Optimal Set Points Regulation of Distributed Generation Units in Micro-grids under Islanded Operation G. Graditi*, M. G. Ippolito°, E. Riva Sanseverino°, G. Zizzo° * ENEA Portici Napoli ° DIEET University of Palermo
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Abstract-The present work studies the problem of optimizing the power production levels of dispersed generation units in islanded microgrids. The problem is intrinsically multi-objective with non linear objectives and constraints, thus the solution approach is based on evolutionary optimization and uses the Non dominated Sorting Genetic Algorithm II. The objectives are calculated based on the solution of the load flow problem. The latter problem is more complicated when in the considered system a physical node with a sufficiently large production capability is not available, because all the generation node of the systems have similar and limited generation capability. In this paper, the issue has been solved including into the optimization string also the slack bus identifier. This idea, together with the use of a suitable multiobjective technique, allows to reach interesting results and to optimally dispatch the power from the different generating units.
I.
INTRODUCTION
In the last years a huge transformation has involved the distribution networks that are evolving towards active networks characterized by a high penetration of distributed generation (DG) units. The latter are based on technologies such as internal combustion engines, small and micro gas turbines, fuel cells, photovoltaic and wind plants. A way to realize the emerging potential of DG is to take a system approach that views generation and associated loads as a subsystem named “microgrid”. Microgrids are small MV or LV electric distribution systems with enough local distributed energy resources (DER) to supply entirely a local load demand and able to work both in grid-connected and in islanded mode (similar to power systems of physical islands). For DER must be intended electric generating units (in microgrids typically in the range of 3 kW to 200 kW), parallel to the electric utility or stand-alone, located within the electric distribution system at or near the end user. DER also involves power electronic interfaces, as well as communications and control devices for efficient dispatch and operation of single generating units, multiple system packages, and aggregated blocks of power. Intra-system cross-supply and communal management standards differentiate a microgrid from a group of independent but physically proximate small generators. In a
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microgrid any generator supplies any load, although economic and technical constraints can result in preferred configurations and schedules. In order to optimize the power flows in the branches of the distribution systems, a microgrid is equipped with Load Controllers (LC) and Microsources Controllers (MC), that are interfaces to control interruptible loads and microsources (active and reactive generation levels), and a MicroGrid Central Controller (MGCC) that promotes technical and economical operation and provides set points to LC and MC. During the grid-connected operation mode the MGCC interfaces with MC, LC and performs studies (forecasting, economic scheduling, Demand Side Management functions, etc.). During the island operation mode the MGCC changes the output control of generators from a dispatch power mode to a frequency mode, performs a secondary control (storage devices, load shedding, etc.) while LC and MC are performing the primary control, and, eventually, disconnects some loads according to a well precise function. Fig.1 shows the typical layout of a MV microgrid. Currently, the interest in the issue of managing these systems is quite high. The interest in these systems is motivated by the possibility to implement on a large scale renewable energy sources (RES), to limit green house gas (GHG) emissions, also reducing the transmission power losses, and to delay or even prevent the construction of new energy infrastructures. The co-ordination of all these generating and loading units is a quite challenging issue requiring distributed intelligence applications; for this reason these modern distribution systems are also referred to as Smart Grids. In the technical literature a few articles propose operational solutions for microgrids because of the need of interdisciplinary knowledge. Some papers [2] are devoted to designing optimal management strategies. In [2] an optimization algorithm able to individuate the subdivision of a given distribution network into an optimized number of sustainable microgrid is proposed. The method provides the best configuration of microgrids in an existing distribution system: the optimal arrangement is the one that maximizes the sum of the savings in both the cost of energy purchasing and the cost of service interruptions. Other strategies are devoted to the identification of control strategies. [3] proposes a control strategy for inverter based DGs and a
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protection scheme are carried out and a coordination between them is proposed to control both voltage and frequency during islanded operation. While in [4] an efficient control system for microgrids management is proposed. The control system manages both the transient and the steady state features of the electrical system. The application is devoted to the implementation on a small Low Voltage test facility at the CESI (Centro Elettrotecnico Sperimentale Italiano, Milan, Italy). In [5] the issue of the autonomous control of Microgrids is treated. Finally, in [6] several schemes for sharing power between generators in microgrids are compared and the minimization of fuel use in a microgrid with a variety of power sources is then discussed. In this paper, the issue of optimal real and reactive power dispatching and the underlying load flow problem is faced. The problem is non linear, constrained and multiobjective. Knowing the hourly upper and lower production limits of each unit and the hourly loading level of each bus, the objectives to be achieved are: • the minimization of the power losses;
• the minimization of the overall production costs; • the minimization of the voltage drops. The unknowns of the problem are the hourly power productions of the DG units. The problem is dealt with using a multiobjective evolutionary approach based on non dominance (NSGA-II [7]). When in a microgrid a physical node with a sufficiently large production capability is not available, the choice of the slack bus for the Load Flow solution becomes more complicated. In this paper, the issue has been solved including into the optimization string also the slack bus identifier. In the following, after a review on the load flow and on the power dispatching problem (Section II), the problem formulation (Section III) and the NSGA-II algorithm (Section IV) are briefly presented. Finally application examples on small and medium size test systems (Section V) are provided.
MC
DER
LC DER Load MC
MC LC
LC
Load
Load
HV Network
DER
MGCC MC
HV
DER
MV Load
MC
MC
DER
DER LC Load
Fig. 1. Typical MV microgrids with control devices.
II.
THE DISPATCHING AND LOAD FLOW PROBLEM
The technical economical power dispatching consists in the identification of the optimal set points of the generating units of an electrical system. Typically the objectives are connected to the minimization of the production cost of these units, although also power quality objectives can be considered within the optimization. Identifying the generated power of each unit giving the minimum production cost and the best operating indices requires the solution of the load flow problem. The load flow equations solution allows the knowledge of all the significant voltages and currents in every bus and branch of the network. The load flow problem
has as inputs the generated power of each unit and as outputs the power flows in all the branches and therefore the power losses and voltage profiles. The solution of the load-flow problem requires that the total generated power of a network matches the total demand plus the power losses. However, as such losses can not be determined beforehand, it is necessary to have at least one bus, named slack bus, whose real power generation can be rescheduled to supply the difference between total system load plus losses and the sum of active powers specified at generation buses, named ‘system imbalance’[8]. Usually voltage magnitude and displacement are considered as reference in the slack node. However, while it is irrelevant
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for the load-flow solution which bus is taken as phase origin, the total system imbalance, and hence, power losses, will be affected to a certain extent by the slack bus selection. Since in power dispatch problems the operation costs include the power losses as well, the choice of the most appropriate slack bus for the load flow solution is not trivial. The load-flow problem for microgrids in power dispatch problem formulations has not been treated in the literature with sufficient interest, and mainly the problem was referred not to the absence but to the physical limited capacity of the slack bus. In this paper, exploiting the potential of evolutionary computation, which is based on a guided ‘trial and error’ approach it is possible to include in the solution string the slack bus identifier together with the set of generated power at the voltage controlled buses. The slack bus identifier (chosen among the generation buses) is thus part of the optimization string and the possible exceeding of the production limit is treated as the violation of a constraint that produces the elimination of the considered solution. In the next section, the mathematical formulation of the problem is proposed. III.
minimizing the following objectives: Joule losses Ploss in the system:
obj[1] = min( Ploss ) = min X
obj[2] = min
DG
]
(1)
∑ CPr i ( Pi g ) ⋅ Pi g ⋅ Δti
X i =1, N DG
(3)
where CPri(Pgi) is the fuel consumption cost of the ith source, Pgi the power output of the ith source, considered constant in time interval Δti; - Absolute mean value of the voltage deviations with respect to the rated value Vset: obj[3] = min
THE PROBLEM FORMULATION
X = [ P1g , P2g ,......PNg
(2)
where nbr is the number of branches in the system, Ri is the ith branch resistance and Ii is the ith branch current; - Fuel consumption costs at every time period:
X
The problem studied in this paper is that to optimally manage a microgrid that works under islanded operation. The problem that will be described below is thus managed hour by hour by the MGCC located at one of the generation buses. At this unit the following features are considered as inputs: • estimation of real and reactive power required by the loads in the subsequent time interval, Δt; • estimation of real power production by the DG nodes in the subsequent time interval, Δt. Based on these data, the MGCC elaborates a set of control signals that are sent to the DG units. These signals are turned by suitable transducers into actions over the regulating systems that modulate the power injections at the DG units. First the system must check whether loads are smaller or greater than generated power. If they are greater, a load shedding procedure is activated that disconnects the lower priority loads. At this point, it is possible to identify the optimal set points of the DG units in order to minimize operation costs. Of course, it is hypothesized that these units can store the excess of energy produced at each hour of the day, if these are based on renewables. A N-bus microgrid system is considered with: Nfix load or generation nodes with fixed forecasted real and reactive power demands or injections; NDG controllable distributed generation units. The problem is that to identify the operating points at the voltage controlled buses:
∑ Ri ⋅ I i2
X i =1,n br
1 Vi − Vset N 1=1,...N
∑
(4)
The typical constraints are: • upper and lower limits of the values of the controlled variables, namely the DG units power outputs, taking into account the required power reserves: Pjgmin ≤ Pjg ≤ Pjgmax (5) Q gj min ( Pjg ) ≤ Q gj •
≤ Q gj max ( Pjg )
power transfer limits in the network branches. In (5): - P jg , P jgmin , P jgmax
respectively represent the active
production and the minimum and maximum limits of real power at the jth DG unit; - Q gj , Q gjmin , Q gjmax respectively represent the reactive production and the minimum and maximum limits of the reactive power at the jth DG unit. Based on the above issues, the optimization variable is a record including: - a real valued vector X (1); - the Id of the current slack bus. In this way, the problem of the absence of a real slack bus is treated within the optimization algorithm, since the load flow calculations are carried out with a different slack bus position for each different solution. Of course, when the power transfer limits at the current slack bus are violated, the solution is penalized, following the constraints (5). For this
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constraint violation, the penalization of the solution is carried out by giving an extremely high value to the main objectives and thus eliminating it from the subsequent calculations. The DG units can be equipped with storage units whose operation cost is not considered in the paper. It is well known that such cost is strictly dependant on the charging and discharging cycles; thus, a more precise formulation should include another term of cost including this element. IV.
THE OPTIMIZATION ALGORITHM
The algorithm used for solving the optimization problem is the Non dominated Sorting Genetic Algorithm II, NSGA-II [7]. The concept of non-dominance is one of the basic concepts in multiobjective optimization. For a problem having more than one objective function to minimize (say, fj, j=1,…,m and m>1) any two multidimensional solutions x1 and x2 can have one or two possibilities: one dominates the other or none dominates the other. A solution x1 is said to dominate the other solution x2, if both the following conditions are true: a) The solution x1 is no worse than x2 in all objectives, fj(x1)≤fj(x2), for all j=1….m. b) The solution x1 is strictly better than x2 in at least one objective, or fj*(x1)
