## 1. Introduction

Over the last decade, there has been a clear focus in the European Union (EU) on promoting low-carbon generation technologies and renewables. To ensure the EU meets its climate and energy goals, the 20-20-20 targets aim to cut the emission of greenhouse gasses by

$20\%$ compared to the 1990 level, achieve a

$20\%$ share of renewables in the total energy consumption, and improve the energy efficiency by

$20\%$. In many countries, feed-in tariffs for eligible technologies have guaranteed returns for investors, and this along with other forms of market support have contributed to a reduction in technology costs and an increasing penetration of renewable energy resources (RESs) into distribution networks across Europe. This growth of renewable energy is expected to maintain since by 2030 the EU aims for

$27\%$ of the final energy consumption to come from renewable sources. The progress of the EU and its member states towards 2020 climate and energy targets are summarized in [

1].

These trends are impacting the operation of distribution networks, making the Distribution System Operators’ (DSOs) mission of providing secure electricity supply and high quality of service increasingly challenging. The historical “fit-and-forget” strategy of distribution networks was consistent with the unidirectional power flows from substations to end consumers and their predictable load profiles. When connecting significant amounts of RESs to the network, the assumption of unidirectional power flows is not always valid anymore. The generated power of RESs can reverse the power flows in the grid, what could lead to a rise of the voltage profiles beyond the allowed limits. Moreover, intermittent and unpredictable nature of renewables increases the complexity of controlling the distribution networks. A comprehensive overview of the impacts of the renewable energy and information and communications technology (ICT) driven energy transition on distribution networks is presented in [

2]. To maintain a high security of supply and quality of service, DSOs have to find new strategies to control their networks.

A transition towards active management strategies would be capable of maintaining the voltage profiles of distribution networks within acceptable limits to comply with the European standard EN 50160 [

3] while minimizing, deferring, or even avoiding any capacity upgrades. Additionally, valuable flexibility of prosumers can be embedded in the operational management of the networks, to allow the prosumers to participate in supporting the grid as kind of ancillary service. Details of the most effective and efficient ways for managing the future active distribution networks, to address the 21st century challenges of transitioning to low-carbon electricity, are discussed in [

4].

The need for managing distribution networks actively by employing smart grid solutions and creating innovative investments and business models are the reasons for launching the EU funded Peer-to-Peer Smart Energy Distribution Networks (P2P-SmarTest) project. The project was launched in 2015 and continued until the end of 2017. The idea of the project consists in developing intelligent control, trading, and communication algorithms through a “Peer-to-Peer” concept; to facilitate the integration of demand side flexibility and to ensure optimal operation of RESs within the network while maintaining quality and security of supply. The deliverables of the project can be found on the website of the project [

5]. In [

6], the view to Peer-to-Peer (P2P) approach for smart grid operation adopted in P2P-SmarTest project is presented. The P2P control paradigm used in the project is presented in [

7].

The approach adopted in P2P-SmarTest project to regulate voltage profiles of active distribution networks is based on distributed optimization techniques and P2P communication. Distributed optimization, as an alternative approach to solve challenges of the centralized optimization mechanism, has attracted increasing attention recently [

8]. A Distributed optimization-based control system is characterized by the complete absence of a central controller. Every RES is considered to be an autonomous control agent where all agents are equally important. To overcome the absence of the central decision making controller, the agents communicate with each other in a P2P fashion. With communication, they are able to make the correct control decisions in every particular situation. Failure of one controller in distributed control system does not lead to an inability to control the system. The work in [

9] describes fundamental concepts and approaches within the field of distributed control systems that are appropriate to power engineering applications.

Centralized control systems often suffer from serious computation, robustness, and communication issues for power networks with many controllable devices. Distributed control is perhaps the only viable strategy for such networks. Nevertheless, these centralized systems can achieve high performance. In a centralized control system, there is only one controller, which receives all necessary data, and based on all available information the multi-objective controller can achieve a globally optimal performance. An interesting question is whether P2P distributed control systems can achieve a comparable good performance to the centralized one. Most research studies appearing in the literature attempt to answer this question by means of simulators, as reviewed in [

10,

11,

12]. For instance, in [

13] a gradient descent method has been used to distribute a centralized optimization problem over agents participating in the voltage control, a push-sum gossip algorithm is implemented to enable P2P communication between the agents. Simulink (MATLAB, version R2016a, The MathWorks, Inc, Natick, MA, USA) has been used to model a 5-bus microgrid and to validate the performance of the proposed algorithm. In [

14], a dual decomposition technique is used to design a P2P-based voltage control system. A backward/forward sweep power flow calculation algorithm, coded in MATLAB, has been used to model a low voltage, 62-bus, semiurban feeder and to test the ability of the algorithm to control the voltage effectively within limits. In [

15], openDSS simulator (version 2017, EPRI, Palo Alto, CA) has been used to validate the effectiveness and robustness of a fully distributed voltage control algorithm that has been developed based on the Alternating Direction Method of Multipliers and consensus protocol (consensus ADMM). The same method has been used in [

16] and validated using CVX software (version 2014, CVX Research, Inc., Stanford, CA, USA) (convex programming). Distributed Energy Storage Systems (DESSs) are used in [

17] to control the voltage profiles of active distribution networks in a distributed way. The proposed methodology is based on network partitioning strategy. Linear programming and voltage sensitivities are used to define the areas for which each DESS maximizes its influence. To study the performance of the proposed algorithms, MATLAB has been used to code the algorithms and to model an IEEE 123 nodes test system. The concept of network partitioning is also used in [

18] to implement a decentralized voltage control system that regulates reactive power of photovoltaic (PV) inverters. The proposed methodology of [

18] is based on Lyapunov theory and has been validated via Matlab/Simulink environment.

The concepts of transactive energy (TE), home microgrids (H-MGs) and coalition formation are used in [

19] to design an algorithm for optimal use of electrical/thermal energy distribution resources, while maximizing profit of H-MGs. The algorithm is based on an optimization problem in which an objective function is based on economic strategies, distribution limitations and the overall demand in the market structure. MATLAB was used to solve the optimization problems of the proposed algorithm. The same concepts have been used in [

20] to design an optimal, autonomous, and distributed bidding-based energy optimization scheduling algorithm to maximize profit and energy balancing efficiency of H-MGs under residential loads. A comprehensive simulation study was carried out to reveal the effectiveness of the proposed method in lowering the market clearing price, increasing H-MG responsive load consumption, and promoting local generation. Optimal management system of battery energy storage is proposed in [

21] to enhance the resilience of a PV-based commercial building while maintaining its operational cost at a minimum level. The methodology is based on linear optimization programming problem with Conditional Value at Risk (CVaR) incorporated in the objective function. CVaR is used to account for the uncertainty in the intermittent PV system generated power and that in the electricity price. MATLAB simulation studies were carried out to evaluate the performance of the proposed method.

There are few studies in existing literature addressing the experimental validation of distributed control algorithms. Experimental evaluations of real deployments are thus lacking. In [

22], a gossip- based P2P voltage control has been tested in a pilot site, the work is part of the European Commission FP7 DREAM project. Six households were equipped with smart control agents, which measure the households’ consumption and control the households’ flexible loads. Each agent is connected to a local Wi-Fi router (internet gateway) and a virtual private network is then used to enable P2P communication between the neighboring agents. In [

23], a multi-agent platform has been implemented and used to test a dual-decomposition-based optimization method for controlling the prosumers’ flexibility. The distributed agents are implemented in Raspberry Pi computers. The agent-based control algorithm of each agent is implemented in Python and executed via Matlab calls. The setup is part of Local Intelligent Networks and Energy Active Region (LINEAR) project [

24]. In [

25], a gossiping P2P semantic overlay network is implemented by a toolbox, Agora+, enabling P2P communication between agents. The toolbox has been used to implement a distributed tertiary control algorithm, which allows groups of generators to operate at an economical optimum. In [

26], distributed reactive power control has been implemented and tested using real power inverters. Each inverter is considered to be an agent where coordination between the agents is obtained by exchanging information via an IP-based communication network.

This paper discusses the results of the experimental validation of a dual-decomposition-based P2P voltage control algorithm developed within the P2P-SmarTest project. A simulation already demonstrated the effectiveness of this algorithm [

14] and this paper demonstrates it experimentally. The voltage control problem is formulated as an optimization problem. The proposed method calculates the minimum change in reactive power and active power needed to maintain the voltages within the limits. The dual-decomposition method decomposes an optimization problem (with separable cost functions and coupled constraints) into sub-problems, suitable for distributed control. Dual-decomposition applies the theory of Lagrangian multipliers and duality to convert a centralized constraint optimization problem into a fully distributed constraint optimization problem. The proposed dual-decomposition method differs from the classical dual-decomposition. In classical dual-decomposition [

27], there is a need for a central agent to calculate the Lagrangian multipliers (control signals), whereas in the proposed dual-decomposition method, the Lagrangian multipliers are calculated locally and each agent communicates its Lagrangian multipliers to the other agents in a P2P fashion.

Our main contributions can be summarized as follows. (1) We present the design, development and hardware setup of a laboratory-based P2P voltage control testbed; (2) Secondly, we propose the use of a fully distributed dual-decomposition method to design a P2P voltage control system; (3) Thirdly, we propose the use of Long Range Wide-area network (LoRaWAN) technology to design a device-to-device communication system. The device-to-device communication is used to enable P2P data interchange between agents of the proposed voltage control system; (4) Finally, we validate experimentally that the proposed P2P voltage control system can indeed provide satisfactory regulation of the voltage profiles.

The testbed presented in this paper provides realistic and pragmatic solution for evaluating P2P smart grid applications. The testbed is used to evaluate the performance of the proposed dual-decomposition-based voltage control system. It can also be used to evaluate other distributed applications for grid management. The testbed allows for re-using of the existing simulator code, while still facilitating accurate integration of power and communication effects on a real hardware platform.

The rest of this paper is organized as follows. The laboratory-based P2P voltage control testbed is described in

Section 2.

Section 3 presents the P2P-based voltage control algorithm. Drive of the inverters is presented in

Section 4. The Device-to-Device (D2D) communication modules used to enable P2P communication between the agents are described in

Section 5.

Section 6 presents the experimental results and the key performance indicators. Finally, the paper is concluded in

Section 7 with future work.

## 2. Testbed Architecture

The architecture of the P2P voltage control testbed is depicted in

Figure 1. The testbed consists of four different layers which interact with each other: (1) microgrid layer; (2) control layer; (3) communication layer; and (4) monitoring layer. The microgrid layer consists of programmable inverters (label 1 in

Figure 1); connected to DC power supplies (label 2). The inverters emulate prosumers with photovoltaic (PV) installations, they are connected to the grid by resistors in series with inductors (label 3). The resistors and inductors are used to emulate a low voltage feeder. The control layer consists of inner control systems (label 4) that drive the power inverters, and grid voltage support functions (GVSFs) that control the voltage profiles of the micogrid (label 6). The communication layer consists of D2D communication modules (label 7) that are used to disseminate the status of the voltage profiles in a P2P fashion. The monitoring layer consists of voltmeters (label 9) and data acquisition platform (label 11).

The P2P voltage control testbed consists of three types of agents: (1) actuators; (2) observers; and (3) a monitor. Each GVSF is connected to a D2D communication module and together they form an actuator agent (label 5). The actuator agents are connected to the programmable inverters through the inner control systems (control loops) and participate actively in voltage control by calculating the change in reactive power and active power that each inverter should follow to maintain the voltage profiles within specified limits. The set-points of the change in reactive and active power of the inverters are determined based on an optimization problem solved in a fully distributed way.

The observer agent (label 8) consists of a voltmeter connected to a D2D communication module through a Raspberry Pi (R.Pi) computer (label 10). The voltmeter periodically measures the voltage of its bus, and the R.Pi fetches the latest reading. The R.Pi of each voltmeter hosts a software that was developed for interfacing with both the communication module and the voltmeter. The R.Pi calculates the control signals (further referred to as Lagrangian multipliers) based on the latest voltage measurement, according to a procedure described later. These control signals are broadcasted through the D2D modules. The actuators communicate with the observers in a P2P fashion to receive the control signals. The actuators then determine how to react based on these control signals and based on their impact on the observed voltages (the impact on the voltages is expressed by voltage sensitivities). They also take into account the cost of dispatching a change in active and reactive power.

The third type of agent, the monitoring agent (label 11), represents a data acquisition platform. This additional agent is not required for the operation of the P2P voltage control algorithm. The observers and actuators record several variables from the algorithm that they execute, together with timestamps. These recordings are cached locally. Periodically, the observers and actuators transfer the cached recordings to the monitoring agent in a robust way. Therefore, even if the data acquisition network is temporarily offline, no data will be lost. The monitoring agent hosts a web service, through which all recorded data is visualized in several dashboards.

The overall schematic of the testbed is depicted in

Figure 2. The microgrid is connected to the main grid through 400 V (line-to-line voltage (L-L)), 64 Amps (A) busbar.

## 3. Dual-Decomposition-Based P2P Voltage Control Algorithm

The proposed P2P voltage control algorithm regulates the voltage within allowed limits based on an optimization problem. The algorithm uses a minimum change in reactive and active power consumption or injection of some participating inverters installed in the microgrid to control the voltage. The derivation of the algorithm is presented in [

14] and here we present the algorithm in a more practical way.

Without compensation, each inverter injects a certain amount of active power into the system. In reality, this active power originates from the solar energy received by the photovoltaic cell. The inverter can additionally inject reactive power, as long as the total apparent power does not exceed the inverter rating. The inverter has an additional degree of freedom; it can curtail a fixed percentage of the active power. Therefore, the actuator agent can take two actions: reducing the active power (by an amount $\Delta P$) and injecting or absorbing reactive power (by an amount $\Delta Q$).

Each actuator agent solves the following optimization problem to find

$\Delta {P}_{d}$ and

$\Delta {Q}_{d}$ :

where

$d\in \mathcal{D}$ is the number of the actuator agent (

$\mathcal{D}$ is the set of actuators participating in the voltage control).

$i\in \mathcal{N}$ is the number of the observer agent (

$\mathcal{N}$ is the set of observers participating in the voltage control).

${c}^{\mathrm{P}}{(\Delta {P}_{d}^{\left(t\right)})}^{2}$ represents the quadratic cost of a change in active power of inverter

d with an amount

$\Delta {P}_{d}$ at time step

t, while

${c}^{\mathrm{Q}}{(\Delta {Q}_{d}^{\left(t\right)})}^{2}$ represents the quadratic cost of a change in reactive power of inverter

d with an amount

$\Delta {Q}_{d}$ at time step

t.

${c}^{\mathrm{P}}$ and

${c}^{\mathrm{Q}}$ are constant factors used to penalize the control variables

$\Delta {P}_{d}$ and

$\Delta {Q}_{d}$. These factors define the priorities for the control actions. It is supposed that reactive power control of the inverter is cheaper than cutting its active power. Therefore,

${c}^{\mathrm{P}}$ should be greater than

${c}^{\mathrm{Q}}$ in a sense that gives priority of the control action to the reactive power. When the reactive power of the inverter is not sufficient, active power curtailment of the inverter will be used to regulate the system voltages. In our control system, we set

${c}^{\mathrm{P}}=200$ and

${c}^{\mathrm{Q}}=1$. Active power curtailment can be penalized more to minimize its use, but having higher

${c}^{\mathrm{P}}$ would decrease the speed of convergence when the curtailment is used to return the voltages back to the limits. It is worth mentioning that the factor

${c}^{\mathrm{Q}}$ can be calculated to incorporate losses on the network (related to reactive power compensation) and other costs. In reality, reactive power provision can lead to some additional losses in the network. An approximate cost factor can include the additional losses in the inverter [

28]. Incorporating the grid losses however would require a more complete network model.

${v}_{d,i}^{\mathrm{P}}$ and ${v}_{d,i}^{\mathrm{Q}}$ are the sensitivity of the voltage at bus i (observer i) to the change in the active power and reactive power (respectively) of inverter d. ${c}_{r}$ is the curtailment factor. In this paper, ${c}_{r}$ is set to $30\%$. In reality, ${c}_{r}$ can be set based on how much the prosumer would like to curtail the active power. ${\left({P}_{d}^{\mathrm{profile}}\right)}^{\left(t\right)}$ is the active power generated by inverter d at time step t. ${S}_{d}$ is the rated apparent power of inverter d.

${\left({\lambda}_{i}^{\mathrm{max}}\right)}^{(t-1)}$ and

${\left({\lambda}_{i}^{\mathrm{min}}\right)}^{(t-1)}$ are the control signals of violating the maximum and minimum (respectively) allowed voltage at bus

i. They are calculated at the previous time step

$t-1$ and considered in the optimization of time step

t. Mathematically speaking, they represent the Lagrangian multipliers. Each observer measures the voltage at its bus and updates these control signals based on the following equations:

where

${\left({\lambda}_{i}^{\mathrm{max}}\right)}^{\left(t\right)}$ and

${\left({\lambda}_{i}^{\mathrm{min}}\right)}^{\left(t\right)}$ are the updated control signals calculated at time step

t and considered in the optimization of time step

$t+1$.

${\left({V}_{i}^{\mathrm{meas}}\right)}^{\left(t\right)}$ is the measured voltage at bus

i after applying the decisions

$\Delta {P}_{d}^{\left(t\right)}$ and

$\Delta {Q}_{d}^{\left(t\right)}$.

${V}^{\mathrm{max}}$ and

${V}^{\mathrm{min}}$ are the maximum and minimum allowed voltage, respectively. We set

${V}^{\mathrm{max}}=1.1$ p.u. (per unit) and

${V}^{\mathrm{min}}=0.9$ p.u. according to the European standard EN50160. The parameter

$\alpha $ is the step size of the dual decomposition method. Because of the Karush-Kuhn–Tucker conditions (KKT), the Lagrangian multipliers cannot be smaller than zero. This explains the use of maximum operator in (

2).

The control algorithm goes through the following steps:

Each observer agent measures the voltage. If the voltage exceeds the upper voltage limit, it will increase ${\lambda}_{i}^{\mathrm{max}}$. If the voltage is lower than the upper limit, it will decrease ${\lambda}_{i}^{\mathrm{max}}$, at most until it reaches zero. A similar procedure applies to ${\lambda}_{i}^{\mathrm{min}}$. The parameter $\alpha $ determines how large the updates to the control signals will be.

The actuator agents receive updates of ${\lambda}_{i}^{\mathrm{max}}$ and ${\lambda}_{i}^{\mathrm{min}}$ periodically. They will adjust their compensation to take the new values of the control signals into account.

The voltage changes due to the actions of the actuator agents. The observer agents update again their ${\lambda}_{i}^{\mathrm{max}}$ and ${\lambda}_{i}^{\mathrm{min}}$, and the whole process repeats. The communication from observer to actuator takes place through the D2D communication modules, while the feedback path goes through the electrical network.

From this explanation, it is clear that this process is based on feedback. As long as the voltage problem persists, the observer agents will increase the control signals to get more compensation from the actuator agents. The effect of $\alpha $ is similar to a gain in control theory. The trade-off in its selection is similar: a low value can lead to slow convergence, while a too large value can lead to instability.

## 6. Results of the Experiment

To test the performance of the P2P distributed voltage control system, one needs to create a voltage rise (or drop) problem and solve it in a P2P fashion. To create a voltage rise problem in a laboratory-based microgrid, a high-power injection from the inverters back to the grid can be used. Alternatively, the impedance of the feeder depicted in

Figure 2 can be oversized to create such a problem with low-power injection. In the following experiments, R1 and R2 are set to 8

$\mathsf{\Omega}$, L1 and L2 are set to 5 mH.

Figure 9 shows the generation profile applied at both inverters. The active power generation starts at zero, and increases to a maximum of 1200 W. At the higher generation, the voltage is expected to rise above the maximum voltage limit. To comply with the European standard EN 50160, the voltage limits

${V}^{\mathrm{max}}$ and

${V}^{\mathrm{min}}$ are enforced to be

$\pm 10\%$ of the nominal phase voltage.

Two experiments are carried out to compare the voltage profiles with and without voltage control. The comparison helps in quantifying the performance of the P2P voltage control.

#### 6.1. First Experiment: Without P2P Voltage Control

The generation profile described by

Figure 9 is applied at both inverters of the setup.

Figure 10 shows that this leads to voltages exceeding the upper limit of 1.1 p.u. at both the first and second node. The agents remained idle during this experiment.

#### 6.2. Second Experiment: With P2P Voltage Control

The inverters apply the same generation profile, but now the agents execute the distributed voltage control algorithm. This leads to the voltage profile shown by

Figure 11. When an increase in generation causes an over-voltage issue, the agents bring the voltages back to the defined limits (

$\pm 10\%$) within 3 min.

The actions of the observer and actuator agents are reflected in

Figure 12. The evolution of the control signals over time are presented in

Figure 12c,d. The control signals for under-voltages (

${\lambda}^{\mathrm{min}}$) are zero, because no under-voltages beyond the limits occur during this experiment. The control signals for over-voltages (

${\lambda}^{\mathrm{max}}$) however, increase sharply after an increase in the voltages above

${V}^{\mathrm{max}}$. One can notice that the control signals

${\lambda}^{\mathrm{max}}$ return back to zero when the voltages return back to normal values without compensation, due to a decrease in the generation profiles.

Figure 12a,b shows the actions taken by the actuator agents. As soon as an over-voltage occurs, nearly all reactive power is dispatched. This behaviour depends on the values of

$\alpha $,

${c}^{P}$ and

${c}^{Q}$. The step size

$\alpha $ controls mainly how fast the control signals will increase, and hence how fast compensation is dispatched. Since the cost of active power is set to be a lot higher than the cost of reactive power, the algorithm will dispatch first the available reactive power.

$\alpha $ is set high enough to get a fast response in the active power dispatch. However, this causes the dispatch of reactive power to be nearly instantaneous.

$\Delta P$ and

$\Delta Q$ return back to zero when the voltages return back to normal values without compensation.

When the measured voltage

${V}_{i}^{\mathrm{meas}}$ is less than

${V}^{\mathrm{max}}$,

${\lambda}_{i}^{\mathrm{max}}$ starts to decrease till it reaches zero. One can explain this based on Equation (

2). The Lagrangian multipliers drop back to zero because the underlying profile of the inverters change. The active power injection drops, and the voltage drops with it. The Lagrangian multipliers adapt to the new situation. When both

${\lambda}_{i}^{\mathrm{max}}$ and

${\lambda}_{i}^{\mathrm{min}}$ are zero at each observer, problem (

1) can be written as:

One can notice that the solution of the above optimization problem is: $\Delta {P}_{d}^{\left(t\right)}=0$ and $\Delta {Q}_{d}^{\left(t\right)}=0$. Hence, a stop mechanism can be designed to stop the solver of the optimization problem whenever the Lagrangian multipliers are zero at each observer. This should decrease the computational burden of the algorithm.

#### 6.3. Key Performance Indicators

There are three key performance indicators (KPIs) considered in this work: (1) Convergence time; (2) Voltage quality; and (3) Communication delays.

The first KPI, convergence time, is a measure for how long it takes the algorithm to solve the voltage problem. Voltage quality reflects how well the control algorithm can mitigate the voltage rise (or drop) problems. Finally, the communication delays depend on the communication infrastructure. Below follows an explanation of how each of these KPIs is quantified in practice.

#### 6.3.1. Convergence Time

The voltage control algorithm is online and adjusts itself continuously. When a change in the generation profile occurs, there are two possibilities: either there is a voltage problem or not. If there is no voltage problem, the control algorithm stays idle. However, if there is a voltage problem, then the agents start to undertake action. The observer agents change the control signals until the voltage problems are resolved. If they succeed, then the control signals converge to a stable value, and the voltages converge to a value within the limits. In this paper, we define the convergence time as the time it takes from a moment when the voltage exceeds the limits until the moment when the voltage is restored within the limits. As demonstrated in

Figure 11, it takes the algorithm around 3 min to regulate the voltages within the defined limits, which is an acceptable time for voltage problems.

It is worth mentioning that the intervention time of the interface protection relay of Triphase inverter is much less than the convergence time. The intervention time of the interface protection relay of Triphase inverter is less than 1 ms. The Triphase inverter is configured to trip at 280 V. This means that there is 27 V as voltage margin, since the algorithm starts regulating the voltage when the PCC voltage is higher than 253 V. Hence, the inverter in our setup is able to correct the voltages before reaching 280 V. If an inverter trips at 253 V (maximum voltage defined by the standard EN 50160), then ${V}^{\mathrm{max}}$ of the proposed algorithm should be set to a value lower than 253 V (i.e., 240 V), in a way to make sure that the convergence time is sufficient to correct the PCC voltages before reaching the maximum voltage at which the inverter trips.

#### 6.3.2. Voltage Quality

The voltage quality is quantified by the metric

$E\ge 0$ defined by Equation (

4). The metric

E integrates the over and under voltages as shown in

Figure 13. This means that both the duration of a voltage problem and its severity will increase the metric

E. A value of zero is the best possible value and indicates that there are no over or under voltage issues: the higher the

E, the worse the voltage problem.

Table 1 shows a comparison between the regulated and the unregulated voltage profiles based on the voltage quality metric.

E is the sum of the metrics

${E}_{0}$,

${E}_{1}$ and

${E}_{2}$ of the nodes 0, 1, and 2, respectively. The P2P voltage control reduced the metric

E from 58.724 to 2.633.

E of the regulated voltage profiles is slightly higher than zero, because it takes the algorithm some time until it has resolved the voltage issues.

#### 6.3.3. Communication Delays

For the observer agents, the delay is defined as the time between consecutive updates of their control signals, which they broadcast periodically to the actuator agents. For the actuator agents, the delay is defined as the time between consecutive updates of the set-points which are sent to the Triphase power hardware.

Figure 14 shows the delays between the iterations of the control algorithm, for each agent individually. The observer agents are implemented by dedicated single-board computers with few other processes running in the background. They manage to update the control signals every 1.5 s, with little deviation. The actuator agents however experience longer control delays, with large differences between both actuators. There are two main causes for these additional delays. Firstly, the actuator agents solve an optimization problem at each iteration. Secondly, the actuator agents are implemented by laptops. These laptops run additionally control software for the Triphase Rapid Prototyping Inverter System, which requires rather heavy processing. The laptop running actuator 2 is older, which shows in the performance. Adapting the implementation of the algorithm for the actuator agents can lower the delays. The lower limit for the delays is 1.5 s, which is the period with which the observer agents send updates of the control signal.

Overall, the delays are as expected. Only the delays for actuator 2 could be shorter to be in line with the other devices. Upgrading actuator 2 to hardware similar to actuator 1, should resolve these additional delays.

#### 6.4. Discussion

The proposed P2P voltage control system managed to increase the voltage quality of the voltage profiles. Some over-voltage issues remain, because the control algorithm needs around 3 min to bring back the voltages within the limits. However, it is in line with the European standard EN50160 as all 10 min mean rms values of the voltages are within the range $[{V}^{\mathrm{n}}-10\%,{V}^{\mathrm{n}}+10\%]$, where ${V}^{\mathrm{n}}=1$ p.u.

The key question motivating this research, was whether fully distributed voltage control systems are a technically effective alternative to centralized ones. The results discussed in this paper show that fully distributed P2P voltage control systems can indeed provide satisfactory regulation of the voltage in distribution networks.

Technically, the P2P approach has shown good characteristics to be considered by DSOs to deliver high quality power to customers. The proposed P2P system could help in delivering easier access to prosumers’ flexible supply and demand by making their active participation in the grid possible. This can be used to alleviate grid stress and defer or avoid grid upgrades, and consequently will help the DSOs to host more RESs.