A Multi-Agent Framework for Voltage Regulation Control in Distribution Systems

Sumith Madampath Sreechithra and Panida Jirutitijaroen, IEEE Senior Member Department of Electrical and Computer Engineering

National University of Singapore Singapore-119077

elesms@nus.edu.sg; elejp@nus.edu.sg

Abstract—As the penetration of distributed generation (DG) increases in distribution power systems, it causes voltage rises and voltage fluctuations in the systems. The DG units can be properly controlled to mitigate these power quality issues. There are several methods of controlling the DG units for achieving acceptable voltage profile. This paper investigates a decentralized control approach to handle voltage regulation problems in the distribution systems. The objective of this paper is to discuss the design of a multi-agent framework for a decentralized voltage control in the distribution systems. We discuss the selection, coordination and interaction of agents required to achieve the desired voltage profile.

Keywords—Distribution system voltage control, Multi-agent framework, Photovoltaic agents

I. INTRODUCTION Electric power grids around the world are in a state of

evolution with the use of communication technologies and information technologies for advanced monitoring, metering, and control [1]. This transformation is driven by the need for environmental compliance and energy conservation. This need arises from the efforts to find renewable energy alternatives against depleting fossil fuel, efficient transmission and distribution for serving the ever increasing energy demand, and safe and reliable operation for the ageing infrastructure. The changes are more prominent in the distribution power systems which experience increases in penetration of distributed generation, distributed storage and electrical vehicles every year [2-3].

The distributed generation (DG) resources such as solar photovoltaic (PV) and wind power plant, cause voltage rise in the system when the generation is high and system demand is low. The stochastic nature of these resources causes voltage fluctuations which is harmful for the safe of operation of end customers and utility equipments. Several studies have indicated that the power electronic interfaces in grid-connected DG systems can help them to provide ancillary services such as reactive power support, load leveling, and peak power sharing [4-6]. These power electronics converters can absorb or inject reactive power from or to the utility grid. By adjusting the reactive power injection capabilities, these converters can keep the bus voltages within the operating limits at their locations and the neighboring areas [5]. There are different approaches to control these devices for achieving voltage regulation in the

utility grid such as centralized, hierarchical, decentralized and completely local control strategies. In centralized control strategy, all the control decisions are taken at a centralized control station such as distribution substation and these decisions are sent to individual controlling devices. On the other hand, in hierarchical control, control decisions are made at several controllers arranged in hierarchical manner. The control decisions are taken at a controller and sent only to the next following controller in hierarchy. In decentralized control, decisions are made at several controllers or control groups and the centralized controller intervenes the decisions of the decentralized controller/ control group infrequently. In completely localized control, each control device works separately and without the intervention of any centralized controllers.

As the number of DG units connected to utility increases, it is difficult to control each of them individually from a substation control centre. Reference [6] presents a completely distributed voltage control strategy where every PV node will try to maintain its nodal voltage within the operational limits by injecting or absorbing the reactive power according to the local nodal voltage magnitude. However, they fail to explore the influence of reactive power injection at its node on the voltage profiles of its neighboring nodes. Reference [7] proposes a hierarchical, decentralized voltage control with a centralized coordinating controller. Reference [8] proposes a distribution system where each distributed generator (DG), capacitor, On Load Tap Changing Transformer (OLTC) has an inherent remote terminal unit (RTU) fitted on them so that they can communicate to each other. However, they still haven’t explored the voltage regulation capabilities of individual DGs. Reference [9] develops a novel decentralized voltage control for the secondary distribution systems connected with DGs. This paper describes the grouping of the DGs based on the relative influence that one exerts on the others in the network. Once the grouping is over, each group will perform the voltage control action in their respective boundaries independent of the other control groups. A multi-agent based, consensus algorithm is developed for the voltage regulation in reference [10]. This paper models each DG node as an individual agent and each agent possesses little knowledge about the neighboring agents. When some part of the network experience voltage violation, the DG agents coordinate with each other to collectively inject

This work is supported by Ministry of Education Academic Research Fund, Grant No. WBS R-263-000-691-112.

106978-1-4799-1075-5/13/$31.00 c©2013 IEEE

the required amount of reactive power demanded by the network.

Our literature survey indicates that there is a growing trend of employing decentralized voltage control approach based on the multi-agent framework. However, these papers do not provide clear guidelines on the design and implementation of the multi-agent used in their respective problems. The focus of this paper is to discuss the design of a multi-agent system for voltage regulation control in the distribution systems with high penetration of PV. A three-level, hierarchical voltage control framework are proposed in this work to represent control actions of the existing voltage control devices in the system such as tap changing transformers, voltage regulators and switching capacitors.

The reminder of this paper is organized as follows. Section II presents an overview of the multi-agent architecture. Section III briefly illustrates the voltage control algorithm employed and section IV gives an illustration of the multi-agent framework in a distribution test system. Conclusion and future works are presented in section V.

II. MULTI-AGENT ARCHITECTURE This paper considers the distribution systems with high

penetration of PV resources and all the analysis are conducted on the basis of control aspects of PV generators. However, one can extend the analysis by including other DG’s such as wind, micro generators etc. and distributed storage resources such as batteries and electric vehicles and incorporating the respective control strategies associated with them.

The PV generation is stochastic in nature and requires a proper control strategy to reduce its impacts on the utility grid. Fig. 1 illustrates three different control strategies that could be employed in typical distribution systems. The centralized control strategy which is utilized in most traditional power system control is shown in Fig. 1a. This form of control gives the best overall system performance; but as the penetration of PV increases, it will be increasingly difficult to manage the communication between numerous PV generators and the central controller. A hierarchical control topology is shown in Fig. 1b where several PV generators communicate with others to form a group and each group communicates with a higher level controller located at a centralized position. Fig 1c shows a completely distributed control where each PV generator has a local controller and each controller operates independent of each other. Since the local controllers might not possess the knowledge of the overall system and the operation strategies of its neighbors, this type of control will result in non-optimal solutions for the overall system. Therefore, a hierarchical control strategy is proposed based on the following assumptions: 1) communication infrastructure in the distribution system is limited in bandwidth 2) each PV generator act as an individual agent 3) each agent has limited knowledge about other agents and the system topology 4) an agent can have its local interest in mind when it agrees to cooperate with other agents.

The PV agents in the distribution systems utilize the communication infrastructure to share information among themselves and several agents from independent groups. Each

of these independent agent groups can communicate with a higher level controller located at a feeder level or at a distribution substation level. The information flow in this control hierarchy is depicted in Fig. 2. Any command from the central controller or the feeder level controller is communicated to some of the PV agents. Once the command is received by PV agents, they start communicating with the neighboring PV agents to form an autonomous group. Within each group, the participating agents reach consensus on individual resource allocation (i.e., active power or reactive power) and adjust the power electronic controller to modify their output according to the new set point. This type of hierarchical control has minimum communication requirements compared to the fully centralized control strategy where each agent communicates with the central controller. The following subsections illustrate the guidelines for grouping the PV agents, locating the optimum position for higher level controller (leader) and the requirements of local communication among the agents and between the agents and the leader.

Fig. 1. Control strategies in distribution system. a) Centralized control. b) Distributed control. c) Decentralized control

Fig. 2. Control hierarchy in the proposed multi agent system

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A. Grouping of PV Agents The voltage- VAR relations have a noticeable local

property so that the voltage at a specific bus is more controlled by the reactive power injection from the neighboring nodes than the reactive power injection from the farther nodes. In normal operating conditions, the control effects of the distant reactive power injections on a local bus voltage can be neglected [11]. This localized property of voltage- VAR control capability is used to partition a large network into smaller subsystems. The agents in each group will try to communicate with other agents in the same group only. The concept of electrical distance can be employed for partitioning the network. Electrical distance is used as a measure of physical dependency between two nodes in the same network [12].

A standard assumption used in transmission system analysis is that the active power injections primarily affect voltage angles and the reactive power injections directly affect the bus voltage magnitudes. However, in a typical distribution power system with high ratio (line resistance to line reactance ratio), the nodal voltage magnitude is sensitive to both active power injections and reactive power injections. However, reference [11] reports that the variation of nodal voltage magnitude, , with respect to small variations in active power, , is around 3% when the system operates around standard operating conditions and hence one can neglect this factor without compromising the accuracy of calculation. A small change in reactive power injection, , is related to as in (1).

(1)

In this paper, all PV nodes are considered as controllable, negative load and hence all the nodes are of PQ type. Rearranging equation (1), the small change in voltage magnitude can be expressed in (2).

(2)

If the nodes in the system are indexed as , and a small variation of voltage magnitude and reactive power injection at any bus is represented by and respectively, the voltage dependency of the bus, , on the other bus, , could be expressed as in (3) and the voltage dependency of the bus, , on the other bus, , could be expressed as in (4).

(3)

(4)

where and are the voltage dependency factor of bus on bus and vice versa and it can be seen that . The electrical distance between any two individual buses in a network must be the same and equation (5) represents the function which maps the voltage sensitivities to electrical distance.

(5)

The logarithm function helps to normalize the electrical distance between any two buses in the system within (0,1). The electrical distance of any bus from itself is 0 and the electrical distance matrix has all the diagonal elements equal to 0.

Once the electrical distance matrix is determined, the network can be grouped into autonomous clusters based on the electrical distance radius, . It can be observed that as the radius increases from the minimum electrical distance observed in the matrix to the maximum electrical distance

, the number of control areas will be reduced from n, (equivalent to completely distributed control wherein each bus represent one group) to 1 (equivalent to completely centralized control wherein the network is undivided). The right choice of radius can be chosen according to the number of control areas needed or the physical distance that the communication between controllers are allowed. The following subsections discuss the guidelines for choosing a leader node in each cluster and the algorithm used for clustering and choosing the leader in each cluster.

B. Leader Node Selection A leader node is chosen in each cluster such that the local

voltage magnitude at its node represents the overall voltage profile of the cluster. In this analysis, the leader node in each cluster is selected as the node that gives the minimum total electrical distance from itself to the others in the same cluster. The leader node is the one which satisfies equation (6).

(6)

where is the set of all nodes in the given cluster.

During normal operating conditions, the controller connected to leader node will monitor the voltage of the leader node terminal and if any voltage violation is found it will ask for reactive power from the DGs connected in the cluster. In practical cases, one has to ensure that the cluster has enough reactive power support capability to maintain its leader node’s voltage profile within the operational limits. If any of the clusters has insignificant reactive power capacity connected within it, it is recommended to redraw its boundaries. The case studies presented in this paper assume that the cluster has sufficient reactive power support.

C. Clustering Algorithm The nodes in the distribution system can be aggregated to

different clusters based on the electrical distance. The K-mean clustering algorithm [13] is used to accomplish this task.

Assume that the system is to be partitioned into clusters. Then, the network with nodes can be clustered into groups using following steps:

1) Prepare initial clusters by arbitrarily assigning the nodes into each cluster. Calculate initial cluster means, , where corresponds to cluster ,

. 2) Obtain the electrical distance from each data point

to the th cluster mean . 3) Assign each data point to the nearest cluster with the

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minimum distance for recalculate the cluster mean by (7).

(7)

where is the number of data points in the th cluster. 4) Repeat steps 2 and 3 until each and every remains

unchanged between two iterations.

D. Requirement of Local Communication The communication system bandwidth in the distribution

system is assumed to be limited and thus the PV agents can communicate only with its peers assigned in the same cluster and its cluster leader agent. This information sharing may be intermittent, asynchronous and of varying topology. The instantaneous communication topology is described by a matrix as in (8) [14].

(8)

In this matrix, , an individual element can take a value of 1 or 0 depending on whether there is a connection existing or not. The first column represents the connectivity between the leader node with other PV agent nodes at any time instance, t. For other elements, represents the connectivity between th and th PV agents in the same cluster. If the output of th agent is known to th agent at time ,

, otherwise . Since an individual PV agent has the knowledge about its own output, it must be used in all the calculations made at that agent. This essentially means that each of the element, equals to 1. If all the elements in the matrix are 1, it represents the centralized control strategy.

The consensus based cooperation theory explained in [14] states that the minimum requirement for ensuring convergence of a consensus based coordination is that the communication topology matrix must be sequentially complete. This means that, if directed graphs are drawn among the connected nodes, there must be a traceable path from a leader node to any other nodes in the network. Fig. 3 illustrates the concept of sequential completeness in a 5-node network. In Fig. 3a, every node can be traced from the leader node 0, but in Fig. 3b, node-2 is not traceable from the leader node 0.

In each cluster, the agents cooperate with each other to supply the reactive power demanded by the cluster leader based on a fair utilization profile. The global information recovery assumes the form (9).

(9)

where is the information discovered by agent at time , is the information possessed by any agent at time t, which communicates with agent and is the weight of individual information exchanged between agent and agent at time t. In this analysis, we use equal neighbour weight rule i.e. each agent assigns equal weight to its own information and the information received from the other agents at time t .Thus the weighting factor is determined from communication topology matrix as given in equation (10).

(10)

Based on the convergence analysis in [14], all will converge to (11), as long as the communication is piecewise, sequentially complete.

, for (11)

If represents the instantaneous reactive power contribution, represents the instantaneous maximum reactive power capacity of th PV agent in a cluster, and

represents the total reactive power demanded from that cluster, the fair utilization profile for agents results in (12) and (13).

(12)

(13) The next section illustrates the voltage control model based

on this multi-agent framework in a distribution test system.

III. VOLTAGE CONTROL MODEL The decentralized voltage control scheme employed in this

analysis has three level hierarchies: a higher level control by leader node, a middle level control by PV agent clusters and a lower level control by individual PV agents.

In the normal operating conditions, if the higher level controller detects any voltage violation (i.e. the nodal voltage is either above the maximum operating voltage limit or below the minimum operating voltage limit) at leader node, it will estimate the reactive power required to clear the voltage violation. If the leader node has a local PV agent connected to it, the controller will check if this PV agent has the capability to inject (or absorb) the estimated reactive power. Otherwise, if the leader node has no PV agent connected to it or the PV agent connected to the leader node cannot inject (or absorb) the estimated reactive power, it will initiate the middle level control through agent coordination. The leader node will send the PV agent coordination request to one more PV agents along with the estimated reactive power demand based on the available communication channels between the leader node and PV agents. If any of the contacted PV agents has the enough reactive power capacity as demanded from leader node, it will adjust its power injections accordingly. Otherwise, the contacted PV agent (agents) will try to establish connections with other peer PV agents in its own

Fig. 3. a. (left) Sequentially complete network; b. (right) Sequentiallyincomplete network

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cluster and initiate an information exchange according to (9). During each discrete time slot, each of the PV agents will transfer three pieces of information with its neighbor agent such as local reactive power demand from the leader node, its minimum reactive power capacity and its maximum reactive power capacity. Once the coordination process converges, each of the agents will decide their reactive power contribution according to formulations (9)-(13). The lower level controller located at each PV agent will try to modify the power injections accordingly.

IV. CASE STUDY The test system in this case study is adapted from the IEEE

13 bus distribution test system. The original IEEE 13 bus system is modified as a balanced, single phase system with significant PV penetration. The system topology with the PV generator is shown in Fig. 4. The test system line data and load data are taken from the IEEE 13 bus distribution test feeder data [15]. All the three phase and two phase loads are converted into single phase equivalent load. Similarly, all the line segments are assumed to be single phase. DG penetration is assumed to be 30% and all the DG’s have equal capacity. All the PV units can operate up to 0.8 power factor (lagging or leading) and their kVA capacity is chosen accordingly. The essential system data is given in Table I.

The multi-agent grouping and leader node selection process is illustrated based on this 13 bus system. Load flow program is run at normal operating conditions and the electrical distances are estimated between the nodes. Table II indicates the electrical distance of node 13 from other nodes in the network. It shows that node 12 is the electrically closest node (Note that electrical distance of a node from itself is 0 and we do not consider this case) and node 4 is the electrically farther most node from node 13. This result can be easily verified from the system topology as well.

The number of clusters is to be provided before partitioning the network based upon the electrical distance for grouping the PV agents. Based on the required number of clusters, the network partitioning is done and in each cluster the leader node is decided. Table III tabulates the agent grouping results for different number of clusters required. Fig. 5 shows the network partition and the leader node location when the system is clustered into 2 subsystems. When the number of cluster is 1, the system control is centralized and the centralized controller

located at node 2. As the number of clusters increases, the network is controlled in decentralized manner and when the number of clusters equal to the number of nodes in the system, the control strategy becomes distributed. Under this distributed control, each node has its own controller located at their location.

Next, we illustrate the implementation of the voltage control algorithm based on the multi-agent framework developed. In this example, the network is partitioned into 2 clusters. Fig. 6 shows the evolution of voltage at the leader node 08 at some arbitrary time instances (for convenience, the time instances are labeled from 1 to 10). The maximum and minimum limits of nodal voltage are fixed at 1.04 pu. and 0.96 pu. respectively. At time instance 3, the leader node detects a voltage violation at its local node and it estimates the reactive power required to clear the violation to be 0.012 pu. Since

Fig. 4. 13 bus system topology

Table I 13 BUS SYSTEM DATA

System voltage

(kV)

Connected load PV penetration

(%)

Individual DG rating

(kVA) P (kW)

Q (kVAR)

4.16 1288 545 30 100

Table II ELECTRICAL DISTANCE OF NODE 13 FROM OTHER NODES

Node Electrical distance Node Electrical

distance 2 0.4357 8 0.2106 3 0.6296 9 0.2688 4 0.7144 10 0.4088 5 0.5790 11 0.2372 6 0.6863 12 0.0664 7 0.1433 13 0

Table III NETWORK PARTITIONING AND LEADER NODE SELECTION FOR 13 BUS SYSTEM

Number of cluster Cluster group Leader node Nodes included

1 2 All nodes

2 2 2,3,4,5,6 8 7,8,9,10,11,12,13

3 3 2,3,4 6 5,6 7 7,8,9,10,11,12

Fig. 5. Illustration of 13 bus system partitioned into two clusters. Dotted line represents the coverage of respective cluster and the stripped node representsthe leader node for the respective cluster.

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there is no PV unit connected at leader node 8, the leader node reach out to agents connected at node 9, 11, 12 for the reactive power support based on the communication channels available at that time instance. These PV agents will start sharing information such as local reactive power demand estimate and its maximum and minimum reactive power capacity with the peer agents. In each iteration, individual PV agents will estimate the utilization ratio similar to (12)-(13) and finally converge to a common value. Fig. 7 represents this convergence process occurring at the coordination process at time instance 3 and it can be seen that the utilization ratio converges to 0.67. The individual reactive power contribution is calculated as the individual maximum reactive power capacity times the utilization ratio. The power electronics controllers at the individual PV units will make the changes in power injections according to the new operating point. From Fig. 6 it can be seen that the voltage violation is cleared as the result of the reactive power adjustments.

V. CONCLUSION In this paper, we developed a multi-agent framework for

voltage regulation control in distribution systems. We discussed the relative merits of different voltage control schemes such as centralized control, hierarchical control, decentralized control and distributed control and choose a three

level, hierarchical control for our problem. This paper described the choice of agents, grouping of agents, choice of leader node in each agent group and the properties of local communication within each group. A 13 bus distribution system was used for illustrating the methodology. Finally we implement the voltage control algorithm on this multi-agent framework.

The main contribution of this work is that it demonstrates how the multi-agent framework can be applied to coordinate the control actions in the distribution networks. This multi-agent frame work is versatile and can be extended to other problems in the distribution power systems. Future work includes the decisions making process of each agent and how their decisions can be coordinated with other agents in lower hierarchy as well as with higher level voltage regulators such as tap changing transformers, voltage regulators.

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Fig. 6. Voltage profile at node: 08- Dotted curve indicates the voltage profilebefore reactive power coordination and the solid curve indicated the voltageprofile after reactive power coordination.

2 4 6 8 101 3 5 971.025

1.03

1.035

1.04

Time instances (discrete)

Vol

tage

(pu.

) : N

ode

08

Fig. 7. Convergence of reactive power utilization ratio estimated by PV agentsfor the coordination process initiated at time instance 3 in Fig. 6.

2 4 6 81 3 5 7 90

0.5

1

Iterations

Util

izat

ion

ratio

est

imat

e

DG 3DG 1DG 4

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