# Secondary Control for Storage Power Converters in Isolated Nanogrids to Allow Peer-to-Peer Power Sharing

^{1}

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## Abstract

**:**

## 1. Introduction

- Grid-forming DERs, i.e., those DERs responsible for keeping proper and stable frequency and voltage values within the microgrid, are connected (either directly or through radial feeders) to the same Point of Common Coupling (PCC), where the loads are also connected [13]. In this case, voltage setpoint is the same for every DER and virtual impedance is usually required to decouple Active Power-Frequency and Reactive Power-Voltage dependence relationships.
- Power sharing obeys to individual energy ratings, thus avoiding circulating currents among DERs. Therefore, power interchange due to economic agreements is usually discarded in isolated mode.

- P2P energy trading between prosumers is addressed in islanded microgrids, from the point of view of the voltage and power setpoint generation and how the DER converter can follow them. Power flow among prosumers is guaranteed due to different voltage setpoint in each prosumer’s load bus.
- A novel secondary control based on power flow algorithm in microgrids is proposed to reach classical secondary control target as well as allow energy interchange between DERs.
- A residential nanogrid is simulated with all the necessary control loops to perform hierarchical control, starting from previously mentioned setpoints.

## 2. Proposed Control Strategy

- Tertiary control aims to optimize the energy use inside the nanogrid. Starting from generation and demand forecasting, demand and storage systems are managed at this stage to match power and energy balance in the isolated nanogrid with optimal resource exploitation. Energy interchange among the resources within the nanogrid presents a clear importance when it is grid-connected, with the aim of obtaining economic advantages and improving self-consumption and self-sufficiency. Another scenario for this tertiary control is P2P energy interchange, which schedules energy sharing under agreement in both grid-connected and isolated situation.
- Secondary control determines the electrical magnitude setpoints for the DERs. In the context of isolated nanogrids, the target of this stage is usually to restore the voltage and the frequency in a unique PCC, with a power-sharing strategy that aimed at using the available resources to keep secure and stable electrical conditions, without considering the economic or agreement-based energy interchange among DERs. In this paper, the P2P energy interchange concept is taken into account at this control stage to allow for complying with economic or energy agreements among different prosumers.
- Primary control acts automatically to obtain stable frequency and voltage magnitudes when power balance mismatching occurs due to unexpected changes in demand or generation. A decentralized droop control is the most frequently used strategy for this stage, whose formulation strongly depends on the resistive/inductive character of the system.

#### 2.1. Nanogrid Tertiary Control

- P
_{G-TERCi}: hourly average active power setpoint for tertiary control (W) - Q
_{G-TERCi}: hourly average reactive power setpoint for tertiary control (VAr) - P
_{Gi}: hourly average forecasted PV generation power, once curtailed (W) - P
_{Bi}: hourly average scheduled battery power (positive values when charging, negative when discharging) (W) - Q
_{Di}: hourly average forecasted reactive power demanded by load in bus i (VAr)

#### 2.2. Nanogrid Secondary Control

_{B0i}) is obtained by linear interpolation between consecutive hourly scheduled power values, whereas the generated (P

_{G0i}) and demanded (P

_{D0i}) power values are both measured and values of the previous minute are used to obtain secondary control setpoints. In the case of communication fault, measured values can be substituted by an interpolation of forecasted values, with the consequent decrease in accuracy, which will be compensated by primary control.

- There is no slack bus in microgrids, as there is not a bus with a powerful generation capacity that assures stable frequency and provides power losses. Two kind of buses are usual in microgrids: PQ (load or grid-following generation buses) and droop buses (this is a new kind of bus, which shares the responsibility to keep stable and proper frequency values).
- Frequency value of the system is not guaranteed, but it is a variable of the problem.
- Active and reactive power generation is governed by droop rules.

#### 2.2.1. Element Modelling for Power Flow Algorithm

- R
_{ij}: line resistance (Ω) - X
_{ij}: line reactance (Ω) - L
_{ij}: line inductance (H) - f: nanogrid frequency (Hz)

- P
_{D-SECi}: active power demand estimation for secondary control (W) - Q
_{D-SECi}: reactive power demand estimation for secondary control (VAr) - U
_{i}: RMS value of the voltage in bus i (V) - U
_{n}: rated voltage (230 V in low-voltage single-phase systems) - f
_{n}: rated frequency (50 Hz) - α, β: active and reactive exponents
- k
_{pf}, k_{qf}: sensitivity factors of active and reactive power to frequency (pu/pu)

- P
_{G-SECi}: active power setpoint for the converter output, for secondary control (W) - Q
_{G-SECi}: reactive power setpoint for the converter output, for secondary control (VAr) - m
_{p}, m_{q}, k_{p}, k_{q}: droop coefficients

#### 2.2.2. Power Flow Algorithm Formulation

_{SECi}) and reactive (Q

_{SECi}) power in bus i are calculated in (6).

- U
_{SECi}, δ_{SECi}: RMS value (V) and phase angle (rad) of i-bus voltage - Y
_{ik}, γ_{ik}: magnitude (S) and phase angle (rad) of ik-element of Ybus admittance matrix

_{SECi}and δ

_{SECi}) and (8) for droop buses (unknown variables P

_{SECi}, Q

_{SECi}, U

_{SECi}and δ

_{SECi}). One of the droop buses acts as phase angle reference (δ

_{SEC}

_{1}= 0), whereas frequency f is an unknown variable. Therefore, the same number of equations and variables are provided.

#### 2.3. Nanogrid Primary Control

_{1}and L

_{2}and capacitance C constitute the LCL output filter of the converter. Setpoints in prosumer’s load bus have been provided by secondary control. Primary control firstly obtains setpoints for capacitor voltage and the power injected in L

_{2}, necessary to perform primary control.

_{c-PRIMi}, δ

_{c-PRIMi}) and the active and reactive power setpoints (P

_{G-PRIMi}, Q

_{G-PRIMi}) in the input terminal of reactance L

_{2}.

**i**

_{L}

_{2}is the current in the filter inductance L

_{2}and * denotes complex conjugate.

**u**

_{ci_ref}, according to measured values and droop characteristic in (4):

**u**_{ci-ref}: reference voltage signal in the filter capacitor of the ith converter- U
_{ci-ref}: RMS value of**u**_{ci-ref}(V) - θ
_{ci-ref}: angle signal of**u**_{ci-ref} - P
_{i}: measured active power in the filter reactance L_{2}of the ith converter (W) - Q
_{i}: measured reactive power in the filter reactance L_{2}of the ith converter (VAr).

#### 2.4. Power Converter Inner Voltage and Current Control Loops

_{n}is the reference angular frequency, in this case, 2π50 rad/s.

_{P-PR}= 0.001 and k

_{R-PR}= 100, as was previously mentioned.

_{P-PR}= 20 and k

_{R-PR}= 2000. The voltage and the current PR controller coefficients were both tuned by means of the guidelines provided in [30].

**u**

_{ci}is the measured voltage signal in the filter capacitor of the ith converter and

**i**

_{L}

_{1}is the current in the inverter-side reactance of the LCL filter.

#### 2.5. Battery DC/DC Converter Control Loop

- i
_{bati-ref}: reference charging current for the ith battery (A) - i
_{bati-refP}: power-reference charging current for the ith battery (A) - U
_{DC-ref}: reference value for the DC-link voltage of the ith converter (V) - U
_{DCi}: measured value for the DC-link voltage of the ith converter (V) - i
_{pvi}: measured value for the ith PV generator current (A) - u
_{bati}: measured value for the battery voltage (V)

- d
_{bati}: duty cycle for the ith battery DC/DC converter - i
_{bati}: measured value for the battery current (A) - L
_{bat}: filter inductance (H) - R
_{bat}: filter resistance (Ω) - T
_{s}: sampling period (s)

## 3. Case Study and Simulation Parameters

^{2}cross-section, 20 m long two-wire cable. As PV generation is not the matter of study in this work, it has been modelled as a DC current source that is assumed to be working at MPP at each house. However, battery ESS consists of a battery source and a DC/DC converter, whose control strategy has been discussed in Section 2.3. A common inverter connects both PV generation and ESS to the load bus of each prosumer. The nanogrid is islanded, i.e., it is disconnected from the main grid. Figure 5 depicts the nanogrid schematic and Table 2 shows the simulation parameters. It can be observed that the droop constants used in primary control are the same or proportional (scaled for stability reasons) to those of secondary control, but changing the relationship between Reactive Power-Frequency and Active Power-Voltage (in resistive line between prosumers for secondary control) and between Active Power-Frequency and Reactive Power-Voltage (in inductive filter for primary control).

## 4. Simulation Results and Discussion

^{®}. Table 4 depicts the time sequence of the simulation. It is the same for both prosumers.

_{2}is a filtered version of current in L

_{1}. They are both quite sinusoidal and their amplitude and phase-shift are consistent with the power setpoints of each converter.

**u**

_{ci}) and measured current in filter L

_{2}reactances (

**i**

_{L}

_{2}). Setpoints for active and reactive powers in primary control (P

_{G-PRIMi}and Q

_{G-PRIMi}) are also depicted in the dashed line in the figure, under their calculated values. It can be observed that the calculated power values reach their initial setpoints once the inverter is connected, after a short transient period. Subsequently, loads change starting from 1.2 s of simulation and droop control shares increment in both active and reactive powers, pushing the calculated powers aside from setpoints. Once the setpoints are updated (1.6 s), the calculated power values reach again their new setpoints with a proper accuracy.

## 5. Conclusions and Future Works

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Acronyms | |

DER | Distributed Energy Resource |

DG | Distributed Generation |

DSM | Demand Side Management |

EMS | Energy Management System |

ESS | Energy Storage System |

MPP | Maximum Power Point |

PCC | Point of Common Coupling |

PR | Proportional-Resonant |

PV | Photovoltaic |

PWM | Pulse Width Modulation |

RPP | Reference Power Point |

SoC | State of Charge |

Variables | |

C | Capacitance of the LCL Filter |

C_{0} | Capacitance of the DC-link capacitor |

d_{bati} | Duty Cycle of the ith Prosumer’s Battery Converter |

f | Frequency |

f_{n} | Rated Frequency |

i_{bati} | Charging Current of the ith Prosumer’s Battery |

i_{bati-ref} | Reference Charging Current of the ith Prosumer’s Battery |

i_{bati-refP} | Power-Reference Charging Current of the ith Prosumer’s Battery |

i_{L1} | Current Signal in the Inner Filter Reactance of the ith Prosumer |

i_{L1-ref} | Reference Current Signal in the Inner Filter Reactance of the ith Prosumer |

i_{L2} | Current Signal in the Outer Filter Reactance of the ith Prosumer |

i_{pvi} | Current of the ith Prosumer’s PV Generation System |

k_{p} | P-U Droop Coefficient |

k_{pf} | Sensitivity Factor of Active Power Load to Frequency |

k_{P-PR} | Proportional-Term Constant of Proportional-Resonant Controllers |

k_{q} | Q-f Droop Coefficient |

k_{qf} | Sensitivity Factor of Reactive Power Load to Frequency |

k_{R-PR} | Resonant-Term Constant of Proportional-Resonant Controllers |

L_{1} | Converter-Side Inductance of the LCL Filter |

L_{2} | Grid-Side Inductance of the LCL Filter |

L_{bat} | Inductance of the Battery Filter |

L_{ij} | Line Inductance of Feeder Between ith and jth Prosumers |

m_{p} | P-f Droop Coefficient |

m_{q} | Q-U Droop Coefficient |

P_{B0i} | 1 Minute-Resolution Interpolation of P_{Bi} |

P_{Bi} | Charging Power of the ith Prosumer’s Battery |

P_{D0i} | Last-Minute Measured Active Power Demand of the ith Prosumer |

P_{Di} | Hourly Average Active Power Demand Forecasting of the ith Prosumer |

P_{D-SECi} | Active Power Estimation of the ith Prosumer’s Demand, for Secondary Control |

P_{G0i} | Last-Minute Measured Power PV Generation of the ith Prosumer |

P_{Gi} | Hourly Average Power PV Generation Forecasting of the ith Prosumer |

P_{G-PRIMi} | Active Power Setpoint for the ith Converter Output, in Primary Control |

P_{G-SECi} | Active Power Setpoint for the ith Converter Output, in Secondary Control |

P_{G-TERCi} | Active Power Setpoint for the ith Converter Output, in Tertiary Control |

P_{i} | Measured Active Power in the Outer Filter Reactance of the ith Converter |

P_{SECi} | Net Injected Active Power in the ith bus, in Secondary Control |

Q_{Di} | Hourly Average Reactive Power Demand Forecasting of the ith Prosumer |

Q_{D-SECi} | Reactive Power Estimation of the ith Prosumer’s Demand, for Secondary Control |

Q_{G-PRIMi} | Reactive Power Setpoint for the ith Converter Output, in Primary Control |

Q_{G-SECi} | Reactive Power Setpoint for the ith Converter Output, in Secondary Control |

Q_{G-TERCi} | Reactive Power Setpoint for the ith Converter Output, in Tertiary Control |

Q_{i} | Measured Reactive Power in the Outer Filter Reactance of the ith Converter |

Q_{SECi} | Net Injected Reactive Power in the ith bus, in Secondary Control |

R_{bat} | Resistance of the Battery Filter |

R_{ij} | Line Resistance of Feeder Between ith and jth Prosumers |

S_{G-PRIMi} | Complex Power Setpoint for the ith Converter Output, in Primary Control |

S_{G-SECi} | Complex Power Setpoint for the ith Converter Output, in Secondary Control |

t | Time |

T_{s} | Sampling Period |

u_{bati} | Voltage of the ith Prosumer’s Battery |

u_{ci} | Voltage Signal in the Filter Capacitor of the ith Converter |

U_{ci} | RMS Value of the Voltage in the Filter Capacitor of the ith Converter |

u_{ci-ref} | Reference Voltage Signal in the Filter Capacitor of the ith Converter |

U_{ci-ref} | Reference RMS Value for the Voltage in the Filter Capacitor of the ith Converter |

U_{c-PRIMi} | RMS Value of the Voltage Signal in the Filter Capacitor of the ith Converter, in Primary Control |

u_{c-PRIMi} | Voltage Signal in the Filter Capacitor of the ith Converter, in Primary Control |

U_{dci} | Voltage in DC-Bus of the ith Converter |

U_{dc-ref} | Reference Voltage of DC-Bus |

U_{i} | RMS Value of the Voltage in the ith bus |

u_{i} | Voltage Signal in the ith bus |

U_{n} | Rated Voltage |

u_{SECi} | Reference Voltage Signal in the ith bus, in Secondary Control |

U_{SECi} | RMS Value of the Voltage in the ith bus, in Secondary Control |

X_{ij} | Line Reactance of Feeder Between ith and jth Prosumers |

Y_{ik} | Module of the ik-element of the system admittance matrix |

Z_{ij} | Line Impedance of Feeder Between ith and jth Prosumers |

α | Sensitivity exponent of Active Power Load to Voltage |

β | Sensitivity exponent of Reactive Power Load to Voltage |

δ_{c-PRIMi} | Phase Angle of the Voltage in the Filter Capacitor of the ith Converter, in Primary Control |

δ_{SECi} | Phase Angle of the Voltage in the ith bus, in Secondary Control |

γ_{ik} | Phase Angle of the ik-element of the system admittance matrix |

θ_{ci-ref} | Reference Angle Signal of the Voltage in the Filter Capacitor of the ith Converter |

ω_{n} | Reference Angular Frequency |

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**Figure 7.**Voltage in the load bus and current in both reactances of converter LCL filter: (

**a**) Prosumer 1; (

**b**) Prosumer 2.

**Figure 8.**Droop control performance: (

**a**) Voltage droop reference in the filter capacitor; and, (

**b**) Frequency droop reference.

**Figure 9.**Active and reactive power output in both inverters, calculated from measured voltage and current values.

Season | α | β | k_{pf} | k_{qf} |
---|---|---|---|---|

Summer | 1.2 | 2.7 | 0.7 | −2.3 |

Winter | 1.7 | 2.6 | 1.0 | −1.7 |

Parameter | Value |
---|---|

R_{bat} | 0.3 Ω |

L_{bat} | 8 mH |

C_{0} | 1.1 mF |

L_{1} | 3.6 mH |

L_{2} | 4.2 mH |

C | 2 µF |

Rated U_{DC} | 400 V |

Rated AC voltage | 230 V |

Rated u_{bat} | 48 V |

Rated frequency | 50 Hz |

m_{p}_{1} = k_{q}_{1}/5 | 3.3 × 10^{−4} Hz/W or Hz/VAr |

m_{q}_{1} = k_{p}_{1} | 1.1 × 10^{−3} V/VAr or V/W |

m_{p}_{2} = k_{q}_{2}/5 | 3.1 × 10^{−3} Hz/W or Hz/VAr |

m_{q}_{2} = k_{p}_{2} | 2.5 × 10^{−3} V/Var or V/W |

Prosumer 1 | Initial Value | Updated Value | Prosumer 2 | Initial Value | Updated Value |
---|---|---|---|---|---|

P_{D-SEC}_{1} | 445.15 W | 545.15 W | P_{D-SEC}_{2} | 571.00 W | 571.00 W |

Q_{D-SEC}_{1} | 146.31 VAr | 146.31 VAr | Q_{D-SEC}_{2} | 187.68 VAr | 217.68 VAr |

P_{G-SEC}_{1} | 341.54 W | 413.46 W | P_{G-SEC}_{2} | 674.62 W | 702.71 W |

Q_{G-SEC}_{1} | 146.31 VAr | 146.31 VAr | Q_{G-SEC}_{2} | 187.68 VAr | 217.68 VAr |

U_{SEC}_{1} | 229.99 V | 229.99 V | U_{SEC}_{2} | 230.02 V | 230.03 V |

δ_{SEC}_{1} | 0 | 0 | δ_{SEC}_{2} | 0 | 0 |

P_{G-PRIM}_{1} | 341.54 W | 413.46 W | P_{G-PRIM}_{2} | 674.62 W | 702.71 W |

Q_{G-PRIM}_{1} | 149.59 VAr | 150.88 VAr | Q_{G-PRIM}_{2} | 199.32 VAr | 230.53 VAr |

U_{c-PRIM}_{1} | 230.79 V | 230.80 V | U_{c-PRIM}_{2} | 231.08 V | 231.25 V |

δ_{c-PRIM}_{1} | 9.8 × 10^{−3} rad | 8.1 × 10^{−3} rad | δ_{c-PRIM}_{2} | 1.6 × 10^{−2} rad | 1.7 × 10^{−2} rad |

Time | Event |
---|---|

0 s | Battery setpoint to control U_{DC} is generated |

0.02 s | PWM of battery DC/DC converter is activated |

0.5 s | SPWM of inverter is activated |

0.6 s | Current and voltage control of inverter are activated Power-reference for battery is generated |

0.65 s | Droop control is activated |

0.9 s | PV generation is connected |

1.2 s | Unexpected change in loads occurs |

1.6 s | Secondary control setpoints are updated |

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**MDPI and ACS Style**

González-Romera, E.; Romero-Cadaval, E.; Roncero-Clemente, C.; Ruiz-Cortés, M.; Barrero-González, F.; Milanés Montero, M.-I.; Moreno-Muñoz, A.
Secondary Control for Storage Power Converters in Isolated Nanogrids to Allow Peer-to-Peer Power Sharing. *Electronics* **2020**, *9*, 140.
https://doi.org/10.3390/electronics9010140

**AMA Style**

González-Romera E, Romero-Cadaval E, Roncero-Clemente C, Ruiz-Cortés M, Barrero-González F, Milanés Montero M-I, Moreno-Muñoz A.
Secondary Control for Storage Power Converters in Isolated Nanogrids to Allow Peer-to-Peer Power Sharing. *Electronics*. 2020; 9(1):140.
https://doi.org/10.3390/electronics9010140

**Chicago/Turabian Style**

González-Romera, Eva, Enrique Romero-Cadaval, Carlos Roncero-Clemente, Mercedes Ruiz-Cortés, Fermín Barrero-González, María-Isabel Milanés Montero, and Antonio Moreno-Muñoz.
2020. "Secondary Control for Storage Power Converters in Isolated Nanogrids to Allow Peer-to-Peer Power Sharing" *Electronics* 9, no. 1: 140.
https://doi.org/10.3390/electronics9010140