TSO-DSO Interaction: Active Distribution Network ...

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TSO-DSO Interaction: Active Distribution Network Power Chart for TSO Ancillary Services Provision Florin Capitanescu

Abstract—Within the timely framework examining interaction modes at the interfaces between transmission system operator (TSO) and distribution system operators (DSOs), this letter proposes the new concept of active-reactive power (PQ) chart, which characterizes the short-term flexibility capability of active distribution networks to provide ancillary services to TSO. To support this concept, an AC optimal power flow-based methodology to generate PQ capability charts of desired granularity is proposed and illustrated in a modified 34-bus distribution grid. Index Terms—active distribution network, PQ capability chart, demand flexibility, optimal power flow, TSO-DSO interaction.

I. I NTRODUCTION Enhanced cooperation between transmission system operator (TSO) and distribution system operators (DSOs) is a timely key factor, underpinned by growing research initiatives [1]– [3], [5], to facilitate a safe massive integration of renewable energy sources (RES) in power systems. For example, several coordination schemes modelling potential interaction modes between TSO and DSOs at their interface have been investigated [3], [4]. To support TSO-DSOs cooperation, the letter proposes the new concept of active-reactive power (PQ) chart (or feasible region) to characterize the flexibility capability of active distribution networks (ADNs) [6] to provide ancillary services (e.g. frequency control/power balancing, congestion management, or voltage support/security [3]) at the TSO-DSO interface so as to aid the secure operation of the transmission network. The concept is examined in short-term basis, i.e. up to tens of minutes ahead operation, where uncertainty could be neglected. Without loss of generality, this work assumes a TSO-DSOs interaction mode in which each DSO provides to the TSO, at some agreed time horizon, the proposed PQ flexibility chart for which ADNs constraints are met. The TSO can then optimally activate (e.g. for balancing purposes) this flexibility and notify the DSOs to change the setpoints accordingly in the ADNs. Iterations between TSO and DSOs may be possible to ensure that constraints are satisfied in the combined transmission/distribution system via, among others, shared use of ADNs flexibility. The proposed PQ chart concept shares some similarity with the approach in [7], where the range of RES reactive power capability is aggregated (for a given active power exchange) at the TSO-DSO interface. This letter leverages significantly the concept to PQ charts in a comprehensive manner by considering an optimal management of ADNs via centralized active network management (ANM) schemes [6] including: The author is with Luxembourg Institute of Science and Technology (LIST), Belvaux, L-4422, Luxembourg (e-mail: [email protected]).

on load tap changer (OLTC) transformers, RES active/reactive power, voltage-led demand reduction [10] assuming a voltage dependent load model, and demand response (DR). While this letter was under review, the similar concept of estimating the active and reactive power flexibility area at the TSO-DSO interface was proposed [8]. This concept was further developed in [9], which explores the impact of discrete variables on the flexibility area, showing that the latter may be composed of disjointed parts corresponding to different values taken by discrete variables. This letter differs from these works [8], [9] mainly in terms of: problem formulation (rectangular vs polar voltage coordinates), approach to generate the PQ chart (ε-constraint vs tangent lines), and a few modelling aspects (e.g. voltage dependent load models, flexibility cost, etc.). II. T HE P ROPOSED M ETHODOLOGY To address this new operation need and generate the PQ capability chart of an ADN, the proposed methodology relies on solving a sequence of tailored AC optimal power flow (OPF) problems. These latter are formulated using complex voltage rectangular coordinates1 (i.e. ei + jfi at bus i), to enable application to both radial and meshed ADNs. For the sake of illustration and formulation simplicity one assumes: balanced operation, a single transformer at the TSO-DSO interface (see Fig. 1) and RES curtailment is allowed for all objectives. A. AC Optimal Power Flow Problem Formulation 1) Objective function and control variables: Depending on the stage of the proposed methodology the objective of the OPF problem concerns one of the following power flow exchange at the TSO-DSO substation interface (see Fig. 1): PijT D min = PijT D max = QTijD min = QTijD max =

min

PijT D

(1)

max

PijT D

(2)

min

QTijD

(3)

max

QTijD

(4)

T D ,QT D ,e ,f rij ,Pgi ,Qgi ,zi ,Pci ,Qci ,Pij i i ij

T D ,QT D ,e ,f rij ,Pgi ,Qgi ,zi ,Pci ,Qci ,Pij i i ij

T D ,QT D ,e ,f rij ,Pgi ,Qgi ,zi ,Pci ,Qci ,Pij i i ij

T D ,QT D ,e ,f rij ,Pgi ,Qgi ,zi ,Pci ,Qci ,Pij i i ij

where (1) and (3) minimize the active power PijT D and reactive power QTijD drawn/imported from the transmission system, or 1 The reader is referred to [11] for a thorough study of the pros and cons of polar and rectangular voltage coordinates for AC OPF problems. This reference brings empirical evidence that rectangular coordinates presents slighly better computational performances than polar coordinates.

2

TSO HV

DSO

expressed at each MV bus i as follows: X gij Pgi − Pci − (e2i + fi2 ) j∈Ni

MV

+

X

rij [gij (ei ej + fi fj ) + bij (fi ej − ei fj )] = 0

(7)

j∈Ni

Qgi − Qci + (e2i + fi2 )[bsh i +

X

(bsh ij + bij )]

j∈Ni

−

X

rij [bij (ei ej + fi fj ) − gij (fi ej − ei fj )] = 0

(8)

j∈Ni

where, bsh i is the susceptance of the shunt bank at bus i, a line is a particular case of branch where rij = 1, and the load active and reactive powers of the load connected at bus i vary according to a voltage-dependent exponential model: Pci = (1 − zi )Pci0 {(e2i + fi2 )/[(e0i )2 + (fi0 )2 ]}α/2

(9)

(fi0 )2 ]}β/2

(10)

Qci = (1 − Fig. 1. Modified 34-bus distribution grid and TSO-DSO interface.

equivalently maximize the power injected/exported into the transmission system, while (2) and (4) maximize these powers. The OPF problem considers the following control variables (flexibility options): OLTC transformer ratio rij , RES reactive power Qgi , RES curtailment of active power Pgi , load active/reactive power shift factor zi , voltage dependent load active and reactive powers Pci and Qci , power flows at the TSO-DSO interface PijT D and QTijD . Other optimization variables are the voltage real and imaginary parts ei and fi . 2) Constraints: The active and reactive powers flows at the HV bus i interfacing the transmission system and distribution system can be expressed as follows:

PijT D =(e2i + fi2 )

X

gij

zi )Q0ci {(e2i

+

fi2 )/[(e0i )2

+

in which Pci0 /Q0ci is the initial active/reactive powers consumed at the initial voltage values (e0i and fi0 ), α and β are parameters of the exponential load model and where the load shift factor zi obeys the constraint: zimin ≤ zi ≤ zimax ≤ 1

(11)

and can take positive values, corresponding to demand reduction, or negative values, corresponding to (partly or fully) satisfaction of energy requirements of other time slots. In particular, the choice of zimax requires some beforehand analysis to assess if the shifted energy can be safely satisfied later on. The apparent power flow at the interface TSO-DSO is max limited by the OLTC transformer rated power Sij : max 2 ) (PijT D )2 + (QTijD )2 ≤ (Sij

(12)

The operational limits on (longitudinal) branch current and bus voltage magnitude take on the form: q
 2  2 + b2 2 (e2 + f 2 ) − 2r (e e + f f ) gij ei + fi2 + rij ij i j i j ij j j max ≤ Iij

(13)

j∈Ni

−

X

rij [gij (ei ej + fi fj ) + bij (fi ej − ei fj )] (5)

(Vimin )2 ≤ e2i + fi2 ≤ (Vimax )2 .

(14)

j∈Ni

QTijD = − (e2i + fi2 )

X

(bsh ij + bij )

j∈Ni

+

X

rij [bij (ei ej + fi fj ) − gij (fi ej − ei fj )] (6)

j∈Ni

where gij , bij , and bsh ij are the conductance, susceptance, and half shunt susceptance, respectively, of the branch ij linking buses i and j, and Ni is the set of buses linked with bus i. The active and reactive power balance equations can be

Simple physical limits of RES active/reactive powers are: min 0 max Pgi ≤ Pgi ≤ Pgi , Qmin gi ≤ Qgi ≤ Qgi ,

(15)

0 where Pgi is the current RES active power production. More realistic RES reactive power capability can be included [7]. OLTC ratio value is assumed for simplicity continuous: min max rij ≤ rij ≤ rij .

(16)

The proposed AC OPF formulation detailed above constitutes a non-convex nonlinear programming (NLP) problem.

3

B. The Methodology

7 6 5 4 Q (MVAr)

The proposed methodology generates a desired number of points 2M + 4 of the ADN PQ capability chart, in an εconstraint fashion, and provides a piece-wise linear approximation of it by performing the following steps: 1) Compute the four extreme points of the chart by solving an AC OPF which optimizes one objective at the time among (1), (2), (3), or (4) subject to constraints (5)-(16). 2) For k = 0, . . . , M − 1, solve an AC OPF problem which optimizes (1) subject to constraints (5)-(16) and (17):

III. N UMERICAL R ESULTS A. Building Up the Base Case The proposed methodology is illustrated using the popular 34-bus and 12.66 kV benchmark radial distribution grid [13] (whose one-line diagram is shown in Figure 1), which is modified by adding the following equipment: • 8 identical wind power RES units (G1 to G8) producing at the base case 0.2 MW and 0 MVAr, and with the following limits: Pgmin = 0 MW, Pgmax = 1 MW, Qmin = −0.75 MVAr, and Qmax = 0.5 MVAr; g g • one 10 MVA HV/MV OLTC transformer at the substation min linking buses 33 and 0, whose ratio limits are rij = max 0.87 p.u. and rij = 1.11 p.u., respectively. Initially both the OLTC ratio and its MV controlled voltage (at bus 0) are set to 1 p.u. and load is modeled as constant power (the overall base case load is 3.715MW/2.3MVAr [13]). The base case is obtained by running a power flow program. The optimization experiments described hereafter rely on this base case and make the following assumptions. A voltage dependent load model is assumed (9)-(10), where α = 1.0, β = 2.0, and the initial voltages and powers correspond to those of the non-modified original network (without RES) [13]. The percentages of load shifting are set to zimin = −0.1 and max zi = 0.2. The upper voltages limits is set to 1.05 p.u. at all nodes, while the lower voltage limit is set to 0.90 p.u. to all nodes, except of node 0, where the minimal bound is of 0.95 p.u..

2 1 0

initial OLTC OLTC,Q OLTC,Q,P OLTC,Q,P,DR

-1

QTijD ≥ QTijD min + k(QTijD max − QTijD min )/(M − 1) (17)

-2 -3 1

1.5

2

2.5

3

3.5

4

4.5

5

P (MW)

Fig. 2. PQ chart linear approximation relying on the 4 extreme points.

7 6 5 4 Q (MVAr)

3) For k = 0, . . . , M − 1, solve an AC OPF problem which optimizes (2) subject to contraints (5)-(16) and (17). The number of points of the PQ chart can be set by TSO-DSO agreement, e.g. given the granularity of interface power flows difference between two successive points (e.g. 1 MW/MVAr). All AC OPF problems in this methodology have been coded in GAMS [14] and solved by the generic NLP solver CONOPT. Although, due to problem non-convexity, in theory, generic NLP solvers provide an (at least local) optimal solution on feasible problems, in practice, they most often provide the global optimum [12]. The PQ chart may hence be more conservative than the real feasible region. The computations in each step can be performed in parallel. The chart can be updated every few minutes, as major sudden changes occur in ADN, or as requested by the TSO.

3

3 2 1 0 -1

OLTC,Q OLTC,Q,P OLTC,Q,P,DR

-2 -3 1

1.5

2

2.5

3 P (MW)

3.5

4

4.5

5

Fig. 3. PQ chart linear approximation using 20 points.

The apparent power limit of lines is set to 6.6 MVA (which corresponds to a current of 300 A). B. Illustration of the Proposed Methodology Fig. 2 shows a raw PQ chart linear approximation of the ADN, for various growing sets of flexibility options, and relying on the (up to) 4 extreme points generated in the first step of the proposed methodology. The labels OLTC, Q, P, and DR correspond to OLTC ratio, RES reactive power, RES active power curtailment, and demand response, respectively. Load reduction/increase option is common to all sets since a voltage dependent model is assumed. Fig. 3 displays a more refined approximation of the PQ chart (for the most effective flexibility options only), after generating 16 extra points, according to the second and third steps of the proposed methodology. In both figures, as expected, the larger the set of flexibility options, the larger the surface of the PQ chart. However, it can be observed that increasing the flexible options set does not fully expand the approximated chart, some parts shrinking.

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This is due to the coarse granularity of the approximation, experiments with fine granularity clearing this apparent issue. Note that demand response and RES active power curtailment are much more effective than other options. In particular, due to the limited control options, the chart in the case OLTC is reduced to a line (see Fig. 2). Both figures highlight the interest and value of ADN PQ flexibility chart to support TSO with ancillary services. IV. C ONCLUSIONS

AND

F UTURE W ORKS

In support to the new concept of TSO-DSO interaction, this letter has proposed an AC OPF-based methodology to generate PQ capability charts of desired granularity characterizing the short-term flexibility capability of ADNs to provide ancillary services to TSO. The charts can be integrated in TSO tools to manage security issues in the transmission network and in future ancillary services markets under definition [3]. If operation security is not harmed, in some markets, the cost function of altering the interfaces power flows could be further required. Future work is planed to adapt the proposed model to provide a piece-wise linear approximation of this cost. The methodology is not limited to the assumed presence of a centralized ANM scheme to meet ADN operation constraints. The piece-wise linear PQ charts require low computing effort (0.1s per point on a regular PC for the 34-bus grid). The short-term PQ chart can be further developed to include other flexibility options (e.g. storage, network reconfiguration) as well as to address longer time horizons, with non-negligible uncertainty levels, extending thus the concept to energy charts. R EFERENCES [1] D. Mayorga Gonzalez, L. Robitzky, S. Liemann, U. Hager, J. Myrzik, and C. Rehtanz, “Distribution Network Control Scheme for Power Flow Regulation at the Interconnection Point between Transmission and Distribution System”, IEEE ISGT-Asia conference, Melbourne, Australia, 2016. [2] A. Saint-Pierre and P. Mancarella, “Active distribution system management: a dual-horizon scheduling framework for DSO/TSO interface under uncertainty”, IEEE Trans. Smart Grid, vol. 8, no. 5, 2017, pp. 2186-2197. [3] G. Migliavacca, M. Rossi, D. Six, M. Dzamarija, S. Horsmanheimo, C. Madina, I. Kockar, and J.M. Morales, “SmartNet: a H2020 project analysing TSO-DSO interaction to enable ancillary services provision from distribution networks”, CIRED, Glasgow (Scotland), June 2017. [4] A. Papavasiliou, I. Mezghani, “Coordination Schemes for the Integration of Transmission and Distribution System Operations”, PSCC conference, Dublin (Ireland), 2018. [5] F. Capitanescu, “AC OPF-based Methodology for Exploiting Flexibility Provision at TSO/DSO Interface via OLTC-Controlled Demand Reduction”, PSCC conference, Dublin (Ireland), 2018. [6] A. Keane, L. Ochoa, C. Borges, G. Ault, A. Alarcon-Rodriguez, R. Currie, F. Pilo, C. Dent, and G. Harrison, “State-of-the-Art Techniques and Challenges Ahead for Distributed Generation Planning and Optimization”, IEEE Trans. Pow. Syst., vol. 28, no. 2, 2013, pp. 1493-1502. [7] P. Cuffe, P. Smith, and A. Keane, “Capability chart for distributed reactive power resources”, IEEE Trans. Pow. Syst., vol. 29, no. 1, 2014, pp. 15-22. [8] J.P. Silva, J. Sumaili, R.J. Bessa, L. Seca, M. Matos, V. Miranda, M. Caujolle, B. Goncer-Maraver, M. Sebastian-Viana, “Estimating the Active and Reactive Power Flexibility Area at the TSO-DSO Interface”, IEEE Trans. Pow. Syst., in press, 2018, doi: 10.1109/TPWRS.2018.2805765. [9] J.P. Silva, J. Sumaili, R.J. Bessa, L. Seca, M. Matos, V. Miranda, The challenges of estimating the impact of distributed energy resources flexibility on the TSO/DSO boundary node operating points, Computers and Operations Research, vol. 96, 2018, pp. 294-304. [10] A. Ballanti and L. Ochoa, “Voltage-Led Load Management in Whole Distribution Networks”, IEEE Trans. Pow. Syst., vol. 33, no. 2, 2018, pp. 1544-1554.

[11] G.L. Torres, V.H. Quintana, “An Interior-Point Method for Nonlinear Optimal Power Flow Using Rectangular Coordinates”, IEEE Trans. on Power Syst., vol. 13, no. 4, 1998, pp. 1211-1218. [12] F. Capitanescu, “Critical review of recent advances and further developments needed in AC optimal power flow”, Electric Power System Research, vol. 136, 2016, pp 57-68. [13] M.E. Baran and F.F. Wu, “Network Reconfiguration in Distribution Systems for Loss Reduction and Load Balancing”, IEEE Trans. Power Delivery, vol. 4, no. 2, 1989, pp. 1401-1497. [14] B.A. McCarl, “GAMS User Guide”, Version 23.8, 2012, www.gams.com.