_{1}

Different droop control methods for PV-based communal grid networks (minigrids and microgrids) with different line resistances (
*R*) and impedances (
*X*) are modelled and simulated in MATLAB to determine the most efficient control method for a given network. Results show that active power-frequency (
*P-f*) droop control method is the most efficient for low voltage transmission networks with low X/R ratios while reactive power-voltage (
*Q-*
*V*) droop control method is the most efficient for systems with high
*X/R* ratios. For systems with complex line resistances and impedances, i.e. near unity
*X/R* ratios,
*P-f* or
*Q-V* droop methods cannot individually efficiently regulate line voltage and frequency. For such systems,
*P-Q-f* droop control method, where both active and reactive power could be used to control PCC voltage via shunt-connected inverters, is determined to be the most efficient control method. Results also show that shunt-connection of inverters leads to improved power flow control of interconnected communal grids by allowing feeder voltage regulation, load reactive power support, reactive power management between feeders, and improved overall system performance against dynamic disturbances.

A PV-based communal grid can be defined as a collection of distributed PV systems, distributed energy storage devices, and distributed loads, operating as a single and controllable system capable of supplying power to an area of service. They should be operable in both grid-connected and islanded modes. Power electronics interfaces and controllers are used in communal grids to ensure quality, reliable and independent power supply at all times. A control system must be able to disconnect and reconnect the communal grid from the utility grid, maintain voltage and frequency levels in islanded mode of operation, and facilitate a black start after a system failure [

Droop control method is the most widely used in PV power systems to enable automatic load sharing between different distributed PV systems and to extend operating range of active (P) and reactive (Q) power ratings of a given inverter [

The power produced at the generator terminal is expressed as [

P = E R 2 + X 2 [ X V sin δ + R ( E − V cos δ ) ] (1)

Q = E R 2 + X 2 [ − R V sin δ + X ( E − V cos δ ) ] (2)

where δ is the voltage angle.

Since HV networks have high reactance (X) and low line resistance (R), and thus high X/R ratios, the line resistance can be ignored and Equations (1) and (2) reduced to [

P = V E sin δ X (3)

Q = E 2 − V E cos δ X (4)

Usually, δ is very small (zero) and therefore cos δ ≅ 1 and sin δ ≅ δ . Equations (3) and (4) can therefore be simplified further to [

δ ≈ P X V E (5)

E − V ≈ Q X E (6)

The reactive power Q can therefore be controlled by the difference in voltage between E and V, and the active power P, by the voltage angle δ . The voltage angle δ can be expressed in terms of angular frequency ω (radians/second), and therefore in terms of electrical frequency f (hertz) as [

δ = ∫ Δ ω d t = 1 2π ∫ Δ f d t (7)

The relationship outlined above allows automatic load sharing between many synchronous generators (SGs) when combined with P-f droop control as shown in

Inverters are used to interface communal grids with utility grids and can be classified according to modes of operation as PQ or V-f (also known as voltage source inverter (VSIs)). A PQ inverter controls the real (P) and reactive (Q) power by adjusting the magnitude of the output real and reactive current. It therefore operates as a voltage controlled current source [

chosen depending on a communal grid’s architecture and control strategy, and may change depending on whether the communal grid is islanded or grid-connected. Unlike synchronous generators, inverters do not have rotors and thus no natural connection between frequency and active power. To achieve stable operation with multiple distributed PV systems, the inverters are controlled so that they mimic the characteristics of synchronous generators with P-f and Q-V droop controls [

As opposed to a synchronous generator that uses its rotor speed as the frequency input for the P-f droop controller, a PQ inverter does not set the frequency, but rather measures the grid frequency using a phase lock loop (PLL) and then operates at that measured frequency [

P ( f ) = P 0 − ( f s e t − f ) k f (8)

where P 0 is the power delivered by the inverter at setpoint frequency f s e t and k f is the gradient of the droop, which determines how much the active power P will change in response to a change in frequency f. When a Q-V droop is used, the PQ inverter measures the terminal voltage and compares this to the reference value. The reactive power is adjusted by altering the reactive component of the inverter current [

Q ( V ) = Q 0 − ( V s e t − V ) k v (9)

where Q 0 is the reactive power delivered/consumed by the inverter at setpoint voltage V s e t and k v is the gradient of the droop, which determines how much the reactive power Q will change in response to a change in voltage V.

A VSI with droop control uses measured active power output to generate the VSI frequency and measured reactive power output to generate the VSI voltage [

f ( P ) = ( P 0 − P ) k p − f s e t (10)

where k p is the gradient of the droop, which determines how much the frequency will change in response to a change in power P.

V ( Q ) = ( Q 0 − Q ) k q − V s e t (11)

where k q is the gradient of the droop, which determines how much the voltage will change in response to a change in reactive power Q.

The conventional droop control relies on the inductive nature of transmission lines and is thus based on the assumption that the line resistance (R) is much less than the reactance (X), i.e., high X/R ratio and therefore active power flow is predominately a function of the voltage angle ( δ ) [

For systems with LV transmission networks and thus high line resistance, the low X/R ratio causes a coupling effect between active and reactive power, rendering Q-V droop control method ineffective in achieving required voltage regulation in such systems [

Consider a communal grid with two-feeder distribution systems as shown in _{4}; parallel connection of the inverters enables them to control both active and reactive power flow through shunt-connected transformers, leading to overall improved system performance [

Type of line | R (Ω/km) | X (Ω/km) | R/X |
---|---|---|---|

Low voltage | 0.642 | 0.083 | 7.7 |

Medium voltage | 0.161 | 0.190 | 0.85 |

High voltage | 0.06 | 0.191 | 0.31 |

through a look up table based on the PCC voltage level. A real-time integration inductor-capacitor-inductor (LCL)-filter with a virtual inductance is used to actively damp the inverter output without the need for extra sensors to feedback measured signals. Impact of DC link voltage and resonance frequency on stability would then be analysed.

The PV system does not produce real power during the night and therefore switches S_{5} and S_{6} can be opened. During the day when the PV system generates power, switches S_{2} - S_{6} are closed, while switch S_{1} is kept open in order to operate the system as interline-PV (I-PV), controlled through an interline power flow controller (IPFC) [_{pcc1} and V_{pcc2}, respectively. The active and reactive powers injected or absorbed by feeders 1 and 2 are expressed as P_{inv1}, Q_{inv1}, P_{inv2} and Q_{inv2} respectively. The reactive powers supported by the inverters are shown as positive quantities since they are leading, while the reactive powers are shown as negative quantities since they are lagging. For simplicity, the simulation results are expressed in per unit (pu), with base voltage of 25 kV and base power of 1 MVA. Feeders 1 and 2 line parameters are: 0.08 + j0.04 ohm/km and line lengths: L_{1} = L_{2} = 20 km.

_{th} represents the feeder as well as inverter coupling impedance, ϕ is the phase angle difference between PCC and grid voltages, while θ is the impedance angle due to Z_{th}.

The following equations are used to control the active and reactive power flows ( S = P + j Q ) from inverter 2 (the power source) to feeder 2 (the grid):

P = V t h Z t h [ ( E P V cos ϕ − V t h ) cos θ + E P V sin θ sin ϕ ] (12)

Q = V t h Z t h [ ( E P V cos ϕ − V t h ) sin θ − E P V cos θ sin ϕ ] (13)

Since ϕ is usually very small, i.e., cos ϕ ≈ 1 , and sin ϕ ≈ ϕ , the equations above are reduced to:

P = V t h Z t h [ ( E P V − V t h ) cos θ + E P V ϕ sin θ ] (14)

Q = V t h Z t h [ ( E P V − V t h ) sin θ − E P V ϕ cos θ ] (15)

Equations (14) and (15) show the dependency of delivered active and reactive power on the impedance angle θ and the phase difference angle ϕ .

This method is suitable for networks with high resistive values and low reactance, i.e. low X/R ratios. This makes the impedance angle θ equals to zero hence, from Equation (14), the active power delivered by the inverter is proportional to the voltage difference (E_{PV} - V_{th}) and thus proportional to the inverter E_{PV}. The reactive power of inverter 2 is proportional to the phase difference angle ϕ , i.e. proportional to the frequency f of the system. It should be noted that ϕ is varying within a small range. P remains constant irrespective of any change in ϕ while Q significantly changes with changing ϕ . On the other hand, P significantly increases with increasing E_{PV} while Q is hardly affected by changes in E_{PV}.

This method is suitable for networks with high X/R ratios, i.e. low line resistance and high reactance and thus the impedance angle θ goes to 90˚. The reactive power of the inverter is proportional to the inverter voltage E_{PV} and the active power is proportional to the frequency f. P significantly changes with changing ϕ while Q remains constant regardless of any changes in ϕ . On the other hand, P hardly changes with changing E_{PV} while Q significantly changes with E_{PV}. The Q-V droop control method is one of the widely used methods for voltage regulation; unlike the P-f droop method where additional provision for real power is required; Q-V droop method does not need such a source of real power for generating the necessary Q for compensation.

This method is suitable for systems with complex line impedances, i.e. where neither the line resistance nor the reactance is more significant over the other and therefore neither can be ignored. In such systems, the X/R ratio is near unity and therefore neither the P-f nor the Q-V droop method is sufficient to regulate the PCC voltage. In this system both the active and reactive power are simultaneously affected by changes in voltage magnitude E_{PV} and the phase difference angle ϕ . Since in these systems both active and reactive power affect the voltage magnitude, the system can be represented by the following equation [

V = V p c c – ( n L ∗ P ) – j ( m L ∗ Q ) (16)

where n L and m L are the electric load droop coefficients while V_{pcc} is the voltage before compensation and is given by

V p c c = V r e f + ( n d ∗ P ) + j ( m d ∗ Q ) (17)

where n d and m d are the active and reactive power coefficients for the proposed P-Q-V droop method while V r e f is the desired reference value of PCC voltage, i.e. 1 pu (25 kV).

For simplicity only feeder 2 in _{1} (0.0 S), inverter 2 starts operation to regulate feeder 2 PCC voltage based on P-f, Q-V, or P-Q-V droop control methods with normal loads. At t_{2} (0.5 S) feeder 2 PCC is increased above 5% due to active power injected from another PV source. At t_{3} (1.0 S) feeder 2 PCC voltage is decreased below 5% limit due to increased load and no additional active power injection.

_{1}, t_{2}, and t_{3}. The PCC voltage is regulated according to the P-f droop control method. _{1} to t_{2}, the PCC voltage is 1.035 pu, and it is reduced to 1.015 pu using P-f droop method; 0.6 pu of active power is absorbed through inverter 2 and is drawn from feeder 1. From t_{2} to t_{3}, the PCC voltage is increased to 1.089 pu and it is reduced to 1.06 pu. This is done by absorbing 1 pu active power. Even though inverter 2 could absorb up to 2 pu to regulate the PCC voltage, it has been limited to a maximum of 1 pu for active power injection in order not to overload feeder 1 and thus to maintain its voltage within acceptable limits. From t_{3} to 1.4 sec, the PCC voltage falls to 0.925 pu due to heavy load on feeder 2. Inverter 2 then injects maximum allowable 1 pu active power to improve the PCC voltage from 0.925 to 0.945 pu. The droop coefficient for this method is 0.02 pu/MW for all the operating conditions.

_{1} to t_{2} the PCC voltage is reduced from 1.035 pu to 1.02 pu as shown in _{2} to t_{3}, the PCC voltage is regulated at around 1.055 pu by absorbing 2 pu inductive reactive power capacity of inverter 2 as shown in _{3} to 1.4 seconds, the PCC voltage is raised from 0.925 to 0.948 pu by injecting capacitive reactive power of 2 pu as shown in

_{1} to t_{2} the PCC voltage is reduced from 1.035 pu to 1.025 pu as shown in _{2} to t_{3}, the PCC voltage is regulated at 1.04 pu by absorbing 1.4 pu inductive reactive power and 0.8 pu active power as shown in _{3} to 1.4 seconds, the PCC voltage is increased from 0.925 pu to 0.96 pu by injecting 1.4 pu capacitive reactive power and 0.7 pu active power simultaneously as shown in

In this article, different droop control methods for PV-based communal grid networks with different line resistances (R) and impedances (X) have been modelled and simulated in MATLAB to determine the most efficient control method for a given network. The results show that active power-frequency (P-f) droop control method is the most efficient for low voltage transmission networks with

low X/R ratios while reactive power-voltage (Q-V) droop control method is the most efficient for systems with high X/R ratios. Results also show that P-f or Q-V droop control methods cannot individually efficiently regulate line voltage and frequency for systems with complex line resistances and impedances, i.e. near unity X/R ratios. For such systems, P-Q-f droop control method, where both active and reactive power could be used to control PCC voltage via shunt-connected inverters, is determined to be the most efficient control method. Results also show that shunt-connection of inverters leads to improved power flow control of interconnected communal grids by allowing feeder voltage regulation, load reactive power support, reactive power management between feeders, and improved overall system performance against dynamic disturbances. The necessary active power for the compensation is drawn from the interconnected feeders via the inverters. The controller then circulates minimum active power between the feeders while the active and reactive power droop coefficients are adjusted online through a look up table based on the PCC voltage level. A real-time integration inductor-capacitor-inductor (LCL)-filter with a virtual inductance is used to actively damp the inverter output without the need for extra sensors to feedback measured signals.

・ P-f droop control method is suitable for networks with low X/R ratios.

・ Q-V droop control method is suitable for networks with high X/R ratios.

・ P-Q-f droop control method is suitable for networks with near unity X/R ratios.

・ Shunt-connected inverters lead to improved system performance.

This research was funded by Leeds International Research Scholarship.

The authors declare no conflicts of interest regarding the publication of this paper.

Opiyo, N.N. (2018) Droop Control Methods for PV-Based Mini Grids with Different Line Resistances and Impedances. Smart Grid and Renewable Energy, 9, 101-112. https://doi.org/10.4236/sgre.2018.96007