Network Reconfiguration on a System with Distributed Generators in Multi-objective Framework

Gokturk Poyrazoglu

Electric Power Research Institute Power Delivery & Utilization

gokturk.p@gmail.com

Rao Fu The State University of New York at

Buffalo Department of Electrical

Engineering raofu@buffalo.edu

HyungSeon Oh* The State University of New York at

Buffalo Department of Electrical

Engineering hso1@buffalo.edu

Abstract— Network reconfiguration in distribution systems has been studied for more than 20 years. This study extends the problem with a scenario of having significant integration of distributed generators in the middle of radial topology structure. The benefits of Semi-Definite Programming for radial systems are utilized in this study with different objective functions. Later, GridLAB-D has been used with more details to verify the feasibility of all solutions. The analysis reveals that, in contrast to expectation, the minimization of power loss and the minimization of operating cost conflict with each other in network reconfiguration problem. Multi-objective framework is adopted to demonstrate the conflicting objectives. The resultant Pareto optima show that there is a tradeoff between operating the system in the most economical manner or in the most efficient way in terms of power loss.

Keywords— Network reconfiguration, Distributed generation, Power system economics, Power system management, Renewable energy sources.

I. NOMENCLATURE 𝑃"# : Real power demand at Bus k 𝑄"# : Reactive power demand at Bus k 𝑃"% : Real power generation at Bus k

𝑃"% : Max. real power generation at Bus k

𝑃"% : Min. real power generation at Bus k

𝑃"&'( : Real power injection at Bus k 𝑄"% : Max. reactive power generation at Bus k

𝑄"% : Min. reactive power generation at Bus k

Tr : Trace operator C : Cost vector of generators W : Positive semi-definite variable matrix Φ" : Constructed matrix from the admittance matrix Ψ" : Constructed matrix from the admittance matrix Λ" : Constructed matrix from standard basis vectors 𝑉" : Maximum allowable voltage magnitude at Bus k 𝑉" : Minimum allowable voltage magnitude at Bus k p.f. : Power factor

II. INTRODUCTION Number of distributed generators integrated to distribution

system keeps increasing due to their improved efficiencies and reduced costs along with governmental subsidies. As a result, the operation paradigm needs an update to optimally utilize such generation capabilities in a way to enhance the system reliability and to keep the system cost down. This need is integrated into a mathematical formulation – so called Optimal Power Flow (OPF) problem. OPF problem is a nonlinear problem with a nonconvex feasible region in nature, which makes OPF an NP-hard problem. However, recent research activities [1, 2] showed that a poly-time algorithm can solve a relaxation approach of OPF to the global optima. This relaxation may find the global optima of original OPF problem under certain conditions; otherwise, the operating conditions cannot be reconstructed from the solution. However, these conditions are proven to hold in Ref. [3] if the transmission topology is in radial structure.

Distributed generation (DG) can now be described as dispersed, decentralized, small scale on-site generation system [4]. DG's capacity is very diverse, and its capacity can range from several kilowatts to hundreds of megawatts. As long as more DG systems have been utilized in the power system, more accurate and efficient system analysis algorithms are needed to precisely analyze the impact of the DG system on different types of power grids and distribution networks [5].

Grid-connected photovoltaics (PV) system has the advantage of more efficient conversion and utilization of the generated energy [6]. Practically, the PV generation system is one of the fastest growing technologies in the renewable energy field, and this trend will continue to develop over the next few years [7, 8].

Some of the most common impacts of PV integration on distribution systems are: (1) reverse power flow, (2) voltage rise, (3) voltage fluctuations, (4) interaction with voltage-controlled capacitor banks, (5) feeder loading, and (6) power losses [5, 9]. With the technology improving, the system needs to be standardized to ensure that production and application do not create safety and quality issues [10].

A simulation tool is very helpful for the following situations: (1) providing detailed analysis of system performance under the

actual operating conditions, (2) exploring the effects of different load curves, (3) testing system size and determining the optimum dimensions for PV modules, (4) evaluating the capabilities of PV systems in terms of energy production and system life cycle costs [11]. Various simulation tools are used in the literature for PV simulations [12-17].

GridLAB-D simulation software is being widely used by many utilities and distribution system designers and operators, which are taking advantage of the latest energy technologies [18]. This open source software package is considered a cutting-edge simulation and analysis tool with the most advanced modeling techniques in distribution systems [19]. The potential and benefit of deploying distributed energy resources are studied in this paper using GridLAB-D [20, 21].

In this paper, network reconfiguration problem in the form of semi- definite programming (SDP) is formulated. Network topology is now allowed to be a variable instead of being a parameter in network reconfiguration problem while minimizing the selected objective. Network reconfiguration method is first studied on loss reduction by Baran [22] and simultaneously studied by Civanlar [23]. Later, effective solving of loss minimization problem with network reconfiguration was studied in Refs. [24] and [25]. Recently, effect of distributed generators on the price of electricity was studied in Ref. [26]. Lastly, Das [27] presented an algorithm for network reconfiguration with multi-objective problem approach. In order to extend the previous studies on the topic, and fill the gap to solve the problem to the global optima, the SDP framework as well as multi-objective selection are utilized in this study.

Reconfiguration operations may enhance the system reliability, reduce the power losses, and reduce the operating cost of the system. The SDP problem formulation seeks for the global optimal network topology while considering various objectives like minimizing operating cost, minimizing wasted renewable energy, or minimizing real power losses under multi-objective framework [28, 29]. To keep the complexity of the intended problem in a manageable way, a branch-and-bound method with parallel computation capability is adopted.

The rest of the paper is structured as follows. Section III introduces the concept of network reconfiguration and provides insights on operating cost variability. Section IV discusses the traditional unidirectional flow approach on radial systems and introduces the modifications made to the test case to address the impact of distributed generators. Section V and VI serves as case studies performed to study those impacts on single and multi-objective framework. Section VII represents the GridLAB-D implementation and the feasibility analysis of the resultant solutions. Finally, Section VIII concludes the study with the core findings of this paper including the conflicting objectives observed in multi-objective framework and the positive impact of the proposed policy on operations of distribution systems in terms of reliability and economy.

III. EFFECT OF NETWORK RECONFIGURATION ON COST WITH VARIOUS LOAD LEVEL

In power system operation, the electric demand is considered constant for a given time horizon. If network topology is also a constant, there is a maximum amount of load that the assumed

topology can serve, which is called the maximum service capacity. Total power load in the system may vary by external effects i.e. weather, temperature. A power system operator should forecast power demand for the near future and prepare the system for this demand. Here, we would like to show the effect of network reconfiguration on the maximum service capacity while operating the system in the most economical manner. Fig.1 shows a 3-feeder radial power network with three tie-lines in the status of normally open (NO). In order to keep the radial structure of the network, when a decision of closing a tie-line is made, a consecutive line must be opened. For example, if we decide to close (connected) Branch A, then we must open (disconnected) either Branch D or Branch E. The same rule is applied for the tie-line B and C, and the corresponding branches are F-G and H-J respectively. Hereinafter the topology having three tie-lines (A, B, C) open will be called the original topology or Topology 27. And the rest of the topologies that can be created by reconfiguration of the switches will be called Topology X where { }1, , 26X = .

Table I shows the assumed cost of energy, and allowable maximum and minimum voltage magnitude levels at each feeder. Table II shows the assumed real and reactive power demand at each bus in the system at load factor 1.0.

The load factor may vary during the day so that we will assume the normal load level is specified when the load factor is equal to 1. We are interested here to choose a topology with a minimum operation cost to operate our system with various load factors. Fig.2 shows the minimum operation cost of the system with the best 4 topologies and the original topology for comparison.

Figure 1. 16-bus 3-feeder distribution system, Topology 27

TABLE I – COST OF ENERGY

Feeder I Feeder II Feeder III

Cost of Energy ($/MWh) 60.00 30.00 100.00

V_max (p.u.Volts) 1.00 1.00 1.00

V_min (p.u.Volts) 0.95 0.95 0.95

The figure also shows the topology’s maximum service capacity. Fig.3; moreover, shows the decision tree of which topology to use under various load levels. In order to show the effect of network reconfiguration, the original topology is also included into the figure. The original topology can only meet up to 4% increase on the total load; however, there are possible topologies that can serve efficiently even in the case of 12% increase on the total demand.

This small exercise shows that the network reconfiguration may decrease the total operation cost of the system. It also shows that the topology control is a decision support tool for a distribution system operator to have flexibility to serve high power demand. These two motivations prove the concept of this paper, yet we also want to see the impact of network reconfiguration on the system when there are distributed generators that are connected to some buses.

IV. DISTRIBUTED ENERGY GENERATOR INTEGRATION A distribution system is generally operated in a radial

structure. A radial structure is configured like a tree where each

bus is connected to only one feeder in the system, and there is traditionally one source of supply, which hereinafter be called feeder. Distribution systems usually have a few tie lines that connect a radial system to another. These tie lines can be reconfigured in case of emergency to keep the system in service while preserving the radial system structure. The consequence of having a radial system in operation is the ability to easily track the voltage level at which the customers are being served. Because of the radial structure, power can flow only from the feeder to the loads. Kirchhoff’s laws dictate that the power flows only between two points which have potential difference, and the direction of flow is from the high voltage node to the low voltage node. Therefore, the highest voltage node in a radial system must be the feeder so that the power can flow from the source to the loads. Same law applies for each bus in the system, and it leads us to a general conclusion. A radial system with one feeder always has a unidirectional power flow. This basic phenomenon generally goes unnoticed in distribution system studies; however, it will be the main contributor on the proposed formulation.

In this study, we are interested in a distribution system having a radial system structure including one feeder and a few distributed generators. Fig.4 shows the same distribution system in Fig.1 including extra 3 distributed generators located at Bus 6, Bus 9, and Bus 15. We will consider the case where having a distributed generator is widely adopted by the customers, and for simplicity we assume that they have rooftop photovoltaic arrays. Each bus in this distribution system actually represents a substation serving a neighborhood, not just one customer. So that the represented distributed generators at Bus 6, 9, and 15

Figure 2. Minimum operation cost for best five topologies w.r.t. load level

Figure 3. Decision tool for topology selection

TABLE II – REAL AND REACTIVE POWER DEMAND AT LOAD FACTOR=1.0 BUS ID 4 5 6 7 8 9 10 11 12 13 14 15 16

2.1 3.15 2.1 1.575 4.2 5.25 1.05 0.63 4.725 1.05 1.05 1.05 2.205

1.68 1.575 0.84 1.26 2.835 3.15 0.945 0.105 2.1 0.945 0.735 0.945 1.05

can be considered as an aggregated rooftop solar arrays in that neighborhood.

V. DISTRIBUTION SYSTEM OPERATION WITH UNI-DIRECTIONAL FLOW

As mentioned in Section III, traditional operation of the distribution system accepts the fact that there is only one feeder so that the power has a unidirectional flow, which can be rephrased as a flow from the feeder to the loads. Hereinafter we will call this type of operation as the current policy. The current policy dictates that the voltage at the From Bus should be greater than the voltage at the To Bus in order to keep the unidirectional flow. This phenomenon is usually disregarded in studies of the distribution system, mainly because the traditional assumption of no power injection in between the feeder and the load. However, recent developments on renewable energy generation and highly motivational federal and state incentives promote customers to have a renewable energy generator. Widely adoption of renewables or distributed generators may increase the power injection at a distribution bus, as well as make the power injection positive. Power injection is defined as the difference of power generation and the power demand at a bus as is shown in Eq. (1). So, a bus with a positive power injection has greater production than the load at that bus. We will consider the bus with positive power injection as a second feeder in the radial structure.

inj g dk k kP P P= − (1)

The bus voltage is directly proportional to the power injection at that bus. An increase on power injection rises the voltage. As discussed earlier, the direction of flow is related with the neighboring voltages, so that the change on the status of the bus from being a load bus to being a feeder bus may affect the direction of the flow. If there is a bus located in the middle of the radial system and having a higher voltage than the both buses connected to it, one of the branches must have a reverse power flow. In such case, a reverse flow is obviously a violation of current policy of having a unidirectional flow. In order to satisfy the current policy in our simulations, extra constraints are implemented to keep the system in radial structure with the unidirectional flow. These constraints put a limitation on the maximum generation from distributed generators, and evidently lead to waste of energy.

We are here interested in finding a feasible operation state for our distribution system while minimizing the operation cost of the system. We modeled the problem as an AC Optimal Power Flow (ACOPF) in the form of SDP as shown below.

(2a) and (2b) models the real and reactive power balance equalities for each Bus k∈Κ . (2c) models a box constraint for voltage magnitude for each Bus k∈Κ to be in between a maximum and minimum allowable limit. (2d) and (2e) are the ACOPF variable representation in the form of SDP. The former forces the variable W to be a positive semi-definite matrix and the latter is a necessary condition to recover a meaningful solution for ACOPF. Keeping the latter in the constraint set also

proves that the solution of (2) is actually the global optimizer of ACOPF problem. (2f) is our additional constraint explained earlier in this section. It puts a constraint on the voltage magnitude at From Bus to be always greater than the voltage magnitude at To Bus. This inequality represents the current policy in ACOPF so that the solution of problem (2) always satisfies the unidirectional flow requirement.

Here the question of interest is that is there any impact of current policy on the ability of injecting all available renewable energy. The problem with each 26 topologies and the original topology with a constant solar power availability parameter as given in Table III is solved. The expectation is that even though a significant energy generation is available from distributed generators, due to high availability of sun, the current policy of unidirectional flow prevents the whole energy being injected. This occurs because more power injection means high voltage

Figure 4. The location of DGs introduced to the test system

(2)

(2a)

(2b)

(2c)

(2d)

(2e)

(2f)

magnitude, but the mathematical programming has an additional constraint on the voltage magnitude.

TABLE III – AVAILABLE ENERGY GENERATION FROM DISTRIBUTED GENERATORS

Bus 6 Bus 9 Bus 15

Available Energy Generation (MWh) 4.00 8.00 4.00

Fig.5 shows a 100% stacked chart for injected and wasted energy when a specific topology is used. Additionally, the minimum operation cost of the system is also illustrated in black line and markers for each topology. The wasted energy is defined as the difference between available energy and the injected energy; the former is a parameter given in Table III and the latter is a variable calculated out of the SDP. As shown in the figure, 13% in average is wasted because it is not possible to inject all available energy to the system due to the unidirectional flow rule.

Another observation from Fig.5 is that there is no direct relation between the minimum operating cost and the amount of wasted energy. The expectation was to observe an increase on the cost when there is an increase on the wasted energy; however, at the time changing the topology of the system from Topology 10 to Topology 11 for example, an increase on the wasted energy is observed but not on the operating cost. This unexpected observation leads this study to focus more on this subject by using multi-objective optimization. The further findings are discussed in Section V in detail.

This case study shows that the existence of current policy of unidirectional flow on distribution network causes up to 20%

wasted energy, so the question of interest is now what if a new policy is assumed that allows bidirectional flow in the distribution system while keeping the radial structure of the system. In order to simulate the proposed policy, the constraint (2f) from the problem’s constraints set is dropped.

Fig.6 shows a 100% stacked chart for injected and wasted energy when a specific topology is used under the proposed policy. As before, the minimum operating cost of the system is also illustrated in black line and markers on the figure. Visual observation of Fig. 5 and Fig. 6 reveals that the wasted energy is reduced significantly after the unidirectional flow policy is dropped from the simulations. There is; however, still some wasted energy on various topologies stating that the unidirectional flow is not the only challenge on injecting power from DGs. The location of the DG is also playing a key role on the amount of power injection to serve the reliable voltage level to all customers in the system.

VI. MULTI-OBJECTIVE OPTIMIZATION In this section of the paper, the objective function is

modified from being minimization of the total operating cost to be minimization of real power loss. The case study focuses on the current policy on distribution systems, so that we will keep the whole constraint set, but the objective function is replaced with Eq. (3) being the minimization of total power losses.

1min { }

K

kW kTr W

=

Φ∑ (3)

An interesting observation is made here: an opposite direction of improvement between power loss and operation cost. The operation costs of the system when Topology 7, 21,

Figure 5. Wasted energy percentage with different topology usage and uni-directional flow constraint

Figure 6. Wasted energy percentage with different topology usage and bidirectional flow constraint

and 22 are deployed are the bottom 3 out of all topologies; however, the highest three power loss cases are observed at the exact same topologies. Fig.7 shows the results for each Topology X in a chart with two y-axes. The left axis related to the blue line represents the total power loss, and the right axis related to the green line represents the minimum total operating cost. In contrast to expectation of having same improving direction within both minimization of power loss and operating cost, this example shows an unexpected opposite improving direction. When the topology is a variable that can be re-configured in distribution system rather than being constant, the minimization of power loss and the minimization of operating cost are no longer converge to the same operating conditions. When there are two conflicting objective functions as in this study, the preferable approach is utilizing multi-objective framework. In these situations, there is no single solution that simultaneously optimizes the two conflicting objective functions but infinitely many inferior solutions, the Pareto optima, for the problem.

For each topology, two individual objective function values are illustrated in a scatter chart to visually observe the Pareto optima of this problem. 27 results for 27 different topologies are illustrated in Fig.8. Operating the system under Topology 7 is found to be the most economical way of operation; however, it leads to almost 150% increase on the real power losses. In contrast, operating the system under Topology 10 has the lowest power losses among all topologies; however, the operating cost is increasing 50% in comparison to the most economic case. One more pareto optimal is also observed for this case study being use of Topology 4. In that case, neither the total power loss nor

the operating cost is minimized; but there has been a tradeoff between them.

VII. FEASIBILITY VERIFICATION USING GRIDLAB-D GridLAB-D has the abilities to help system designers and operators observe that, if we make a change to one part of the distribution system, what impacts it may have on the rest of the grid [18]. Compared with MATPOWER, the models in GridLAB-D are built on detailed physical information of all devices in the system. Taking line parameters as an example. MATPOWER uses resistance, reactance, and line charging susceptance. Yet in GridLAB-D, line distance, conductor configuration, and line spacing can be applied to represent an actual line. Besides that, GridLAB-D can schedule load operation plans depending on load changing through time. Therefore, such models may be considered as a pre-design to verify system feasibility. For example, the project in Ref. [30] used GridLAB-D to calculate the power flow due to its significantly detailed analysis. However, GridLAB-D does not contain a few certain features which MATPOWER owns.

Figure 7. Minimum operation cost and real power losses with different topology usage

Figure 8. Multi-objective optimization with Pareto optimal solutions

MATPOWER is able to run optimal power flow, and the results include not only power flow and power loss data, but also generator costs. GridLAB-D does not have such capability. Its primary function is still simulating traditional power flow. In our case, using network configuration showed in Fig.4, we built the system as shown in Fig.9.a (Topology 27) in MATLAB. After running GridLAB-D simulation, a voltage contour plot in Fig.9.b. can be obtained.

Overall, from voltage contour plots of all 27 topologies, no critical low voltages (below 0.95 per unit) have been detected in

any topologies, which indicates that all 27 topologies are feasible according to GridLAB-D simulation outcome. If we set the power factor of all the inverters to be 0.85, the best voltage scenarios are Topology 10, 23, and 24, with the same lowest voltage on Bus 12 at 0.988 per unit, while the worst scenarios are Topology 7, 21, and 22, with the same lowest voltage on Bus 5 at 0.975 per unit.

Described in previous statement, three solar panel models are placed on Bus 6, Bus 9 and Bus 15 along with inverter models. [31] indicates that, power factor of grid-connected solar

Fig 9. Network configuration in Fig.4 and its voltage contour plot

Fig 10. Voltage contour plots of Topology 10, which is the best voltage scenario among all 27 topologies. From left to right, power factor of PV is 0.8, 0.85

and 0.9. With power factor increasing, reactive power is decreasing, as well as the voltage on Bus 12.

Fig 11. Real power loss (a) and reactive power loss (b) of all 27 topologies from GridLAB-D power flow simulation

inverter can be set to 0.8, 0.85 and 0.9. As we know, smaller power factor provides larger reactive power, which has more positive influence on bus voltage.

On the other hand, if real power is fixed, higher reactive power means higher maximum power point tracking (MPPT). More power needs to be converted from the solar. Thus, if lowest bus voltage can still meet the voltage requirement, higher power factor is more effective to send the real power to the loads. Also, real and reactive power losses have been collected from the GridLAB-D power flow simulation as shown in Fig.11. If we compare the real power loss in Fig.7 with Fig.11.a, we could see that the power losses from two different simulation tools are similar to each other.

VIII. CONCLUSION Network reconfiguration is a widely used operational tool in distribution systems to provide reliable and economic service to all end users. This study extends the previous works published on the subject by introducing the distributed generators in a scenario of having significantly large capacity in the middle of a radial network. While the maintaining the radial structure is secured in the simulations, the unidirectional flow limitation is observed to be a challenge to inject all available renewable energy. However, the allowance of bidirectional flow in the radial structure while making sure the acceptable voltage levels are maintained at the service bus reduces the wasted energy significantly. The analysis of the test cases also reveals that the minimization of power loss and the minimization of operating cost is no longer accord with one another. Therefore, a multi-objective framework is utilized to present the Pareto optima in network reconfiguration that enables tradeoff between economics and efficiency of the system. GridLAB-D software is also used to simulate the network under realistic parameters, and thus the feasibility of the operating conditions found from the utilized semi-definite programming approach is verified. With visualized interface and contour plots, all 27 topologies are found to be feasible and Topology 10 has the lowest power loss, both in real and reactive power. This matches the findings from the multi-objective optimization approach.

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