Background

A smart grid can be considered as an advanced and radically evolved version of traditional power systems. The term ‘smart’ in the smart grid exemplifies the use of advanced technology such as bi-directional communication, artificial intelligence (Tokody et al. 2018), Complex systems theory (Iantovics et al. 2018), modeling and simulation, and more, all employed with the goal of converting the legacy power grid into an advanced proactive and reactive system. At the lowest level, the Smart grid can be considered as an integrated system made up of a variety of interacting components—ranging from smart appliances and smart storages to smart generators, Internet of Things (IoT) (Fortino et al. 2017), and beyond. Another key focus area of the Smart grid is in the integration of renewable energy resources, such as, but not limited to, wind turbines and solar panels (Wong and Pinard 2017). By integrating advanced communication and information systems, Smart grid components can communicate and coordinate with each other with the goal of constructing a sustainable and efficient energy production system (Gungor et al. 2011) for the future.

An increase in the size of smart grid has unexpected consequences. This increase is coupled with a corresponding increase in its intrinsic complexity (Cintuglu et al. 2017). Firstly, it is important to understand that smart grid implies complexity (Monti and Ponci 2010). To understand this complexity, consider the fact that, in any modern large-scale power system, each component is often times, dynamic in nature. As such, the states of the system also vary temporally. The reason for that is that the states are not only a function of, but also, are the result of emergent properties of the same numerous interacting components. Thus the result of what we see at the macro-level cannot thus be easily discernible as a direct function of the micro-level components. This behavior can thus be considered as the outcome of numerous interactive events occurring in relation to each component—quite similar to a natural complex adaptive systems (CAS) (Iantovics 2013; Amin and Wollenberg 2005).

With so much complexity at hand, it is clear that modeling the smart grid certainly needs considerable number of practical examples and case studies (Pagani and Aiello 2014). It is also evident that developing various types of formalisms for the domain is needed. This will allow for the selection of better and more elegant solution to models—which in turn can be used to develop a better understanding of the complex domain. Essentially, modeling any system can be considered as an activity which allows for a better understanding of the system. In the smart grid domain, better modeling approaches can not only simplify system complexity but also allow for a better understanding and implementation of the system. Besides, it can also allow for ensuring a reduction in system failures.

Formal methods provide facilities for the modeling of each component of any complex system (Hall 1990). It allows for developing models for each component of the system allowing for a clear focus on understanding consistency as well as semantic correctness. The behavior of each system can be analyzed and observed with the help of these formal models. A key benefit to this approach is that it helps in the detection of faults and flaws in the design phase of system development, thereby considerably improving system reliability.

In previous studies, formal specification framework has been successfully applied for the mathematical modeling of different CAS ranging across various domains. Some key examples of such work includes a formal specification used for the modeling of AIDS spread using agent-based modeling (Siddiqa and Niazi 2013). Likewise, it has been developed for modeling the progression of researchers in their domain (Hussain and Niazi 2014), and for the modeling of wireless sensor networks (Niazi and Hussain 2011a). The use of formal specification models for modeling CAS also include studies such as (Zafar and Afzaal 2017; Afzaal and Zafar 2016). Suggestions to use formal specification for the Smart grid have also previously been mentioned in literature (Hackenberg et al. 2012). Another example is the use of state machine formalism (Turner 2014). However, to the best of our knowledge, the same approach has not been applied much in the domain of the smart grid domain. It is thus clear that there is a growing need to model the key components in a smart grid by means of an elegant formal framework among other tools such as noted previously (Rohjans et al. 2014). Such a prudent approach allows for a better understanding of the domain besides allowing for systems to be verified using the given specification.

In this paper, we present first steps towards a basic formal specification modeling framework for smart grid components. We first consider different types of entities and then elaborate their detailed formal specifications.

The rest of the paper is structured as follows: first, basic concept of a formal framework and a smart grid scenario is discussed. This is followed by formal specification of different entities of smart grid system. The paper ends with a conclusion section.

Theoretical foundation

In this section, we present the theoretical foundations needed for understand the presented formal specification model.

Formal frameworks

A formal specification is a software engineering approach that is used for mathematical modeling of different components of a system (Hall 1990). During engineering of any system, it is important to ensure that all the system components are integrated and working correctly without any error. A formal specification provides this facility to accurately specify each requirement of the system before going to the real implementation (Woodcock and Davies 1996).

A formal specification decomposes the large system into the subsystem. Then provides a specification for each individual subsystems. It follows two approaches; one is the algebraic approach in which each operation and relationships can be described, second is a model-based approach which concerns with the state and transitions of each individual components. The model-based approach uses the Z language specification which involves the utilization of mathematical notations, sets, sequences, and states (Bowen 1996).

Scenario of the smart grid

We can think of a smart grid as a complex system in which different consumers and generation units are connected through power communication lines (Milanovic and Zhu 2017). Generation units generate power and transmit toward consumer’s side. Consumers demand energy according to their usage profile and generation units response according to the consumer’s demand (Yang et al. 2017).

On the consumer’s side, the process of monitoring and controlling consumer’s demand energy usage profile is called home energy management (HEM) (Hosseini et al. 2017). This process involves the use of smart meters, smart appliances, information and communication technology etc. the smart meters collect data about consumer’s demand at the different time period and transmit this collected data to the power generation unit. On the power generation unit side, this data is analyzed and response according to the consumer’s demand. Sometimes, consumer’s demands exceed from available energy power at the grid side. This creates unbalance situation of the power system. To handle this issue, the concept of demand response management (DRM) (Soares et al. 2017) has been introduced.

DRM is the process of adjusting consumer’s demand in response to the price of energy and incentives from grid side. The generation unit sends their energy cost pattern of different time periods. The time in which power cost is high is called high peak hour and the time in which power cost is low is called off peak hour. So during high peak hour, consumers can keep their flexible appliances off and run at low peak hour.

To reduce burden on generation unit, the concept of renewable energy sources (RES) is also introduced in a smart grid application (Park et al. 2017). RES can be in the form of photo-voltaic (PV) or wind energy sources. These energy sources can be installed and provide energy to the consumer’s side. Consumers can use this energy at an off-peak hour, so this solves the energy unbalance as well as high-cost issues. The energy collected from RES can be stored using storage devices. Sometimes, if the available energy is larger than consumer’s demands, then it can be sold back to the grid unit by using some buyback mechanism (Chiu et al. 2017). However, RES has unpredictable nature and depends on weather and time. PV energy can only be produced during the daytime i.e. at sunny day. Wind energy can only be produced in windy environments.

Regarding RES, a new concept has also been included in a smart grid called electric vehicles (EVs) (Ahmadian et al. 2017). These EVs are using energy storage devices which can be charged either using PV or electric station. The stored energy is then used for drive vehicles. In case if the energy demands of consumers exceed at grid unit. These EVs can also provide energy to the grid unit by using the vehicle to grid (V2G) mechanism.

Formal specification framework

In this section, we present formal specification models for the smart grid components. In our study, we consider four different entities in a smart grid system. These entities are: appliance, solar, turbine, and storage devices. Each entity has different states as well as associated events that cause state transitions. In Table 1, summary of each object, states and events are given.

Table 1 Smart grid components, their states and events
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Smart appliance

An appliance object has three distinct states along with events associated with states. As we can see in Fig. 1, Whenever an unplugged event occurs, the appliance enters in the disconnected state. By plugged-in event, the appliance enters in the connected state. And whenever an in-use event occurs, the appliance remains in the running state.

Fig. 1
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Statechart depicting the life of an appliance

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Next, we present formal specification for an appliance object.

A free type “APPLIANCESTATE” is used to represent different states of an appliance that are disconnected, connected and running.

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Next, we define an appliance schema that contains “appState” variable of type “APPLIANCESTATE”. The value of “appState” can be either disconnected, connected or running.

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As we have defined appliance state and appliance schema. Now we can move towards operational schemas.

First, we start by presenting initialization schema named as InitAppliance. In this schema, we declare “Appliance” schema as a variable. In predicate section, we say that on initialization, the state of an appliance must be equal to disconnected.

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As the plugged-in event occurs, the state of an appliance becomes connected. To show this transition, we define an operational schema called PluggedInAppliance. In the schema, the changing state of an appliance is shown by a delta sign \((\Delta ).\) In predicate, we say that the state of an appliance is changed from disconnected to the connected state.

figure e

The state of an appliance is also changing whenever an in-use event occurs. Then the appliance remains in a running state. This transition is shown by defining InUseAppliance. Here, again we declare the changing state of an appliance with a delta sign. In predicate, first an appliance must be in the connected state, then we say that the state changes to the running state.

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As we noted before, when an unplugged event occurs, an appliance goes to the disconnected state. This transition is shown by another schema called UnPluggedAppliance. In the predicate section, we can see that the state of an appliance changes from connected to the disconnected state.

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An appliance can be in connected but not in use state. This operation is shown by introducing another schema called NotInUseAppliance.

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There can be some scenario in which a schema can be success or there may some error. To understanding the success and error conditions of schemas, we present free type definitions in the form of Table 2. In the given table, for each schema we define the success and failure conditions.

Table 2 Success and error outcomes of the schemas for an appliance entity
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Wind turbine system

A wind turbine object has three distinct states named as turbine not running, turbine slow running, and turbine fast running. There are also different events associated with each state that causes a state transition. In Fig. 2 we can see that when there is no wind, the turbine enters in the “turbine not running” state. When there is slow wind, turbine runs slowly. And if there is fast wind, the turbine is running fast.

Fig. 2
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Statechart depicting a Wind turbine life

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Next, we present formal specification for a turbine object.

First, we start by defining a free type “TURBINESTATE” set. This set comprises of a turbine different states that are “turbineNotRunning, turbineSlowRunning, and turbineFastRunning”.

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Now, we define a wind turbine system schema by presenting WindTurbine. This schema consists of a variable “trbState” of type TURBINESTATE. The value of this variable can be either “turbineNotRunning”, “turbineSlowRunning”, or “turbineFastRunning”.

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As we have defined turbine’s states and turbine’s schema, now we move to operational schemas.

First, we start by initializing a turbine entity by presenting InitTurbine schema. In the schema, first, we call the WindTurbine schema. Then in the predicate, we say that the initial state of a turbine must be equal to “turbineNotRunning” state.

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As we noted in the state diagram when during slow wind, the state of a turbine becomes “turbineSlowRunning”. This transition is shown by defining SlowWind schema. In the schema, we call the WindTurbine schema with a delta sign. In predicate, we say that the state of a turbine is changing from “turbineNotRunning” to the “turbineSlowRunning”.

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In case of fast wind, a turbine runs fast. To show this process, we present another schema called FastWind. In the schema, again we call WindTurbine schema with a delta sign. In predicate, we say that the state of a turbine changes from slow to fast running.

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A turbine’s state also changes to not running when there is no wind. This transition is shown by introducing NoWind schema. The schema shows that a turbine’s state is changed from slow running to not running state.

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The schemas of the turbine entity can be success or fail when errors occur. So to understand the success and error conditions of each turbine’s schemas, we present free type definitions in Table 3.

Table 3 Success and error outcomes of the schemas for a wind turbine entity
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Solar system

A solar object has three distinct states named as “no energy generation, partial energy generation, and full energy generation”. There are also different events associated with each state that causes a state transition. The states and it’s associated events have shown in Fig. 3.

Fig. 3
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Statechart for a solar energy system

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Next, we present formal specification for a solar object.

First, we begin by introducing a free type “SOLARSTATE” that is used for presenting different states of a solar entity. This set comprises of “noEnergyGeneration, partialEnergyGeneration, and fullEnergyGeneration” states.

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Here, we present a solar system by introducing SolarPanel schema. The schema takes a variable “slrState” of type SOLARSTATE. The value of this variable can be either “noEnergyGenreation”, “partialEnergyGeneration” or “fullEnergyGeneration”.

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As we have defined solar state and schema, now we move towards the operational schemas.

The initialization process is shown by presenting InitSolar schema. First, the schema calls the SolarPanel schema in the declaration part. In predicate, we defined that the state of a solar is “noEnergyGeneration” at the initial time.

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As we know that when there is a cloud at daytime, then the solar generates partial energy. During this time period, the solar remains in a partial energy generation state. This process is shown by introducing DayAndCloudy schema. In the schema, the changing state of a solar is shown by a delta sign. In predicate, it shows that the state of solar changes from no generation to the partial generation.

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In case of the sunny day, a solar remains in a full generation state. This process is shown by defining DayAndSunny schema. Here, we again define the changing state of a solar with delta sign. In predicate, we say that the state of solar changes from partial to full energy generation.

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As we know that a solar does not generate any energy during night time. At this time period, solar remains in a no generation state. Here, we present another schema called “Night”. In the schema, we say that the current state of a solar can be partial or full energy generation. Then we change solar state to the no energy generation state.

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The success and failure conditions for the solar’s schemas is summarized in Table 4.

Table 4 Success and error outcomes of the schemas for a solar entity
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Storage system

A storage device also has different states as well as events that cause the transition of states. As we can see in Fig. 4 that there are three states named as “charging, discharging, and not in use” of a storage object. When a store energy or battery low event occurs, the storage enters in the charging state. In case of energy consumption, the state of storage becomes discharging, In case remove event, the state of storage becomes not in use.

Fig. 4
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Statechart for a storage system

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Next, we present formal specification for a storage system.

First, we start by defining a free type STORAGESTATE set that comprises of different state of a storage device.

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Here, we define a storage system schema. In the schema, we declare a variable “strState” of type STORAGESTATE that has any single value from the storage state set.

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As we have defined storage state and system schema. Now, we move towards operational schema.

First, we start by introducing an initialization schema called InitSorage. This schema calls the StorageDevice schema as a variable. In predicate, it shows that the state of a storage is “notInUse” at the initial time.

figure w

As we noted before, when a store energy event occurs, a storage goes to the charging state. This process is shown by StoreEnergy schema. The changing of a storage is shown by a delta sign. In predicate, it shows that the current state of a storage is “notInUse” which is changed to the “charging” state.

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We also know that when a consume energy event occurs, a storage device goes to the discharging state. This process is shown by presenting ConsumeEnergy schema. In the schema, we can see that the state of a storage changes from charging to the discharging state.

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A storage can also enter in the charging state whenever the storage state is low. This process is presented by means of BatteryLow schema.

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When a storage is removed from the system, then it goes to the “notInUse” state. This process is shown by introducing another schema called RemoveStorage. In the schema, we can see a storage can be in either charging or discharging state. Then it’s state changes to the “notInUse” state.

figure aa

The schemas of the storage devices can be success and may be there some errors at the execution time. So there is also need to define the success and error criteria for schemas. Here, in Table 5, we summarized all success and failure conditions of the storage’s schemas.

Table 5 Success and error outcomes of the schemas for a storage entity
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Comparison with previous work

In this section, we discuss different related work carried out in the smart grid domain using formal method approaches. We highlight their objectives and key contributions to the smart grid technology. However, the previous studies do not consider modeling of different key components of the smart grid as presented in this paper. Some of the key papers are discussed as follows.

In paper (Pózna et al. 2018), the author used a colored Petri net approach for modeling electrical network. The network is composed of feeders and sources. The proposed work effectively diagnose and locate unbalance situation on the network.

In the paper (Mhadhbi et al. 2018), a distributed energy management model is proposed that capable of handling neighbors surplus energy. The system is modeled using colored Petri net approach which achieved system balancing.

The smart microgrid is an effective way of using renewable energy resources. As the number of component increases, its complexity also increases. To handle the complex scenario of the smart microgrid, in the paper (Halim 2018), the author proposed the new hybrid Petri net approach. The proposal modeled power balance in a bus. This work showed various operations strategies that are useful for achieving network balancing.

Another use of Petri net approach is discussed in the domain of smart grid (Jiang et al. 2018). In this work, a hybrid distributed control system for modeling smart grid network. They used supervisors and local solutions for fault handling. The proposal is capable of detecting and locating fault using colored Petri net approach.

In paper (Loia et al. 2017), a multi-agent approach is used to monitor states of the smart grid as well as its components. The objective was to define optimal power flow on the network. The Fuzzy transform approach is applied on a large operational dataset of the smart grid. This work reduces storage needs in the network. By deploying agents, a reliable system is achieved.

In paper (Sultan et al. 2017), the author proposed the use of the formal method for smart grid components. In the study, two components that are smart meter and transformer are used. The states and operations of the components are modeled using UML notations. In this work, the VDM-SL language is used.

In previous studies, the smart grid architecture approach is used for modeling, requirement engineering, and analysis in different literature. In the paper (Neureiter et al. 2016), SGAM is integrated with a formal method for security requirement. In this study, different security classes, risk, and vulnerabilities are identified and modeled using a formal method along with SGAM.

In the smart grid, there involves heterogeneous components and complex interaction among them. In a large-scale power system, the power flow and interaction among different entities lead to the emergent behavior of the system. In paper (Kolen et al. 2018), the author focused on the distribution aspect of the smart grid. This study proposed DistAIX modeling paradigm for power distribution system. The proposed model comprises of power lines, communication, control, interaction.

Discussion and future work

The idea in this paper was primarily to identify and specify key components of the smart grid.  This included an identification of their different states, in addition to events resulting in a state transition. In this regard, we have considered appliances, solar system, turbine, and storage as the key components and presented formal models of each component. The formal specification using the ‘Z’ language is a state-based approach useful for defining and developing mathematical models of different entities with dynamic behavior. However, there is more work that needs to be performed especially in the domain of integration of different entities and components into a single system. In cases such as smart homes, additinal techniques such as artificial intelligent algorithms (​Crişan et al. 2017) in general and agent-based computing (Niazi and Hussain 2011b) in particular can be especially useful. Agent-based modeling allows to develop an abstract model of any complex system allows for a clear understanding of the model, behavior of each component, thus results in understanding the global behavior of the system. The optimization approaches are needed to create optimal decisions on energy consumption at the consumer side.

Conclusions and future work

In this paper, we focused on formal specification of smart grid components. We considered four different components of a smart grid system. We identified states and events which cause state transitions of each individual component. Then we modeled each component of the smart grid system by using a formal specification approach. This provides a clear understanding the behavior of each component involved in the system. The presented formal framework clearly demonstrates the utility of using a formal specification approach to modeling complex systems including technological systems such as the smart grid.

Here we would like to mention that the presented framework currently considers only four key smart grid components. However, the same can be further expanded for a large number of devices. For example, the same approach can be applied to the smart home energy management system. A smart home is an integrated energy system comprises of different and a large number of smart objects such as sensors, smart meters, smart appliances etc. The smart home also integrates solar panels and storage devices Thus, a smart home can be considered as an integrated system consists of various objects and system. In such a system, each component communicates and interact with each other. The users demands and available energy needed adaptive strategies. In such scenarios, the Petri net approach is also useful. Petri net approach is an interval-value based specification approach and deals with uncertain situations that is useful for modeling integrated systems such as a smart home. Modeling of the smart home leads to clear understanding the overall behavior of the smart grid.