Goal-Based Holonic Multiagent System for Operation of ... - IEEE Xplore

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Goal-Based Holonic Multiagent System for Operation of Power Distribution Systems Anil Pahwa, Fellow, IEEE, Scott A. DeLoach, Member, IEEE, Bala Natarajan, Senior Member, IEEE, Sanjoy Das, Ahmad R. Malekpour, Student Member, IEEE, S M Shafiul Alam, Student Member, IEEE, and Denise M. Case, Member, IEEE

Abstract—Large-scale integration of rooftop solar power generation is transforming traditionally passive power distribution systems into active ones. High penetration of such devices creates new dynamics for which the current power distribution systems are inadequate. The changing paradigm of power distribution system requires it to be operated as cyber-physical system. A goal-based holonic multiagent system (HMAS) is presented in this paper to achieve this objective. This paper provides details on design of the HMAS for operation of power distribution systems. Various operating modes and associated goals are discussed. Finally, the role of HMAS is demonstrated for two applications in distribution systems. The first one is associated with control of reactive power at solar photovoltaic installations at individual homes for optimal operation of the system. The second deals with the state estimation of the system leveraging different measurements available from smart meters at homes. Index Terms—Cyber-physical system (CPS), multiagent system (MAS), optimization, power distribution system, smart grid, solar power, state estimation.

I. I NTRODUCTION DVANCES in computer and communication technology have been continuously integrated into power systems resulting in more robust and reliable systems. Although power distribution systems are a large part of power systems, integration of cyber systems into power distribution system operation and control have lagged behind those of generation and transmission systems. Progress on power distribution system automation has been relatively slow due to the investment needed to automate these systems with their potentially vast number of components. As a result, most of the operation and planning of power distribution systems have relied on heuristics and archived information. Now with emergence of smart grid [1], [2] new challenges and opportunities are appearing for operation and control of power distribution systems. Additionally, newer devices

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Manuscript received May 15, 2014; revised October 11, 2014; accepted December 28, 2014. This work was supported by the National Science Foundation under Grant CNS-1136040. Paper no. TSG-00452-2014. A. Pahwa, B. Natarajan, S. Das, A. R. Malekpour, and S M Shafiul Alam are with the Department of Electrical and Computer Engineering, Kansas State University, Manhattan, KS 66506 USA (e-mail: [email protected]). S. A. DeLoach and D. M. Case are with the Department of Computing and Information Science, Kansas State University, Manhattan, KS 66506 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSG.2015.2404334

such as electric vehicles and rooftop solar generation are gaining popularity. High penetration of such devices creates new dynamics for which the current power distribution systems are inadequate. For example, intermittent clouds can cause rapid fluctuations in solar power production [3], which in turn cause fluctuations in power flow from the grid and voltage fluctuations at customer-end [4]. With the large number of active devices in the system, power distribution systems become very complex, which requires them to be operated as a cyber-physical system (CPS) with seamless integration of cyber and physical aspects. A power distribution system is, by nature, highly distributed and hierarchical in structure. The requirement for reactive and proactive adaptivity across a highly distributed system naturally fits the realm of multiagent systems (MASs). The autonomous nature of agents [5] allows them to make decisions based on local knowledge and constraints thus allowing the system to adapt quickly and efficiently to its changing environment. The hierarchical nature of power distribution systems naturally suggests a multilayer hierarchy such as holonic MASs (HMASs). While MASs have had some prior attention in power systems, HMASs are just starting to be introduced to power distribution systems [6]–[10]. An HMAS is a type of MAS, where the system can be decomposed hierarchically into a system of nested agents called holons. Each holon may manage and represent an entire lower-level organization while acting as a participant in an organization higher up the control hierarchy. Holonic design enables the reuse of control logic at each level and provides a means for propagating multiple distributed local optimizations up the hierarchy (called a holarchy in an HMAS) to support increasingly centralized control objectives. There are many issues that need to be explored to operate power distribution systems as CPSs. A summary of these research questions is given below. 1) Goal-Based, Holonic Architecture: How can we define goals at each level of the architecture that are consistent between levels? How can we design organizations to support proactive and reactive adaptive functionality while incorporating security? How can we learn and use various profiles and factors to predict behavior? How should we define protocols for negotiations and information sharing? 2) Information-Enabled Modeling: How much information is required for system state estimation and what is the

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cost of that information? How can the communication network adapt to provide required information for estimation, inferencing, and control? How is control optimality affected by local actions? How much information uncertainty (delay, errors) can be tolerated before the system becomes unstable? This paper provides details on design of the HMAS for operation of power distribution systems. Various operating modes and associated goals are discussed. Finally, the role of HMAS is demonstrated for two applications in distribution systems. The first one is associated with control of reactive power at solar photovoltaic (PV) installations at individual homes for optimal operation of the system. The second deals with state estimation of the system leveraging different measurements available from smart meters at homes. II. M ODES OF O PERATION AND G OALS Although attempts to automate power distribution systems have been ongoing for many years, in most cases very little real-time information is available to operators from the system at this level. Therefore, most of the planning and operation is based on archived information available from load research. These statistical sample data provide information for operation and planning. Generally, the only real-time measurement available is from the feeder gateway at the substation. As a result of that, system settings are set based on operators’ experience and heuristics. Hence, most power distribution systems currently operate in a nonoptimum mode and have difficulties in recovering from abnormal events. With recent technological advancements and increased awareness of renewable energy by customers and society, the current level of automation is not sufficient. Thus, utilities are beginning to focus on advanced distribution automation within the smart grid paradigm to make power distribution systems more robust and resilient. In addition, customers are becoming more willing to participate in activities that result in energy conservation and generation of electricity from renewable resources. Power distribution systems of the future [16] will have homes with smart meters to monitor energy consumption, on-site grid-connected solar or wind generation, battery storage, and plug-in vehicles. The feeders will have advanced power electronic switching devices to control the system, sensors at strategic locations to measure flow of real and reactive power, voltage, and current. Similarly, the substation will have power electronic controls, measurements, and protection to operate the system more efficiently and reliably. The system will have a seamless communication layer from the utility’s control room to customers and it will be integrated with advanced cyber systems to enable its operation. Substantially, more real-time information will be available to facilitate their operation and control. We envision three time-based modes, each requiring finer levels of information granularity with finer levels tending to require more information with detailed calculations and faster decisions. Metrics identifying key features of these modes are shown in Table I.

TABLE I M ODES OF O PERATION AND A SSOCIATED M ETRICS

A. Normal Mode In this mode all the devices operate as expected and the goal is to optimize system performance to minimize losses, maximize reliability, and maximize benefits to the customers. Since the system does not see many changes under normal operation, information sampled over a longer time periods (e.g., 1–15 min) is sufficient to make control and operation decisions. An example of this mode is a sunny day with no fluctuations in output of solar panels. The goal in this mode is to optimize system performance, such as loss minimization. B. Minor Event Mode In this mode, either a small set of devices fail or some external conditions in the system change suddenly. For example, the movements of intermittent clouds can suddenly reduce power output from rooftop solar panels simultaneously, thus stressing the system as the power deficiency must come from the grid into the power distribution system. Control actions and adjustments to keep system within operating limits will require faster actions over intervals of 1 s to 1 min. The goals in this mode are to minimize fluctuations in voltage at customer-end and fluctuations in power flow from the grid. C. Major Event Mode In this mode, a large change in system conditions takes place, such as loss of grid connection due to equipment failure, natural disasters, or terrorist acts. Microgrid operating standards are evolving and in future a power distribution system would be able to operate as an islanded microgrid with its own resources. Specific guidelines currently do not exist on how to maintain the balance between load and generation, to manage frequency and voltage, or to keep the distributed generators synchronized. The fact that many distributed generators have no rotating components or inertia makes the job of meeting these requirements very complex. The devices and control processes must react over intervals of one cycle to 1 min. The goals in this mode are to provide electricity to customers for essential needs for as long as possible until the connection to the grid can be restored. III. A PPROACH Our approach uses holonic design principles to formulate the control problem and develop a computational architecture appropriate for intelligent power distribution systems using HMAS. HMAS control systems are being applied in areas

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Fig. 1. Representation of a power distribution system as a three-level holarchy.

such as manufacturing and transportation systems [11]–[13] and supply chain management [14], [15]. Power distribution systems and CPS in general, can use the holonic approach when the associated physical system can be recursively decomposed from the top-level (a super-holon reflecting the entire system) into set of sub-systems, eventually resulting in the lowest level sub-systems that consist of the low-level physical devices. In power distribution systems, the top level is typically a substation, while the lowest level devices and agents may represent the individual consumers or homes. Some homes may have grid-connected rooftop PV systems with smart inverters installed. It is assumed that in the event of disconnection from the grid, distribution of power from the PVs between the consumers is possible. An example of modeling a power distribution system in this way is shown in the three-level holarchy of Fig. 1. Each white (unshaded) oval encapsulates an organization, or group of agents working together, while the gray (shaded) ovals encapsulate a level in the system, i.e., the substation, feeder, and neighborhood levels. Each node labeled with a number represents an agent in that particular organization. Each agent at one level may actually be composed of several agents at the next lower level, which may again be composed of agents at next lower level. Atomic (nondecomposable) agents may exist at any level. Each organization at the same level is the same type of organization, and each organization is populated with different agents based on the physical configuration of the power distribution system. As organizations cooperate toward the achievement of their goals, these goals become the chief control and feedback mechanism within the system. For instance, assume

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that at the substation level, the system only has access to p MW of power. Thus, the substation organization would have the goal of sufficiently distributing p MW of power. Instead of dividing p evenly among the agents (the sub-systems) for distribution, the agents can negotiate amongst themselves to determine exactly how best to distribute the power based on the needs of the individual agents (sub-systems). Thus, each agent at substation level would be assigned the goal of efficiently distributing its negotiated amount pi of power such that p = pi . Subsequently, each organization represented by an agent at the substation level would attempt to achieve its assigned goal, pi , by decomposing it into individual goals that are assigned to agents in the organization. While similar to traditional hierarchical control systems where control passes from the top level to the lower levels, there are differences. A hierarchical organization of intelligent agents can be made to operate autonomously, but in holonic systems, each subsystem or holon is inherently endowed with the ability to operate independently as well as take input from above. The primary difference in employing a holonic approach is the benefit associated with reusing key design elements at every level of the hierarchy. Rather than designing multiple level-specific agents, we design a core control holon that can be reused from the highest substation level to the lowest levels of the power distribution system (in our case, a home). Each holon from the sub-organization represents its sub-organization at the higher level and takes part in the decision-making process at both levels. Each level consists of one or more analogous organizations of agents, cooperating to achieve their given objectives. If a connection is lost between levels, each holonic organization will continue to operate autonomously and pursue their local goals. For instance, if a neighborhood organization (e.g., agents 65–74) get disconnected from the feeder and the feeder-level organization (agents 63 and 64), the neighborhood can still function and attempt to distribute the power that may be available from local distributed sources such as rooftop PVs. Control information is captured in goals that flow from the top of the hierarchy to the lowest level agents, while information on the status of the system flows up from the lowest levels to the top level (see Fig. 1). The substation-level organization takes the overall system goal and decomposes it into a set of sub-goals that is distributed to each agent in the substation organization (consisting of agents 1–35). Agents that represent lower-level organizations (e.g., agent 32, which represents the feeder-level organization consisting of agents 39–42) passes that goal to its feeder-level organization, where the goal is further decomposed into goals for the individual agents (agents 39–42). This process is repeated until goals get assigned to the lowest level agents, which in this case are the agents representing individual homes at the neighborhood level (e.g., agents 58–62). Agents equipped with control devices may then execute control actions based on their goals. Conversely, information flows from the neighborhood level to the substation level, being aggregated at each level. This aggregate information is used at each level to provide local control. Within each organization regardless of the level, there is an organization level goal that is either provided by the



operators (at the substation level) or assigned by the organization’s parent organization (at the feeder and neighborhood levels). Each organization uses status information provided by its agents (potentially gathered by lower-level organizations) to determine how to decompose the organization level goal into individual goals for its agents. Thus, each level uses its status information in order to optimize its operation given the control information (goals) provided from the next higher level. This holonic agent-based architecture induced unique requirements on the agents in the system; agents that represent their organization at the next higher level must be able to participate in two organizations simultaneously. For example, in Fig. 1, agent 42 is an agent in a feeder-level organization while agent 58 is its associated agent in the neighborhood-level organization. In a holonic design, these two agents are actually combined into a single agent. Thus, an agent must be able to fully participate in multiple organizations. To provide implementation support for this requirement, we had to extend our existing agent architecture used in previous organizationbased MAS to support multigroup agents, i.e., agents capable of participating concurrently in more than one group or organization. Multigroup agents must manage potentially conflicting demands among multiple local groups while concurrently supporting the needs of the larger distribution system as a whole. Interested readers are referred to [17] for more information on our multigroup architecture. IV. H OLONIC O PTIMIZATION S CHEME A. Holonic Representation of Power Distribution System As shown in Fig. 1, power distribution system can be described as a three-level hierarchical ordered system where every level is a specific part of the power distribution system, i.e., substation, feeder, and neighborhood level. A modified version of the IEEE 37 node test feeder [18] is used to demonstrate the proposed holonic loss minimization approach. The substation level represents the original three-phase primary feeder and laterals branching out of the primary feeder distributing power in a district network. The feeder level embodies the single-phase laterals tapped off the primary feeder and passing through a community (e.g., nodes 39–42). The final power journey from substation to the homes is represented by neighborhood level, where short stubs or line-segments branch off a pole- or pad-mounted transformer distributing energy to a neighborhood consisting four homes (e.g., nodes 43–47). The conductors and overhead cables used to expand the system are described in detail elsewhere [4]. The system consists of 144, 144, and 160 homes in phases A, B, and C, respectively, with 50% rooftop PV penetration in each phase, which were selected randomly for each phase. For example, the neighborhood level PV-enabled homes are located at nodes 44, 46, 52, 55–57, 59–62, 66, and 71–73 in Fig. 1. Each home selected for PV was assumed to have an associated smart inverter that would allow setting the amount of reactive power at the inverter. The home agent responsible for reading the load and demand for the home is also assumed to have ability to execute a control action to set the reactive power setting at the inverter. The home agent determines the setting given the

Fig. 2.

Holonic power distribution system decomposed into three levels.

device capacity, the available margin given the local conditions at the home, and the request for reactive power provided to the home by the upper-level neighborhood agent. B. Implementing Holonic Optimization Fig. 2 shows the representation of power distribution system as decomposed into three levels. The holonic loss minimization is initiated at neighborhood level. From a substation/feeder holon perspective, the adjacent node at the feeder/neighborhood level is modeled as a pseudo production/consumption (prosumption). From a feeder/neighborhood holon perspective, the adjacent node at the substation/feeder level supplying the feeder/neighborhood level is modeled as an infeed bus. 1) Step 1—Initialization. a) Each feeder holon looks down and aggregates the neighborhood sub-holons prosumptions as Ux Ux Ux Ux PUx N , QN , and PGN , where PN , QN represent the pseudo active/reactive power demand, PGUx N is the pseudo generation connected to the adjacent node at the feeder level, and x denotes the ABC or either of A, B, or C phases. b) The substation holon looks down and aggregates Ux the feeder sub-holons prosumptions as PUx F , QF , Ux Ux Ux and PGF , where PF , QF represent the pseudo active/reactive power demand and PGUx F is the pseudo generation connected to the adjacent node at the substation level. 2) Step 2—Top-Down Optimization: Holarchy is Explored From Whole to Parts. Ux Ux a) Knowing the values of PUx F , QF , PGF , the substation holon runs a three-phase optimal power flow (OPF) and finds at each node: i) the optimal reactive power generation/absorption from pseudo Ux generators (QGUx F ); ii) voltages and angles VF , Ux θF ; and iii) real and reactive power injected to the infeed bus PxS , QxS in substation network. b) Substation holon passes down calculated target valUx Ux ues VFUx , θFUx , PUx F , QF , QGF to the feeder holons. Ux Ux Lx Lx Considering VF = V F , θF = θ F , feeder holons


run a single-phase OPF and find at each node: i) the optimal reactive power generation/absorption from pseudo generators (QGUx N ); ii) voltages and angles VNUx , θNUx ; and iii) real and reactive power injected Lx to the infeed bus PLx F , QF in feeder network. c) Feeder holons pass down calculated target values Ux Ux VNUx , θNUx , PUx N , QN , QGN to the neighborhood Ux Ux Lx holons. Considering VN = V N , θNLx = θ N , neighborhood holons run a single-phase OPF and find at each node: i) the optimal reactive power generation/absorption from rooftop PV generators (QGN ); ii) voltages and angles VN , θN ; and iii) real and Lx reactive power injected to the infeed bus PLx N , QN in neighborhood network. 3) Step 3—Bottom-Up Aggregation: Parts are Used to Aggregate Into Wholes. a) Each neighborhood holon passes up its aggregated Lx prosumption to the feeder holon i.e., PLx N , QN . Each feeder holon looks down and see if there is active/reactive power flow mismatch between the Ux Lx Ux pairs (PLx N , PN ), (QN , QN ). If so, it readjusts the Lx Lx Ux target values such that PN = PUx N , QN = QN . b) Each feeder holon passes up its aggregated proLx sumption to the feeder holon i.e., PLx F , QF . The substation holon looks down and see if there is active/reactive power flow mismatch between the Ux Lx Ux pairs (PLx F , PF ), (QF , QF ). If so, it readjusts the Lx Lx Ux target values such that PF = PUx F , QF = QF . Steps 2 and 3 are executed until the power and voltage mismatches at the adjacent nodes become lower than the specified threshold. C. Problem Formulation Mathematically, the loss minimization problem can be expressed as given below. Minimize f =

N N 1 abc Pij + Pabc ji 2 i

s.t.

g (x) = 0 h (x) ≤ 0

j, i=j

(1)

where f is the objective function (total power losses or equivalently the real power injected to the network from substation abc are three phase active and reactive transformer), Pabc i , Qi power injected at bus i and N is the number of buses. g(x) = 0 and h(x) ≤ 0 incorporate equality and inequality constraints. The aim is to determine the reactive power injection/absorption of inverter-based PV units (vector of decision variables x) while maintaining safe operation. g(x) = 0 represents the power balance in each phase while h(x) ≤ 0 denotes the maximum/minimum reactive power capability of renewables, voltages, and branch flows. So far, most optimization problems are solved under the assumption that power distribution system is a balanced three-phase system [19]–[23] by using a singlephase equivalent model. However, distribution lines are rarely transposed due to economical and practical purposes and massive integration of rooftop solar generators at home level will

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TABLE II R ESULTS F ROM THE C ENTRALIZED AND THE D ECENTRALIZED A PPROACHES

Fig. 3.

Total power losses.

add further imbalance to the power distribution system in terms of loading levels in each phase. Hence, in this paper, both three-phase and single phase OPF are formulated to minimize power losses in each level of the holonic architecture. There are major differences in optimization problem formulation at substation level and feeder/neighborhood levels. At the substation level, three-phase OPF determines the optimal reactive power injection of renewables by incorporating the full three-phase unbalanced line configurations and loading levels. The problem is solved subject to three-phase equality and inequality constraints and phase imbalance limits. At the feeder and neighborhood levels, single-phase OPF is used intending to minimize the power losses by finding the reactive power injection of renewables. Single-phase equality and inequality constraints are incorporated and there is no phase imbalance constraint considered. D. Results Table II gives the active/reactive power losses obtained from the proposed holonic approach as well as those obtained using a centralized approach. From the comparison, it can be observed that active/reactive power losses of the proposed approach are very close to those obtained from the centralized approach. Fig. 3 shows the total power loss reduction in phases A, B, and C, respectively, through the iterations. Fig. 4 shows the power mismatch in line connecting node 63 in the feeder holon and node 65 in the neighborhood holon. Power mismatch between the aggregated demand from the feeder holon and pseudo generation from the neighborhood holon converges to a unique value after four iterations. It can be seen that there is an increase in aggregated demand/pseudo generation as the mismatches are rebalanced up to higher levels through the iterative process. This leads to voltage reduction in node 63 (phase B) as shown in Fig. 5.



Fig. 4.

Power mismatch in lines 63–65.

Fig. 5.

Voltage at node 63.

Due to its complexity, the majority of execution time is spent on solving the substation level. The computational times are 93 s for the distributed approach and 225 s for the centralized approach, which shows significant reduction in computation with minor degradation in the results. The presented OPF for each holon is a nonconvex optimization problem. To ensure convergence, the problem is converted to convex form using Taylor series expansion described in detail in [24]. Under the assumption of convexity, convergence of the hierarchical optimization has been proven in [25] and [26]. The iteration is terminated when the power mismatches at the adjacent nodes are smaller than the user-defined termination tolerance ε. In this paper, ε is set to 0.001. Obviously, the number of iterations will increase with decrease in ε. V. H OLONIC F RAMEWORK FOR S TATE E STIMATION Static state estimation in power systems can be carried out either centrally or in distributed fashion. In the central approach, the real and reactive power measurements are collected from each end user and sent to the substation level fusion center for computing the voltage magnitude and angle estimates. These measurements can be efficiently aggregated using the compressed sensing approach, which exploits the correlated characteristics of renewable energy sources and loads, geographically distributed over the distribution network [27]. Once transmitted to the fusion center, the compressive measurements can be directly used for static state estimation [28]. This approach not only reduces the communication overhead but also allows efficient storage of the raw measurements obtained in real-time from an ever expanding network of power distribution.

Distributed state estimation relies on a set of dedicated sensors distributed over the network. In this architecture, each sensor node observes only a distinct portion of underlying physical system and makes a local estimate of overall system states by exchanging information with neighboring nodes. In this regard, the weighted least square (WLS) method is reported to be the most popular one for distributed state estimation in power transmission systems [29]. Other notifiable methods include factorized WLS [30], global consensus combined with local least squared innovation [31], and alternating direction method of multipliers [32], [33]. It should be noted that, so far the distributed approach of state estimation is reported specially for interconnected power transmission systems having over-determined local observation space as well as low degree of state overlaps among sub networks. On the other hand, distribution systems are typically of radial structure that causes poor convergence while applying transmission system state estimation methods. In the near future, massive deployment of smart energy meters is expected throughout the distribution network for better monitoring and control. The observation space of these communicable meters is nonlinear and underdetermined as manifested by the radial topology as well as the physics of electricity. Unlike interconnected power transmission systems, the distribution network also entails very high degree of state overlaps among smart meter observation spaces, thus making the distributed estimation problem quite challenging. The states of an electric power system are usually defined in terms of either system node voltage phasors or branch currents [34], [35]. These states form a system of nonlinear equations with the real and reactive power information available from smart energy meters. Furthermore, estimation of the states can be performed in static manner as long as the power measurements get updated at a higher rate than the underlying system dynamics. As seen in Fig. 1, the power distribution system can be modeled as a three level network of agents. The estimation of local state elements is simultaneously carried out by the home agents with reference information from the radial feeder node. At the next layer, the radial feeders have real and reactive power information aggregated from respective home agents. The aggregation also considers the active power loss incurred from home to radial feeder level. At the feeder level, states of feeder nodes are estimated by the corresponding agents through relevant neighborhood communication and with reference information from respective starting feeder node of each radial subsection. The same procedure is repeated at the substation level, where the feeder nodes estimate their states with reference information from substation. It should be noted that, the neighbors of an agent are defined based on existing physical connections. In this setup, an agentwise local consensus of static estimation can be performed, when: 1) each agent’s observation space is nonlinear and underdetermined and 2) each state element of the system is shared at least between two agents [36]. In the holonic multiagent framework, the effect of neighbors can be incorporated in local consensus with the help of


binary projection matrices. These matrices project the neighboring agents’ state vector with correct sign and orientation onto the local state vector to accomplish distributed local consensus. Let us consider a MAS consisting of N agents. Each agent’s set of measurements map to a distinct subset of global state information. Let us assume that the set of measurements available to the ith agent is stored in the mi -dimensional vector yi . Each entry of this vector nonlinearly relates to the corresponding subset of global states–denoted by the ni -dimensional vector xi . This nonlinear mapping between measurements and states can be described in a system of nonlinear equations. Thus, for the ith agent, we get the following noiseless measurement model: yi = hi (xi )

(2)

where hi represents a vector of nonlinear functions which map the ith agent’s state information to each of the measurement entry available to that agent. Mathematically, hi : Rni → Rmi . Furthermore, in the absence of a central fusion center and estimator, each agent is interested in only a limited portion of global awareness. Consequently, the observation space for each agent is at most fully determined (i.e., mi ≤ ni ). Since the agents are observing some portion of the overall system, they may share some of the state elements and are considered as neighbors to each other. Let, Si denote the set of physical neighbors of agent i. This is defined based on the overlap/sharing of state elements. Mathematically (3) Si = j : Pj,i xj projects onto Lj,i xi where Pj,i and Lj,i are ni × nj and ni × ni binary projection matrices, respectively. By default, Pi,i = Li,i = Ini . As an illustrative example, we consider a three-agent system having a set of global state elements {a, b, c, d, e}. The Venn diagram in Fig. 6 shows the agent-wise distribution of the state elements for this system. According to the mathematical model just described, the dimensions of the state vectors are n1 = 4, n2 = 3, and n3 = 1. The set of neighbors for agent 1 are S1 = {2, 3}; agent 2 are S2 = {1}, and for agent 3 are S3 = {1}. And the projection matrices for the agents are as follows: ⎡ ⎡ ⎤ ⎤ 0 0 0 0 0 0 0 ⎢1 0 0⎥ ⎢0 1 0 0⎥ ⎢ ⎥ ⎥ Agent 1: P21 = ⎢ ⎣ 0 1 0 ⎦, L21 = ⎣ 0 0 1 0 ⎦ 0 0 0 0 0 0 0 ⎡ ⎤ ⎡ ⎤ 0 0 0 0 0 ⎢0⎥ ⎢0 0 0 0⎥ ⎢ ⎥ ⎥ P31 = ⎢ ⎣ 0 ⎦, L31 = ⎣ 0 0 0 0 ⎦ 1 0 0 0 1 ⎤ ⎡ ⎡ ⎤ 0 1 0 0 1 0 0 Agent 2: P12 = ⎣ 0 0 1 0 ⎦, L12 = ⎣ 0 1 0 ⎦ 0 0 0 0 0 0 0 ⎡ ⎤ ⎡ ⎤ 0 0 0 0 P32 = ⎣ 0 ⎦, L32 = ⎣ 0 0 0 ⎦ 0 0 0 0

Agent 3: P13 = 0 0 0 1 , L13 = [1]

P23 = 0 0 0 , L23 = [0].

Fig. 6.

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Venn diagram for a three-agent system.

For each agent, the static state estimation is performed through a weighted combination of agent consensus and iterative Gauss–Newton algorithm. Using the projection matrices and measurement model, we can thus write the (k+1)th update for the ith agent in the following way: (k+1) (k) † y = x(k) + α (k)H (k) − H(k)x xi i i i i i (k) (k) Lj,i xi − Pj,i xj (4) − β(k) j∈S i

where αi (k), β(k) > 0 are the time varying coefficients, which represent relative weights to measurement update and agent consensus, respectively. Hi (k)† represents the pseudoinverse for a full row rank local Jacobian matrix. Mathematically, this can be expressed as −1 . (5) Hi (k)† = Hi (k)T Hi (k)Hi (k)T It can be observed from (4) that the system observability depends upon the measurements acquired by each agent. If the agents are allowed to share measurements among neighbors, each agent is expected to have accurate estimation with faster convergence. However, issues such as security and privacy have to be considered in defining the type of information the neighboring agents can share. Furthermore, the choice of values for αi (k) and β(k) is another important factor that determines the rate of convergence of the proposed method. Interested readers are referred to [36] for detailed convergence analysis in this regard. A. Case Study of 560 Node Distribution Network The proposed method of holonic multiagent state estimation is applied to the test distribution network discussed in Section IV. Initially, classical Newton–Raphson method is used to determine states at home and distribution transformer level. The consensus-based approach is used next for each of the feeder subsection as well as at the substation level. As an illustration, Table III shows the estimated voltage magnitudes and angles for eight homes under two feeder nodes 65 and 70. The home-level voltages are estimated with reference to known voltages at the respective upstream feeder nodes 65 and 70. The results are truncated to the fourth decimal place due to space restrictions. The average home-level estimation error for voltage magnitudes are calculated in terms of mean absolute error (MAE) N 1 xi − xi∗ × 100. (6) MAE = N xi i=1



TABLE III VOLTAGES E STIMATED AT H OMES U SING THE H OLONIC A PPROACH

in distribution system is under progress at present and the results will be presented in future publications. D ISCLAIMER The views expressed in this paper are those of the authors and have not been endossed by the funding agency. R EFERENCES

The average error in voltage angle estimation is represented using mean integrated absolute error (MIAE) [28] MIAE =

N 1 xi − xi∗ . N

(7)

i=1

For 444 homes, MAE is obtained to be 0.0380% and MIAE is 0.0003 radian. The results clearly show that the estimated home-level voltages are very close to those obtained through classical Newton–Raphson power flow method. In the next step, this information can be used to calculate the aggregated real and reactive powers injected at individual feeder nodes. With a reference voltage from the starting node of each feeder network, the feeder node voltages can then be adjusted from the previous values (used in home-level estimation). Using similar steps, we can aggregate real and reactive power injection from bottom to top levels and then estimate the voltages at individual nodes from top to bottom levels. It should be noted that the time taken to communicate load/generation information is much smaller than the 15-min resolution period commonly used for measuring customer demands. In addition to that, the effect of faulty communication is addressed in a recent paper and it is found that the consensus approach is more robust than the diffusion of neighborhood information under the influence of lossy network [37]. VI. C ONCLUSION Characteristics of distribution systems under different operating modes with high penetration of distributed PV generation are discussed. Design of an HMAS to operate the power distribution system as a CPS is presented in this paper. The holonic approach presented follows the natural physical structure of the distribution system, which makes it very attractive for their automation. Examples of system optimization with reactive power injection and state estimation in normal mode with HMAS are presented. The results illustrate that HMAS can be used successfully for these cases. It was assumed that the time taken to communicate information is much smaller than the 15-min resolution period for loss minimization and state estimation in the normal mode of operation used in this paper. In other modes of operation, where faster communication and computations will be required, these issues will become important and will be appropriately addressed. Research on application of HMAS to other operating modes

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Anil Pahwa (F’03) received the B.E. (Hons.) degree in electrical engineering from the Birla Institute of Technology and Science, Pilani, India; the M.S. degree in electrical engineering from the University of Maine, Orono, ME, USA; and the Ph.D. degree in electrical engineering from the Texas A&M University, College Station, TX, USA, in 1975, 1979, and 1983, respectively. Since 1983, he has been with Kansas State University, Manhattan, KS, USA, where he is currently a Professor and holds the Logan-Fetterhoof Chair of the Electrical and Computer Engineering Department. His current research interests include distribution automation and intelligent computational methods for distribution system applications.

Scott A. DeLoach (M’96) received the B.S. degree in computer engineering from Iowa State University, Ames, IA, USA, in 1982, and the M.S. and Ph.D. degrees in computer engineering from the Air Force Institute of Technology, Hobson Way, OH, USA, in 1987 and 1996, respectively. He joined the Department of Computing and Information Sciences, Kansas State University, Manhattan, KS, USA, after 20 years in the U.S. Air Force. His current research interests include distributed adaptive systems, where agents cooperate as a part of a team to achieve an overarching goal.

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Bala Natarajan (S’98–M’02–SM’08) received the B.E. degree from the Birla Institute of Technology and Science, Pilani, India, and the Ph.D. degree from Colorado State University, Fort Collins, CO, USA, in 1997 and 2002, respectively, both in electrical engineering. Since 2002, he has been a Faculty Member with the Department of Electrical and Computer Engineering, Kansas State University, Manhattan, KS, USA, where he is currently a Professor and the Director of the Wireless Communication and Information Processing Research Group. He was also involved in telecommunications research at Daimler Benz Research Center, Bangalore, India, in 1997. His current research interests include spread spectrum communications, multicarrier code division multiple access and orthogonal frequency division multiplexing, multiuser detection, cognitive radio networks, sensor signal processing, distributed detection, and estimation and antenna array processing. He published the Multi-carrier Technologies for Wireless Communications (Kluwer, 2002) and holds a patent on customized spreading sequence design algorithm for CDMA systems.

Sanjoy Das received the Ph.D. degree in electrical engineering from Louisiana State University, Baton Rouge, LA, USA, and the Post-Doctoral degree from the University of California–Berkeley, Berkeley, CA, USA, and the Smith-Kettlewell Institute, San Francisco, CA, in 1994 and 1997, respectively. Since 2001, he has been with the Electrical and Computer Engineering Department, Kansas State University, Manhattan, KS, USA, where he is currently an Associate Professor. His current research interests include multiagent systems, machine learning, computational game theory, quantum computing, bioinformatics, and applications to power systems and smart grids.

Ahmad R. Malekpour (S’06) received the B.S. and M.S. degrees in electrical engineering from Shiraz University, Shiraz, Iran, in 2003 and 2006, respectively. He is currently pursuing the Ph.D. degree from Kansas State University, Manhattan, KS, USA. From 2003 to 2009, he served as a Lecturer at several academic institutions in Fars, Iran. From 2009 to 2011, he was an Engineer at Fars Regional Electric Company, Shiraz, where he managed various distribution and transmission planning studies, as well as distributed generation interconnection and integration analysis. His current research interests include renewable energy, smart grids, and stochastic electric power system optimization. Mr. Malekpour is a Member of Eta Kappa Nu, Tau Beta Pi, and Sigma Xi.

S M Shafiul Alam (S’03) received the B.Sc. and M.Sc. degrees in electrical engineering from the Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh, in 2008 and 2011, respectively, where he is currently pursuing the Ph.D. degree in communication and signal processing theory applied to smart grid distribution and control. He has three years of undergraduate teaching experience at BUET. His current research interests include compressed sensing, statistical signal processing, and smart grid. Mr. Alam is a Member of Eta Kappa Nu.

Denise M. Case (M’10) received the B.S. (Hons.) degree in chemical engineering from the University of Missouri, Columbia, MO, USA, and the Master’s degree in software engineering from Kansas State University, Manhattan, KS, USA, in 1985 and 2013, respectively. She has been a Consulting Engineer for 20 years, focusing on information management and analytics in critical infrastructure industries. Her current research interests include distributed artificial intelligence, smart infrastructure, and adaptive systems. Ms. Case is a Licensed Professional Engineer in the State of Kansas, and a Member of the Association for Computing Machinery, Alpha Chi Sigma, Omicron Delta Kappa, and Tau Beta Pi.