Assessing the impact of incentive regulation on distribution network investment considering distributed generation integration

Electrical Power and Energy Systems 89 (2017) 126–135

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Assessing the impact of incentive regulation on distribution network investment considering distributed generation integration Yalin Huang ⇑,1, Lennart Söder Teknikringen 33, KTH Royal Institute of Technology, Stockholm, Sweden

a r t i c l e

i n f o

Article history: Received 30 June 2016 Received in revised form 29 November 2016 Accepted 25 January 2017

Keywords: Network investment Distributed generation Incentive regulation Revenue cap regulation Performance incentive regulation

a b s t r a c t In a deregulated power system, incentive regulations for network owners are designed to direct the network investment. An innovative method that assesses the incentive regulation in distribution networks is proposed in this paper. The method quantifies the interplay between incentive regulation, network investment, and network performances. It allows regulators and the distribution system operators (DSOs) evaluating the economic effects of investments within the incentive regulation framework. Considered network investments include the investment in network infrastructure and performance improving. The assessment is based on a network investment optimization model considering multiperiod optimal power flow and regulatory constraints. The main contributions of this paper include the modeling of the incentive regulations and the quantification of the impacts of incentive regulation on network infrastructure investment and performance improving investment. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction 1.1. Motivation In a deregulated power system, power system operators transit from cost-based regulation to incentive regulation. This transition can impact on distribution system operators’ (DSOs’) investment decisions [1]. Incentive regulation has shown an impact on shortterm innovation and cost reduction, but the impact on long-term infrastructure investment has proven to be limited [2]. However, incentive regulation should be designed to encourage efficient long-term infrastructure investment to achieve a sustainable energy sector [1]. At the same time, more and more distributed generation (DG) is connecting to the distribution systems, and DG should be considered by DSOs as an alternative to network expansion, according to the EU Electricity Directive Article 14/7 [3]. Therefore, regulations of DSOs should recognize the impact of DG on DSO performance since the DG penetration affects the economic benefit and costs for the DSO [4]. Moreover, investigating metrics for the quantification of the most important performances is recommended by the Council of European Energy Regulators (CEER) [5]. Therefore, it is important to analyze and quantify the interplay between the incentive regulation, network investment

⇑ Corresponding author. 1

E-mail address: [email protected] (Y. Huang). The financial support for this project from Energiforsk is greatly acknowledged.

http://dx.doi.org/10.1016/j.ijepes.2017.01.018 0142-0615/Ó 2017 Elsevier Ltd. All rights reserved.

and network performance. Moreover, the quantification has been studied by individual DSOs or by a case-to-case approach, but not much academic research has been found to the authors’ best knowledge.

1.2. Literature This paper presents the results of interdisciplinary research. It combines regulatory economics and power system engineering. The literature focusing on both research areas regarding incentive regulations is reviewed below. Papers [6,7] discuss the design of incentive regulation from the point of view of economic theory. The advantages and disadvantages of different regulatory schemes are analyzed theoretically. Regulatory impact on infrastructure investment is analyzed in [8]. Review studies on how investment decision in an energy utility changes with the change of regulatory schemes in European countries can be found in [1,9]. The studies show that the investment is sensitive to regulatory settings in the incentive regulation. Moreover, many empirical studies are found regarding incentive regulation in distribution networks. An empirical model, using input distance functions, is developed in [10] to estimate the relationship between efficiency gain and investment under the incentive scheme. A statistical model, Bayesian Model Averaging, is used in [11] to consider the uncertainty around the response of the regulated firms to different incentive instruments. Data Envelopment Analysis technique is used in [12] to study the impact of incentive

Y. Huang, L. Söder / Electrical Power and Energy Systems 89 (2017) 126–135

127

Nomenclature

x x1 x2 x02 kloss

a

bE bP

c B0 Bt C cap t C oper t

adjusted incentive for network utilization improvement during the regulatory period incentive from loss reduction during the regulatory period incentive from network load factor increase during the regulatory period limited incentive from network load factor increase during the regulatory period energy price for losses DSO’s share of benefit from loss reduction network fee for the consumed energy to the upper stream grid (€/kW h) network fee for the subscribed peak power to the upper stream grid (€/kW,yr) limit on the total incentive in percentage of the allowed return on costs reference value of fee paid to the upper stream grid fee paid to the upper stream grid during year t annual network investment annual operational cost which includes the cost for losses and curtailment

regulation of quality of service in the UK distribution networks. Benchmarking analysis is used in [13] to study the impact of incentive regulation on network security. Besides these quantitative economic studies, some studies using an engineering modeling approach considering the incentive regulation in power systems are also found. Many researches have earlier studied DGs impact on distribution network investment [14–17], regulation impact on DG connection [18,19], and distribution network investment considering active demand management [20,21]. In addition, there are some studies that evaluate the impact of regulatory framework including incentives for network performances [2,22–25]. A network load flow model and a financial spreadsheet model are combined to study the incremental net impact of DG on DSOs in [22]. However, the physical planning model does not consider the economic regulation or the investment timing. Distribution network investment strategies for incentive regulation in a Finnish case are studied in [23]. The incentive regulation on network losses in distribution networks in Spain is analyzed in [24]. Both papers use a cost-benefit analysis in a case-to-case manner. A systematic method to evaluate the impact of the regulatory framework in the UK is presented in [2]. The DSO in the model has the possibility to select the type and number of wind turbines to be allocated. However, this possibility is not always allowed in an unbundled distribution network, even though the DG ownership for DNOs can be beneficial [19,26]. Moreover, the network upgrade is not considered in [2]. The analysis is only based on the current network without reinforcement. Network upgrade solutions are considered in [25] together with specific alternative solutions (non-traditional network investment solutions); however, the focus is on the network investment including the specific alternative network upgrade solutions rather than evaluating the impact of the regulatory framework. In this paper, we develop a model to study another regulatory framework, the Swedish one. The developed model optimizes the network upgrade and DG connection subject to the technical constraints and the incentive regulation. We use the developed model to evaluate the effectiveness of the regulation and the sensitivity of some parameters in the regulation.

D Eloss 0 EQ0 EQ mfp m Pdav g b0 P b P bd P Rt b R b EG R

number of days considered reference value of the energy loss reference value of the energy flow through the feeding point Q energy flow through the feeding point Q during the regulatory period load factor at the feeding point load factor at the load point average power at the feeding point in a day during the regulatory period reference value of the peak power at the feeding point peak power at the feeding point during the regulatory period peak power at the feeding point in a day during the regulatory period annual revenue in during year t allowed return on costs during the regulatory period revenue cap for a more efficient grid during the regulatory period

1.3. Contribution There is relatively little academic analysis of the effects of the incentive regulation mechanisms on the performance of DSOs exante [6,25], especially considering DG integration, compared to empirical works that examines the effects of incentive regulation ex-post. All the ex-ante studies [2,22–25] do not establish a cost benchmark for investment in improving the performance based on the incentive regulation framework. The studies focus on some specific investment alternatives, for example demand response-based smart solutions. The here proposed method establishes a contribution to quantify the cost benchmark ex-ante in order to improve the performances based on the given incentive regulation framework. In the assessment, we propose a modeling approach as shown in Fig. 1. One of the main contributions in this paper is that we model the incentive regulations and have effectively combined it into the network investment model. The model provides quantitative and systematic assessment. On the one hand, the model is able to consider the physical constraints, fluctuating load and DG, load shedding and DG curtailment (due to network limits); on the other hand, it considers the regulatory constraints due to incentive regulations. The modeled incentive regulations are revenue cap regulation, and performance incentive regulation for loss reduction and load factor increase. The other main contribution is the implication for the regulatory policy design. The implication is obtained from the quantifying costs as benchmarks for investing in performance improvement. The benchmarks can assist the DSOs in evaluating different investment options that relate to performance improvement. Furthermore, these benchmark can assist the regulators in determining the correct incentives for network performance considering DG integration. The studied performance incentive regulation aims to reduce the losses in the system and to increase the load factor by engaging in demand side management (DSM) or other innovative solutions from DSOs. It induces DSOs to recognize the potential of the DG and consumers in order to invest and operate the network more efficiently. This is in line with the aim of EU smart grids regulation targets [27] and is currently applied in Sweden. We examine the impact of applying the Swedish incentive regulation in distribution networks with

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Input data The investment model: Obj: max profit s.t. Regulatory constraints Technical constraints Opmal soluon

Outputs: Opmal infrastructure investment

Network performance

Benchmark prices for invesng in performance improvement

Fig. 1. Flowchart of the assessment; contributions are highlighted in red. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

and without DG, based on numerical applications of the model. The modeling approach for the Swedish performance incentive regulation is able to extend to other performance incentive regulations. 2. Distribution network investment background A traditional way of investing in network infrastructure is to dimension the network for the ‘‘worst case” of the load profile, which is usually the highest load case [28]. With more and more DG in the network, the ‘‘worst case”, which can be when the load is the highest or the DG is the highest, is no longer as obvious. Furthermore, the generation from some renewable sources can vary a lot in a short time, for example wind power. If the network is designed according to the very short time ‘‘worst case”, the infrastructure investment would be high and the capacity of the network is not used most of the time [29]. Otherwise, the capacity of the network may not be enough and some generation needs to be curtailed for certain time periods. DG curtailment has been recommended to be allowed in [30]. Curtailment practice for renewable energy has been reviewed in [31,32]. Some innovative curtailment schemes are quantitatively analyzed in [33]. In this paper, the curtailed energy is allowed and compensated by the DSO according to the agreement between the DSO and the DG owners. The distribution network infrastructure investment is modeled as a two-stage decision making optimization problem. The investment decisions considered in the model are choices of new DG connection routes, conductors of the connection lines, substations updates and reinforcements in the existing lines. These as well as the optimal timing of these decisions are represented by integer variables. These decisions are made at the first stage under uncertainties of load and DG. When the uncertainty is disclosed, the second stage decisions are taken. In this model, the second stage decisions are the timing and amount of DG curtailment. Load shedding is assumed not to be allowed. These decisions depend on the current in each line and voltage in each node, which are determined when the uncertain load and DG production are realized. The investment model considers essential network constraints such as voltage, thermal limits and power balance. It also properly addresses the economic constraints from economic regulation as presented in the following sections. 3. Regulatory background for the model-incentive regulation for distribution networks in Sweden 3.1. Revenue cap regulation Under the revenue cap regulation, the maximum yearly revenue that the DSO is allowed to receive in a year is limited by the rev-

enue from the previous year considering inflation and performance for a period of several years [34]. The components in the Swedish revenue cap for the current regulatory period of years 2016– 2019 is illustrated in Fig. 2. The revenue cap defines the maximum total revenue that a DSO can receive for the regulatory period. Efficiency change defines the efficiency improvement on the operations. The power quality and network utilization indices are defined by the regulator to be used to quantify the incentives for qualified and efficient network investment. The calculation for the allowed return on costs is presented in [35], the performance incentive from the quality regulation is presented in [36], and the calculation and motivation for the performance incentives from network utilization are presented in [37]. In this paper, the focus is on the performance incentives for the network utilization. The performance of the DSO depends not only on DSO’s investment decision, but also on objective reasons such as the geography of the network, the types of consumer or DG and the size of the company. In order to limit the impact of the objective reasons, the Swedish regulator sets a limit on the sum of economic incentives each DSO can obtain.

3.2. Performance incentives for efficient network utilization The performance incentives for distribution networks utilization are calculated based on two performance indices [37]. One is to motivate the DSO to reduce losses in the network, the other is to motivate the DSO to increase the load factor. Network losses can be affected by the DSO’s investment decision. An incentive to reduce the losses can benefit the network users, since the cost of losses will be recuperated from them; and can benefit the society, since less energy will be produced to cover the losses. The economic incentive from loss reduction is shared by the DSO and the customers. The ratio to share is determined by the regulator. A similar formulation of incentives for loss reduction can be found in many other European countries, for example Austria and Spain [27]. The load factor of the network is the ratio between the average power and the peak power on the feeding point (the connection point to the upper stream grid) of a distribution network in a certain period. It is considered as an index for efficient utilization of the networks in the Swedish regulation. This is because an effective way of using the network is to level off the flow profiles, considering there is load and generation in the network. The load factor defined in the Swedish regulation is the yearly mean value of the daily ratios during a regulatory period. A decrease of the average flow variation leads to an increase of the load factor. Furthermore, increasing the load factor of the network is economically attractive

Y. Huang, L. Söder / Electrical Power and Energy Systems 89 (2017) 126–135

• Controllable cost

•

DSO’s input

• Efficiency change Regulator’s input

Regulator’s

•

Noncontrollable cost

•

Depreciation

129

•

Performance measures (Quality and network utilization)

Capital base

•

•

Performance indices (Quality and network utilization)

Return of capital

• Revenue cap = Allowed return on costs + Adjusted incentives (quality and network utilization)

output

Fig. 2. Swedish revenue cap regulation framework.

for the DSO. Therefore, this incentive aims to encourage DSOs to recognize the contribution from the DG or DSM to the network. By levelling off the flows in the network, the peak power in the network and also the losses are reduced, giving the total energy unchanged. Therefore, it can lead to network investment reduction. The loss reduction can be doubly rewarded by these two incentives. However, they are still different incentives. The loss reduction incentive provides a static value for the loss reduction at any time; the loss reduction in the peak load moments provides a more dynamic value for the loss reduction. Therefore, the loss reduction at times of peak load is more beneficial than that at other times. This reflects different benefits of the loss reduction at different times.

x1 ¼ kloss

Eloss 0 EQ0



Eloss

!

EQ

EQ  a

ð2Þ

where

x1 = Incentive from loss reduction during the regulatory period. kloss = Energy price for losses.

Eloss = Reference value of the energy loss. 0 Eloss = Energy loss during the regulatory period. EQ0 = Reference value of the energy flow through the feeding point Q. EQ = Energy flow through the feeding point Q during the regulatory period. a = DSO’s share of benefit from loss reduction.

4. The model 4.1. Revenue cap The revenue cap is modeled as two parts [37]. One part is the adjusted incentives, the other one is the allowed return on costs as shown in Fig. 2.

b EG ¼ R bþx R

mined from historical data. The difference is valued by the electricity price. The incentive for loss reduction is modeled as [37]:

ð1Þ

where b = Allowed return on costs during the regulatory period. R

x = Adjusted incentive for network utilization improvement during the regulatory period. b EG = Revenue cap for a more efficient network utilization durR ing the regulatory period. In this paper, the adjusted incentive are modeled only from performance incentives for network utilization. 4.2. Performance incentives for efficient use of the network 4.2.1. Incentive for loss reduction The economic incentive from loss reduction in the regulation is defined based on a self benchmark approach. The loss is normalized by the total imported or exported energy in the network and this normalized loss serves as an indicator for loss reduction. This indicator is compared with a reference value which is deter-

In the model, the energy loss is calculated based on power flows. In reality, the losses are defined by two measurements. One is the measurement on the network user’s side, the other is at the feeding point. The difference between these two measurement is considered as losses. Therefore, the losses that are calculated from the measurement contain the losses from power flows and the losses from electricity thefts and not metered electricity consumption. Therefore, the modeled losses is a conservative approximation of the incentives from loss reduction. 4.2.2. Incentive for load factor increase In the regulation, the economic incentive from the load factor increase is related to the network fee DSOs paid to the upper stream grid. The total fee is normalized by the total imported or exported energy in the network. This normalized sum is compared with a reference value which is determined from historical data. If the sum increases, the incentive is set to zero. If the sum decreases, the incentive will increase accordingly with the load factor. This sum can decrease due to wind power integration [38]. The incentive for network load factor increase is defined as [37]:

x2 ¼ mfp ¼

B0 EQ0



B

!

EQ av g

D Pd 1X bd D d¼1 P

EQ mfp

ð3aÞ ð3bÞ

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Y. Huang, L. Söder / Electrical Power and Energy Systems 89 (2017) 126–135

where

x2 = Incentive from network load factor increase during the regulatory period. B0 = Reference value of fee paid to the upper stream grid. B = Fee paid to the upper stream grid during the regulatory period. mfp = Load factor at the feeding point. Padv g = Average power at the feeding point in a day during the regulatory period. b d = Peak power at the feeding point in a day during the regulaP tory period. D = The number of days considered. The network fee paid to the upper stream grid is modeled by two parts [39]; one part is related to the subscribed capacity, the other part is related to the transported energy as shown in (4). The subscribed capacity is decided by the DSO for the coming year. It is assumed that the DSO always subscribes the capacity according to the peak power in the network. The price of the network fee to the upper stream grid is assumed unchanged from the reference years and the considered regulatory period. In order to model this incentive (3b) linearly, the load factor at the load point is used. Modeling the load factor at the load point is also reasonable, because the DSM devices are implemented at the load points. The load factor at the load point and the feeding point are the same if the network is lossless and there is no DG in the network.

b 0 þ bE EQ bP P 0

x2 ¼

EQ0



b þ bE EQ bP P EQ

!

EQ m ¼

b0 P EQ0

!

b Q bP m EQ  P

ð4Þ

where bP = Network fee for the subscribed peak power to the upper stream grid (€/kW,yr). bE = Network fee for the consumed energy to the upper stream grid (€/kW h). b 0 = Reference value of the peak power at the feeding point. P b = Peak power at the feeding point during the regulatory P period. m = Load factor at the load point. 4.2.3. The limit on the total incentive The limit on the total economic incentive each DSO can obtain is defined as a percentage (c) of the allowed return on costs in the Swedish regulation [37]. Furthermore, the incentive for the load factor is only counted if it is positive in the Swedish regulation. These constraints are modeled as follows: (see Fig. 3)

8 b b > if x1 þ x02 P c  R > < c  R; x ¼ x1 þ x02 ; if  c  Rb 6 x1 þ x02 6 c  Rb > > : b b c  R; if x1 þ x02 6 c  R 

x2 ; if x2 P 0 0; if x2 < 0

x02 6 Dpos  M x02 6 x2 þ ð1  Dpos Þ  M

ð8aÞ ð8bÞ

4.3. Optimization formulation The infrastructure investment decision of the DSO is based on maximizing the total profit in a regulatory period. The profit is the net present value (NPV) of the revenue minus the cost. The revenue is limited by a revenue cap considering performance incentives. The allowed return on costs which is not influenced by the incentives is assumed to be defined by the procedure in [35]. The objective for the DSOs is

maxNPV

X

  Rt  C cap þ C oper t t

! ð9Þ

t

where Rt = Annual revenue in the regulatory period. = Annual network investment. C cap t C oper = Annual operational cost which includes the cost for t losses and curtailment. The DSOs have to consider a combination of economic regulatory constraints, as e.g. incentive regulation, together with engineering standards, as allowed voltage variation. The economic incentive in the model is quantified by the network performances, which links the two aspects of constraints. This objective is subject to regulatory constraints as follows: 1. The total revenue in a regulatory period is not higher than the b EG as in (1) revenue cap R 2. The incentives are calculated based on the performance indices as in (2) and (4) 3. The limit on the total incentive is modeled as in (7) and (8) The objective is also subject to a number of technical constraints as listed in the following. 1. Kirchhoff current law and Kirchhoff voltage law. 2. Capacity constraints on the substation and on the electrical lines. 3. Voltage limits on each bus. 4. Logical constraints on network infrastructure investment. 4.4. Solution method

ð5Þ

where

x02 ¼

In order to model the constraint (6) linearly, a binary variable (Dpos ) is introduced for each regulatory period.

ð6Þ

In order to model the constraint (5) linearly, two positive variables (Z 1 ; Z 2 ) are introduced with a penalty in the objective function:

x ¼ x1 þ x02 b 6 x þ Z1  Z2 6 c  R b cR EG b þ x þ Z1  Z2 b ¼R R

ð7bÞ

Z1 P 0

ð7dÞ

Z2 P 0

ð7eÞ

ð7aÞ ð7cÞ

The input for the model, as shown in Fig. 1, consists of scenarios for load and DG in the planning period, the technical data of the network and the regulation. The problem is formulated as a twostage stochastic programming. The first-stage variables represent the decisions, such as line reinforcement, that must be taken before the realization of the uncertain inputs. These decisions can be implemented in the next stage. The second-stage decisions, such as the timing and the amount of DG curtailment, which should ensure the system operation is within the constraints dictated by the investment decisions. The regulatory constraints are modeled linearly, and the non-linear technical constraints are linearized by the successive linear IV ACOPF algorithm developed in [40]. Therefore, linear optimal power flow (OPF) subproblems are solved successively, and the convergence criteria are designed by the guidelines developed in [40].

Y. Huang, L. Söder / Electrical Power and Energy Systems 89 (2017) 126–135

131

Fig. 3. The limits on the total incentive.

5. Model application To apply the proposed model, a radial network with 21 load nodes and two DG plants which have asked for connection is created. The type and size of the DG are not decided by the DSO; however, the connection points to the network are modeled as investment decisions. The mixed integer optimization programming is performed in the General Algebraic Modeling System (GAMS) 23.9 using CPLEX solver. The distribution network is displayed in Fig. 4a. It operates at 24.9 kV. Two wind farms are in the pipeline to be connected. In the figure, the square node represents the feeding substation, the wind turbines represent wind farms, and the circles are the load points and wind farm locations (N22 and N23). Continuous lines denote the existing network and dashed lines are candidate routes for new connections. The system details (node data and line data) can be found in [41]. Investment for one regulatory period of four years is considered in the case study. A DG owner applies for a connection to N22 in year 2 and another DG owner applies for a connection to N23 in year 3. The installed capacity of DG accounts for 47% of the total load. In this grid, all lines have two alternatives for upgrade, AL1 is the initial line and AL2; AL3 are the alternatives to upgrade. The cost of upgrading is higher when the capacity is larger. There are three paths to connect each new wind farm into the network. L8; L13, and L21 are for N22. L9; L15, and L24 are for N23. Each new path has three alternatives. The time-varying characteristics of load and DG are modeled by clustering the data into different levels according to seasons, weekdays or weekends. Therefore, six representative days are identified

for a year. Scenarios in each year are obtained by discretizing the distribution function in each representative day. The scenario, which represents the combination between DG and load demand values, is characterized by the number of hours over a year. This number represents the time during which each combination DG/ demand occurs in a year. The scenarios for the following years are generated taking into account the load/DG growth. It is assumed that the stochasticity in each level remains the same in the following years but the magnitude changes. Therefore, the six levels that identified in the first year evolve to next year on one path, which constitutes a so called scenario fan; cf. Fig. 4b. Twenty scenarios are generated from the probability density functions in each representative day; therefore, in total 480 scenarios (120 scenarios for each year) have been considered. The price for losses (kloss ) is set as the mean electricity price in Sweden in 2013, which is 0.052 €/kW h according to a distribution system operator [42]. Network fee for the subscribed peak power (bP in (4)) is set as 30 €/kW,yr according to the data published by the Energy Inspector in Sweden [43]. The ratio a in (2) is set to 0.5 as in the Swedish regulation [37], c in (5) is set to 5%, and allowed b is set to 800  105 € for the regulatory period. return on costs ( R) The discount rate is set to 8%. The reference network in the case study is when there is no DG connection but the same load increase.

6. Results and discussions The application looks into the DSOs’ investment decisions and performances under the Swedish incentive regulations. In the application, the input load profiles are with three different load

Fig. 4. Sketches for the studied network and scenario generation.

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Y. Huang, L. Söder / Electrical Power and Energy Systems 89 (2017) 126–135

factors (m) but the same total yearly energy consumption at each load point. Load shedding is assumed to be not allowed. DG curtailment is compensated by the electricity price. The network infrastructure investment cost is calculated for two situations, with DG and without DG.

6.1. Results for impact of the incentive for load factor increase Table 1 presents quantified interplay between the incentive for load factor increase, network investment and network performance including the load factor at the feeding point, the loss as a percentage of the consumption, the incentives (x1 and x2 ), the NPV of total allowed incentives and the profit in a regulatory period. Load factor at the feeding point, which is the load factor that is measured at the feeding point according to the definition in the Swedish regulation, is different from the m values in that it is simulated at the load point. This is because the load factor at the feeding point aggregates the network losses and the correlations among nodes. The difference is larger in the cases with DG connection. This can be due to the fact that the DG reduces the average consumption but hardly the peak consumption observed at the feeding point. The Investment cost, which is the net present cost (NPC) of the network infrastructure investment, decreases as the m value increases. For example, the infrastructure investment cost decreases by 24% and 37% when the m increases from 0:5 to 0:6 in the case with and without DG respectively. This means that the increase of the load factor leads to a lower cost investment decision. This is because by levelling off the flows in the network, the peak power in the network reduces, given that the yearly load energy is kept the same for different m values. With the same m value, the investment cost is lower in the system with DG than that without DG. This is true in all case studies, because the DG in the system delays some of the reinforcements. The Loss percentage increases with the increase of the m value. Therefore, the loss reduction incentive (x1 ) decreases. For example, the loss percentage increases 0:8% when the m increases from 0:5 to 0:6 in the case with DG. This is due to the avoided reinforce-

ment: fewer lines that are needed to be upgraded, for example L4 and L5; some of the upgrades are postponed, for example L10 and L23. If the investment is kept unchanged, the loss percentage decreases and x1 increases. However, the increasing incentive due to the loss reduction is less than the saved investment cost. With the same m value, the loss percentage is lower in the system with DG than without DG. Some of the reinforcements are unnecessary in the system with DG, for example L14, L25 and L26 in the case when m ¼ 0:5. It means that DG decreases the losses in this case study. The loss reduction incentive x1 decreases with the increase of m value, because the loss increases as explained in the previous paragraph. Because DG decreases the losses in this case study, the loss reduction incentive x1 in the cases with DG is higher than that without DG. For example, when m ¼ 0:5 the loss incentive in the case with DG is 1:07  105 € higher than that in the case without DG. This reflects the value of DG integration on losses. Thus, the loss reduction sends out a higher economic incentive for systems with DG in this case study. Furthermore, the load factor increase incentive x2 increases with the increase of m. An example of this is, increasing m from 0.5 to 0.6, x2 increases 2:72  105 € and 4:86  105 € in the case with DG and without DG respectively. This is expected since an increase of m means a decrease of the peak power at the load point and can lead to a decrease of the subscripted peak power level at the feeding point. The increase is smaller in the system with DG than without DG. One reason is that the increase of m has bigger impact on the decrease of the peak power in the feeding point, b Q in (4) in Section 4, in the system without DG. Besides which is P that the gain from the decrease of the subscribed peak power level is multiplied by m; the bigger the m is, the higher the x2 is. Furthermore, with the same m, the load factor increase incentive x2 is lower in the system with DG than without DG. One reason is that the imported energy from the upper grid is lower in the system with DG than in the system without DG, therefore EQ in (4) is smaller. Another reason is the load factor at the feeding point is lower in the system with DG. The Total incentive, the sum of the loss reduction and load factor increase incentive, increases with the increase of m value. With the

Table 1 Results for different load factors at the load nodes. Results

Load factor at the feeding point Investment cost (105 €) Loss percentage (%) Loss reduction incentive x1 (105 €)

m = 0.5

m = 0.6

m = 0.7

With DG

Without DG

With DG

Without DG

With DG

Without DG

0.38 329.67

0.42 612.78

0.5 251.09

0.55 388.88

0.56 143.55

0.6 269.53

1.9 8.22

3.1 7.15

2.7 7.37

3.6 6.72

3.3 7.00

4.9 5.59

Load factor increase incentive x2 (105 €)

2.57

5.37

5.29

10.15

7.02

13.70

Total incentive (105 €)

10.79

12.52

12.66

16.87

14.02

19.29

Profits (105 €)

373.89

109.37

458.20

336.74

569.70

456.25

Investment decisions

L1,AL3,T1 L2,AL3,T1 L3,AL2,T3 L4,AL2,T1 L5,AL2,T3 L6,AL2,T2 L7,AL2,T1 L10,AL2,T1 L14,AL3,T2 L16,AL2,T3 L19,AL2,T2 L20,AL2,T2 L21,AL3,T2 L23,AL2,T2 L24,AL1,T3

L1,AL3,T1 L2,AL3,T1 L3,AL2,T3 L4,AL3,T1 L5,AL2,T2 L6,AL3,T2 L7,AL3,T1 L10,AL2,T1 L16,AL2,T3 L17,AL2,T4 L18,AL2,T2 L19,AL2,T2 L20,AL2,T2 L23,AL3,T2 L25,AL3,T4 L26,AL2,T4

L1,AL2,T1 L2,AL3,T1 L3,AL2,T4 L10,AL2,T2 L14,AL3,T2 L15,AL1,T3 L16,AL2,T4 L19,AL2,T4 L20,AL2,T4 L21,AL3,T2 L23,AL2,T3

L1,AL2,T1 L2,AL3,T2 L3,AL2,T4 L4,AL3,T1 L5,AL2,T4 L6,AL2,T2 L7,AL2,T2 L10,AL2,T2 L14,AL2,T2 L16,AL2,T4 L18,AL2,T3 L19,AL2,T3 L20,AL2,T3 L23,AL2,T3

L1,AL2,T1 L4,AL3,T1 L10,AL2,T2 L21,AL2,T2 L23,AL2,T4 L24,AL1,T3

L1,AL2,T1 L2,AL3,T2 L4,AL3,T1 L6,AL2,T2 L7,AL2,T2 L10,AL2,T2 L14,AL2,T2 L18,AL2,T3 L19,AL2,T4 L20,AL2,T4 L23,AL2,T4

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same m value, the total incentive is lower in the system with DG than without DG. This is due to the low load factor increase incentive x2 in the system with DG. This total value is limited by the regulation. In this case the limit is 5% of the allowed return on costs. This parameter should be so low that the DSO does not over-invest in the network. The infrastructure investment would be higher than necessary just for a higher profit. It should also be high enough for the obtained reward to be higher than the infrastructure investment which is needed to increase the performance. This is further analyzed in Table 3. The Profit also increases with the increase of m value in both with and without DG cases. By comparing profits between different m values, the cost benchmark of investment in increasing m values is obtained. If the investment to increase m is lower than the benchmark, it is profitable to invest in increasing m. For example, the cost benchmark to increase m from 0:5 to 0:6 is 84:31  105 €, and the benchmark to increase m from 0:6 to 0:7 is 122:20  105 € if there is DG in the system. By comparing these two benchmarks, the incentive to increase load factor from medium to high is higher than from low to medium in the system with DG. In the systems where there is no DG, the cost benchmark of increasing m from 0:5 to 0:6 is 227:37  105 €, and the cost benchmark of increasing m from 0:6 to 0:7 is 119:51  105 €. By comparing these two benchmarks, the incentive to increase load factor from low to medium is higher than from medium to high in the system with DG. Furthermore, the economic incentive for the DSO to invest in increasing the load factor, for example through DSM, are high, accounting for more than 18% of the profits, in systems with or without DG. With the same m value, the profit is higher in the system with DG than without DG. However, the profit in the system with DG is over-estimated because the allowed return on costs is assumed to be the same as in the system without DG. This overestimation can be limited if the allowed return on costs takes the effect of infrastructure investment delay due to DG into account. 6.2. Results for impact of the incentive for loss reduction By implementing the regulation as the revenue cap without incentives and revenue cap with only the incentive for loss reduction, the infrastructure investment costs and profits of the DSO are shown in Table 2. The infrastructure investment costs do not vary nor do the operational costs, but the total profits do. This means that the economic incentive is not high enough to change the infrastructure investment decisions. The reward/penalty for reducing losses in /kW h can be estimated for a given network. In this example, comparing the case with and without the incentive for loss reduction, the gain due to loss reduction is 7:37  105 € in the case with DG and 6:72  105 € in the case without DG. The incentives shown here are the same as the incentive of x1 shown in Table 1. This is because the optimal infrastructure investment costs and curtailments are the same in these regulatory frameworks. The reward/ penalty price for loss reduction/increase, which is the incentive x1 divided by the reduced losses in kW h, is 0.053 €/kW h in this case for the system with DG. It is 0.001 €/kW h higher than the

expected electricity price. The reward/penalty price for loss reduction/increase is 0.048 €/kW h in this case for the system without DG, which is 0.004 €/kW h lower than the expected electricity price. These prices can be used as a benchmark to evaluate the cost to reduce losses. 6.3. Sensitivity analysis The level of the economic incentives depends on many parameters which are set by the regulation. One of the parameters is the upper and lower limits on the total incentive. Different limits can result in different solutions as shown in Table 3. By changing the limit on the total incentive c in (5), the infrastructure investment cost does not change in this case study. The DSO would not invest more just to obtain higher incentives or invest less due to too low allowed incentives. Thus the limits on the total incentive do not distort the optimal solution from the infrastructure investment point of view. This also shows that the incentives that a DSO can receive is limited by the definition of each indicator rather than the limits on the total incentive. 6.4. Strength and limitations The main strength of the presented model is that it is technology neutral. The investment in the network which improves the performance is incentivized according to the regulation. Given the desired performances, the cost benchmark of investment in any technology to achieve these performances is obtained from the proposed model. This benchmark can be used to evaluate the effectiveness of the incentives for investments in innovation. A cost benchmark of reaching a certain performance is the maximum cost that the DSO can benefit by investing in alternative solutions to reach a certain performance giving the respective performance incentive. It can be used to evaluate the alternative solutions other than the traditional network investment solutions which can reach at least the same performance. If the cost in investing in an alternative solution is lower than the cost benchmark, it is beneficial to choose the alternative solution. It can also be used to evaluate whether the incentive is effective. If the benchmark is lower than any available alternative solution, then the incentive will not be effective in investing in innovative solutions. Last but not the least; the cost benchmark can be used to direct the development of the innovative solution developers. It can give signals for the developer to decrease the costs and develop more desirable functions according to the incentives. Another strength is the flexibility of the model. Given available technologies and devices, for example on-load tap changers (OLTCs), automatic voltage control (AVC), energy storage systems (ESSs), etc., to invest in for improving the performances, they could be modeled as decision variables and corresponding impacts in power flows. Furthermore, if a specific allowance due to the innovative investment is given by the regulation, the corresponding cost function can be modified in order to take that incentive into account. This method has been developed to study the impact for one regulatory period. Therefore, the strategical investment for multiregulatory periods is not considered. The allowed return on costs

Table 2 The impact of loss reduction incentive in systems with m ¼ 0:6. With DG

Without DG

Investment cost (105 €)

b R 251.09

b + x1 R 251.09

b R 388.88

b + x1 R 388.88

Profit (105 €)

445.55

452.92

330.02

336.74

Revenue cap

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Table 3 The impact of incentive limits in a system with DG and m ¼ 0:6. Limits on the total incentive 5

c ¼ 0:02

c ¼ 0:05

c ¼ 0:2

No c

Investment cost (10 €)

251.09

251.09

251.09

251.09

Profit (105 €)

458.13

458.20

458.20

458.20

is simplified and the incentive for quality is not considered in order to study only the impact from the incentives for loss reduction and load factor increase. Moreover, in the case study the load factor at the DG connection point is not controllable. This is because regulating production from DG is related to many other regulations which are outside this paper’s scope. Different DG curtailment regulation and connection tariff may have an impact on the analysis. Further studies considering this aspect are needed. The performance incentives modeled in this paper are based on the Swedish incentive regulation. However, the modeling approach is able to extend to other performance incentives which are regulated as a reward or penalty in deciding the revenue cap.

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