Multi-Objective Optimal Power Management in

Multi-Objective Optimal Power Management in Microgrids: A Comparative Study Dany Mauricio Lopez-Santiago

Eduardo Francisco Caicedo-Bravo

Escuela de Ingeniería Eléctrica y Electrónica Universidad del Valle Santiago de Cali, Colombia [email protected]

Escuela de Ingeniería Eléctrica y Electrónica Universidad del Valle Santiago de Cali, Colombia [email protected]

Abstract— In microgrids the Energy Management System (EMS) design involves important technological challenges, especially when two or more objectives must be reached. Several multiobjetive optimization algorithms (MO) can address optimal power management in microgrids, but only partially. This because a decision-maker (DM) must choose, not only the microgrid final set-point, but before, the more convenient MO algorithm applied to the process. This paper presents a comparative study among four MO algorithms: MOGA, NSGAII, SPEA2 and IMOPSO to propose a first comparative framework to ease choosing of MO algorithm. The study proposes five criteria to evaluate the performance average of selected techniques: total operation costs, total emissions, energy share, runtime and non-dominated solutions in grid-connected mode. Results show differences of performance under each criterion, implying each MO algorithm is applicable to different operating scenarios in microgrids.

∈ ∈

1, 2 , … ,

Index Terms-- decision maker, energy management system, microgrids, multi-objective optimization, optimal power management.

I.

INTRODUCTION

Microgrids are a new concept of power system, developed to avoid illness an unsuitability of conventional power grids. However, expectation for microgrids deployment includes optimal performance in terms of lower operational costs, lower pollutant emissions, a safety operation, among others objectives [1]. Under this criteria, the above means microgrids must properly manage power output of all distributed generators that comprise it [2]. This task is commonly known as an optimal power management in microgrids. To perform it, an specialized and qualified system is looked for and known as energy management system (EMS) [3], [4]. Recently, several researches have proposed to base the EMS optimization core using constrained multi-objective optimization (MO) [5], getting promising results. Nevertheless, MO gives a solution-set instead a single optimal one solution. This approach implies to develop a design process, in which a decision-maker (DM) must select, not only a solution and apply it to microgrid state. This project is co-financed by the Administrative Department of Science, Technology and Innovation in Colombia (COLCIENCIAS) and Universidad del Valle, Santiago de Cali, Colombia.

,

, ∑

, , 1

DG01 MT01 FC01 BG01 BG02 BG03

n-dimensional decision variable Vector to optimize Number of objective functions n-dimensional feasible set of an optimization problem Inequality constraint Equality constraint Number of inequality constraints Number of equality constraints Output power of generating unit Operation cost of microgrid [$/h] Overall total emissions of NOx, SOx and CO2 [kg/h] Power vector of decision variables Number of generating units Emission type (NOx, SOx , CO2) Fuel cost of generating unit . Fuel consumption rate of generating unit Operation and maintenance cost for Generating unit Cost of imported energy from main grid Cost of exported energy to main grid Type emission factor of generating unit Constant externality cost for type emission Parameters of characteristic emission of Generating unit Total power generated by generating units Power load demand Output power of photovoltaic array PV Output power of wind turbine WT Output power of small hydro-power SHP Output power of distributed store DS Power of main grid Minimum set-point of generating unit Maximum set-point of generating unit Diesel generator number one Micro Turbine generator number one Fuel Cell generator number one Biodiesel generator number one Biodiesel generator number two Biodiesel generator number three Figure 1. Nomenclature

This paper presents a comparative study about four MO algorithms applied to optimize two conflictive objectives over the same microgrid model i) minimize economical costs in the microgrid and ii) minimize overall pollutant emissions (CO2, SOx and NOX). The MOGA , NSGAII, SPEA2 and IMOPSO algorithms are part of this study. The paper proposes an approach of methodology to perform the comparative study through five criteria to evaluate performance of each MO algorithm: total operation costs, total emissions, energy share, amount of non-dominated solutions delivered average and runtime average. The remainder of this paper is organized as follow: section II presents problem formulation and some relevant previous research. Section III presents our comparison methodology in terms of microgrid model, MO algorithms applied to manage its power and the framework used to evaluate performance. Section IV shows all results obtained using the proposed comparison framework and opens discussion about new criteria and new comparative studies. II.

PROBLEM FORMULATION AND STATE OF THE ART

An specialized EMS for microgrids can base its optimal power management core using MO [7]. Researches have considered this kind of formulation, among other features, due MO allows to depict this problem through follow formal definitions: Minimize: Subject to:

1

, 0, 0,

2

,…,

(1)

1,2, … , 1,2, … ,

(2) (3)

Interest in modeling the optimal power management problem using MO has raised in recent years, with satisfactory results. In some of these studies, different MO algorithms face two or more non-lineal objective functions to depict a minimization of operational costs and greenhouse emissions [8]–[13]. In others, economical costs and maximization of DG use [14], minimization of lost in transmission lines and fuel consumption [15], or maximization of profits and risk minimization due to price variability [16] are proposed. Nevertheless, when MO is involved is necessary to consider two design aspects related with design concepts and alternative concepts. The alternative concepts, due the output of a MO algorithm is not a single solution, but a set, implies that a DM must choose only one solution from the set and apply it to microgrid state. However before this occurs, DM should make

a decision about which MO algorithm to use to perform the most convenient optimization. From work of Mattson and A. Messac in [6], these aspects are respectively called design alternatives and design concepts. Thereby, a methodology to compare performance among different design concepts could be a convenient tool to ease DM labor. The state of the art refers some studies which include a different methodology about design concepts to ease DM work, however they are tailored for another specific areas of engineering [17], [18] or in the field of math [19], [20], without direct relation with optimal microgrids operation. III.

COMPARISON FRAMEWORK

A. Microgrid Model Proposed microgrid model is based in a cluster of electrical power loads, fed by a group of distributed generators: distributed energy resources (DER: DG01, MT01, FC01, BG01, BG02 and BG03) and alternative energy distributed generation (AEDG: Photovoltaic array–PV, Wind Turbine–WT and Small Hydro Power–SHP). Fig. 2 shows a conceptual scheme for this model, included maximum power of each distributed generator. Main Grid

Microgrid

DG01 20kW

PV 5kW

MSC

MT 20kW MSC

MSC

CB

Microgrid LV bus

But first, due several and different algorithms of MO can address the problem, DM faces the challenge of choosing an MO algorithm to perform the best optimization process [6]. In this manner, a common comparison methodology could be a convenient tool to choose the more appropriate MO algorithm. Specialized literature shows some approaches, however each one has its own framework, and the absence of optimization parameters hinders comparison among algorithms. In fact, as far as known, very few comparative studies among MO techniques applied over optimal microgrid power management in microgrids have been published.

FC01 10kW

BG01 15kW

PL

MSC

CB

MSC

WT 60kW

CB

TRAFO PL

PL

BG02 15kW

EMS

SHP 10kW

MSC CB PL: Power load MSC: Micro-source controller CB: Circuit Breaker EMS: Energy Management System

PL

BG03 15kW

MSC

PL

PL

MSC

PL

Figure 2. Microgrid conceptual scheme [21]

B. Objective Functions From model of Fig. 2, this section describes cost function optimization model, based on operation cost, emission and constraints. See [21] for more details of the model. 1) Economic cost function: Equation (4) shows operation cost function where fuel, operation and maintenance (O&M), energy importation/exportation and externality costs (due pollutant gases, NOx, SO2 and CO2, see Table I) are aggregated in the follow expression: ∑

1

∑

1∑

1

(4)

2) Emission function: Equation (5) shows emissions of NOx, SO2 and CO2, like a function of power output in each DER unit and main grid energy imported. In Equation (5), L is the number of DER units plus one, L=N+1:

∑

1 10

2

2

exp

TABLE II.

(5) Source

TABLE I. Emission Type NOx SO2 CO2

EXTERNALITY COSTS AND EMISSION FACTORS

α [$/kg]

DG/GRID [kg/kWh]

FC [kg/kWh]

MT [kg/kWh]

BG [kg/kWh]

4.200 0.990 0.014

0.021800 0.000454 0.001432

0.000030 0.000006 0.001078

0.000440 0.000008 0.001596

0.030800 0.000000 0.000750

DG/BG /GRID MT FC

α

EMISSION COEFICIENTS

β

γ

ζ

λ -6

0.2125

0.2404

0.2809

8.70x10

0.0110 0.212x10-3

0.0120 0.240x10-3

0.0140 0.014x10-3

4.35x10-7 4.35x10-10

0.1237 0.0062 0.62x10-5

3) Constraints: For a secure operation, a balance among output power must be introduced. At same time, each generating unit must be bounded between its own output power limits. See Equations (6-7). ∑

1



, ∀

1, … ,

(6) (7)

C. MO Algorithms From the good performance shown in specialized literature, four MO algorithms are used in this study: the non-domination sorting genetic algorithm–NSGAII [22], the multi-objective genetic algorithm–MOGA [23], the strength pareto evolutionary algorithm–SPEA2 [24] , and the improved multiobjective particle swarm optimization–IMOPSO [25]. Previous algorithms have been used in different optimization approaches for many areas of engineering, obtaining satisfactory results.

Figure 3. Power load demand and AEDG power output

D. Performance Criteria Based on work of López-Santiago in [21], a new comparison framework among MO algorithms is proposed to evaluate average of: costs [$/h], emissions [kg/h], distribution of energy (energy share), runtime and non-domination, in 24h operation, from evaluation of 10 test (24 runs for each day, 4 algorithms, 10 test, total 960 simulations). According to Zitztler in [26], metrics about non-domination (ND) solutionset can be depicted according to Equation (8). Figure 4. Curves of sale and buy prices

′

,

′′



a ′′

∈

′′

; ∃a ′ ∈ ′ : a ′ ≼ a ′′ | ′′ |

(8)

Where ′ , ′′ ⊆ , are two decision vector set. a′′ and a are individual solutions from ′ , ′′ respectively. Function ′ , ′′ to the interval [0, 1]. maps ordered pair ′ , ′′ 1, means all solutions in ′′ are dominated or ′ are equals to solutions in ′ . , ′′ 0, means no ′ ′ , ′′ is not solutions are dominated by set. Note that ′′ ′ , . necessarily equal to 1 ′

E. Input Information The Fig. 3 shows how power load demand (PL) is not covered with only AEDG resources. In case like this, is necessary to carry up a power management strategy using a combination among DER units and even main grid. The Fig. 4 presents price evolution of energy bought and sold to the main grid. Between curves, there is a commercial brokerage rate close to 30%.

F. Optimization Strategy 1) At the beginning of each hour, calculate output of renewables generation units. 2) Calculate total power load demand. 3) Run MO algorithm over constraints, operation cost and emission, and to obtain a solution-set . Equations (4–7). 4) From solution-set to choose only one solution (setpoint).This set-point can be formed by only DER units or by a combination with grid. DM makes selection based on follow rules: i. Calculate cost [$] of importing all energy deficits from grid. This implies equal to zero all output power in DER units (total importation strategy). ii. From MO solution-set, select first individual which operation cost value is lower or equal to the value calculated in i. 5) Apply selected set-point. 6) Repeat for next hour until 24h. 7) Repeat 10 times steps 1–6.

IV.

RESULTS AND DISCUSSIONS

A. Costs average: A comparative chart among costs average is showed in Fig 5. IMOPSO delivers cheaper performance with $395.61 of average, followed by results that are more expensive: SPEA2 (10.35% more), MOGA (12.01% more) and NSGAII (21.89% more). See Table III.

shutdown diesel/biodiesel sources, while IMOPSO shows a trend to match same production in all sources.

Figure 7. Energy share average comparison. MOGA (a), NSGAII (b). SPEA2 (c). IMOPSO (d). TABLE III.

Figure 5. Cost average comparison.

PERFORMANCE INDEX

Performance Index

MOGA

NSGAII

SPEA2

IMOPSO

Total cost av. [$] Total emission av. [kg] Runtime average [s] Coefficient of variation

443.13 33,536.54 22.40 1.48%

482.23 36,338.02 30.27 1.59%

436.55 35,340.94 107.75 2.28%

395.61 35,325.87 164.45 1.99%

D. Runtime average Table III shows runtime average from 24h operation among MO algorithms. MOGA is the fastest (22.40s), followed by NSGAII (35.15% slower), SPEA2 (381.10% slower) and IMOPSO (334.25% slower) respectively. Coefficient of variation shows similar data consistency for the algorithms. E. Non-domination average Table IV shows first comparison about amount of nondominated solutions average based on Equation (8). In summary, IMOPSO offers more non-dominated solutions since it exceeds the amount of non-dominated solutions of other algorithms. In that order, SPEA2, MOGA and NSGAII complete ranking. Sensitive data variation is perceived when the amount of non-dominated solutions tends to be smaller. TABLE IV. Figure 6. Emissions average comparison.

B. Emissions average A comparative chart among total emissions (GRID+DER) average is showed in Fig 6. MOGA shows the greener performance with 33,536.54 kg of gases thrown to atmosphere, followed by results that are more pollutants: IMOPSO (5.34% more), SPEA2 (5.38% more) and NSGAII (8.35% more). See Table III. C. Energy share average Fig. 7 shows how energy has been distributed from DER sources. SPEA2, MOGA and NSGAII presents a trend to

Study MOGA vs NSGAII NSGAII vs MOGA MOGA vs SPEA2 SPEA2 vs MOGA MOGA vs IMOPSO IMOPSO vs MOGA NSGAII vs SPEA2 SPEA2 vs NSGAII NSGAII vs IMOPSO IMOPSO vs NSGAII SPEA2 vs IMOPSO IMOPSO vs SPEA2

NON-DOMINATION STUDY Non-Domination Average

Coefficient of Variation

0.78608 0.00008 0.00542 0.70984 0.01317 0.69646 0.00000 0.84629 0.00004 0.84242 0.07438 0.52496

5.49368% 200.02899% 42.49079% 5.48675% 22.51955% 3.41146% 0.00000% 4.23911% 300.00000% 3.99599% 8.64725% 1.60025%

After results, IMOPSO presents best features to obtain lower costs and solutions where a more combined mix of DER generation units is used. These performances are explained because IMOPSO provides a greater amount of non-dominated solutions. However, use of this technique could be limited by runtime, in cases where a lower sampling time is needed. Although MOGA, in literature review is an evolutionary algorithm which tends to disuse, it offers the best performance in emissions average and a competitive performance in cost average. Furthermore, its use can take advantage in cases where on-line behavior is more critical. At same time, MOGA provides the lower Coefficient of Variation, which means a more Nonetheless, DM must choose the more convenient algorithm before start optimization, but time expended to asses performance can limit quality of results. In these cases, an evaluation off-line could be recommended, at least to select best algorithms for performance according to nature of microgrid model. This could means that the DM should make decisions on two different stages, first in off-line mode and probably after in on-line mode. Beyond this, extend the methodology to include other performance index is a convenient tool to make best evaluations and therefore more accurate decisions, before or after microgrid operation is started. At same time, new studies should incorporate other MO algorithms to wide possibilities of DM to approach optimum performance.

[12] [13]

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[16]

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[20]

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