1.2pt

# Robust dynamic operating envelopes for flexibility operation using only
local voltage measurement

Md Umar Hashmi1**  |, and Dirk Van Hertem1 *  | Corresponding author email<EMAIL_ADDRESS>Umar Hashmi and Dirk Van Hertem are with KU Leuven, division Electa & EnergyVille, Genk, BelgiumThis work is supported by the H2020 EUniversal project, grant agreement ID: 864334 (https://euniversal.eu/) and the Flemish Government and Flanders Innovation & Entrepreneurship (VLAIO) through the Moonshot project InduFlexControl (HBC.2019.0113) and project IMPROcap (HBC.2022.0733).

###### Abstract

With growing intermittency and uncertainty in distribution networks around the
world, ensuring operational integrity is becoming challenging. Recent use
cases of dynamic operating envelopes (DOEs) indicate that they can be utilized
for network awareness for autonomous operation of flexibility, maximizing
distributed generation integration, coordinating flexibility in different
power networks and in resource planning. To this end, a novel framework is
presented for generating decentralized DOEs in real-time using only the nodal
voltage measurement and partially decentralized, risk-averse, robust DOEs in a
time-ahead setting using voltage forecast scenarios. Chance constraint level
is analytically implemented for avoiding extremely restrictive time-ahead DOEs
with insufficient feasible regions for local energy optimization. Since the
proposed DOE calculation framework uses none or limited centralized feedback,
it is resilient to cyberattacks, communication failures, missing data and
errors in network layout information.  Numerical results showcase the DOE
calculation framework in real-time using voltage magnitude measurements and in
day-ahead timeframe using forecasted voltage scenarios. Furthermore, the DOEs
are extended to form P-Q charts while considering power factor and converter
capacity limits.

###### Index Terms:

Flexibility, network-aware, dynamic operating envelopes, decentralized
control, autonomous operation.

###### Contents

  1. I Introduction
    1. I-A Related literature
    2. I-B Contributions and organization of the paper
  2. II Methodology for network awareness
    1. II-A Dynamic operating envelopes
    2. II-B Generating of robust time-ahead DOEs
      1. II-B1 M1: Apply CC on voltage levels
      2. II-B2 M2: Apply chance constraint on DOE
    3. II-C Performance indices
    4. II-D Algorithm for DOE calculation
  3. III Numerical results
    1. III-A Case study 1: Methods for DOE calculation
    2. III-B Case study 2: Comparison of DA-DOE with FNA
    3. III-C Case study 3: PQ charts
  4. IV Conclusions and future directions

##  I Introduction

Flexible resources participating in energy markets would impact the operating
states of the distribution network (DN) to which it is connected to. Dynamic
operating envelopes (DOE) provide a feasible range for operating flexible
resources while considering local DN objectives for preserving the network
integrity by ensuring voltage and line loading are within permissible bounds.
The use cases for DOE are detailed in Fig. 1. Based on prior literature, these
use cases are classified into four objectives: (1) providing network operation
for autonomous operation, (2) maximizing distributed generation (DG)
integration to the DNs, (3) applicability of DN flexibility resources for
solving upstream network issues in medium and high voltage networks and also
for neighbouring DNs, and (4) use case of DOE for resource planning. The
substantial amount of prior works, [1, 2, 3, 4, 5, 6, 7], address the first
two use case for DOE in Fig. 1, i.e., concerning network awareness and
maximizing DG integration of flexible resources while avoiding network
congestion incidents.

###  I-A Related literature

Operating envelopes for power system flexibility are introduced in [8]. The
research in the domain of DOE is widely used in Australian DNs [1, 2] and
gradually gaining traction worldwide where DG penetration in DNs is high. In
the USA, with the FERC order 2222, [9], allowing distributed energy resources
(DERs) to participate in wholesale electricity markets, the relevance of DOEs
is going to grow drastically, this is exhibited in the panel session at PES
General Meeting 2022 [10]. Recent literature showcases the applicability of
DOEs in building energy management [11], and demand response [12]. The
fairness attribute of DOEs is dealt with in [13, 14]. Liu and Braslavsky in
[15] use centralized optimal power flow (OPF) based robust DOE calculation. A
framework for calculating probabilistic operating envelopes is introduced in
[16]. The dynamic active (P) and reactive (Q) power DOE calculation using
centralized OPF is elaborated in [17].

These DOEs are similar to P-Q charts, which essentially define the feasible
operating region for flexibility resources. Novel frameworks for P-Q charts
are introduced in [18, 19, 20].

Figure 1: Use cases for DOEs in distribution and transmission networks.

Many smart meters already measure the voltage magnitude at the point of common
coupling (PCC). Prior works such as [21, 22] show that voltage violations
precede line loading limit violations. Therefore, voltage magnitude is a
strong indicator of DN congestion, thus, voltage magnitude measurement and
forecast is used for DOE generation in this work.

TABLE I: Centralized vs presented decentralized DOE generation Centralized DOE calculation |  Proposed decentralized DOE
---|---
|
$\bullet$ Communication infrastructure needed eg. 4G, PLC etc |  $\bullet$ No communication needed as only voltage magnitude at PCC is used
$\bullet$ Centralized (optimal) power flows are used for DOE calculation [5, 15] |  $\bullet$ Con: Lack of centralized coordination, may lead to convergence issues leading to over and/or under compensation of corrective action
$\bullet$ High observability is needed for measurement feedback $\forall$ the nodes |  $\bullet$ Suitable for low observability networks: distribution/transmission
$\bullet$ Prone to communication delays, cyberattacks, missing information |  $\bullet$ Cyber-secure & resilient to communication failures, missing data
$\bullet$ Higher accuracy for the calculation of DOE. Simultaneous coordination of resources can be performed in case of centralized intervention. |  $\bullet$ Suitable for autonomous operation for applications such as: (a) peer-to-peer (P2P) trading without centralized interference & DN awareness, (b) decentralized flexibility activation for congestion mitigation
$\bullet$ Accurate information of network topology is crucial, |  $\bullet$ Network topology info (line impedance, phase connectivity): not needed.

###  I-B Contributions and organization of the paper

The goal of this paper is to provide a novel framework for calculating DOEs,
using only local voltage magnitude measurement and/or forecast at the PCC. A
summary of the pros and cons of DOE calculation using centralized versus the
presented (partially) decentralized DOE calculation is summarized in Tab. I.
The key contributions of this paper are:
$\bullet$ Real-time DOEs using only voltage measurement: To the best of our
knowledge, this is the first work that proposes a decentralized DOE
calculation without any centralized feedback.
$\bullet$ Time-ahead DOEs using voltage forecast: we use centralized power
flows for generating voltage forecast. Two methods for calculating DOEs are
presented: M1 applies chance constraint on the voltage values and calculates
the DOE for each node and time, and M2 applies chance constraint on the
envelopes calculated based on each of the scenarios of voltage. Numerically,
we observed that M1 is more than two times faster computationally compared to
M2, while substantially reducing the data communication needs.
$\bullet$ Robust DOE calculation framework is proposed using nodal voltage
forecast in time-ahead setting. A chance constraint (CC) level is implemented
analytically, similar to [23, 24, 25]. The CC avoids over-conservative
envelopes that would be restrictive for local objectives of the flexibility
devices, such as (a) energy cost, (b) loss cost minimization, (c) energy
market revenue, (d) social welfare, (e) quality-of-service maximization, etc.
$\bullet$ Numerically, we show that day-ahead DOE calculated temporally
resembles the flexibility needs assessment (FNA) identified in [26], implying
the efficacy of the presented framework. Furthermore, we extend the calculated
DOEs to form nodal and temporal P-Q charts that also consider (a) power factor
limit [27], and (b) the capacity of the inverter.

This paper is organized as follows. Section II, describes the formation of
robust dynamic operating envelopes for network awareness. Section III, details
the numerical case studies. Section IV concludes the paper.

##  II Methodology for network awareness

In this work, a decentralized and a partially decentralized mechanism for
generating DOEs is proposed that takes as input the voltage measurement in
real-time and for time-ahead setting, power flows are performed for different
load scenarios depending on the forecast of load and distributed generation
and associated forecast errors, refer to [26] for details on scenario
generation. We present two models for generating DOEs in a time-ahead setting,
requiring different levels of communicated data. Note that in time ahead time
setting, communication latency is not a concern as small delays will not
impact DOE generation. Fig. 2 shows the inputs and output of the DOE
generation proposed.

Figure 2: Time-ahead and real-time DOE generation framework

The proposed DOE builds on our prior work on projecting traditional volt-var
and volt-watt inverter policies for identifying the feasible range for
operating resources [28]. In [28] we identify an active and reactive power
range selection policy that reduces the locational discrepancy of such
flexible resources. This work proposes a methodology for generating DOE for
flexibility services, considering local DN constraints. These DOE subsequently
be used for optimizing operational states of flexible resources based on the
service performed in the energy market(s). The proposed real-time or close to
real-time DOE (RT-DOE) generation framework for a node is a function of nodal
voltage levels at the PCC. In many DNs the network topology is not accurately
known, for such DNs, the proposed RT-DOE generation mechanism can be directly
applied as only PCC measurement of voltage is required. Further, since RT-DOE
is generated locally, no additional communication is needed, making the
proposed DOE generation inherently resilient to cyberattacks. However, for
time-ahead DOE generation nodal voltage forecast is needed. In this work,
power flows are performed at the centralized level for different loading
scenarios and the voltage forecast is communicated to each node. DOEs are
generated locally based on these voltage levels communicated. Although voltage
forecast scenarios in this work are calculated centrally, local and
distributed voltage forecasting methods can also be utilized.

Next, we describe the DOE generation framework. Subsequently, two methods of
generating robust envelopes is proposed while considering a CC or risk level.
The CC is used in order to avoid too conservative solutions, which would
provide little to no room for optimizing flexible resources.

Figure 3: Active power DOE based on [28]. (a) Volt-watt or P(U) control and
(b) envelope for active power, P. $U_{\min}$ and $U_{\max}$ denotes minimum
and maximum voltage levels allowed, $\Delta_{\text{perm}}$ denotes permissible
voltage fluctuation, $P_{\min},P_{\max}$ are the minimum and maximum active
power output and $Q_{\min},Q_{\max}$ are the minimum and maximum reactive
power output, $pf$ denotes the power factor lower limit.  Figure 4: Reactive
power DOE. (a) volt-var or Q(U) control and (b) envelope for reactive power, Q
[28].

###  II-A Dynamic operating envelopes

P(U) and Q(U) inverter control are also referred to as volt-watt and volt-var
control. The use of P(U) and Q(U) inverter control in standalone and/or in
combination are popular practices for the operation of radial DNs. It uses the
drooping behavior to limit excess active and reactive power injection
(capacitive) or consumption (inductive) thus, not aggravating grid voltage
further. In [28], two adaptations of volt-var and volt-watt inverter policies
are proposed, referred to as positive reinforcement control (PRC) and avoiding
negative reinforcement control (ANRC). PRC outputs more restrictive operating
envelopes compared to ANRC. We observed that ANRC projections used for active
power (P) and PRC used for setting reactive power (Q) set points reduce the
locational discrepancy [28]. In this work, we will extend the hybrid
projections used for P and Q for generating DOE. Fig. 3 and Fig. 4 show the
range selection mechanism used for generating DOE. The feasible region is
shown as traffic-light control with green as no reduction in the feasible
region, yellow shrink the feasible region, and red shrink it even further, see
Fig. 3(b) and Fig. 4(b). The volt-watt and volt-var plots shown in Fig. 3(a)
and Fig. 4(a). The operating region for the inverter is defined based on the
voltage magnitude $U_{i,t}$. For active power, we denote the region as
$R_{P}(U_{i,t})\equiv[R^{U_{i,t}}_{P_{\min}},R^{U_{i,t}}_{P_{\max}}]$, and for
reactive power, as
$R_{Q}(U_{i,t})\equiv[R^{U_{i,t}}_{Q_{\min}},R^{U_{i,t}}_{Q_{\max}}]$. where
$R^{U_{i,t}}_{P_{\min}}$, $R^{U_{i,t}}_{Q_{\min}}$ denote the lower operating
envelopes and $R^{U_{i,t}}_{P_{\max}}$ and $R^{U_{i,t}}_{Q_{\max}}$ denote the
upper operating envelopes for P and Q respectively. Note that these ranges are
modified based on the zone, the voltage magnitude and control type. Fig. 3(b)
and Fig. 4(b) are directly used for P and Q DOE generation for real-time
setting based on the voltage measurement at PCC.

###  II-B Generating of robust time-ahead DOEs

In Sec. II-A we detail the DOE generation using voltage measurement. This
method does not consider voltage fluctuations due to forecast errors. In the
time ahead flexibility planning, parameter uncertainty needs to be considered
in the form of load and DER scenarios for centralized power flow. The voltage
magnitude time series for these scenarios is then communicated to the nodes
(partially in model M1 and fully in M2). For M1, an empirical cumulative
distribution function (ECDF) is identified for nodal voltage distribution for
each time instant. We use non-parametric ECDF for risk assessment [26].
Envelopes generated for the absolute worst case of probable voltage
fluctuation would indeed make the flexible resource operation robust. However,
such realizations of the worst case are highly improbable. This motivates us
to use CC. Based on the distribution of data, different levels of robust
solutions can be created. The CC for this robust formulation is analogous to
the risk. It is governed by the incentive of participating and the penalty for
not ensuring healthy network operation. In this work, we assume the CC level
is fixed at 5%.

Figure 5: Nodal voltage statistical attributes. (a) the histogram and an
approximately normal distribution fit for nodal voltage scenarios, and (b)
ECDF for all the nodal voltage scenarios.

We propose two methods, M1, M2 for calculating risk-averse robust DOEs based
on the sequence of CC implementation.

####  II-B1 M1: Apply CC on voltage levels

In this method, the CC level is applied to all the voltage scenarios for each
node and time. Based on the voltage distribution shown in Fig. 5(a), ECDF is
identified as shown in Fig. 5(b). $U_{L}$ and $U_{H}$ voltage time series are
communicated to each node for the look-ahead time horizon. These risk-averse
voltage levels are used to calculate DOEs.  Fig. 6 summarizes the M1 method,
where time-ahead DOE is the intersection of DOEs for inputs $U_{L}$ and
$U_{H}$.

Figure 6:  The upper and lower levels of voltage are used for envelope
generation. The intersection of these envelopes is the output for the M1
method of robust envelope generation.

####  II-B2 M2: Apply chance constraint on DOE

In this method, DOE is calculated for all scenarios for each time and node.
Thus, all voltage time series for all scenarios needs to be communicated to
the prosumer node. The ramp up and ramp down P and Q robust DOE is identified
by applying CC level, as shown in Fig. 7 for the DOE calculated.

For centralized voltage scenario calculation, M1 compared to M2 DOE generation
would be more efficient as only $U_{L}$ and $U_{H}$ time-series needs to be
communicated to the prosumer node.

Figure 7:  Feasible range calculated using M2

###  II-C Performance indices

Numerical results use the following performance indices

  * •

For comparing M1 and M2:

    1. 1.

Sum of absolute error in DOEs generated by methods M1 and M2, given as

$\displaystyle\Delta
P_{E}\text{=}\sum_{t}\sum_{i}\\{|R_{P_{\min}}^{\text{M1},i,t}-R_{P_{\min}}^{\text{M2},i,t}|+|R_{P_{\max}}^{\text{M1},i,t}-R_{P_{\max}}^{\text{M2},i,t}|\\},$
(1) $\displaystyle\Delta
Q_{E}\text{=}\sum_{t}\sum_{i}\\{|R_{Q_{\min}}^{\text{M1},i,t}-R_{Q_{\min}}^{\text{M2},i,t}|+|R_{Q_{\max}}^{\text{M1},i,t}-R_{Q_{\max}}^{\text{M2},i,t}|\\}.$
(2)

  1. 2.

Computation time in seconds.

  * •

Comparing DOE and FNA: For comparing the decentralized DOE framework proposed
compared to the centralized method, we use the flexibility needs assessment
output generated based on [26]. It is assumed that the shrinking of the
feasible region of DOE is an indicator of the flexibility needed by DN.

###  II-D Algorithm for DOE calculation

Algorithm 1 outlines the procedure to identify DOEs in time-ahead and close to
real-time frames.

Inputs: Nodal voltage forecast, voltage measurement
Output: Dynamic operating envelopes in day-ahead & real-time,

1:Generate day-ahead dynamic operating envelopes (DA-DOE),

  * •

Perform power flows & communicate nodal voltage scenarios

  * •

Use these voltage values for generating the DA-DOE based on M1 and M2 models
detailed in Section II-B.

2:Calculate DOEs in real-time (RT-DOE) using voltage measurement at PCC. DOE
calculation is based on Section II-A.

Algorithm 1 DOE in time-ahead & real-time

##  III Numerical results

The DN considered is an adaptation of one of the Spanish LV feeders described
in [29]. The DN consists of 76 nodes and 75 branches connecting the nodes. 52
loads are connected in 28 DN nodes. The DN diagram is shown in Fig. 8. The DN
used in this work along with load profiles can be found on GitHub [30].

Figure 8: Network diagram [31] for the 76 bus Spanish DN. The substation is
indicated with a blue circle.

###  III-A Case study 1: Methods for DOE calculation

The case study outline is as follows:

  * •

Objective: Evaluation of DOE calculation methods M1, M2,

  * •

Data used: 76 bus Spanish DN,

  * •

Methodology used: Proposed in Section II,

  * •

Outcome: M1 is computationally better compared to M2.

Figure 9:  DOE for active and reactive power of a given node in real-time
based on nodal voltage measurement time-series, shown in (a). (b) shows the
reactive power DOE is based on PRC, and (c) shows the active power DOE based
on ANRC in per unit value of flexibility.

The visualization for P and Q DOE based on voltage time series measurement in
real-time (RT-DOE) is shown in Fig. 9. The parameters used are
$U_{\max}=1.08,U_{\min}=0.92,\Delta_{\text{perm}}=0.04$, and ANRC is used for
P DOE and PRC is used for Q DOE. The shaded region in Fig. 9(b) and (c) shows
the feasible region of operation.

DA-DOE’s are calculated using voltage forecasted scenarios calculated at a
centralized level. The voltage forecast scenarios are generated based on load
forecast scenarios used for performing power flows. 1000 scenarios are
generated for load profiles, see [26] for details on load profile scenarios.
For comparing DA-DOE generating methods M1 and M2, we calculate the sum of
absolute errors using (1) and (2): $\Delta P_{E}=0$ and $\Delta Q_{E}=0.23$.
The computation time comparison for 1000 Monte Carlo simulations is shown in
Fig. 10. Using, these performance indices, we can draw a conclusion that M1 is
computationally at least 2 times better compared to M2, while no significant
difference is observed in the sum of absolute errors. Further, M1 requires
only 2 ($U_{L}$ and $U_{H}$) time series to be communicated to each node. On
the contrary, M2 requires 1000 (for each scenario) times series to be
communicated for each node. Thus, subsequently, we use model M1.

Figure 10:  Comparison of computation time for models M1 and M2 for 1000 Monte
Carlo simulations.

###  III-B Case study 2: Comparison of DA-DOE with FNA

The objective of this case study is to compare the DA-DOEs with day-ahead FNA
identified in [26]. Clearly, from Fig. 11, the active power feasible ranges
are more restrictive for some nodes compared to others, see nodes 48 to 52.
The reason for this inherent unfairness is due to the different voltage levels
observed by the DN nodes.

Note that DA-DOEs are a preventive strategy and FNA is a corrective framework,
pointing towards corrective action. Fig. 12(a) the temporal DOEs and Fig.
12(b) shows the temporally aggregated nodal FNA. Clearly, the time periods
where flexibility is needed are coinciding with the shrinking of DOEs implying
the need for preventive action from such resources.

Figure 11:  Nodal variation of the active power DOE for a 24-hour period.
Figure 12:  Comparison of DA-DOE with FNA calculated based on FNA-OPF proposed
in [26]. (a) shows the temporal nodal DA-DOE, (b) shows the temporal FNA for
the 76-bus DN.

###  III-C Case study 3: PQ charts

Fig. 13 shows feasible spaces in shaded regions. In (a) the P-Q chart based on
calculated DOE is shown. (b) shows the feasible space due to power factor
constraint, which limits the ratio of reactive and active power. For this
demonstrative example, the power factor limit of 0.9 is considered. (c) shows
the feasible space due to the converter limit. Plots Fig. 13(d), (e) and (f)
show the P-Q charts for three-time instants of Fig. 9. Note that for plot Fig.
13(f) the power factor limit could lead to a null set with no feasible region.

Figure 13:  P-Q chart considering DOE and power factor limit and inverter size
limit. (a) P-Q plot feasible space based on (a) DOE, (b) power factor limit of
0.9, and (c) inverter size of 1 per unit. Plots (d) to (f) denotes the P-Q
charts for 3 different time instants on Fig. 9.

The P-Q charts thus identified can be used for LV flexible resources to
contribute towards solving upstream network issues. These charts can be used
for TSO-DSO coordination for flexible resource sharing.

##  IV Conclusions and future directions

Risk-averse robust partially decentralized and fully decentralized framework
in the context of time-ahead and real-time frames, respectively, for
calculating dynamic operating envelopes (DOEs) is presented. Real-time DOEs
(RT-DOE) are calculated based on local voltage measurement, with no additional
information exchange between neighboring nodes or centralized substations,
thus eliminating the need for communication infrastructure. Due to the
decentralized RT-DOE calculations, the framework is inherently resilient to
cyberattacks, communication failures, missing data, low levels of DN
observability, and lack of network topology information. For day-ahead DOE
(DA-DOE) calculation framework, the voltage signals are communicated to the
nodes, where DOEs are calculated, thus partially decentralized.  In numerical
evaluations, we apply the proposed DA-DOE calculation frameworks. Using
performance indices, we show that applying risk-averse levels in the form of
analytical implementation of chance constrained on voltage scenarios followed
by DOE calculation leads to similar results when compared with chance
constraints applied on all DOEs for all voltage scenarios. We also numerically
extend the DOEs calculated to form P-Q charts considering power factor and
converter capacity limits.

In future works, we will quantify the optimality gap between decentralized
DOEs with centralized DOEs in the real-time frame. Subsequently, we will apply
the DOE calculation frameworks for the autonomous operation of distribution
networks and industrial flexibility for solving congestion incidents and
energy market participation. Furthermore, we will also apply DOEs for
decentralized network-aware peer-to-peer trading.

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