converges when the DER’s kvar injection results in the grid voltage equal to the expected curve voltage. For instance, under the condition when

V1<Veq<V2

the equilibrium voltage can be defined as follows:

Veq=(V2*GS+Vinit x |droop|)/(GS+|droop|)                                                      (6),

where

V2 – Minimum target voltage,

GS –  Grid sensitivity factor

Vinit  –   Initial voltage before the additional kvar injections.

The equilibrium kvars can be defined as follows:

Qeq = (V2-Veq)/|droop| = (Veq-Vinit)/GS       (7)

Let us consider some examples based on the IEEE 4-nodes test feeder [2], (Figure 5). A DER with a smart inverter is added to node 4. The rated kVA of the DER is 3000kVA, the power factor is 0.9. The load in node 4 is presented as a load shape with the peak load 5400 kW and power factor 0.9. The load shapes and the DER kW injections are presented in Figure 6.

Figure 6. Load shapes.

The grid sensitivity of this circuit related to node 4 is about 0.12 V/kvar, while the droop of the DER’s volt-var curve changes with the change of the available kvars (Figure 7). As seen in the figure, the droop (absolute value) is smaller than the sensitivity factor of the grid during the entire day.

Figure 7. The droop of the volt-var curve (Figure 1) and of the sensitivity factor of the grid to the DER’s kvar for the above circuit

The results of the simulations for the above load shapes under conditions (1) and (2) are presented in Figure 8. As seen in the figure, the process either did not converge for some hours, or was stuck on the current limit of the kvars of the DER.

Figure 8. Results of simulations under conditions (1) and (2) of the curves of Figure 2 for the circuit with large sensitivity factor.

Another simulation was performed for a grid with a sensitivity factor smaller than the droop of the volt-var curve. In this case, the lengths of the lines were reduced by the factor of 10, and the step-down transformer’s rated kVAs were changed to 25000 kVA. As a result of these changes, the grid sensitivity factor was reduced to about 0.023 V/kvar, which is smaller than the values of the droop of the volt-var curve for all hours of the day (Figure 9).

Figure 9. The droop of the volt-var curve (Figure 1) and the sensitivity factor of the grid to the DER’s kvar for the circuit with reduced sensitivity factor.

The results of the simulations for the circuit with the reduced sensitivity factor under conditions (1) and (2) are presented in   Figure 10.  As seen in the figure, the process converges for all hours of the day.

Figure 10. Results of simulations under conditions (1) and (2) of the curves on Figure 2 for the circuit with small sensitivity factor.

In order to achieve the conditions when |droop|> Gs, the volt-var curve of the smart inverter should be less “aggressive” [3]. It can be done by setting a lower var limit or by changing other setting of the volt-var curve. Such a curve, with a 100% var limit, is presented in Figure 11, and the relationship between the droop and the sensitivity factor for the original 4-node circuit is presented in Figure 12 .

Figure 11. A volt-var curve with a greater droop

Figure 12. The droop of the “gentle” volt-var curve (Figure 11) and the sensitive factor of the grid for the circuit with large sensitivity factor.

The results of the simulations for the original circuit with the large sensitivity factor and with the “gentle” volt-var curve under conditions (1) and (2) are presented in Figure 13.  As seen in the figure, the process converges for all hours of the day.

Figure 13. The results of simulations for the original circuit with the “gentle” volt-var curve

Figure 14 shows the results of the last (converged) simulation. As seen in the figure, the target voltage is not reached, although there still are available kvars from the DER.

Figure 14. Equilibrium voltages and DER’s kvars achieved based on the “gentle curve”

Another simulation of the volt-var control for the 4-node circuit was performed based on the following equations:

Q(DER)h, i+1 =(V2–Vi, h) / |droop|h + Q(DER)h,I  ≤ Qmax(DER) h, i+1   for  V1< Vi, h< V2       (1a)

Q(DER) = Q(DER)init, i    for V2 <Vi <V3                                                                                                     (3a)

Q(DER)h, i =(V3 –Vi) / |droop|h + Q(DER)h, i ≥ Qmin(DER) h, i+1   for  V3 <Vi< V4                (4a)

In this case, the injected DER’s kvars at iteration i are used for the initial DER’s kvars for iteration i+1.

The convergence of this simulation is presented Figure 15, and the final kvars and voltages are presented in Figure 16.  As seen in the figures, the volt-var control process converges without oscillations, and either the target voltages are reached when there are sufficient available kvars, or all available kvars are utilized when the target voltages cannot be reached.

Figure 15. Convergence of volt-var control process based on (1a) – (4a)

Figure 16. Final voltages and DER’s kvars of the volt-var control simulations based on (1a) – (4a)

Conclusions.

1. This paper addresses autonomous volt-var control by a smart DER’s inverter in one node  based on droop control

2. The settings of the volt-var control curve cannot be chosen independently of the volt-to-var sensitivity  of the relevant nodes of the subject  circuit.  This means that the settings should be different for different nodes and they may need to be  changed when the connectivity of the circuit changes.

3. The simulations of the volt-var control described in this paper show that the volt-var control based on the recursive equations (1a) – (4a) provide better convergence and a more efficient  utilization of the available DER’s kvars than control based on a constant Qinit.

References.

1. CEC and CPUC, SIWG Phase 3 DER Functions: Recommendations to the CPUC for Rule 21, Phase 3 Function Key Requirements, and Additional Discussion Issues, March 31, 2017.  Available: https://www.energy.ca.gov/electricity_analysis/rule21/documents/phase3/SIWG_Phase_3_Working_Document_March_31_2017.pdf

2. IEEE  4  Node  Test Feeder.  Available: https://www.scribd.com/document/100557391/IEEE-4-Node-Test-Feeder-Revise...

3. Jens Schoene and Muhammad Humayun, Volt-Var Control Settings for Smart PVs. Available: https://www.energycentral.com/c/cp/volt-var-control-settings-smart-pvs