Evaluating the Curtailment Risk of Non-Firm Utility-Scale Solar Photovoltaic Plants under a Novel Last-In First-Out Principle of Access Interconnection Agreement

: AbstractsWith the increasing share of distributed energy resources on the electric grid, utility companies are facing signiﬁcant decisions about infrastructure upgrades. An alternative to extensive and capital-intensive upgrades is to offer non-ﬁrm interconnection opportunities to distributed generators, via a coordinated operation of utility scale resources. This paper introduces a novel ﬂexible interconnection option based on the last-in, ﬁrst-out principles of access aimed at minimizing the unnecessary non-ﬁrm generation energy curtailment by balancing access rights and contribution to thermal overloads. Although we focus on solar photovoltaic (PV) plants in this work, the introduced ﬂexible interconnection option applies to any distributed generation technology. The curtailment risk of individual non-ﬁrm PV units is evaluated across a range of PV penetration levels in a yearlong quasi-static time-series simulation on a real-world feeder. The results show the importance of the size of the curtailment zone in the curtailment risk distribution among ﬂexible generation units as well as that of the “access right” deﬁned by the order in which PV units connect to the grid. Case study results reveal that, with a proper selection of curtailment radius, utilities can reduce the total curtailment of ﬂexible PV resources by up to more than 45%. Findings show that non-ﬁrm PV generators can effectively avoid all thermal limit-related upgrade costs.


Introduction
Electric power distribution systems are traditionally designed and planned to move energy from the distribution substation to end users. In this design, all the energy needs from consumers are centrally supplied. With the increased interest in distributed energy resources (DERs), distribution system operators (DSOs) are receiving increasing numbers of customer generation applications. These customers, commonly referred to as prosumers, own generation assets on their premises. Often, these assets are solar photovoltaic (PV) plants as a result of their modularity, decreasing solar panel prices, and state incentives. The size of such installations varies as a function of customer type (residential, commercial, or industrial), socioeconomic standing, etc. For a DSO or utility company, the challenge is to evaluate the potential impacts each customer-owned generation asset might have on the safe and reliable operation of the distribution system, which was originally conceived assuming one-way power flow. That is the aim of the interconnection studies DSOs perform as part of the interconnection application review process. Two main interconnection categories have been implemented to date: firm interconnection and flexible interconnection.
Firm interconnection is the most common and most widely adopted option worldwide. In this category, applications are reviewed considering all potential technical challenges. Applicants that pass the tests are given unrestricted access to the network within the limits of the regulation that governs such interconnections. Interconnection applications that fail one or more screening tests are rejected or recommended mitigation strategies that would alleviate the violations suspected. Network constraint mitigation strategies can be costly and can make the project economically nonviable [1]. If the applicant is willing and able to pay for the needed upgrade, the application will be given due attention and the upgrades implemented before interconnection; otherwise, the application is denied, or the project is cancelled. Connected firm generators are not subject to curtailment signals from the DSO.
To relieve the burden of high connection costs on energy project developers and optimize the use of existing network infrastructure, flexible interconnection options have recently emerged and have been more frequently implemented in Europe via so-called active network management platforms [2]. Flexible interconnection options offer an applicant the opportunity to avoid upgrades by accepting that its system's real power output might be subject to curtailment as necessary to avoid system violations. These options generally include DER management systems, in which optimal active and reactive power set points are determined through online system operational optimization; and principles of access (PoA), in which the real power output of interconnected variable resources is curtailed as needed according to market-or nonmarket-based approaches. A market-based approach suggests the creation of a curtailment market where flexible generators bid for curtailment and get compensated according to the established market rules [3]. This approach is impractical in the short term at the distribution level because it requires a formal distribution power market arrangement. Nonmarket approaches include [4]: • Last-in, first-out (LiFo): the last non-firm generator to connect is the first to be curtailed in case a network constraint is violated, and the first to connect is the last to be curtailed if the violation persists. • Pro rata: the required curtailment volume is equally distributed among all nonfirm generators. • Shedding rota: curtails non-firm generators in a predefined rotational order updated on a regular basis (e.g., every day). • Technical best: curtailment is assigned to non-firm generators based on their contribution to the network constraint violation. • Greatest carbon benefit: curtailment is assigned to non-firm generators based on their carbon emission levels with the objective to minimize overall carbon emission. • Most convenient: generators are curtailed based on the DSO's preference, i.e., which could be because of convenience and effectiveness. • Generator size: the first generator to be curtailed is the one with the highest output that is contributing to the violation.
These options have been explored in the United Kingdom. In the United States, the City of New York is currently piloting the flexible interconnect capacity solution with two DER projects: one 2 MW PV plant and one 450 kW farm waste digestor [5]. A detailed survey of different arrangements and associated issues is presented in [4,6,7]. Additionally, based on the U.K. experience, the LiFo, pro rata, or a combination of both methods, with generators placed in tranches with different levels of maximum curtailment according to when they interconnected have previously, been the most acceptable options. LiFo has been the most prevailing form in distribution networks in the United Kingdom [8,9], even though it might not always be the most economically efficient option [10]. In fact, LiFo presents many drawbacks. UK Power Networks, a distribution system operator, investigated alternative arrangements in the Flexible Plug and Play project. The study concluded that despite the simplicity of the LiFo arrangement, pro rata curtailment would be more attractive for subsequent non-firm renewable generators [4]. One drawback of LiFo is that it does not account for generator location when defining curtailment priorities, as highlighted in [11]. This leads to systematically high curtailment risk for later connected non-firm generators, even if they are not contributing to a given grid constraint. Potential solutions to this issue include the use of power flow sensitivity factors, as proposed in [12]. Although combining this approach with LiFo would yield a better performance than the current LiFo approach, it would be more computationally expensive and might become infeasible for implementation in large distribution systems. In addition, the most attractive feature of the LiFo, which is simplicity, might be lost. To be "fairer" in the LiFo curtailment allocation, this paper introduces a novel electric distance-based, last-in, first-out (ed-LiFo) PoA. In this approach, curtailment signals, instead of being solely based on the rank of access to the distribution network, consider the proximity of candidate generators to the location of the thermal overloads as a proxy for their contribution level to the network constraints. The aim of this work, beyond the innovative ed-LiFo option, is to assess the curtailment risk of non-firm, large-scale PV plants. In addition to thermal violations, voltage issues can arise with distributed resource integration [13]. These might not always be resolved using the LiFo curtailment scheme. Therefore, in this paper, we use an advanced inverter with autonomous Volt-VAR settings to control the voltage at PV nodes.
In summary, the contribution of this paper is twofold: • First, we introduce a novel flexible interconnection scheme based on the LiFo framework with the objective to minimize unnecessary curtailment of non-firm generation resources while considering the access rights of individual flexible generation units.

•
Second, we evaluate the curtailment risk distribution among flexible units at different PV penetration levels in an annual quasi-static time-series (QSTS) distribution system simulation framework.
The remainder of this paper is organized as follows. Section 2 presents the methodology of the proposed non-firm interconnection scheme. Section 3 describes the distribution test system and the test setups considered in our case study. Section 4 analyses the observations from the case study results, and discusses the insights derived. Section 5 concludes the paper.

Methodology
The proposed flexible interconnection option, ed-LiFo, refers to a non-firm PV connection scheme that schedules PV real power curtailment according to the non-firm generators' network access order (as in the traditional LiFo) while considering their proximity to the thermal violation observed. Section 2.1 presents the concept of electrical distance considered in this paper.

Electrical Distance
Klein and Randić introduced the concept of resistance distance, generally referred to as electrical distance [14]. Considering a connected graph, G, defined by a set of vertices, V, and a set of edges, the authors placed a unit resistance on each edge (i, j). The resistance distance between two vertices is the effective resistance (or Thevenin resistance) obtained using the standard series and parallel equivalents reduction techniques. For the sake of quantifying the proximity of two nodes, we consider the distribution network as a conductance (inverse of the resistance) weighted graph G. The adjacency matrix A of G, assuming n vertices, has the form given in (1), where g ij is the conductance that connects vertices i and j. g ij is nonzero only if the edge i-j exists.
As shown in (1), A is a square matrix with diagonal filled with zeros. We define a diagonal matrix called "degree" matrix D, which features the strength of ties of a node i in G. The degree of node i is the sum of the conductance elements that connect i to other nodes, with elements D ii given by (2): The Laplacian matrix derived from this representation is shown in (3) and is the conductance matrix, or the "real part" of the classic admittance matrix in electric circuit theory, as given in (4): The electrical distance matrix E is defined by (5): where E ij is the resistance distance between nodes i and j; L † is the pseudo-or group inverse of the Laplacian matrix L. As the Laplacian matrix (conductance matrix, in our case) is real-symmetric, the existence of its pseudo-inverse is guaranteed [15][16][17]. The relationship between L and L † is defined by the properties shown in (6) [18]:

ed-LiFo PoA
The aim of the proposed ed-LiFo is to reduce unnecessary curtailments, i.e., the curtailment of generators that do not contribute to the thermal constraints experienced. In fact, with the traditional LiFo scheme, early connected non-firm generators, even if sited in constrained network areas, would be exposed to relatively less curtailment risk, whereas the later connected non-firm generators located in less restricted areas are exposed to increased curtailment risk. The proposed ed-LiFo is based on active curtailment zone formation. A violation zone is dynamically identified as the union of a set of nodes within a given radius of all nodes directly connected to an overloaded line within the distribution system. Figure 1 is an illustration of a violation zone formation-physical distances are used in this illustration for easy visual representation.
We define a diagonal matrix called "degree" matrix D, which features the strength of ties of a node in G. The degree of node is the sum of the conductance elements that connect to other nodes, with elements given by (2): The Laplacian matrix derived from this representation is shown in (3) and is the conductance matrix, or the "real part" of the classic admittance matrix in electric circuit theory, as given in (4): The electrical distance matrix E is defined by (5): where E is the resistance distance between nodes and ; † is the pseudo-or group inverse of the Laplacian matrix . As the Laplacian matrix (conductance matrix, in our case) is real-symmetric, the existence of its pseudo-inverse is guaranteed [15][16][17]. The relationship between and † is defined by the properties shown in (6) [18]:

ed-LiFo PoA
The aim of the proposed ed-LiFo is to reduce unnecessary curtailments, i.e., the curtailment of generators that do not contribute to the thermal constraints experienced. In fact, with the traditional LiFo scheme, early connected non-firm generators, even if sited in constrained network areas, would be exposed to relatively less curtailment risk, whereas the later connected non-firm generators located in less restricted areas are exposed to increased curtailment risk. The proposed ed-LiFo is based on active curtailment zone formation. A violation zone is dynamically identified as the union of a set of nodes within a given radius of all nodes directly connected to an overloaded line within the distribution system. Figure 1 is an illustration of a violation zone formation-physical distances are used in this illustration for easy visual representation.  In this illustration, lines (c, f ) and (h, j) experience thermal violation. Hence, the set of nodes that are directly connected to any thermal violation is DCN = {c, f , h, j}. With a preset curtailment zone radius, ρ, individual violation areas represented by ρ-radius discs centered in each directly connected node are determined. Any non-firm generator located at a node that falls on a disc is a candidate for curtailment. The set of nodes CCN at which non-firm generators are subject to curtailment is given by (7): In Figure 1, the set of curtailment candidate nodes is CCN = {c, f , g, h, j, m}. The set of PV units, candidate to curtailment in their LiFo order, is given by (8): Consequently, any non-firm generator located at any CCN node might receive a curtailment signal from the distribution system operator. This assumes that this feeder hosts a set four non-firm PV units {PV d , PV f , PV h , PV k , PV m , PV n } located, respectively, at d, f, h, k, m, and n, in order of connection, with PV d the first and PV n the last. As d, k, and n are not in CCN, even though PV n is the last to connect to the feeder, it will not be curtailed unless all curtailment PV candidates have been curtailed and the thermal overloads still exist. In fact, in practice, all non-firm generators that are not curtailment candidates are appended to CCPV in their LiFo order. This way, in case the candidate list is exhausted before overload is relieved, non-curtailment candidates might receive curtailment signals.
The curtailment order will be given by the set of curtailment candidate PV systems CCPV as follows {PV m , PV h , PV f }. The augmented CCPV would include PV n , PV k , and PV d at the end according to their LiFo order. Thus, if none of the candidates can suppress the thermal violation, PV n , PV k , and PV d will receive curtailment signals in this order. The set of curtailment candidates, CCPV, will then be {PV m , PV h , PV f , PV n , PV k , PV d }.
To select the curtailment zone radius ρ discussed in (7), we introduce (9): where µ and σ are, respectively, the average and standard deviation of the set of electrical distance values between any two buses in the feeder, and r is a railing factor. To ensure a feasible choice of curtailment zone radius, r must satisfy constraint (10): where E max is the electrical diameter of the feeder, i.e., the maximum electrical distance between any two buses of the feeder. Figure 2 describes the ed-LiFo PoA framework and its implementation in a QSTS simulation. The shaded boxes identify ed-LiFo processes.
When the system approaches a preset thermal limit, either on lines or transformers, the ed-LiFo PoA control is activated. Curtailment decisions are made and executed until thermal violations are suppressed. This concept is tested in Section 3. When the system approaches a preset thermal limit, either on lines or transformers, the ed-LiFo PoA control is activated. Curtailment decisions are made and executed until thermal violations are suppressed. This concept is tested in Section 3.

Case Study
To evaluate the proposed flexible interconnection option and determine the curtailment risk incurred by non-firm generators, we consider an example on a real-word test feeder, a PV scenario as well as the ed-LiFo design described in Sections 3.1 through 3.3.

Distribution Feeder
The study presented in this paper applies to the utility distribution feeder shown in Figure 3, the same as Feeder A studied in [19]. It is a 12.47 kV distribution system feeding 291 residential customers and 334 commercial customers, for a total load of 7.65 megawatts. The farthest customer is at 9.7 km from the substation. The primary bus X/R ratio ranges from 0.669 to 5.71 with an average of 2.206. In this test feeder, voltage support is provided by 6 capacitor units totaling 4800 kVAR in capacity. It should be noted that no line regulator nor load tap changer is present. The electrical connectivity within the studied feeder is presented in Figure 4, by means of the cumulative density function of the electrical distance given in Equation (5) and features the electrical distance between any two buses. The normalized load profile used in this case study is obtained from supervisory control and data acquisition system measurements. We use a single PV profile based

Case Study
To evaluate the proposed flexible interconnection option and determine the curtailment risk incurred by non-firm generators, we consider an example on a real-word test feeder, a PV scenario as well as the ed-LiFo design described in Sections 3.1-3.3.

Distribution Feeder
The study presented in this paper applies to the utility distribution feeder shown in Figure 3, the same as Feeder A studied in [19]. It is a 12.47 kV distribution system feeding 291 residential customers and 334 commercial customers, for a total load of 7.65 megawatts. The farthest customer is at 9.7 km from the substation. The primary bus X/R ratio ranges from 0.669 to 5.71 with an average of 2.206. In this test feeder, voltage support is provided by 6 capacitor units totaling 4800 kVAR in capacity. It should be noted that no line regulator nor load tap changer is present. The electrical connectivity within the studied feeder is presented in Figure 4, by means of the cumulative density function of the electrical distance given in Equation (5) and features the electrical distance between any two buses. The normalized load profile used in this case study is obtained from supervisory control and data acquisition system measurements. We use a single PV profile based on measured irradiation data at a station near the test feeder. We assume that the topology of the feeder does not change throughout the year. on measured irradiation data at a station near the test feeder. We assume that the topology of the feeder does not change throughout the year.

PV Scenarios
We consider a set of three identical large-scale PV units with size starting at 500 kW. The location of the PV systems is randomly chosen and fixed, as shown in Figure 3, across all penetration levels. Higher PV penetration levels (percentage PV to peak load ratio) are obtained by increasing the size of each PV unit by 50 kW at a time. We use real-world load and solar irradiation profiles to conduct a yearlong simulation at a 1-min time resolution. Each PV unit is a three-phase system equipped with a Volt-VAR controlled inverter. The Volt-VAR control satisfies the standard for interconnection and interoperability of distributed energy resources published by the Institute Electrical and Electronics Engineers (IEEE). We use the default IEEE 1547-2018 Category A Volt-VAR curve shown in Figure  5. on measured irradiation data at a station near the test feeder. We assume that the topology of the feeder does not change throughout the year.

PV Scenarios
We consider a set of three identical large-scale PV units with size starting at 500 kW. The location of the PV systems is randomly chosen and fixed, as shown in Figure 3, across all penetration levels. Higher PV penetration levels (percentage PV to peak load ratio) are obtained by increasing the size of each PV unit by 50 kW at a time. We use real-world load and solar irradiation profiles to conduct a yearlong simulation at a 1-min time resolution. Each PV unit is a three-phase system equipped with a Volt-VAR controlled inverter. The Volt-VAR control satisfies the standard for interconnection and interoperability of distributed energy resources published by the Institute Electrical and Electronics Engineers (IEEE). We use the default IEEE 1547-2018 Category A Volt-VAR curve shown in Figure  5.

PV Scenarios
We consider a set of three identical large-scale PV units with size starting at 500 kW. The location of the PV systems is randomly chosen and fixed, as shown in Figure 3, across all penetration levels. Higher PV penetration levels (percentage PV to peak load ratio) are obtained by increasing the size of each PV unit by 50 kW at a time. We use real-world load and solar irradiation profiles to conduct a yearlong simulation at a 1-min time resolution. Each PV unit is a three-phase system equipped with a Volt-VAR controlled inverter. The Volt-VAR control satisfies the standard for interconnection and interoperability of distributed energy resources published by the Institute Electrical and Electronics Engineers (IEEE). We use the default IEEE 1547-2018 Category A Volt-VAR curve shown in Figure 5.
In the ed-LiFo study case, where the active power output of a PV unit can be completely curtailed at times, the maximum reactive power available is limited to 25% of the inverter apparent power rating according to the IEEE 1547-2018 standard ( Table 8, p. 39). This ensures a category A Volt-VAR local voltage support for each PV unit, with reactive power ranges from −25% (absorption) to +25% (injection) of its inverter's apparent power rating, according to the curve shown in Figure 5. In all cases, PV inverter controls are in VAR priority. In the ed-LiFo study case, where the active power output of a PV unit can be completely curtailed at times, the maximum reactive power available is limited to 25% of the inverter apparent power rating according to the IEEE 1547-2018 standard ( Table 8, p. 39). This ensures a category A Volt-VAR local voltage support for each PV unit, with reactive power ranges from −25% (absorption) to +25% (injection) of its inverter's apparent power rating, according to the curve shown in Figure 5. In all cases, PV inverter controls are in VAR priority.

ed-LiFo Parameters
The ed-LiFo PoA controls are issued every 15 min. The control action issued is enforced for the next 15 min, then updated during the next ed-LiFo control iteration.
For the test feeder studied in this paper, according to Equation (10), r must be selected between −0.73 and 9.63. We use two empirically chosen values of : = −0.657 and = −0.58. The resulting curtailment zone radius values are, 0.00225 and 0.0045 Ω, respectively. The pure LiFo case-i.e., the case where all PV units are always considered as curtailment candidates and thus curtailed solely according to their access right-is a particular case in ed-LiFo, with = − , or 9.63 for our test feeder. This corresponds to a curtailment zone radius of 0.175 Ω. The hypothesis in the assignment of access right is that PV1 is the first interconnected and PV3, the last. Therefore, the LiFo curtailment order is {PV3, PV2, PV1}, subject to the overload contribution based on the position of each PV unit with regard to curtailment zones dynamically formed during each ed-LiFo iteration.

Results and Discussion
In this paper, we study voltage and thermal loading impacts of the ed-LiFo PoA as well as the curtailment incurred by non-firm PV units. The ed-LiFo results are benchmarked against two base cases with the same PV units with unity power and default Category A Volt-VAR control, respectively. Moreover, because of the parametric nature of the ed-LiFo concept, we next investigate the sensitivity of each PV unit's annual energy curtailment with respect to the curtailment zone radius. In this paper, the term curtailment, expressed in percent, refers to the annual energy curtailment defined by (11).
where / , is the annual energy produced by a PV unit before the principles of access scheme is applied; and / , the annual energy produced by a PV unit after the principles of access scheme is applied.

ed-LiFo Parameters
The ed-LiFo PoA controls are issued every 15 min. The control action issued is enforced for the next 15 min, then updated during the next ed-LiFo control iteration.
For the test feeder studied in this paper, according to Equation (10), r must be selected between −0.73 and 9.63. We use two empirically chosen values of r: r = −0.657 and r = −0.58. The resulting curtailment zone radius values are, 0.00225 and 0.0045 Ω, respectively. The pure LiFo case-i.e., the case where all PV units are always considered as curtailment candidates and thus curtailed solely according to their access right-is a particular case in ed-LiFo, with r = E max − µ σ , or 9.63 for our test feeder. This corresponds to a curtailment zone radius of 0.175 Ω.
The hypothesis in the assignment of access right is that PV1 is the first interconnected and PV3, the last. Therefore, the LiFo curtailment order is {PV3, PV2, PV1}, subject to the overload contribution based on the position of each PV unit with regard to curtailment zones dynamically formed during each ed-LiFo iteration.

Results and Discussion
In this paper, we study voltage and thermal loading impacts of the ed-LiFo PoA as well as the curtailment incurred by non-firm PV units. The ed-LiFo results are benchmarked against two base cases with the same PV units with unity power and default Category A Volt-VAR control, respectively. Moreover, because of the parametric nature of the ed-LiFo concept, we next investigate the sensitivity of each PV unit's annual energy curtailment with respect to the curtailment zone radius. In this paper, the term curtailment, expressed in percent, refers to the annual energy curtailment defined by (11).
where AnnualEnergy w/oPoA , is the annual energy produced by a PV unit before the principles of access scheme is applied; and AnnualEnergy w/PoA , the annual energy produced by a PV unit after the principles of access scheme is applied.

Sensitivity of Curtailment Risks and System Efficiency to Curtailment Zone Radius
As shown in the illustrative case of Figure 1 and the subsequent discussion of Equations (7) and (8), the selection of the curtailment zone radius is critical to an efficient active network management. In fact, the value of the curtailment zone radius determines the weight placed on a PV unit's responsibility in a given thermal overload. As ed-LiFo operates in a PoA framework, finding the best balance between access right and responsibility vis à vis thermal violations is key for a flexible interconnection paradigm based more on which generators are actually contributing to the constraint. Individual non-firm gener-

Sensitivity of Curtailment Risks and System Efficiency to Curtailment Zone Radius
As shown in the illustrative case of Figure 1 and the subsequent discussion of Equations (7) and (8), the selection of the curtailment zone radius is critical to an efficient active network management. In fact, the value of the curtailment zone radius determines the weight placed on a PV unit's responsibility in a given thermal overload. As ed-LiFo operates in a PoA framework, finding the best balance between access right and responsibility vis à vis thermal violations is key for a flexible interconnection paradigm based more on which generators are actually contributing to the constraint. Individual non-firm generation assets can experience very different curtailment risks under different zone radius settings. Figures 6 through 8 show the curtailment distribution for three zone radius values.  Figure 6 shows the annual energy curtailment of the three utility-scale PV systems under a last-in first-out interconnection agreement as well as the system-wide aggregate curtailment. The index of each PV system reflects its interconnection order. As expected, under this agreement type, where a PV unit's output is curtailed solely based on its interconnection order, the last unit to connect, PV3, incurs the highest curtailment risk, whereas PV1, the first unit to connect, experiences the least curtailment. Under the ed-LiFo agreement, setting the curtailment zone radius to the electrical diameter of the test feeder is equivalent to simply relying on the PV units' interconnection orders or access rights to decide which unit to curtail at a given time. This setting removes the thermal violation contribution factor of individual PV units from the curtailment decision. Note that the aggregate PV energy curtailment is relative to the total PV capacity. As all PV units are of the same size, the aggregate curtailment percentage is the average of the three PV systems. This holds true in Figures 7 and 8.
To account for the proximity of the PV units to potential thermal overloads, Figure 7 shows the curtailment risk distribution among all three flexible PV units under ed-LiFo with a lower curtailment zone radius. The curtailment zone radius is set to 4.5 × 10 −3 Ω. The effect of considering the thermal violation contribution factor is explicitly seen at PV penetrations between 102% and 125% of peak feeder load, where PV1 incurs more curtailment risk than PV2. In fact, PV1 is closer to the overloaded lines more often in this PV penetration range, at the curtailment zone radius of 4.5 × 10 −3 Ω. The main question is: which curtailment radius would be the most appropriate? Based on the ed-LiFo concept, a smaller radius would effectively limit unnecessary curtailment, whereas a higher radius would increase it; however, when no PV unit is found in the vicinity of the thermal overloads, all PV units are curtailment candidates based on their LiFo interconnection order. Therefore, extremely small curtailment radius values would lead to the same results as a pure LiFo case; however, the radius should be small enough that it truly captures, to some extent, the correlation between thermal violation contributions and curtailment risks incurred. Figure 8 presents an ed-LiFo curtailment case where the radius is set to 2.25 × 10 −3 Ω.  Figure 6 shows the annual energy curtailment of the three utility-scale PV systems under a last-in first-out interconnection agreement as well as the system-wide aggregate curtailment. The index of each PV system reflects its interconnection order. As expected, under this agreement type, where a PV unit's output is curtailed solely based on its interconnection order, the last unit to connect, PV3, incurs the highest curtailment risk, whereas PV1, the first unit to connect, experiences the least curtailment. Under the ed-LiFo agreement, setting the curtailment zone radius to the electrical diameter of the test feeder is equivalent to simply relying on the PV units' interconnection orders or access rights to decide which unit to curtail at a given time. This setting removes the thermal violation contribution factor of individual PV units from the curtailment decision. Note that the aggregate PV energy curtailment is relative to the total PV capacity. As all PV units are of the same size, the aggregate curtailment percentage is the average of the three PV systems. This holds true in Figures 7 and 8. would increase it; however, when no PV unit is found in the vicinity of the thermal overloads, all PV units are curtailment candidates based on their LiFo interconnection order. Therefore, extremely small curtailment radius values would lead to the same results as a pure LiFo case; however, the radius should be small enough that it truly captures, to some extent, the correlation between thermal violation contributions and curtailment risks incurred. Figure 8 presents an ed-LiFo curtailment case where the radius is set to 2.25 × 10 −3 Ω. Overall, the PV curtailment is consistently triggered at 102% PV penetration level for all control strategies. The answer to the question "which curtailment radius would be most appropriate, under ed-LiFo?", relies not only on the interconnection order but also on the proximity to the overload area (based on the curtailment zone radius). Although the interconnection order is fixed, the proximity to the overload can be tuned by an appropriate setting of the curtailment zone radius, as demonstrated by Figures 6 through 8. To account for the proximity of the PV units to potential thermal overloads, Figure 7 shows the curtailment risk distribution among all three flexible PV units under ed-LiFo with a lower curtailment zone radius. The curtailment zone radius is set to 4.5 × 10 −3 Ω.
The effect of considering the thermal violation contribution factor is explicitly seen at PV penetrations between 102% and 125% of peak feeder load, where PV1 incurs more curtailment risk than PV2. In fact, PV1 is closer to the overloaded lines more often in this PV penetration range, at the curtailment zone radius of 4.5 × 10 −3 Ω. The main question is: which curtailment radius would be the most appropriate? Based on the ed-LiFo concept, a smaller radius would effectively limit unnecessary curtailment, whereas a higher radius would increase it; however, when no PV unit is found in the vicinity of the thermal overloads, all PV units are curtailment candidates based on their LiFo interconnection order. Therefore, extremely small curtailment radius values would lead to the same results as a pure LiFo case; however, the radius should be small enough that it truly captures, to some extent, the correlation between thermal violation contributions and curtailment risks incurred. Figure 8 presents an ed-LiFo curtailment case where the radius is set to 2.25 × 10 −3 Ω.
Overall, the PV curtailment is consistently triggered at 102% PV penetration level for all control strategies. The answer to the question "which curtailment radius would be most appropriate, under ed-LiFo?", relies not only on the interconnection order but also on the proximity to the overload area (based on the curtailment zone radius). Although the interconnection order is fixed, the proximity to the overload can be tuned by an appropriate setting of the curtailment zone radius, as demonstrated by Figures 6-8. In addition, non-firm generators can incur significant annual energy curtailment risks once a certain penetration level is reached. Figure 9 compares the system-wide aggregate PV curtailments (previously shown in Figures 6-8) of all three presented curtailment radius values.
The aggregate system PV curtailment can be used as an efficiency measure. In fact, the less curtailed energy resource, the better it is for flexible PV unit owners because they would lose less revenue. From a system standpoint, however, if the same thermal violations could be resolved by less resource curtailment, the curtailment scheme deployed would be considered more efficient. Results indicate that more than 45% reduction in total curtailment can be achieved. Even though our case study reveals that the highest curtailment efficiency is achieved with the lowest curtailment zone radius (2.25 × 10 −3 Ω), there is no linear correlation between the efficiency and the radius. The highest radius does not necessarily lead to the lowest efficiency (i.e., the highest aggregate curtailment). The choice of the curtailment radius is critical. Future studies will investigate the radius selection problem, with the objective of increasing curtailment efficiency. In addition, non-firm generators can incur significant annual energy curtailment risks once a certain penetration level is reached. Figure 9 compares the system-wide aggregate PV curtailments (previously shown in Figures 6 through 8) of all three presented curtailment radius values. Figure 9. Comparison of aggregate PV energy curtailments for three curtailment radius values.
The aggregate system PV curtailment can be used as an efficiency measure. In fact, the less curtailed energy resource, the better it is for flexible PV unit owners because they would lose less revenue. From a system standpoint, however, if the same thermal violations could be resolved by less resource curtailment, the curtailment scheme deployed would be considered more efficient. Results indicate that more than 45% reduction in total curtailment can be achieved. Even though our case study reveals that the highest curtailment efficiency is achieved with the lowest curtailment zone radius (2.25 × 10 −3 Ω), there is no linear correlation between the efficiency and the radius. The highest radius does not necessarily lead to the lowest efficiency (i.e., the highest aggregate curtailment). The choice of the curtailment radius is critical. Future studies will investigate the radius selection problem, with the objective of increasing curtailment efficiency.
Given that the PoA schemes are aimed toward reducing thermal overloads, it is important to evaluate the impact of flexible generators on other grid operational parameters, such as voltage and power quality. Hence, in addition to studying the effectiveness of ed-LiFo PoA, Section 4.2 considers the impact of ed-LiFo implementation on voltage across the feeder at different PV penetration levels.

Effectiveness of ed-LiFo PoA at Resolving Distribution Violations
In this section, we present a comparative study of the voltage and thermal loading across the test feeder at different PV penetration levels under three control strategies: (1) all three PV systems are legacy PVs, i.e., their inverter control is set to unity power factor, labeled "base-case, PF = 1" ; (2) all three PV systems are Volt-VAR controlled, with the Volt-VAR curve presented by Figure 5, labeled "base-case, VoltVar"; and (3) all three PV units are considered flexible and controlled by the ed-LiFo scheme introduced in this paper, labeled "edLiFo, VoltVar". The reactive power limit of the Volt-VAR curve in the ed-LiFo case is 25% of the inverter's rated kVA. The ed-LiFo design with radius of 2.25 × 10 −3 Ω (see Figure 8) is used. In the first two strategies, the PV units are considered firm generators. Figure 10 shows the maximum line and transformer thermal loadings by PV penetration for all three control strategies. Regardless of the control strategy, no transformer is overloaded at any time throughout the year at any PV penetration, indicating the effectiveness of the ed-LiFo algorithms at resolving thermal overloading issues. If the PV units were to connect as firm generators, however, they would incur the line reconductoring Given that the PoA schemes are aimed toward reducing thermal overloads, it is important to evaluate the impact of flexible generators on other grid operational parameters, such as voltage and power quality. Hence, in addition to studying the effectiveness of ed-LiFo PoA, Section 4.2 considers the impact of ed-LiFo implementation on voltage across the feeder at different PV penetration levels.

Effectiveness of ed-LiFo PoA at Resolving Distribution Violations
In this section, we present a comparative study of the voltage and thermal loading across the test feeder at different PV penetration levels under three control strategies: (1) all three PV systems are legacy PVs, i.e., their inverter control is set to unity power factor, labeled "base-case, PF = 1" ; (2) all three PV systems are Volt-VAR controlled, with the Volt-VAR curve presented by Figure 5, labeled "base-case, VoltVar"; and (3) all three PV units are considered flexible and controlled by the ed-LiFo scheme introduced in this paper, labeled "edLiFo, VoltVar". The reactive power limit of the Volt-VAR curve in the ed-LiFo case is 25% of the inverter's rated kVA. The ed-LiFo design with radius of 2.25 × 10 −3 Ω (see Figure 8) is used. In the first two strategies, the PV units are considered firm generators. Figure 10 shows the maximum line and transformer thermal loadings by PV penetration for all three control strategies. Regardless of the control strategy, no transformer is overloaded at any time throughout the year at any PV penetration, indicating the effectiveness of the ed-LiFo algorithms at resolving thermal overloading issues. If the PV units were to connect as firm generators, however, they would incur the line reconductoring costs for any PV penetration more than 100% whether they use Volt-VAR control, as shown by the maximum line thermal loading curves under base-case, PF = 1 and base-case, VoltVar. Figure 11 shows the maximum and minimum voltages across the test feeder for different PV penetration levels. The feeder experiences the highest voltages in the legacy PV (PF = 1) case. All minimum voltages are within the ANSI A limits. Although the firm generator cases (control strategies (1) and (2)) would require voltage upgrades well before the 20% PV penetration, the ed-LiFo case would need to participate in voltage regulation upgrades only after 40% PV penetration, when the maximum voltage reaches the 1.05 p.u. upper threshold. costs for any PV penetration more than 100% whether they use Volt-VAR control, as shown by the maximum line thermal loading curves under base-case, PF = 1 and base-case, VoltVar. Figure 10. Line and transformer thermal loading per PV penetration by study case. Figure 11 shows the maximum and minimum voltages across the test feeder for different PV penetration levels. The feeder experiences the highest voltages in the legacy PV (PF = 1) case. All minimum voltages are within the ANSI A limits. Although the firm generator cases (control strategies (1) and (2)) would require voltage upgrades well before the 20% PV penetration, the ed-LiFo case would need to participate in voltage regulation upgrades only after 40% PV penetration, when the maximum voltage reaches the 1.05 p.u. upper threshold.

Conclusions and Future Work
This paper investigated the curtailment risk of large-scale PV power plants connected to the grid under a flexible interconnection agreement, namely, ed-LiFo, a novel PoA interconnection option introduced herein. It has been shown that the curtailment risk distribution across flexible generators is fundamentally sensitive to the selected value of the curtailment zone radius. This design parameter of ed-LiFo is critical not only to individual flexible generators' curtailment risk but also to system operational resource efficiency because it would impact the amount of flexible generation resource that is unnecessarily curtailed because of the inherent access priority enforced in LiFo PoA schemes. The ed-LiFo   Figure 11 shows the maximum and minimum voltages across the test feeder for different PV penetration levels. The feeder experiences the highest voltages in the legacy PV (PF = 1) case. All minimum voltages are within the ANSI A limits. Although the firm generator cases (control strategies (1) and (2)) would require voltage upgrades well before the 20% PV penetration, the ed-LiFo case would need to participate in voltage regulation upgrades only after 40% PV penetration, when the maximum voltage reaches the 1.05 p.u. upper threshold.

Conclusions and Future Work
This paper investigated the curtailment risk of large-scale PV power plants connected to the grid under a flexible interconnection agreement, namely, ed-LiFo, a novel PoA interconnection option introduced herein. It has been shown that the curtailment risk distribution across flexible generators is fundamentally sensitive to the selected value of the curtailment zone radius. This design parameter of ed-LiFo is critical not only to individual flexible generators' curtailment risk but also to system operational resource efficiency because it would impact the amount of flexible generation resource that is unnecessarily curtailed because of the inherent access priority enforced in LiFo PoA schemes. The ed-LiFo Figure 11. Voltage range per PV penetration by study case.

Conclusions and Future Work
This paper investigated the curtailment risk of large-scale PV power plants connected to the grid under a flexible interconnection agreement, namely, ed-LiFo, a novel PoA interconnection option introduced herein. It has been shown that the curtailment risk distribution across flexible generators is fundamentally sensitive to the selected value of the curtailment zone radius. This design parameter of ed-LiFo is critical not only to individual flexible generators' curtailment risk but also to system operational resource efficiency because it would impact the amount of flexible generation resource that is unnecessarily curtailed because of the inherent access priority enforced in LiFo PoA schemes. The ed-LiFo scheme balances the access rights of flexible generators and their estimated responsibility in thermal overloads. The curtailment zone radius is the ed-LiFo design parameter that is used to tune the access right and overload contribution balance to increase the fairness of output curtailment among non-firm generators. The test cases considered reveal that non-firm generators under the ed-LiFo agreement would not trigger any line reconductoring or transformer replacement upgrade. With a proper choice of curtailment zone radius, utilities can reduce their total flexible PV curtailment by up to more than 45%. The study shows that there is no linear correlation between the system efficiency and the curtailment zone radius. The highest radius does not necessarily lead to the lowest efficiency, i.e., the highest aggregate curtailment. Future studies will research the radius selection problem, with the objective of increasing curtailment efficiency. Future work will also investigate the sensitivity of ed-LiFo-induced curtailment to the share of firm generators in overall PV penetration. Further research will focus on the cost-benefit analysis of the ed-LiFo PoA interconnection option for non-firm generators and for utilities. Acknowledgments: This work was authored by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308. Funding was provided by U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Solar Energy Technologies Office. A portion of the research was performed using computational resources sponsored by the Department of Energy's Office of Energy Efficiency and Renewable Energy and located at the National Renewable Energy Laboratory. The views expressed in the article do not necessarily represent the views of the DOE or the U.S. Government. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes.

Conflicts of Interest:
The authors declare no conflict of interest.

A
Electrical adjacency matrix made of conductance parameters CCPV Set of curtailment candidate PV units arranged in their LiFo order CCN Set of curtailment candidate nodes D Electrical "degree" matrix, diagonal matrix DCN Set of nodes that are directly connected to any thermal violation DER Distributed energy resource DSO Distribution system operator E Electrical distance matrix ed-LiFo Electrical distance-based, last-in, first-out principles of access g ij Conductance that connects vertices i and j L Conductance matrix, a Laplacian matrix LiFo Last-in first-out L † Pseudo-or group inverse of the conductance matrix L µ Average electrical distance between any two nodes of a feeder PF Power factor PoA Principles of access p.u.
Per unit PV Solar photovoltaic QSTS Quasi-static time-series simulation ρ Curtailment zone radius σ Standard deviation of the electrical distance between any two nodes of a feeder S Apparent power VoltVar Volt VAR control function X/R X (reactance) by R (resistance) ratio i, j, k, t, z Node indices