Scientific Workflow-Based Synthesis of Microgrids

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Scientific Workflow-Based Synthesis of Microgrids

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A peer-reviewed article of this preprint also exists.

Olga Edeleva

Alexei Edelev

Mikhail Voskoboinikov^*,

Alexander Feoktistov^*

Olga Edeleva

Alexei Edelev

Mikhail Voskoboinikov^*,

Alexander Feoktistov^*

This version is not peer-reviewed

Submitted:

02 November 2024

Posted:

05 November 2024

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Abstract

The nature of multi-energy systems requires the integration of interdisciplinary methodologies and complementary tools in a coherent and systematic manner. Therefore, it is imperative to develop an efficient experimental environment to effectively implement the interaction between different tools for structural and parametric optimization (synthesis) of multi-energy systems and analysis of their operation. Due to the inherent complexity of the energy system optimization model, solving the synthesis problem often leads to significant challenges in terms of required computational resources and runtime. Known synthesis approaches do not fully address these challenges. In this context, we propose a subject-oriented environment for the multi-energy system synthesis in a reasonable time considering the available computational resources. The basis of the environment is a service-oriented application. The modeling and optimization of the studied systems is performed by means of scientific workflows. The execution of the specialized tools for modeling and optimization is done through web services. The pre-selection of these tools, depending on the level of model detail of the systems under study, and the data validation are performed on the specially developed testbeds. Such testbeds are constructed as system workflows. This is one of the distinguishing features of our approach. The application of the proposed environment is demonstrated through a case study on the synthesis of a microgrid (a special case of a multi-energy system). As a result of the study, an optimal microgrid configuration was proposed. It is based on the cogeneration of heat and electricity generation using natural gas.

Keywords:

Subject: Computer Science and Mathematics - Applied Mathematics

1. Introduction

In the 21st century, the development of a reliable, sustainable, environmentally friendly, and cost-effective energy supply is of great importance. However, the inefficient use of fossil fuels has resulted in significant environmental pollution. In addition, the disparate planning and operation of different energy sources has resulted in significant energy waste. The advent of new conversion technologies and several generations of more environmentally friendly energy sources has prompted a re-evaluation of the role of Multi-Energy Systems (MESs) in energy production, transmission, and consumption [1].

A microgrid is a small-scale MES that includes a variety of elements, including combined heat and power (CHP) generators and various types of energy storage systems, as well as distribution networks to deliver heat and electricity to isolated communities [2]. In light of these considerations, it is imperative to synthesize the most effective microgrids.

There are three key terms that are commonly used in the context of microgrid synthesis: optimization model, modeling environment, and configuration.

Optimization models are concrete representations of real microgrids with specific levels of detail of modeling aspects [3], including spatial, temporal, technological, economic, and other dimensions. Such representations may include multiple hard- or soft-linked submodels to enhance understanding of technical, environmental, and policy issues. Models are constructed from model generators that generate them based on a specific analytical and mathematical methodology (e.g., by using a predefined set of equations representing different energy technologies). For example, a methodology might minimize the annualized investment and operating costs of the microgrid while improving the environment by reducing fossil fuel consumption.

A modeling environment can be defined as a structured software toolbox that includes a set of specialized tools, model generators, and specific models (renewable energy models) [3]. It allows us to explore optimal microgrid alternatives from a variety of perspectives.

A microgrid configuration describes the potential infrastructure, which includes energy facilities and associated data on natural, climatic, social, economic, and other factors. For example, renewable energy modeling requires the input of a variety of meteorological data sets, including but not limited to the air temperature, atmospheric pressure, humidity, density, solar radiation, wind speed, and direction.

One of the major problems associated with microgrid optimization models is their inherent computational complexity, which is mainly influenced by the level of detail of different modeling dimensions [4]. The microgrid models are designed to provide a comprehensive system-wide perspective and sufficient levels of detail for effective decision making. In addition, any increase in the level of detail of any of the dimensions leads to an exponential increase in computational time. As a result, computationally tractable microgrid models are characterized by either a narrow perspective with a high level of detail or a broad scope with minimal detail. Such simplifications do not guarantee the establishment of the intended microgrid synthesis, especially with respect to the sustainability of the energy supply. This problem arises from the discrepancies in the level of detail of different dimensions, which in turn affects the practical applicability of microgrid optimization results.

To overcome the discrepancies in the level of detail, a number of strategies have been developed with the goal of reducing the amount of computational resources required. These strategies can be classified as either model-based or solver-based [5]. While each model-based technique implies modifications of a model with respect to the conceptual layer and thus is based on the same solution algorithm, solver-based strategies concern all techniques that can be applied in a solver package. However, they are specific implementations of the same solution algorithms or their adaptation by appropriate parameterization.

Recent microgrid synthesis approaches [6] facilitate the construction of optimization models with different modeling environments, such as ETHOS.FINE [7], which integrate the model-based techniques to reduce the spatial or temporal level of detail. However, these approaches still lack capabilities for intelligent management of available computational resources, and comprehensive testing of model-based and solver-based strategies to strike a balance between model computational complexity and acceptable solution time with little loss of modeling accuracy. For example, one of the main results of testing model-based acceleration strategies in the BEAM-ME project [5] is that the computational time of large models can be reduced by a factor of up to 10 by applying model reduction heuristics. A drawback is the reasonable limitation in accuracy. The next result is related to the development of the solver PIPS-IPM++, which allows the parallel solution of linear optimization problems on High-Performance Computing (HPC) architectures. The progress made in testing HPC solver-based acceleration strategies allows to reduce the solution time of large models by a factor of up to 26 without affecting the accuracy [5].

However, the above and other well-known approaches to the multi-energy system synthesis do not address all existing challenges. In this context, we propose a Subject-Oriented Environment (SOE) for solving a multi-energy microgrid optimization problem. The SOE consists of a service-oriented application for solving the aforementioned problem using the resources of a Heterogeneous Distributed Computing Environment (HDCE) and specialized testbeds for software testing and verification, data validation, and optimization algorithm selection in the context of a specific microgrid model. Problem-solving is based on the design and execution of a scientific workflow that determines a sequence of operations for optimizing a multi-energy microgrid. The operations are implemented as services.

2. Related Work

2.1. Energy System Synthesis

We consider the microgrid synthesis as structural and parametric optimization of local MESs. The objective of such optimization is to select the optimal types of energy equipment and determine their optimal locations for installation. In general, it is formulated as a parametric optimization problem. Accordingly, structural and parametric optimization is a more complicated problem from a mathematical and computational point of view compared to parametric optimization. The objective of MES synthesis is to identify an optimal system configuration. Such a configuration represents the optimal combination of disparate energy technologies with the most appropriate equipment unit sizes for the optimal operation of the selected equipment.

The conventional methodology for MES synthesis involves the manual creation of numerous system configurations that are significantly different from each other. The primary disadvantage of this methodology is the significant subjectivity inherent in the decision-making process, which depends on the expertise and experience of the MES configuration designer.

The two-stage decision-making process inherent in the synthesis problem provides the basis for implementing a two-level methodology to address complex, large-scale problems [8]. The high-level methods determine the investments, placements, and dimensions of the equipment, while the low-level methods are responsible for making decisions about the operation of the equipment units. Optimization of high-level decisions requires the simultaneous consideration of low-level decisions. Accordingly, the computational complexity increases hierarchically from the lowest to the highest level of a methodology.

In the literature, two methodologies are highlighted with respect to automating the MES synthesis problem. These methodologies are based on superstructure-based and superstructure-free synthesis, respectively.

The superstructure-based synthesis includes the following main sequential stages [9]:

Development of a superstructure containing all feasible alternative energy process structures;
Implementation of the superstructure for a mathematical programming solver;
Optimization of a system configuration using the solver.

Unlike to superstructure-based synthesis, superstructure-free synthesis does not use the combinatorial search space to obtain alternative energy process structures. The method dynamically generates these structures and then evaluates them using an Energy System Optimization Model (ESOM). The main advantage of the superstructure-based methodology is the use of rigorous optimization techniques at all stages of synthesis. However, this methodology often results in large, non-convex mathematical problems that are difficult to solve [10]. In many cases, the superstructure-free methodology uses meta-heuristic techniques at the highest level of synthesis. It should be noted that meta-heuristic techniques do not guarantee the optimality of the solution obtained. Nevertheless, these techniques are capable of identifying a highly satisfactory solution in a relatively short time [11].

In contrast to the traditional approach, both types of automated synthesis have the potential to yield a large number of MES configurations. This is a significant advantage in the context of decision support. Decision-makers typically seek to obtain several promising MES configurations of high quality, which can then be further evaluated in light of additional information that may emerge in practice. Accordingly, an optimal but singular MES configuration is typically insufficient.

2.2. The Concept of the Energy Hub

The increasing number of interconnections between microgrids, a consequence of their development, gave rise to the concept of the energy hub [12]. An energy hub is defined as an aggregation of production facilities for multiple energy resources, including conversion and accumulation. An energy hub serves as a conduit between microgrids and consumers, ensuring that the latter receive energy resources of the required quality [13].

The energy hub concept is an effective tool for modeling and analyzing the physical interconnections within microgrids. This is due to the fact that the energy hub concept places a primary emphasis on the detailed study of the energy conversion processes that occur between different energy resource types.

Energy hub modeling is based on optimizing the distribution of energy resource flows, originating at the hub's inputs and terminating at its outputs. The inputs and outputs of the energy hub are connected to the corresponding nodes of the distribution networks. Accordingly, a microgrid can be considered as an energy hub network [14].

3. Microgrid Model

Let the time interval under consideration be composed of

T

periods of the duration

Δ t

. The energy resources are represented by a set

K

, and the energy infrastructure is represented by a network of

H

interconnected hubs.

3.1. Input and Output Flows

Each hub

h = \{1, \dots, H\}

is equipped with the set

M_{h} \subseteq K

of inputs, the set

N_{h} \subseteq K

of outputs, the set

I_{h}^{i n} \subseteq K

of input storages, and the set

I_{h}^{o u t} \subseteq K

of output storages. Additionally, the hub

h

has

J_{h}

converters.

As shown in Figure 1, at the hub

h = \{1, \dots, H\}

in the period

t = \{1, \dots, T\}

, the energy flow

P_{h m}^{t}

at the input

m \in M_{h}

is divided into the flow

Q_{h i}^{t}

of the input energy storage

i \in I_{h}^{i n}

and the flows

F_{h m j}^{t}

to the converters

j = \{1, \dots, J_{h}\}

associated with the input

m \in M_{h}

P_{h m}^{t} = \sum_{j \in Θ_{h} (m)} F_{h m j}^{t} + Q_{h i}^{t},

(1)

F_{h m j}^{t} \leq w_{h} {\bar{F}}_{h m j},

(2)

w_{h} \in \{0, 1\},

(3)

where

{\bar{F}}_{h m j}^{t}

is a throughput of the converter

j

to the input

m

of the hub

h

Θ_{h} (m)

is a set comprising the converter of the hub

h

connected to the input

m

w_{h}

is a binary variable that specifies the hub

h

status.

The formation of the energy resource flow

L_{h n}

at the output

n \in N_{h}

of the hub

h = \{1, \dots, H\}

is shown in Figure 2. During the time interval

t = \{1, \dots, T\}

the energy converter

= \{1, \dots, J_{h}\}

of the hub

h

converts the flow

F_{h m j}^{t}

with a conversion factor of

η_{h m j n}^{c o n}

and directs it to the output

n

. Given the flow

Q_{h i}^{t}

of the output drive

i \in I_{h}^{o u t}

, the flow

L_{h n}^{t}

at the output

n \in N_{h}

is defined as

L_{h n}^{t} = \sum_{m \in M_{h}} \sum_{j \in Θ_{h} (m, n)} η_{h m j n}^{c o n} F_{h m j}^{t} - Q_{h i}^{t},

(4)

L_{h n}^{t} \leq w_{h} {\bar{L}}_{h n}^{t},

(5)

where

Θ_{h} (m, n)

is a set consisting of converters connecting the input

m \in M_{h}

to the output

n

of the hub

h

3.2. Energy Storage Devices

In formulas (3) and (6), the flow

Q_{h i}^{t}

of the storage

i \in I_{h}^{i n} \cup I_{h}^{o u t}

of the hub

h = \{1, \dots, H\}

is formed by the flows of charge

Q_{h i}^{c h g, t}

and the discharge

Q_{h i}^{d i s, t}

in the period

t = \{1, \dots, T\}

L_{h n}^{t} = \sum_{m \in M_{h}} \sum_{j \in Θ_{h} (m, n)} η_{h m j n}^{c o n} F_{h m j}^{t} - Q_{h i}^{t},

(6)

The energy level

E_{h i}^{t}

, stored in

i \in I_{h}^{i n} \cup I_{h}^{o u t}

of the hub

h = \{1, \dots, H\}

at the end of the period

t = \{1, \dots, T\}

, depends on its capacity

{\bar{E}}_{h i}

, the level

E_{h i}^{t - 1}

at the end of the previous period

t - 1

, the charge flows

Q_{h i}^{c h g, t,}

, and the discharge flows

Q_{h i}^{d i s, t}

in the period

t

E_{h i}^{t} = E_{h i}^{t - 1} + (η_{h i}^{c h g} Q_{h i}^{c h g, t} - \frac{1}{η_{h i}^{d i s}} Q_{h i}^{d i s, t}) Δ t,

(7)

0 \leq E_{h i}^{t} \leq {\bar{E}}_{h i},

(8)

E_{h i}^{0} = {\bar{E}}_{h i},

(9)

0 \leq Q_{h i}^{d i s, t} \leq w_{h} {\bar{Q}}_{h i}^{d i s},

(10)

0 \leq Q_{h i}^{c h g, t} \leq w_{h} {\bar{Q}}_{h i}^{c h g},

(11)

where

η_{h i}^{c h g}

is a charge efficiency factor of the storage

i

of the hub

h

η_{h i}^{d i s} i s

a discharge efficiency factor of the storage

i

of the hub

h

{\bar{Q}}_{h i}^{d i s}

is the maximum possible discharge flow value of the storage

i

of the hub h,

{\bar{Q}}_{h i}^{c h g}

is the maximum possible charge flow value of the storage

i

of the hub

h

. Equation (11) assumes that before the start of the operation

(t = 0

) all the storages contain full charge.

Equations (8), (10), and (11) specify technical constraints on the operation of the storage unit

i

in the period

t

3.3. Energy Transportation Networks

Energy hubs are connected to each other and to consumers through energy distribution networks, as shown in Figure 4. Each network is represented as a graph, denoted by

G_{k} = (V_{k}, E_{k})

, where

V_{k}

is a set of nodes,

E_{k}

is a set of oriented arcs, and

k

is an energy resource drawn from the set

K

. Additional constraints may be imposed on the graph

G_{k}

due to the physical laws of distribution of the energy resource

k

The network

G_{k}

may contain the set

V_{k}^{g} \subset V_{k}

of nodes representing the isolated sources of the energy resources

k \in K

that do not belong to any of

H

hubs. For example,

V_{k}^{g}

may be associated with fuel sources that are represented by rectangles in Figure 4.

Let

V_{k}^{d} \subset V_{k}

denote a set of nodes consuming the energy resource

k \in K

. The remaining nodes from the set

V_{k}^{o} = V_{k} \ (V_{k}^{g} \cup V_{k}^{d})

are called as the intermediate nodes. These nodes facilitate the interconnection of energy flows within the distribution network. Each node

v

of the network

G_{k}

must satisfy one of the conditions for the balance of the energy flows

k \in K

at the time

t = \{1, \dots, T\}

g_{v}^{t} + \sum_{(q, v) \in Ψ_{k} (v)} a_{q v} f_{q v}^{t} - \sum_{(v, q) \in Ω_{k} (v)} f_{v q}^{t} = 0, v \in V_{k}^{g}

(12)

\sum_{(q, v) \in Ψ_{k} (v)} a_{q v} f_{q v}^{t} - \sum_{(v, q) \in Ω_{k} (v)} f_{v q}^{t} + u_{v}^{t} = {\bar{d}}_{v}^{t}, v \in V_{k}^{d}

(13)

\sum_{(q, v) \in Ψ_{k} (v)} a_{q v} f_{q v}^{t} - \sum_{(v, q) \in Ω_{k} (v)} f_{v q}^{t} = 0, v \in V_{k}^{o}

(14)

0 \leq u_{v}^{t} \leq {\bar{u}}_{v}^{t}, v \in V_{k}^{d},

(15)

0 \leq f_{v q}^{t} \leq w_{v q} {\bar{f}}_{k v q}, (v, q) \in E_{k},

(16)

0 \leq g_{v}^{t} \leq w_{v} {\bar{g}}_{v}^{t}, v \in V_{k}^{g},

(17)

w_{v q} \in \{0, 1\}, (v, q) \in E_{k},

(18)

w_{v} \in \{0, 1\}, v \in V_{k}^{g},

(19)

where

Ψ_{k} (v) \subseteq E_{k}

is a set of arcs entering the node

v

, and

Ω_{k} (v) \subseteq E_{k}

is a set of arcs leaving the node

v

f_{q v}^{t}

is a flow of the energy resource

k

along the arc

(q, v) \in E_{k}

at the period

t

g_{v}^{t}

represents the production of the energy resource

k

at the node

v \in V_{k}^{g}

at the period

t

, while

{\bar{u}}_{v}^{t}

denotes the demand of the node

v \in V_{k}^{d}

for the energy resource

k

at the period

t

u_{v}^{t}

represents the shortage of the energy resource

k

to the node

v \in V_{k}^{d}

in the period

t

. The term

a_{q v}

denotes a coefficient that characterizes the losses incurred during the transportation of the energy resource

k

along the arc

(q, v) \in E_{k}

. The throughput of the arc

(q, v) \in E_{k}

is represented by

{\bar{f}}_{v q}, (v, q)

, whereas the binary variable

w_{v q}

defines the status of the arc

(v, q)

, the binary variable

w_{v}

in turn, defines the status of the source node

v

If we consider the energy hubs connected to

G_{k}

at the node

v

, then equations (12)-(14) for the period

t = \{1, \dots, T\}

are written as

g_{v}^{t} + \sum_{(q, v) \in Ψ_{k} (v)} a_{q v} f_{q v}^{t} + \sum_{h \in Λ_{k}^{g} (v)} L_{h n}^{t} - \sum_{h \in Λ_{k}^{d} (v)} P_{h m}^{t} - \sum_{(v, q) \in Ω_{k} (v)} f_{v q}^{t} = 0, v \in V_{k}^{g},

(20)

\sum_{(q, v) \in Ψ_{k} (v)} a_{q v} f_{q v}^{t} + \sum_{h \in Λ_{k}^{g} (v)} L_{h n}^{t} - \sum_{h \in Λ_{k}^{d} (v)} P_{h m}^{t} - \sum_{(v, q) \in Ω_{k} (v)} f_{v q}^{t} + u_{v}^{t} = {\bar{u}}_{v}^{t}, v \in V_{k}^{d},

(21)

\sum_{(q, v) \in Ψ_{k} (v)} a_{q v} f_{q v}^{t} + \sum_{h \in Λ_{k}^{g} (v)} L_{h n}^{t} - \sum_{h \in Λ_{k}^{d} (v)} P_{h m}^{t} - \sum_{(v, q) \in Ω_{k} (v)} f_{v q}^{t} = 0, v \in V_{k}^{o},

(22)

where

Λ_{k}^{d} (v)

is a set of hubs whose inputs are connected to the network

G_{k}

at the node

v

P_{h k}^{t}

is a flow of the energy resource

k \in K

arriving at the input

m \in M_{h}

of the hub

h \in Λ_{k}^{d} (v)

at the period

t

Λ_{k}^{g} (v)

is a set of hubs whose outputs are connected to the network

G_{k}

at the node

v

L_{h n}^{t}

is a flow of the energy resource

k \in K

arriving at the output

n \in N_{h}

of the hub

h \in Λ_{k}^{g} (v)

at the period

t

3.4. Environmental Constraints

In the event that constraints on the emission of harmful substances from the plurality

L

are necessary, they may be imposed on the production of the energy resource

k \in K

. Examples of such substances include particulate the matter, sulfur oxide, nitrogen oxide, carbon dioxide, and benz(a)pyrene.

For the source node

v \in V_{k}^{g}

, the emission

e_{l v}^{t}

of a harmful substance

l \in L

at the period

t = \{1, \dots, T\}

is calculated and constrained as follows:

e_{l v}^{t} = λ_{l v}^{t} g_{v}^{t},

(23)

e_{l v}^{t} \leq {\bar{e}}_{l v}^{t},

(24)

where

λ_{l v}^{t}

represents the specific emission of the given harmful substance

l

, as associated with the production of the given energy resource

k

by the source

v

. Meanwhile,

{\bar{e}}_{l v}^{t}

denotes the emission limit of the aforementioned harmful substance

l

for the source

v

For the hub

h = \{1, \dots, H\}

the emission

E_{h m j l}^{t}

of the pollutant

l

at the time

t

is tied to the flow

F_{h m j}^{t}

of the converter

j = \{1, \dots, J_{h}\}

consuming the energy resource

m \in M_{h}

E_{h m j l}^{t} = λ_{h m j l}^{t} F_{h m j}^{t},

(25)

E_{h m j l}^{t} \leq {\bar{E}}_{h m j l}^{t},

(26)

where

λ_{h m j l}^{t}

represents the specific emission of a harmful substance

l

by transducer

j

, while

{\bar{E}}_{h m j l}^{t}

denotes the emission limit of the aforementioned substance

l

for the transducer

j

3.5. Objective Function

The objective of optimizing the functionality of interconnected hubs is to achieve the most comprehensive satisfaction of energy resource needs with the least investment on hubs and distribution networks, while minimizing the operational costs of these systems over the specified period

t = \{1, \dots, T\}

\sum_{h = 1}^{H} Z_{h} + \sum_{k \in K} Z_{k} + \sum_{t = 1}^{T} [\sum_{h = 1}^{H} F_{h}^{t} + \sum_{k \in K} F_{k}^{t} + \sum_{l \in L} E_{l}^{t}] \to m i n

(27)

Z_{h} = b_{h} w_{h},

(28)

Z_{k} = \sum_{v \in V_{k}^{g}} b_{v} w_{v} + \sum_{(v, q) \in E_{k}} b_{v q} w_{v q}

(29)

F_{h}^{t} = \sum_{m \in M_{h}} C_{h m}^{t} P_{h m}^{t} + \sum_{n \in N_{h}} C_{h n}^{t} L_{h n}^{t} + \sum_{i \in I_{h}^{i n} \cup I_{h}^{o u t}} (C_{h i}^{c h g, t} Q_{h i}^{c h g, t} + C_{h i}^{d i s, t} Q_{h i}^{d i s, t})

(30)

F_{k}^{t} = \sum_{v \in V_{k}^{g}} c_{v}^{t} g_{v}^{t} + \sum_{v \in V_{k}^{d}} y_{v}^{t} u_{v}^{t} + \sum_{(v, q) \in E_{k}} c_{v q}^{t} f_{v q}^{t},

(31)

E_{l}^{t} = \sum_{h = 1}^{H} \sum_{m \in M_{h}} \sum_{j \in Θ_{h} (m)} y_{h m j l}^{t} E_{h m j l}^{t} + \sum_{k \in K} \sum_{v \in V_{k}^{g}} y_{l v}^{t} e_{l v}^{t}

(32)

where

b_{h}

represents the investment in the hub

h = \{1, \dots, H\}

b_{v}

represents the investments in the source

v \in V_{k}^{g}

b_{v q}

is the investment in the arc

(v, q) \in E_{k}

C_{h m}^{t}