<PAGE>

                                                                   Exhibit 10.11

                                AMENDMENT NO. 1
                                       TO
                          COMMON FACILITIES AGREEMENT

     This Amendment No. 1 to Common Facilities Agreement (this "Amendment") is
made and entered into this 30 day of March, 2000, by and between Peoples Energy
Resources Corp. ("PERC") and Elwood Energy LLC ("Elwood").

                                    RECITALS

     A.   On April 16, 1999, The Peoples Gas Light and Coke Company ("Peoples")
and Elwood entered into that certain Common Facilities Agreement (the
"Agreement").  By letter dated August 23, 1999, Peoples assigned all of its
rights and obligations under the Agreement to PERC.  Capitalized terms not
otherwise defined herein have the respective meanings given them in the
Agreement.

     B.   Pursuant to the Agreement, PERC and Elwood set forth their mutual
agreement with respect to the shared use of certain facilities on the Property
(the "Services") and the sharing of the costs and expenses with respect thereto.

     C.   PERC and Elwood now desire to amend the Agreement to reflect the
shared use of certain additional Services and the sharing of the costs and
expenses with respect thereto.

     In consideration of the premises and the mutual covenants hereinafter set
forth and for other good and valuable consideration, the sufficiency of which is
hereby acknowledged, PERC and Elwood hereby agree as follows:

     1.   Article II of the Agreement is hereby amended by adding the following
new Sections 2.12, 2.13 and 2.14:

     Section 2.12  Janitorial Services

          (a) PERC's Responsibilities.  Commencing November 1, 1999, PERC shall
              -----------------------
provide to Elwood janitorial services as described in Appendix F.  PERC shall
                                                      ----------
provide all necessary personnel, equipment and materials in connection with
these Services.

          (b) In the event that PERC desires to terminate its obligations under
this Section 2.12, PERC shall provide forty-five (45) days prior written notice
to Elwood and Elwood shall no longer be liable for the cost of such janitorial
activities after the effective date of such termination.
<PAGE>

     Section 2.13  Security Services

          (a)      PERC's Responsibilities. Commencing November 1, 1999, PERC
                   -----------------------
shall provide to Elwood security services as described in Appendix G. PERC shall
                                                          ----------
provide all necessary personnel, equipment and materials in connection with
these Services.

          (b)      Elwood's Responsibilities.  Elwood shall be responsible for
                   -------------------------
ensuring that all security personnel that are provided by PERC pursuant to this
Section 2.13 are given free access to the Premises after the effective date of
such termination.

          (c)      In the event that PERC desires to terminate its obligations
under this Section 2.13, PERC shall provide forty-five (45) days prior written
notice to Elwood and Elwood shall no longer be liable for the cost of such
security services.

     Section 2.14  Snow Plowing Services

          (a)      PERC's Responsibilities. Commencing December 1, 1999, PERC
                   -----------------------
shall provide to Elwood snow removal services as described in Appendix H. PERC
                                                              ----------
shall provide all necessary personnel, equipment and materials in connection
with these Services.

          (b)      In the event that PERC desires to terminate its obligations
under this Section 2.14, PERC shall provide forty-five (45) days prior written
notice to Elwood and Elwood shall no longer be liable for the cost of providing
such snow removal activities.

     2.   Sections 4.1 and 4.2 of the Agreement are hereby amended by deleting
the words "A through F" and inserting in lieu thereof the words "A through H."
Additionally, new Appendices F, G and H, which are attached hereto, are made a
part of the Agreement.

     IN WITNESS WHEREOF, PERC and Elwood have caused this Amendment to be
executed as of the date first written above.

                                    ELWOOD ENERGY LLC

                                    By:  /s/ Tony Belcher
                                         --------------------------

                                         Tony Belcher
                                         General Manager


                                    PEOPLES ENERGY RESOURCES CORP.

                                    By:  /s/ William E. Morrow
                                         --------------------------

                                         William E. Morrow
                                         Vice President
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                          COMMON FACILITIES AGREEMENT
                                   APPENDIX F

                              JANITORIAL SERVICES
                              -------------------

1. Scope of Services:  PERC shall provide general janitorial services.

2. Charges for Services:  PERC shall charge Elwood the sum of $36.88 per hour
per person performing such janitorial services.  Consumable items provided to
Elwood by PERC in the performance of such janitorial services are not included
in this charge and shall be billed to Elwood as an additional cost.
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                          COMMON FACILITIES AGREEMENT
                                   APPENDIX G

                               SECURITY SERVICES
                               -----------------

1. Scope of Services:  PERC shall provide security services for the Premises as
specified in the Guardian Security Services Security Officer Instructions for
Peoples Energy Corporation, McDowell Energy Center-Revised Jan/00, as amended
and supplemented from time to time.

2. Charges for Services:  PERC shall charge Elwood the sum of $31,500 per year
for such security services.
<PAGE>

                          COMMON FACILITIES AGREEMENT
                                   APPENDIX H

                             SNOW PLOWING SERVICES
                             ---------------------

1. Scope of Services: PERC shall provide snow plowing services. In the event
that the quantity of snow is required to be removed from the Premises by hauling
the snow to a location offsite from the Premises, PERC shall provide the
necessary hauling.

2. Charges for Services: PERC shall charge Elwood the following charges,
inclusive of equipment costs, for snow removal services:

   a.  Fixed annual charge in the amount of $2,669.25.
   b.  $35.13 per hour per person performing such snow plowing services. This
       rate includes any and all expenses.
   c.  Additional charges where hauling of snow is required.