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Determination of Real-Time Interdependent Flexibility on Multiple
Grid Connection Points in an Active Distribution Network
Andreas KUBIS*, Ankit SINGH, Giancarlo TORRES-VILLARREAL,
Sasiphong LEKSAWAT
PSI Software AG
Germany
akubis@psi.de
SUMMARY
The continuous and intensive integration of renewable energy sources (RES) and the subsequent
decommissioning of conventional plants result in technical challenges in planning and operation of
electrical networks such as higher uncertainty and absence of reliable ancillary services.
One solution to overcome the current challenges is the effective and smart usage of RES connected to a
distribution grid. The control characteristics of RES could enable the use of RES as sources of flexible
active and reactive power to provide flexibility to a higher voltage network at their interface point.
The flexibility of an active distribution network (ADN) is determined at the grid connection point (GCP)
which is defined as the interconnection point between two networks (e.g. HV/MV or MV/LV networks).
The determined flexibility at the GCP can support in maintaining stability in the power system in terms
of managing the network operation and ancillary services, e.g., congestion management, voltage control,
frequency services, etc. Based upon the available flexibility at a given time and the respective power
flow situation, the calculated flexibility can decrease or increase active and reactive power to suit the
needs. For example, congestion in a transmission line can be solved by utilizing the flexibility that an
underlying distribution network offers by absorbing active power. Additionally, determination and
utilization of flexibility enables effective and efficient grid utilization with the available resources
without the need of expanding the grid; thus, diminishing capital investments.
Awareness and information of mutual flexibility at multiple GCPs can be supported in use cases, such
as congestion management in a meshed distribution network, where multiple GCPs are connected to a
common transmission line. Accordingly, this paper proposes a method for the determination of
flexibility at multiple GCPs with mutual dependency into consideration. The potential usage of the
method from the point of view of grid operator is discussed. The discussion describes a use case and
expected visualization that support grid operations contingency constrained security. The demonstration
results including the hardware-in-the-loop control system environment will be evaluated.
KEYWORDS
Flexibility service mechanism, active distribution networks, optimal power flow, meshed distribution
network, multiple grid connection points, renewable energy sources, parallel optimization
Paper ID: 1108 Session 2022
Active Distribution Systems and Distributed Energy Resources (C6)
Innovative Planning and Operation of Active Distribution Systems (PS2)
1
1. INTRODUCTION
Figure 1 exemplifies a medium voltage (MV) ADN connected to a high voltage (HV) network at their
GCP. The current operating point, indicated in green in the P-Q diagram at the GCP, is the initial point
for the calculation of new possible operating points represented as active and reactive power flow values,
depicted in orange. This group of possible values along with the current operating point represent the
flexibility at the GCP and allow network operators to assess real-time flexibility along with the dispatch
information for the respective flexible points.
Figure 1: Determination and exploitation of flexibility at the GCP [1].
The calculated active and reactive values that represent the feasible points in the ADN consider network
constraints such as generator limits, voltage limits (both magnitude and angle), line flow limits, and
power balance.
The flexibility obtained at the GCP is the outcome of the aggregated results of the different flexibility
providing units (FPU) connected to the ADN. These assets are the source of flexibility in the electric
grid and are defined as a generating or flexible load unit that contains a certain scope of operating within
their own feasible region of operation. The flexibility calculation, thus, contemplate the feasible region
of operation of the flexible assets and their ON-OFF status.
The concept of FPUs and its usage as flexible assets is also described in [1] and [7]. Furthermore, [9]
provides detailed analysis of the technical possibility of the flexibility potential and the regulatory
possibility with reduced flexibility potential. In this paper, total technical capability of the flexible assets
is assumed to maximize the flexibility potential at the GCP.
1.1 Background and research contribution
Flexibility is determined based on the type of flexibility assessment approach or algorithm. The most
common are the Random Sampling (RS) or Monte-Carlo based approach, and the optimal-power-flow
(OPF) based method [2]. Due to the significant computational expense and time, the RS approach is
most suitable with respect to the determination of flexibility for network planning, where the discovered
flexibility range can be used for preventive measures [3-6].
The optimal-power-flow methods enable a cost-based flexibility region at one of the GCPs [7]. These
methods are preferred in various flexibility calculations and consequent improvements to the algorithm.
A variation of this approach is the linearized OPF that aims to improve the computational performance
[8], i.e., smaller calculation time. Similarly, a novel method to improve the assessment of flexibility
through multiple OPFs is proposed in [9].
Another OPF-based method that considers not only economic aspects but also security constraints is
proposed in [1]. It aims to provide a set of feasible operating points based upon the current operating
point, costs and n-1 security criteria.
2
The different previously mentioned methodologies for calculating flexibility [1-9] consider an
individual GCP for the determination of flexibility without the consideration of change in active and
reactive power in other GCPs. This represent a limitation for meshed distribution networks where other
GCPs are also involved in the operation of the electric grid.
In this paper, therefore, the determination of flexibility presented in [1] is extended to meshed grids with
multiple GCPs with mutual dependency. The characteristics of the extended algorithm are as follows:
i. Real-time flexibility assessment: The approach uses the current operating set point as a starting
point for the calculation of the flexibility assessment.
ii. Consideration of mutual flexibility of multiple GCPs: Flexibility is determined considering the
mutual dependency of various feasible power flow situations on different GCPs.
iii. Availability of economic set points as flexibility options: The approach calculates flexible set
points in the form of cost-optimized set points applicable to the current set point at the GCP.
iv. Parallelized computation of OPF functions: The methodology utilizes parallelized computation
capability of the respective platform to distribute multiple instances of optimal power flow
functions and compute in parallel, thereby improving computational performance of the overall
process.
v. De-aggregation: The calculation of flexible set points include the dispatch information of
respective generating or flexible units. This information can enable the system operator to
provide ancillary services such as congestion management in a secure and cost-optimized way.
2. MODELLING OF ACTIVE DISTRIBUTION NETWORK
As stated in the previous section, flexibility estimation aims to optimize the active and reactive power
control of RESs at the GCPs. Therefore, the decision variables considered for optimization are vectors
of voltage magnitude (𝐕𝐦) and angle (𝛉), active (𝐏𝐠) and reactive (𝐐𝐠) power, and active and reactive
power at the GCP. Thus Eq. (1) can be written as
𝒙
=
[
𝜽
𝑽
𝒎
𝑷
𝒈
𝑸
𝒈
𝑮𝑪𝑷
]
(1)
where 𝑮𝑪𝑷 is either the active (𝑮𝑪𝑷𝑷) or reactive (𝑮𝑪𝑷𝑸) power exchange at the GCP bus.
From the operational measures to be optimized, the flexibility estimation consists of several optimal
power flow problems (See the methodology in section Error! Reference source not found.).
Furthermore, the solution is limited by the following standard network constraints:
- Node-voltage limits
- PQ control capabilities of the RESs
- Power flow limits in the lines or branches
- Power balance equations
- Active and reactive power limits of the flexible generators
The derivation of the power flow model starts from considering the apparent bus power injection:
𝑺
𝒃𝒖𝒔
(
𝜽
,
𝑽
𝒎
)
=
𝒅𝒊𝒂𝒈
(
𝑽
)
𝒀
∗
𝑽
∗
(2)
Where 𝑽 = 𝑽𝒎∗ 𝒆𝒋𝜽 and 𝒀 ∈ 𝑪𝒏𝒃×𝒏𝒃 represents the bus admittance matrix. Then, the nodal power
balance equations for the real and reactive power injection at the buses can be derived from the real and
imaginary parts of Eq. (2). The equations are presented in equality constraints as follows:
𝑷
𝒃𝒖𝒔
(
𝜽
,
𝑽
𝒎
)
+
𝑷
𝒅
−
𝑪
𝒈
∗
𝑷
𝒈
+
𝑮𝑪
𝑷
𝑷
=
𝟎
(3)
𝑸
𝒃𝒖𝒔
(
𝜽
,
𝑽
𝒎
)
+
𝑸
𝒅
−
𝑪
𝒈
∗
𝑸
𝒈
+
𝑮𝑪
𝑷
𝑸
=
𝟎
(4)
3
Where, 𝑷𝒃𝒖𝒔(𝜽, 𝑽𝒎) and 𝑸𝒃𝒖𝒔 (𝜽, 𝑽𝒎) are the respective active and reactive bus power injections. 𝑷𝒅
is the load at each node, and 𝑪𝒈∈ 𝑪𝒏𝒃×𝒏𝒈 is the generator connection matrix to map the generators (𝑷𝒈
or 𝑸𝒈) with respect to the buses in the system. 𝑮𝑪𝑷𝑷 and 𝑮𝑪𝑷𝑸 represent the active or reactive power
flexibility demand from the GCP, respectively. Positive values indicate feed-in from the ADN to the
transmission grid and the negative value indicates the opposite.
Additionally, these constrained equations, Eq. (3) and Eq.(4), are complemented with line-flow limits
defined by
𝑺
𝒇
∙
𝑺
𝒇
∗
−
𝑺
𝒇
,
𝒎𝒂𝒙
≤
𝟎
(5)
𝑺
𝒕
∙
𝑺
𝒕
∗
−
𝑺
𝒕
,
𝒎𝒂𝒙
≤
𝟎
(6)
where, 𝑺𝒇 and 𝑺𝒕 are the two sets apparent-power flow of a line. The subscripts 𝑓 and 𝑡 indicate,
respectively, the “from” and “to” ends of a line, whereas the subscript 𝑚𝑎𝑥 denotes the maximum
apparent power limit for the respective end.
3. METHODOLOGY
This section is dedicated to describe the method for the determination of flexibility. The determination
of flexibility is divided into two parts: First, flexibility is determined individually in each of the GCPs
of the electric network; second, the calculation considers the mutual dependency between the different
GCPs of the electric grid.
3.1 Determination of flexibility ‘without’ consideration of mutual dependency
The methodology of the flexibility service mechanism (FSM), described in [1], searches for an initial
active and reactive power exchange limits at the GCP, which are Pmax, Pmin, Qmax, and Qmin, respectively.
This sets the base for flexibility calculation with respect to the current operating point (Pref,GCP, Qref,GCP)
at the GCP under consideration, which acts as a reference point in the nodal power balance equality
constraint. A search precision, which depends on the user, is assumed to search for specific numbers of
cost-optimal active and reactive power operating points at the GCP with respect to the current operating
point (Pref,GCP, Qref,GCP). The initial condition must satisfy the power flow condition for the current
operating point (Pref,GCP, Qref,GCP).
The resulting operating points resemble the specific active and/or reactive power demand from the
transmission network to the ADN. Therefore, the results obtained for flexibility determination with FSM
considering just one GCP or multiple GCPs without mutual dependency is a valid set of cost-optimal
operating points with respect to current operating point as shown in Figure 2 [1]. The green dot
represents the current operating point, whereas the blue dots in the figure represent the valid set of cost-
optimal operating points as ‘flexibilities’.
Figure 2: Determination of flexibility at a GCP without mutual dependency [1]
3.2 Determination of flexibility ‘with’ consideration of mutual dependency
When only one GCP is considered, the power flow in other GCPs is assumed to remain constant. In this
paper, the methodology of the existing FSM is extended to consider possible changes in the power flow
4
of other GCPs, while determining flexibility at the requested GCPs. Similar to the case of one GCP,
possible power flow changes in other GCPs are represented as active and reactive power flexibility.
Figure 3 shows an example of mutual dependency between GCPs of a distribution network and a
transmission network. Assuming flexibility (PGCP1, QGCP1) at GCP1 is being determined, the impact of
GCP2 to GCPn is concurrently taken into account, where n is the total number of GCPs. That is, multiple
power flow situations in the corresponding GCPs are used to determine flexibility at the main GCP,
which is GCP1.
Figure 3: Methodology depicting determination of mutual flexibility at multiple GCPs
Figure 4 illustrates the process of determining flexibility with multiple GCPs. It consists of three main
steps. First, the main GCPi is selected, where i = {1, 2, 3… n}. GCP of bus 1, i.e. GCP1, is set as the
main GCP illustrated in Figure 4.
Figure 4: Step-by-step description of determination of mutual flexibility
Then, independent flexibility Fi of each GCPi, e.g. bus 1, is determined through OPF. At this step, the
FSM considers power flow situations at other GCPs (orange dot in Figure 4). Using the FSM algorithm,
5
each valid power-flow in the corresponding GCPs results in a unique flexibility potential for the GCPi
(green dot). In Figure 4, GCPk represents a corresponding GCP, where k = {1, 2, 3… n, k ≠ i}.
Certainly, not all the power flow situations at the corresponding GCPs are valid as for the determination
of flexibility at the GCPi. Some of invalid power flows will result in infeasibility, or the OPF will not
converge. When all these flexibilities are combined together, an intersection of all these flexibilities with
the most common region depicting the safest flexibilities with all the power-flow situations in the
corresponding GCPs. The region of combined flexibilities ensure that the operation at any operating
point within the region is secure, also for the rest of GCPs.
After the determination of an Fi at the main GCP is done, the process has to be repeated to determine
the mutual interdependent flexibility IFk at the rest of GCPs, where k = {1, 2, 3… n, k ≠ i}. The whole
determination process is done, when the determination of flexibilities is finished for at all GCPs.
With the proposed method, a determination of flexibility is not limited only to one GCP. It allows grid
operators to know flexibility at a GCP with consideration of multiple GCPs corresponding to the grid,
giving more feasibility in having secure operation. This process provides pre-determined mutual
interdependent flexibility at all the GCPs, thereby enabling an awareness of the maximum and safest
potential of flexibility of all GCPs with all the valid power flow scenarios at the GCPs. Once this is
obtained, a flexibility operator can change an operating set point at the main GCP within the pre-defined
flexibility limit during grid operation. In the next section, use cases of the flexibility with consideration
of mutual dependency are discussed.
4. USE CASES AND DISCUSSION
FSM with consideration of dependency between GCPs is expected to support transmission system
operators (TSOs) and distribution system operators (DSOs) to ensure stable and secure grid operation.
As generating units and controllable loads can reside in distribution networks, results from FSM
provides the capability of communicating TSOs and DSOs how much flexibility in the form of active
and reactive power set points (PQ) that DSOs have at each GCP to perform operational planning and
ancillary services. In this paper, a use case of congestion management, which is an ancillary service, is
discussed together with how the results of flexibility from multiple GCPs can be visualized to support
grid operations by TSOs and DSOs.
4.1 Congestion management
Congestion management is a service that can also be achieved via FSM. An example is illustrated in
Figure 5. In real-time situations, the FSM can calculate simultaneous flexibility at both the GCPs with
respect to the current set point by means of the method presented in Section 3.2. Therefore, the
calculated flexibility provides a set of possible new operational set points options to support in the
congestion of the transmission line as shown in the example in Figure 5.
Figure 5: Congestion management as a use case for the mutual FSM.
HV
MV
Q
P
HV
MV
Q
P
Simultaneous change in setpoint at and to manage congestion in
the transmission network
Congestion in
transmission line
Feed-in from
GCP Feed-in from HV
transmission line to GCP
6
Here, congestion detected in the HV transmission line is solved by using the flexibility offered in the
MV distribution network. A change of operating point at both GCPs can be performed securely within
the region of their predetermined flexibilities, which consider mutual dependency between the GCP. In
the example in Figure 5, GCP1 is adjusted to feed-in power to the transmission line to maintain the power
demand, while GCP2 is adjusted to absorb power from the transmission line to relieve the line
congestion.
4.2 Visualization option
To determine flexibility region of a GCP with consideration of its mutual GCPs, a large amount of
results are involved. Visualization, therefore, can provide a better understanding of the resulted
flexibility values to grid operators. To give an example, the IEEE 9-bus system is modified to have two
GCPs at bus 1 and bus 2, as shown in Figure 6. Simulations of 100 different valid power flow scenarios
at GCP1 were conducted to determine 100 different PQ set points flexibility maps at GCP2.
2
1
3
4
5 6
789
Figure 6: A modified IEEE 9-bus test system.
An exemplified visualization of mutual flexibility region determined for GCP2 with respect to GCP1 is
depicted in Figure 7 in the form of density diagram. Figure 7 shows a combination of numerous PQ
flexibility maps for different power flow situations at GCP1. The region showing red marks represents
the most common and safest flexibility region with respect to the power flow situations at GCP1. For
this simulation, 100 different valid power flow situations at GCP1 were used to determine 100 different
PQ flexibility maps at GCP2. From Figure 7, the maximum active and reactive power exchange lay
between -239MW to 392MW and -374MVAR to 421MVAR respectively.
420.862
-374.805
Q [Mvar]
-238.640 391.817
P[MW]
Figure 7: A mutual flexibility region determined for GCP2 with respect to GCP1 in the IEEE Case 9-bus system.
7
When all these flexibilities are combined together, an intersection of all these flexibilities with the most
common region depicting the safest flexibilities with all the power-flow scenarios in the corresponding
GCPs. The region of combined flexibilities ensure that the operation at any operating point within the
region is secure, also for the rest of GCPs.
5. CONCLUSION
Gradual increase in RESs in the ADNs and decommissioning of conventional sources of energy poses
a significant challenge to network operators in maintaining power system balance but at the same time
a remarkable opportunity to contribute in energy transition to greener alternatives.
A viable alternative to support the energy transition is the flexibility service mechanism (FSM). It is an
effective and efficient utilization of distributed energy sources in distribution networks to provide
“flexibility”, or active and reactive power exchange capacity, to maintain stability of power systems.
The focus of this paper is to propose an extension of FSM which can determine flexibility at multiple
GCPs considering their dependency. Step-by-step description of a method to determine mutual
flexibility among GCPs of the same distribution network is presented. In this method, various power
flow scenarios are verified through AC-OPF algorithm to determine flexibility values of the GCPs, while
secure grid operations can be ensured. Under critical circumstances, e.g. congestion of a power lines in
a transmission network, these flexibility values can be then offered to TSOs and DSOs as power set
points to solve the congestion problem. Knowledge of flexibility in two or more GCPs at the same time
can act as a curative measure for performing a redispatch request through flexibility demand from
multiple GCPs when a transmission line is facing congestion. Moreover, an example of a mutual
flexibility region as a result from two GCPs is illustrated. It exemplifies how results from FSM can be
visualized besides displaying calculated flexibility values.
The proposed FSM not only has the capability of providing flexibility to TSOs to manage power
exchange with their underlying distribution network, but also enables active operations in distribution
networks. Thereby, RES-based generating units in a distribution network can be exploited and included
as participants for grid operations.
8
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